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In this paper, we take a design-led perspective on the use of computational tools in the aerospace sector. We briefly review the current state-of-the-art in design search and optimization (DSO) as applied to problems from aerospace engineering, focusing on those problems that make heavy use of computational fluid dynamics (CFD). This ranges over issues of representation, optimization problem formulation and computational modelling. We then follow this with a multi-objective, multi-disciplinary example of DSO applied to civil aircraft wing design, an area where this kind of approach is becoming essential for companies to maintain their competitive edge.
Our example considers the structure and weight of a transonic civil transport wing, its aerodynamic performance at cruise speed and its manufacturing costs. The goals are low drag and cost while holding weight and structural performance at acceptable levels. The constraints and performance metrics are modelled by a linked series of analysis codes, the most expensive of which is a CFD analysis of the aerodynamics using an Euler code with coupled boundary layer model. Structural strength and weight are assessed using semi-empirical schemes based on typical airframe company practice. Costing is carried out using a newly developed generative approach based on a hierarchical decomposition of the key structural elements of a typical machined and bolted wing-box assembly.
To carry out the DSO process in the face of multiple competing goals, a recently developed multi-objective probability of improvement formulation is invoked along with stochastic process response surface models (Krigs). This approach both mitigates the significant run times involved in CFD computation and also provides an elegant way of balancing competing goals while still allowing the deployment of the whole range of single objective optimizers commonly available to design teams.
1. Introduction: the design process, design search and optimization
Design search and optimization (DSO) is the term used to describe the application of formal optimization software to the problem of engineering design. The inclusion of the word 'search' in this term indicates that alongside the desire for optimal designs is the recognition that the design activity is often an exploratory process where there are no fixed endpoints and no obviously optimal solutions to the complex problems being dealt with. Rather, an aerospace design team is typically faced with multiple and competing goals, thousands of constraints and imperfect design tools that are almost never neatly integrated with each other. Moreover, the goals and constraints being dealt with will often not be defined with crisp precision, but instead need interpreting with a great deal of hard won experience. Any of the well-known texts on aircraft synthesis will make such difficulties abundantly clear; see, for example, those by Stinton (1983) or Torenbeek (1984).
Much progress has, of course, been made in the field of aerospace design since the first flight by the Wright brothers a little over a century ago. A great deal of this progress has been achieved by the use of computational tools, primarily in the prediction of the performance of new configurations before they have been built. The two fields of computational structural mechanics (CSM) and computational fluid dynamics (CFD) have been at the forefront of this progress (and this theme issue is dedicated to the latter area). In fact, so important has the use of computational modelling become in engineering design and analysis that a new field, which has been labelled 'computational engineering', has begun to emerge (Keane & Nair 2005). This field spans more than just the modelling of structures or fluid flows: it also tackles the way that high-quality analysis tools can be integrated into the design process, allowing for geometry manipulation and meshing, the application of optimization tools, the interpretation of results coming from varying domains and at differing levels of fidelity and the best use of the (often distributed) computing resources available to the design team. The use of knowledge stores and knowledge application tools is also beginning to impact on this world, so that the large quantities of corporate information accumulated by the world's aerospace companies can be effectively captured and reused during design.
The current state-of-the-art in aerospace computational design typically makes use of1
a geometry manipulation engine that may be process specific or make use of one of the sophisticated parametric CAD engines now available (e.g. Catia, UniGraphics, ProEngineer);
a meshing process that accepts data from the geometry system (using standards such as STEP or IGES, or by direct file transfer) and which produces discretized analysis domains suitable for use by CSM or CFD codes (e.g. GridGen, Gambit);
a collection of analysis codes that work at varying levels of fidelity and deal with various models of the physics encountered (in CFD, these range from simple two-dimensional panel codes, through Euler and RANS solvers up to direct Navier–Stokes codes applied in three dimensions; e.g. VGK, Vsaero, Fluent);
post-processing tools that allow useful engineering metrics to be extracted from the results of analysis, perhaps combining results coming from multiple disciplines as in aero-elasticity (often highly customized and calibrated by the design team, rarely publicly available);
exploration and optimization tools that can be used to modify designs formally in the search for improvement against numerically specified targets, either commercially available such as iSight or DesignExplorer or in-house such as Options (Keane 2004);
process integration tools that allow the preceding components to be linked together and run on heterogeneous and distributed computing platforms, taking into account the very large variations in run times that will be encountered and the team-like nature of those working on the design (e.g. Fiper, ModelCenter, Matlab or Python); and
database tools that allow the collected results of design studies to be stored and efficiently browsed at will (such as Oracle).
Each of these tool types will require significant expertise to use to the standards now expected in aerospace companies. They will thus all need augmenting by large amounts of knowledge—currently, this mostly resides in the heads of the design team, although progress is being made in knowledge-based technologies across all these topics, whether it be in the construction of suitable meshes for accurate CFD solves or the correct choice of optimization strategy to allow for reasonable outcomes in affordable computing time. The linking together of these components into an automated design system to tackle a specific design challenge, preferably spanning multiple domains, is still very difficult. Although much progress has been made, almost all of the steps noted will require manual intervention, often for substantial periods. For example, the production of a high-quality mesh with good boundary layer modelling over a complete aircraft configuration remains a daunting task if accurate drag results are to be recovered—most aerospace companies still insist on full wind tunnel validation of any critical computations.
If the design process envisaged is to allow for a wide-ranging exploration over many possible configurations, the integration of all the relevant modules becomes even more difficult. It is therefore common practice to build the tool chain up for each major configuration as and when it is needed, reusing previous components where possible and customizing where necessary. This 'workflow' construction process can be dealt with in many ways, but typically feels a lot like computer programming whatever system is used: sequences of processes must be assembled, looped over and tested as the design progresses. Moreover, the workflow itself will be adapted as work proceeds and design options become more clearly understood. For example, the baseline geometric model being worked on will be modified in different ways at different points in the design. This may even involve the transition through completely different ways of holding the geometric data from bespoke concept exploration tools that feel much like spreadsheets to full product life-cycle modelling (PLM) systems in which even parametric CAD is just a sub-activity. It is also not uncommon to hold several versions of the same geometry, each specifically tailored to the process in hand: the level of detail needed in a manufacturing drawing is clearly unnecessary for CFD; the mesh used for CSM will differ from that used in CFD; even within CFD, differing resolutions will typically be used for drag recovery work when compared with aero-elastic studies.
A number of further factors combine to make work in this field particularly demanding. First and foremost, the run times needed for the most accurate studies in the most complex regimes can be fearsome. The study of a bird strike on a running aero-engine using large deflection finite element-based CSM codes can take many days on a major parallel computer. A direct Navier–Stokes solve at even modest Reynolds numbers is similarly difficult. Second, design teams will wish to study multiple options, either to trade various desirable and competing goals against each other, or just to allow for a simple design optimization study. Lastly, no engineering product operates in its nominal geometry, under nominal conditions, unchanged throughout its life. Allowance must be made for uncertainty in shape and boundary conditions when carrying out analysis and the consequent stochastic analysis is always more time consuming than a simple deterministic calculation. All these issues point in essentially one direction—attempts must be made to mitigate analysis run time. Sometimes, this is possible through improved solution schemes, sometimes via the use of more powerful processors and sometimes through the deployment of large-scale computing clusters, although such parallel computation brings its own difficulties. Aerospace companies seek to exploit all these avenues.
In this paper, we will concentrate on software methods that enable multiple goals to be studied in an efficient way. We will combine classical drag reduction calculations with modern cost evaluation methods and show how these competing issues can be reconciled via computational models. Before treating specific examples, however, we briefly review a number of the approaches commonly adopted when applying optimization tools to CFD calculations. We then go on to use the Southampton multi-level wing design environment (Keane & Petruzzelli 2000) to study the merits of multi-objective, multi-disciplinary design when applied to three-dimensional CFD solvers over a transonic wing system combined with a cost modelling tool. Here, the aim is to build a multi-objective response surface model (RSM) using CFD data to model variations in drag at fixed lift and a new generative code to describe manufacturing costs as gross changes are made to the overall wing parameters. Currently, such changes are usually assessed using empirical concept design tools that make no attempt to solve the flow conditions over the wings being studied and that use past data to estimate probable costs. Although these concept tools can be extremely accurately calibrated to deal with familiar geometries and processes, they experience difficulties whenever extreme or even moderately novel configurations are considered. They are, however, very easy to use and capable of giving rapid estimates of probable drag levels (Cousin & Metcalfe 1990) and probable costs.
The work reported here attempts to overcome some of these limitations by fusing together data coming from CFD-based drag routines and the costing code using design of experiment (DoE) techniques (Mackay et al. 1979; Mead 1988) and multi-objective Kriging (Jones et al. 1998) to build RSMs (Myers & Montgomery 1995). Variants on these methods have been used in aerospace design for some time. However, so far, they have mostly been used to accelerate single domain, single goal optimization approaches using expensive codes (Keane 2003). It is only relatively recently it has been proposed that they might be helpful in multi-objective analysis (Hutchinson et al. 1994; Liu et al. 1999; Malone et al. 1999; Vitali et al. 1999; Zang & Green 1999). The main aim here is to use the DoE and Krigs to produce a combined RSM that combines multiple goals in a new way.
The techniques described here have recently been incorporated within the Options design exploration system (Options 2006) and the results presented have been produced using that system to drive the Southampton wing design environment (Keane & Petruzzelli 2000).
2. CFD-based optimization
For as long as people have been able to predict the behaviour of aerospace systems via modelling or computation, there have been attempts to use formal schemes to improve their performance. In the world of aerospace CFD, this has often focused on drag reduction or the improvement of lift/drag ratios in some way. In all cases, this has involved trying to specify the geometry in some codified or formalized way that will allow variations in shape to be systematically generated in preparation for performance assessment. To begin with, attempts were made to explore the behaviour of two-dimensional airfoil sections systematically using wind tunnels—leading, for example, to such things as the famous NACA four digit airfoil series (Ladson & Brooks 1975). The first computer-based applications of optimization in design appear to be for structural applications; see, for example, the early work of Schmidt (1960) on structural synthesis. One of the earliest studies to make use of computational approaches to airfoil design was that by Liebeck & Ormsbeef (1970) some 10 years later, using second-order airfoil theory and the calculus of variations. This early work has been followed by a veritable avalanche of publications that have attempted to use ever higher-quality CFD solvers over ever wider ranges of geometry operated over broader ranges of operating conditions.
(a) Parameterization
In each case, a mapping is required between the (preferably few) variables controlled by the designer and the (commonly many tens of thousands of) surface coordinates needed to define the boundaries in the flow. Building such a mapping or parameterization of the geometry can be critical in achieving an efficient design search—if there are too many variables or these interact too strongly, the search landscape can become intractably complex to explore. Conversely, if too few variables or too restricted a mapping is used, it may be impossible to make worthwhile improvements in a design.
For purely local searches, there are some strategies that can overcome this dilemma by allowing an efficient search using all the coordinates of the surface directly. These make use of adjoint schemes (Jameson 1988) that allow one to trade the number of variables being changed against the number of outputs being studied. In a conventional search, one varies a few parameters and then analysis gives flow details at possibly millions of locations in the flow field. In adjoint approaches, all the grid points may be variables but one accepts only overall outputs such as the gradient of drag with respect to these variables. For a local search, this is very attractive since typical downhill methods work very well in such circumstances (Kim et al. 2000). Impressive results have been reported using adjoint schemes to carry out geometry improvements using local and thus limited range searches. The approach is not very useful for large-scale geometric changes and is difficult to use with CAD-based geometries since it requires invasive changes to all the codes being used (or at least the way they are used). This has prevented routine adoption of such approaches by most aerospace companies.
(b) Meshing
Given a parameterization scheme capable of generating the geometries required, the next hurdle faced in building an automated analysis scheme (and such automation is virtually a prerequisite for optimization) is in generating a suitable analysis mesh. Almost all the CFD codes in use today require the fluid domain to be sub-divided (discretized) into meshes consisting of simple shapes such as triangles, tetrahedra, quadrilaterals or bricks. Although various mesh-free schemes have been proposed, these currently remain experimental codes and at the time of writing almost all practical design work is carried out with meshes of some form or another. The meshes may be structured or unstructured, body-fitted or Cartesian and all combinations of these have their pros and cons. The work described later uses non-body fitted structured meshes which are easy to set up over wide ranges of body shapes but which result in rather less efficient solver run times than more complex, but more difficult to create, body-fitted methods.
(c) Solving
Even when a suitable geometry and mesh have been created, the analyst's difficulties are not completely over. Even the most well established of commercial CFD codes have a variety of controls that must be set governing things such as domain division over CPUs, order of solution, number of iterations, turbulence models, etc. It is quite common to find that a certain amount of experimentation is needed to establish the most efficient combination of controls, allocation of processors, usage of memory and settings for convergence parameters. For example, if parallel execution is desired over a given number of processors, the user may need to choose between studying several geometries at one time, each with a few CPUs or instead dedicating all the available processors to each calculation, one at a time. In the work reported here, each solve is handled by its own dedicated CPU, but an optimization scheme allowing 10 simultaneous calculations is adopted to make best use of the 10 available licences for the commercial code used. If commercial codes are being used, total licence numbers can often influence such decisions as much as total available computing power.
(d) Post-processing
Having run a suitable CFD (or any other) solver to acceptable convergence, the designer will wish to decide on how to assess the resulting data. When dealing with the results of CFD, this will commonly involve dealing with integrated quantities such as lift or drag as well as with specific flow features such as the locations of any shocks or separations. Extracting such information automatically and routinely from the flow solution is also non-trivial, particularly if a quantity such as drag is to be calculated with precision and sub-divided into the components of interest to the engineer such as wave drag and induced drag. Some of the most commercially sensitive aspects of aerodynamic analysis can occur in this phase as various calibration coefficients are brought to bear which may encapsulate the results of many experiments and trials carried out over extended periods.
(e) Optimization schemes
Once an automated design analysis capability has been assembled, it is then possible to consider the use of optimization tools. Such methods adjust design variables, seeking to improve goal functions while meeting any specified constraints. They can be as simple as the steepest descent schemes that date back to Cauchy and Newton or complex hybrids making use of surrogate models, evolutionary searches and a whole range of heuristics. All aim to move quickly to improved goals, although some specifically sacrifice global coverage in the aim to quickly converge to a local optimum while others specialize in wide-ranging exploration. There are some fundamental limitations that must be recalled whenever working in this area, however. In particular, the so-called 'no free lunch' theorems show that when averaged over all possible problems, all search methods are equally good (Wolpert & Macready 1997). Thus, if one seeks to make a search faster, it will inevitably become more specialized and thus prone to misbehave on problems for which it has not been carefully set up. Most design teams like to have a range of search tools to hand which they can bring to bear depending on the number of variables, goals and constraints being dealt with, the speed of the analysis process and the nature of the variations in the functions being studied. This topic is considered in more detail in subsequent sections of this paper.
(f) Databases
Since so much analysis is computationally expensive and online storage increasingly cheap, it is now sensible to store as many design calculation results as possible online, so that they can be browsed and reused. Such reuse is not simply a case of caching results to avoid duplication, rather it is often possible to interpolate and regress among existing data to guide future search processes better. This can not only speed up the design process but can also improve its quality. To do this often requires that additional descriptive 'meta-data' be stored with each computational result, so that its provenance can be readily searched by the tools available to the designer. The automated integration of such data stores is currently a very active topic of research.
3. A brief history of optimization methods
The development of nonlinear numerical optimization methods is a very large field, but may be grouped into three main themes: the classical gradient-based methods and hill climbers of the 1960s; the evolutionary approaches that began to appear in the late 1970s; and the adaptation of DoE and response surface methods to computer simulations in the 1980s and 1990s. Classical hill climbers all seek to move uphill (or downhill) from some given starting point in the direction of improved designs. Sometimes, they use simple heuristics to do this (as in the Hooke & Jeeves (1960) search) and sometimes they use the local gradient to establish the best direction to move in (as in quadratic programming Boggs & Tolle 1995). Where needed, such gradients are commonly obtained by finite differencing but can sometimes be obtained directly (e.g. by using an adjoint code). Few new heuristic approaches seem to have found favour in the literature since the early work of the 1960s. Instead, most effort since that time has been focused on improving the speed of convergence of quadratic methods and getting them to deal efficiently with constraints. Perhaps, the best known of these is the FSQP method developed by Panier & Tits (1993).
The so-called evolutionary methods are linked by the common thread of a stochastic approach to optimization. That is, the sequence of designs tested while carrying out the search has some random element—the main benefit is that such methods can avoid becoming stuck in local basins of attraction and can thus explore more globally. The downside is that they are often slower to converge to any optima they do identify. The most well-known methods in this class are the genetic algorithms (GAs), which seek to mimic the processes of natural selection that have proved so successful in adapting living organisms to their environments (Goldberg 1989). A variety of alternative stochastic global search methods have also been developed over the same period and these methods are now much interwoven in their development. For example, a series of developments made in Germany at around the same time led to the so-called evolutionary algorithms (Schwefel 1995) or the work on simulated annealing (Kirkpatrick et al. 1983). Some of these techniques work with populations of designs and are thus efficiently handled by clusters of computers: they are thus increasingly popular owing to developments in modern computing grid architectures where hundreds of processors may be used simultaneously.
Design of experiment and response surface methods are not really optimizers per se: rather, they are techniques that allow complex and computationally expensive optimization problems to be transformed into simpler tasks that can be tackled by the methods outlined in the previous two paragraphs. Essentially, these are curve fitting techniques that allow the designer to replace calls to an expensive analysis code by calls to a curve fit that aims to mimic the real code. Such methods all work in two phases: first, data are gathered on the nature of the function being represented by making a judiciously selected series of calls to the full code, usually in parallel—the placing of these calls in the design space is often best achieved using formal DoE methods, which aim to cover the search space in some statistically acceptable fashion (Montgomery 1997). Then, when the resulting data are available, the second phase consists of constructing a curve fit through or near the data—such curve fits are often termed 'response surfaces' (Myers & Montgomery 1995). The choice of RSMs that may be used is quite wide and will depend on the nature of the problem being tackled and the quantities of data available. Usually, the initial RSM will not be sufficiently accurate in all the areas of interest and so an iterative updating scheme may then be used where fresh calls to the full analysis code are used to provide additional information—various updating schemes have been proposed (Jones et al. 1998), see figure 1. The use of DoE and RSM methods in optimization is relatively recent but, even so, has yielded some impressive results (Sacks et al. 1989; Buck & Wynn 1993).
As probably goes without saying, very many hybrid approaches that try and combine methods from these classes have been experimented with. So much so that current practice is often to use a collection of methods in some complicated workflow to try and achieve results tailored to the problem in hand. Most commercial DSO toolkits support such an approach, often providing powerful graphical workflow editors to set up and control such hybrid searches. At the time of writing, optimization methods from each of these three classes are now sufficiently mature that they are available in commercial optimization packages and are in routine use by designers—academic research is currently more focused on how to deploy optimizers most effectively, given the desire to minimize the use of time-consuming and complex analysis codes, or to search very large design spaces, also to exploit emerging features of analysis methods such as the sensitivities coming from CFD adjoint codes. For example, the published academic research on CFD optimization can be categorized as
work that aims to make modest but detailed changes to refine an existing design via some kind of gradient descent approach on a single, deterministic goal function such as drag—this can involve impressively large CFD jobs using adjoint codes;
inverse schemes that seek to modify a geometry so as to achieve a pre-specified flow behaviour, typically defined as a pressure distribution over the surface of a wing or airfoil—again commonly over very large meshes;
wide-ranging searches over gross dimensions such as span and sweep so as to identify promising wing planforms, etc.—most commonly on modest cost panel or Euler codes;
optimization using multiple operating point schemes or multiple objectives to allow for the fact that more complex design goals are the norm in real design work—less common and rarely carried out with full fidelity calculations; and
models where uncertainty is specifically allowed for, such as where geometry may be uncertain or operating conditions unknown—relatively little work published to date but beginning to emerge.
Here, by way of example, we study planform design using the RSM approach—this technique is currently very popular when carrying out CFD-based optimization, particularly if wide-ranging searches are required.
4. Kriging and probability of improvement
It is no surprise that there are a number of variations and refinements that may be applied to the basic RSM approach—the literature offers many possible alternatives. In this paper, an LPτ DoE sequence (Statnikov & Matusov 1995) is used to generate the initial set of points and a Kriging model applied to build the RSM. The Kriging approach allows the user to control the amount of regression as well as providing a theoretically sound basis for judging the degree of curvature needed to model the user's data adequately. Additionally, Kriging provides measures of probable errors in the model being built that can be used when assessing where to place any further design points. It also allows for the relative importance of variables to be judged.
In Kriging, the inputs x are assumed to be related to the output (response) y by an expensive function fe(x). The response of the code is then evaluated for combinations of inputs generated by the DoE and used to construct an approximation(4.1)
The response at any x is then approximated by(4.2)where μ is the mean of the responses and ϵ(x) is a Gaussian random function with zero mean and variance σ2. In Kriging, ϵ is taken to depend on the distance between corresponding points. The distance measure used here is(4.3)where θh and ph are hyper-parameters tuned to the data in hand. The correlation between points x(i) and x(j) is given by(4.4)where Λ is a regularization constant that governs the degree of regression in the model (when set to zero the Krig strictly interpolates the data supplied) and δij is the Dirac delta function. When the response at a new point x is required, a vector of correlations between the point and those used in the DoE is formed, r(x)=R(x, x(i)). The prediction is then given by(4.5)where the mean μ is found from(4.6)
The hyper-parameters θh, ph and regularization constant Λ are all obtained by maximizing the likelihood, defined as(4.7)where the variance σ2 is given by(4.8)N is the number of points used in the DoE. The mean squared error of the prediction is(4.9)which gives a measure of the accuracy of the Krig at x. Another of the attractions of Kriging is that the θ hyper-parameters produced may be used to screen the variables in the data for relative importance if the input variables are normalized to a unit range before the Krig is tuned. Once tuned, the hyper-parameters simply rank the significance of the variables they represent.
Having built an initial RSM, some thought must be given to how well it models the data used and if this modelling is fit for purpose. Commonly, it is not and some kind of improvement strategy is employed to help refine the process. Suppose that an initial set of training data is made available by running the high-fidelity model at the points generated by a space-filling DoE technique, i.e. D0≡{x(i), y(x(i))}, i=1, 2, …, N0. This dataset is then used to construct a Krig model to approximate the input–output relationship where the mean squared error of the prediction gives an estimate of the uncertainty involved in making predictions using a finite set of input–output data. From the viewpoint of DoE, to improve the accuracy of the baseline surrogate, it is sensible to augment the dataset D0 with additional points where this error is high. However, from the perspective of finding iterates that lead to reductions in the objective function, the aim is to minimize . Statistical improvement criteria attempt to balance these aims in a rational way. Here, we detail the so-called 'probability of improvement' although there are several alternatives (Keane & Nair 2005).
Since a Krig model is a Gaussian process, the probability of any newly calculated design point representing an improvement over the current best design, , is readily calculated from(4.10)where [.] denotes the expectation operator and Φ( ) is the normalized Gaussian distribution function. This quantity is just the area in the tail of the Gaussian distribution below the current best function value and indicates the probability that any new design will represent an improvement over those in the existing training data, but does not indicate how much of an improvement will be obtained. Therefore, to minimize the original objective function fe(x), the procedure set out in figure 1 can be followed: first, a baseline Krig model is constructed using N0 points generated by applying a space-filling DoE technique. Subsequently, a new iterate is generated by maximizing the probability of improvement criteria, i.e. . The high-fidelity model is then evaluated at and the resulting exact function value, , is added to the baseline training dataset to give D1. The augmented dataset is used to update the Krig and its hyper-parameters, which is then used to solve the previous equation for the next iterate. This process is continued until specified convergence criteria are met.
Kriging is not a panacea for all evils, however. It is commonly found that it is difficult to set up such models for more than 20 or so variables and also that the approach is numerically expensive if there are more than a few hundred data points, since the set-up (hyper-parameter tuning) process requires the repetitive LU decomposition of the correlation matrix R, which has the same dimensions as the number of points used. Moreover, the number of such LU steps is strongly dependent on the number of variables and the likelihood is commonly highly multi-modal.
5. Multi-objective design: Pareto fronts
Most real design problems have more than one goal that the designer is trying to improve. In aerospace design, it is common to be aiming for light weight, low-cost, robust, high-performance systems. These aspirations are clearly in tension with each other and so compromise solutions have to be sought. Such compromises inevitably involve deciding on some form of weighting between the desired goals. However, before this stage is reached, it is possible to study design problems from the perspective of Pareto sets. A Pareto set of designs is one whose members are all optimal in some sense, but where the relative weighting between the competing goals is yet to be finally fixed (Fonseca & Fleming 1995). More formally, a Pareto set of designs contains systems that are sufficiently optimized that, to improve the performance of any set member in any one goal function, its performance in at least one of the other functions must be made worse. Moreover, the designs in the set are said to be 'non-dominated' in that no other set member exceeds a given design's performance in all goals. It is customary to illustrate a Pareto set by plotting the performance of its members against each goal function (figure 2). The series of horizontal and vertical lines joining the set members is referred to as the 'Pareto front'—any design lying above and to the right of this line is dominated by members of the set.
There are a number of technical difficulties associated with constructing Pareto sets. First, the set members need to be optimal in some sense—since it is desirable to have a good range of designs in the set, this means that an order of magnitude more optimization effort is usually required to produce such a set than to find a single design that is optimal against just one goal. Second, it is usually necessary to provide a wide and even coverage in the set in terms of the goal function space—since the mapping between design parameters and goal functions is usually highly nonlinear, gaining such coverage is far from simple. Finally, and in common with single objective design, many problems of practical interest involve the use of expensive computer simulations to evaluate the performance of each candidate, and this means that only a limited number of such simulations can usually be afforded.
Currently, there appear to be two popular ways of constructing Pareto sets (Keane & Nair 2005). First, and most simply, one chooses a (possibly nonlinear) weighting function to combine all the goals in the problem of interest into a single quantity and carries out a single objective optimization. The weighting function is then changed and the process repeated. By slowly working through a range of weightings, it is possible to build up a Pareto set of designs. Alternatively, one can try and use a population-based search to locate a whole series of points on the front in one go. Perhaps, the most well known of these schemes is the NSGA-ii method introduced by Deb et al. (2000). In that approach, a GA is used to carry out the search, but the goal function used to drive the genetic process is based on the relative ranking and spacing of the designs in the set rather than their combined weighted performance. More specifically, at each generation, all the designs are compared and the non-dominated designs set to one side. These are assigned rank one. The remaining designs are compared and those that now dominate are assigned rank two and so on. Thus, the whole population is sorted into rank order based on dominance. This sorting into rank-order dominance can be carried out irrespective of the relative importance of the objectives being dealt with or the relative magnitudes and scaling of these quantities.
Having sorted the population of designs into ranks, they are next rewarded or penalized depending on how close they are to each other in goal space (and sometimes also in design variable space). This provides pressure to cause the search to fan out and explore the whole design space, but does require that the competing objectives be suitably scaled—an important issue that arises in many aspects of dealing with multi-objective approaches to design. When combined with the traditional GA operators of selection, crossover and mutation, the NSGA-ii scheme is remarkably successful in evolving high-quality Pareto sets. As originally described, however, no means were provided for mitigating run-time issues arising from using expensive computer simulations in assessing competing designs.
To overcome the problem of long run times, a number of workers have advocated the use of RSM approaches, including Kriging within Pareto front frameworks (Wilson et al. 2001; Knowles & Hughes 2005). It is also possible to combine tools such as NSGA-ii with Kriging (Voutchkov & Keane 2006). In such schemes, an initial DoE is carried out and RSMs built as per the single objective case, but now there is one RSM for each goal function. In the NSGA-ii approach, the search is simply applied to the resulting RSMs and used to produce a Pareto set of designs. These designs are then used to form an update set, and after running full computations, the RSMs are refined and the approach continued. Although sometimes quite successful, this approach suffers from an inability to balance exploration and exploitation explicitly in the RSM construction in just the same way as when using such models in single objective search and greedily seeking for the best designs, although the crowding or niching measures normally used help mitigate these problems to some extent. The central thrust of the probabilistic improvement approach used here is to explicitly tackle this problem.
6. Multi-objective probability of improvement
Assuming that we have an expensive multi-objective search problem that is being tackled using a combined DoE and Kriging approach, it is possible to revisit the ideas of improvement and devise appropriate metrics. To begin with, consider a problem with two expensive goal functions f1e(x) and f2e(x) with outputs (responses) y1 and y2 that must both be minimized. Moreover, for simplicity, assume that x consists of just one design variable x. By constructing a DoE as before, it will be possible to construct a set of training data. This will allow us to identify the initial Pareto set of M0 designs that dominate all the others in the training set
In this set, the superscript * indicates that the designs are non-dominated. We may plot these results on the Pareto front axes as per figure 2 discussed in §5. In figure 2, the solid line is the Pareto front and the hatched area represents locations where new designs would need to lie if they are to become members of the Pareto set.
Given the training set, it is also possible to build a pair of Krig meta-models. Here, it is assumed that these models are independent though it is also possible to build correlated models by adopting the formalism known as co-Kriging (Cressie 1993). The pair of meta-models and will be Gaussian processes as before and each term in the two models will be identified by suffixes 1 and 2, respectively. Given a proposed new design point x, this pair of models will provide a prediction of the two goal function values and also their standard errors, here taken to be uncorrelated. These values may then be used to construct a two-dimensional Gaussian probability density function for the predicted responses that accords with the predicted mean and errors coming from the two Krig models at x.
When seeking to add a new point to the training data, we wish to know the likelihood that any newly calculated point will be good enough to become a member of the current Pareto set and, when comparing competing potential designs, which will improve the Pareto set most. There are a number of metrics that can be considered in these circumstances (see Keane (2006) for a full discussion) here we outline just the simplest; the probability that a new design will be good enough to at least augment the existing Pareto set. This is given by integrating the joint probability density function over the hatched area in figure 2,(6.1)or(6.2)
This metric is, of course, non-dimensional and is the multi-objective equivalent of equation (4.10). Moreover, it works irrespective of the relative scaling of the objectives being dealt with.2
7. A typical aircraft concept design problem: cost versus performance
Having set out the basic tools needed for our multi-level approach, we next illustrate their use in wing design using an Euler-based CFD solver and a generative cost model. Here, the responses being studied are the drag and cost of a transonic civil transport wing. A simple test problem has been constructed with the aim of optimizing the wing for operation at Mach 0.785 and a Reynolds number of 7.3 million. The objective is minimization of wing drag area, also known as drag per unit dynamic pressure, D/q (drag coefficient × wetted area) as calculated by the CFD solver and manufacturing cost in £m with target lift, wing weight, volume, pitchup margin and root triangle layout chosen to be representative of a 220-seat wide-body airliner. Limits are placed on the design variables that are typical of work in this area (although they still admit designs that would be considered radical in practice—it is not common to use sweep angles as high as 45° in a civil aircraft, for example). To make this study sensibly realistic, and also to provide data for the costing process, a relatively detailed structural and weight estimation process is incorporated into the calculation.
(a) Weight estimation
The most common way to calculate the weight of the load-carrying part of the wing is to split the structure into the parts that resist bending and those that resist shear. For the aircraft category under consideration (subsonic transport and executive aircraft), the wing is generally built up from the subparts depicted in figure 3. Here, the wing weight is estimated using an analytical–empirical approach that is a development of Torenbeek's (1992) method developed by Cousin & Metcalfe (1990). In such methods, the wing weight is computed as the sum of several functional components, each of which is estimated via a rational and/or statistical approach. The methods are especially suitable for the preliminary design stage, when sensitivity studies are required on the effects of geometric and other variations on the design characteristics.
Once the wing weight has been evaluated, this has to be included in the aircraft weight build-up. The design aircraft weight can be broken into crew weight, payload weight, fuel weight and operational empty weight (structure, engines, landing gear, fixed equipment, avionics and anything else not considered part of crew, payload or fuel). The crew and payload weights are both known since they are given in the design requirement. The only unknowns are the fuel weight and the operational empty weight, both of which are dependent on the total aircraft weight. Thus, an iterative process must also be used for aircraft sizing. For the purposes of this study, it has been assumed that part of the operational empty weight (i.e. excluding the weight of the wing structure) is fixed (in the range of our search) and that the maximum fuel weight is dependent on the size of the wing box (which houses the fuel tanks). Table 1 gives typical structural design parameters and table 2 the resulting weight estimates.
(b) Drag prediction
Here, drag is computed using the commercial CFD code MGAERO, which is a viscous coupled multigrid Cartesian Euler solver (Epstein et al. 1989). A series of drag recovery routines are incorporated with this code to assess the various drag components in a fashion compatible with typical concept design tools (Squire & Young 1937; Lock 1986; van Dam & Nikfetrat 1992). The input geometries to the CFD solver are created using a set of orthogonal functions derived from NACA transonic foils (Harris 1990; Robinson & Keane 2001). When using Mgaero, the inviscid analysis is coupled with a boundary layer model via surface transpiration. The viscous drag is then calculated using Cooke's (1973) implementation of the Squire & Young (1937) method. The wave drag is computed via Lock's (1986) second-order method. The induced drag is obtained from the integration of vorticity immediately downstream of the trailing edge as dissipation due to the presence of numerical viscosity precludes integration in the Treffitz plane. Of course, such drag values are subject to the usual inaccuracies associated with drag recovery from Euler codes (van Dam & Nikfetrat 1992), and by the standards of the other papers presented in this theme issue, this calculation is somewhat pedestrian; it nevertheless represents typical commercial design office practice. The CFD analysis requires around 30 min on a 3 GHz processor.
(c) Cost modelling
The cost model uses a generic hierarchical modelling tool called DecisionPro developed by the Vanguard Software Corp., Cary NC, USA. The significance of this approach is that it allows libraries of reusable cost objects to be created. This leads to a very efficient and extensible model that is relatively easy to navigate and deploy through a standard web browser. Further details on this methodology applied to gas turbine design can be found in Scanlan et al. (2006).
For the purposes of optimization, the cost model can be viewed as a 'black-box' as illustrated in figure 4. The internal structure of the cost model comprises cost-object libraries of
part types (stringers, spars, ribs and skins);
processes; and
The model includes an aggregation tree to sum the component hierarchy that is produced by a wing-structure model (figure 5). The wing-structure model generates the component hierarchy by instantiating the part-type cost-objects and populating their geometrical properties. Each part-type cost-object calls a set of process functions to determine manufacturing costs for a set of process steps. A particularly useful feature within the DecisionPro software is the ability to define variables in terms of their relevant physical units. The tool is able to undertake dimensional analysis (using SI units) to ensure consistency in any calculations. This eliminates many errors that could be difficult to identify otherwise. A sample search created an initial set of results of varying cost. Figure 6 gives an example of the response of the cost model to two different inputs.
(d) Sample calculation
A typical result from this combined weight, CFD and costing analysis is detailed in the initial value column of table 3 while figure 7 illustrates the equivalent geometry and overall mesh. Note that in this case, the wing is defined by 11 parameters and also that constraints are placed on the wing volume, undercarriage bay length, pitch-up margin and weight. At all times, the angle of attack is set to generate the required lift and the wing weight changes in a realistic fashion, allowing for necessary structural modifications as its dimensions alter. Given this analysis capability, it is possible to carry out a direct search: column 3 of table 3 gives the results of such a study, using a direct GA optimization of 20 generations and a population size of 100 aimed solely at reducing drag and allowing the cost to float. This search represents some 75 days of computing effort; here, carried out on a cluster of PCs running in parallel over a week. The extreme cost of such searches makes them infeasible for everyday use—but they do provide benchmarks against which to compare other results. Here, the design variables are limited by the bounds also shown in the table. Note that the drag is reduced by some 14%, the cost by 11% and that the optimized wing has a significantly larger area. This demonstrates that the initial design can be improved on in both aerodynamic and cost terms, but does not indicate how any further trades might be made between these two aspects.
(e) Multi-objective design optimization
As will be obvious from the previous two calculations, optimizing a design for minimum drag does not always increase cost, particularly if the starting point for the search has not been specifically optimized for minimum cost or weight. To examine what interactions there might be between these two aspects, we therefore next use the probability of the improvement metric and update scheme outlined earlier to produce a Pareto front of nine trade-offs possible between cost and drag (figure 8). This front has been produced using an initial set of 250 analysis runs to build the first Krig database, followed by a further 250 runs in batches of 10 found by searching equation (6.2) for good candidate solutions (the fact that this function is highly multi-modal means that it is always relatively easy to find such batches of good candidates). Of these 500 runs, some 45% fail to yield results either because the CFD meshing scheme being used cannot build an acceptable mesh or because the resulting CFD run does not converge correctly in either the inviscid or viscous coupled solves. These failed points are not included when constructing the Krig, but their presence is allowed for in the update scheme using the concept of imputation (Forrester et al. 2005), which allows the process to be warned that samples have already been taken in a given location. This is necessary to prevent the update process continually revisiting areas of the design space where solutions cannot be generated. Since these 500 runs can be handled in parallel, exploiting the 10 available licences, this search process requires around 5 days of computing effort. Note also that the design previously found by simply optimizing for low drag is not located by the multi-objective search, being slightly less than 1% lower in drag than the lowest drag design found on the front—it could thus be added to make a 10th point in the Pareto set—this is indicated in the figure by the dashed line linking the points mark with Z.
Also shown in figure 8 are the results from the initial 250 point DoE, all the successful update points and the position of the front after the initial DoE. Note that those design points that lie below and to the left of the front are not considered for membership of the front because they violate one or more of the constraints—in this case, either the wing weight or volume constraints are the active aspects in the design. It is clear that the update scheme being used here not only rapidly identifies good designs but also that these are nicely spread along the front, providing designers with a wide range of options from which to choose. Interestingly, one design (the 157th) from the initial DoE remains on the Pareto front even after the update sequence, moreover this also is quite a well-balanced design—its presence demonstrates the benefit of using a good quality space filling DoE at the outset.
Since the designs that make up the final front span a wide range of costs and aerodynamic performance, it is interesting to examine three cases taken from the front in more detail (table 4). Here, information is provided for the designs at either end of the front found by the update search, to illustrate the range of variation possible while still providing some degree of optimality, while the third design represents a reasonable trade-off position of intermediate cost with fairly low drag. Note that these three designs have notably different aspect ratios and weights with the low drag design having longer more slender and more swept back wings which are structurally less efficient and thus heavier and more costly, while the low-cost design has strongly tapered thick and deep inboard sections that lead to a very structurally efficient design of low weight and cost, but at the expense of 27% more drag, though being 35% cheaper. The intermediate design seems a much better compromise with drag only 6% higher than the low drag design, while being nearly 27% cheaper.
All three new designs are significantly cheaper than the baseline geometry or the purely CFD-optimized design (see figure 9 for a breakdown of these costs). Two of the three also offer lower drag than the baseline, showing how far from optimal this initial geometry was. The major cost increase in the low drag design when compared with the other two wings is primarily due to the large increase in skin costs due to the increase in skin thicknesses driven by the cover-weight estimates. The other differences are more minor and are driven by differences in geometry and number of features such as cut-outs, etc. Figure 10 shows the planform shape and upper surface Mach contours for DoE point 157 and it is clear that an enlarged inboard root section that is shock-free has been obtained at the expense of a slight shock in the reduced chord tip areas.
While there is no suggestion that any of these designs should be used in practice, it is hoped that this brief demonstration of what is possible using the latest generation DSO tools will be of value to practising designers, indicating that significant cost savings can often be made at the concept level in exchange for relatively modest penalties in aerodynamic performance.
8. Conclusions
This paper briefly reviews the current state-of-the-art of design optimization as it applies to aerospace engineering. It notes that if design improvements are to be made in a realistic industrial setting, a significant suit of capabilities must be assembled and managed together and that such tasks span CAD, classical engineering and modern computing grids. It then goes on to demonstrate what may be achieved in multi-discipline, multi-objective design by using a three-dimensional Euler CFD code, a modern generative costing approach and the sophisticated use of DoE and response surface optimization techniques formulated using multi-objective expected improvement schemes. This allows physics-based predictions to be brought to bear when attempting to trade-off the conflicting desires for low-cost, high-performance designs.
It is fully anticipated that upcoming developments in RSM, systems integration and parallel CFD methods, coupled with the reducing cost of computational facilities will allow the routine deployment of such multi-objective approaches with tens of goals and hundreds of variables by design staff within the next 10 years.
Development of the Southampton wing design environment used here was supported by the UK Engineering and Physical Sciences Research Council under grant GR/L04733 and by BAE SYSTEMS. Their support is gratefully acknowledged.
One contribution of 9 to a Theme Issue 'Computational fluid dynamics in aerospace engineering'.
↵N.B., here we mention a number of commercial codes by name, all of which are subject to copyright, etc., and all of which may readily be located from a web search—we make no recommendation as to the capabilities of any of them and of course there are many others besides those noted—they do, however, typify current practice in this area.
↵N.B., the subscript aug is used to indicate that this is the probability of augmenting (as opposed to dominating) members in the existing front.
- © 2007 The Royal Society


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http://kidcreatestudio.com/wp-content/uploads/2013/10/Kid-Create-Studio-340-1561.jpg 0 0 Lara Olson http://kidcreatestudio.com/wp-content/uploads/2013/10/Kid-Create-Studio-340-1561.jpg Lara Olson2014-07-29 13:09:422014-08-01 11:48:57September Birthday Party Sale- Save $25.00!
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Achieving that luminous skin is easier said than done. And between hectic work hours, round-the-clock stress and windpipe-chocking pollution, is it really a wonder your skin is 24x7 lifeless and tired? What you need are hacks for glowing skin.
We know, yes we know, time is a luxury and most of us don't seem to have it. That's where these tricks come in. They require literally just five minutes of your time and show results almost instantly.
However, before we further explore these ingenious hacks for glowing skin, you need to do some background work!
And with the background work, we mean tweaking your everyday habits to reap long-term skin benefits.
Quit smoking, as it can make your skin age twice as faster. Chug down that H2O, as it flushes out the toxins from your body, making your skin glow. Avoid touching your face, unless you want to transfer bacteria from your hands to face.
And of course, the most important, apply sunscreen every single day! Yes, do remember this point clearly.
So, here are 7 insanely simple hacks for an instant glowing skin, take a look!
Acne Wiping Spray
Mix a tablespoon of sea salt to a cup of warm water. Transfer the solution to a spray bottle. Shake it well and spritz it on the problem area. Let it get soaked naturally into the skin. It will help heal, repair and dry out the acne.
Caution: Avoid this trick for clear and radiant skin, if you have dry skin.
Illuminating Cheeks With Lip Balm
Want to add an instant shine to your lack-lustre skin? Here is a little trick for quick glowing skin, you will thank us for.
Take your regular tinted lip balm, wipe a thin coat onto your cheeks in an upward stroke. It will give your cheeks that titillating sheen and add a bit of colour. If the lip balm becomes too much, dab on a little face powder with a brush.
Witch Hazel For Under-eye Bags
Nothing can kill your look the way under-eye bags do. Here is what you can do to treat that. Take witch hazel in a cotton pad, apply it gently on the area under your eyes. It will not just reduce the fluids under your eyes and remove eye bags, but also help brighten them.
The Dewy Look Trick
Forget applying foundation the old way, here is a new way that guarantees that dewy glowing skin. Dip a brush coated with foundation with a few drops of facial oil. Apply it to your skin, as you apply your regular foundation. It will give your skin an enviable glow, plus it will look like you have applied no makeup!
Revive Dull Skin With Rose Water
Here is a little pick-me-up for your tired and dull skin at the end of the day. Fill an ice tray with rose water, pop it into the refrigerator to solidify. Once frozen, gently rub it over your skin. It will relax the tired muscles, boost blood circulation, close pores AND tone your skin. Use this homemade remedy for glowing skin every day!
Stand Upside Down
No, we mean literally. Lie horizontally on your bed, with your head hanging out. Maintain the position for 3 to 5 minutes, as long as your comfortable. Then, return. This little trick will send the blood gushing to your face and scalp, giving you an instant glow. Bonus point: It also improves your hair growth!
Instant Tan Remover
Yet another tip on how to get radiant skin instantly. Peel, grate and extract the juice of 1 potato. Mix it with a tablespoon of honey, and apply an even coat to your face and neck. Let it sit till your skin starts to stretch, then rinse it clean with plain water. Bleaching properties and humectant will naturally lighten your skin tone, without making it dry.


text:
- Description
DetailsCeramic Electric Oil Burner in Matt Black Approx. 6cm high x 12cm diameter with approx. 75ml capacity and approx. 675 grams in weight. Water should be added before adding a few drops of your favourite essential oil. Can also be use with wax melts. Features include an on/off switch, a light to indicate burner is on or off. Comes in a great presentation box with all the instructions and safety details. (230v, 50hz, 17w). these are c tick approved and compliant with australian electrical safety standards and deemed to be energy efficient.


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Matt Masson (of the United Kingdom) is huge supporter of the CR Johnson Healing Center and a major fan of CR Johnson. Matt suffered a TBI when he was 23 years old. Recently he and his parents (Anne and Nick) visited High Fives! http://goo.gl/aUcqDj
High Fives Foundation high fived this.


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There is no better way to celebrate being done with school then going out for a skate. @garrett_creamer ripping through Colorado post finals on the Keystone!


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Jealous of the attention Tiger Woods has received over his loose definition of the terms "faithful" and "no sex in the champagne room," media whore and interception enthusiast Brett Favre decided to get involved in what is quickly becoming the single most bizarre sex scandal since the alleged Berenstain Bear/Kim Kardashian sex tape.
According to Us Weekly's crack team of Columbia graduates who get paid to follow celebrities around town (Look, Dad! Bradley Cooper is just like us – he also visits the free clinic after having condom-less sex with Eastern Vietnamese call girls), Elin Nordegren stayed in Favre's Mississippi mansion this month while visiting her husband – Tiger Woods - at a local sex addiction clinic.
This new twist provides an intriguing denouement in this touching, romantic tale:
Boy meets girl
Boy asks another professional golfer to ask out girl for him
Boy marries girl
Boy cheats on girl with anyone who has two legs and text messaging capabilities
Boy enters sex rehab
Girl stays with NFL quarterback in order to visit boy
Boy and girl get back together?
The story broke when one local resident noticed that someone a little too attractive was roaming around town. "She definitely stands out," a local shopkeeper told the magazine. "She was beautiful. She was walking around alone and trying to keep to herself."
While most people are asking "does this mean Tiger and Elin are back together?" it seems that nobody is wondering "Why does Brett Favre live so close to a sexual rehabilitation clinic?"
Source: Harry How/Getty Images Sport/Getty Images
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Steve Mainini had a dream. Or perhaps, better put, it was a vision.
Nearly a decade ago, the Kennedy High School visual arts teacher thought it would be a pretty awesome idea if he started an on-campus silk screening shop that not only taught students about the artistic discipline, but also generated funding that could be recycled back into the school's art program.
Six years passed by before his idea, as Mainini puts it, "fell upon the right ears."
The right ears belonged to former West Contra Costa Unified School District (WCCUSD) Associate Superintendent Wendell Greer, who helped Mainini secure the startup funding to realize his vision.
In 2014, 'Eagle Ink' took flight, which today stands as a student-powered silk screening shop that creates T-shirts, sweatshirts, hoodies, backpacks and the like and is expected to generate approximately $20,000 for the school's art program and scholarships this year.
"We started the program to basically fund the arts," said Mainini. "And then I realized that once we started getting going and once we started building a pretty good profit that we could actually build it into a program that not only supports the arts and offers new opportunities for the students here but also offers the opportunity to give them scholarships that aren't tied down or weighted to going to college," he added.
"We have a lot of kids who want to just go and work—they may not want to go to college right away—so these scholarships that we're offering them are to help get them started," said Mainini. "It's for them—it's for their needs."
At the end of each school year, Mainini allocates a base amount of Eagle Ink's profits for program funding and divides up the remaining funds for scholarships for seniors in his Graphic Arts class.
Mainini says his Graphic Arts class is a "collaborative learning" environment made up of sophomores, juniors and seniors where new students learn from veteran students while creating multicolor silk screens using computers, a dark room and two state-of-the-art shop machines: one four-head and one six-head press.
Students can design the artwork for a job or customers can supply their own artwork.
One veteran student, Melissa Salmeron, age 18, said the program has taught her real-world work skills.
"Eagle Ink has trained me how to act in a more professional job environment, so this is more than a program, it's like a job," said Salmeron. "You do get paid for coming here at the end of your senior year…you have to take it seriously, you have to come to class everyday—it's basically training us for the outside world. No one's gonna tell you when to get up, when to come to class—when to come to work, for example—this whole program is about taking initiative and being a team player."
According to Mainini, the Eagle Ink team can produce up to two T-shirts a minute. "We run it pretty darn smooth now and the students do a remarkable job," he said.
Currently, the students are gearing up for a huge job order: 3,000 T-shirts for teachers working at WCCUSD schools. "Every teacher will get a shirt," said Salmeron.
In the past, Eagle Ink also has created T-shirts for the Golden State Warriors basketball team emblazoned with 'WWKD,' meaning "What would Kerr do?" for when the team's coach, Steve Kerr, was injured and unable to work.
The silk screening shop welcomes orders from the community. Anyone interested can contact Steve Mainini at firstname.lastname@example.com.
"This program is very beneficial to the whole school because we do recycle the money," said Salmeron, who hopes to attend the University of California at Irvine for college.
"I would say if anybody wants to do business with us, they should do it; it's really giving back to the community."


text:
CRISTIANO Ronaldo's Portugal face a struggle to book an automatic World Cup berth after they squeaked a 3-3 draw to Israel overnight.
Portugal is now four points adrift of Group F leaders Russia.
Russia had hoped to bolster that margin with a win away to Northern Ireland but Fabio Capello's men must wait 24 hours after heavy snow in Belfast forced a postponement, with the Windsor Park pitch unplayable.
Despite the presence of the likes of Real Madrid star Ronaldo, Portugal have struggled in recent qualifying tournaments.
Having already dropped four points from their opening four fixtures they again found themselves on the back foot, despite taking a second-minute lead through Bruno Alves.
The Zenit St Petersburg veteran headed in from a corner but after that it was all Israel.
Fine strikes from Tomer Hemed, of Spanish side Mallorca, midway through the first half and Eden Ben Basat on 40 minutes, followed by a Rami Gershon header in the 70th minute left the hosts on the brink of an upset.
But within two minutes former Tottenham striker Helder Postiga had pulled one back and then Fabio Coentrao, who had already hit the crossbar, rescued a point for Paulo Bento's side after Hugo Almeida nodded on a Carlos Martins cross.
The draw leaves both Israel and the Portuguese on eight points from five games, but with only the group winners guaranteed a berth in the finals in Brazil, the Russians appear to hold the whip hand.
Ronaldo had a quiet game by his own exalted standards and, adding to his frustration in front of goal, picked up a yellow card in the second half as the Portuguese showed the kind of shortcomings that marred their route to Euro 2012.
He will miss Tuesday's trip to Azerbaijan as a result.
In Belfast, meanwhile, former England coach Capello and his players had trained ahead of the qualifier, but overnight snow and rain forced Norwegian referee Tom Hagen to call off the match and reschedule it for Saturday.
Originally published as Struggling Portugal, Israel draw


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for Everyoneby A verified traveler
Very good location and rooms are bigPosted May 26, 2017
This hotel is located very convenient. Restaurants and eateries are all within walking distance. The hotel provided upgrades at very reasonable price (with some negotiation). Had one very nice female staff that offered us umbrellas as it was raining. Rooms were very spacious. And it had a very decent and large bathrooms. Only lacking is the breakfast where selection was very limited. Overall excellent hotel. And will recommend to friends.
for Couplesby Chengdulover
Wonderful stayPosted Oct 11, 2014 on HotelClub
We stayed in this hotel for six nights in September at the end of Sichuan tour . The hotel room , the corner lot on the eighth floor G50 is smaller that what I expected ,however, the design is contemporary and tastefully decorated. On arrival, we requested change of room as the cigarette smell was unaberable. We are allowed to view other two rooms before we made the final choice. In this regard, the reception staff is very helpful. Any requests for housekeeping items are being attended almost immediately . Beds are comfortable, wifi in room is good .Breakfasts are excellent covering local and western choices . Location of hotel is perfect, opposite the hotel is bus stop and less than ten minutes walk is Chunxi Rd subway and pedestrian shopping area. Plenty of shopping malls and food choices . As I am mandarin speaking, unable to comment on the English speaking capability of the staff. It would be nice if the G60 room has twin beds . I would be back at this hotel on my next Chengdu visit
for Everyoneby A verified traveler from Lynchburg, VA
New, modern hotel in the heart of ChengduPosted Sep 21, 2014
Pros: Everything. So modern and new.
Cons: The lighting. There are so many built-in lights, and I couldn't get two of them to turn off. So when maintenance tried to fix it, he blew a fuse.
I had a very short time in Chengdu, due to getting delayed by the typhoon in Haikou. so I was so happy when I arrived in Chengdu and had booked such a lovely hotel. Very modern, and the view at night out of the hotel window was marvelous. Even though I hadn't paid for breakfast, they were so nice to include it for free when my trip was delayed. The restaurant in the hotel was wonderful as well. The rooms were huge, with a beautiful marble and glass bathroom, a large closet, two televisions, etc. It was unbelievable! Wonderful beds, and a variety of pillows. And the staff were so nice and accommodating. I wanted to use the business center, but it was closed, so they opened it just for me. Really wonderful service.
by Randy from NJ, USA
Nice modern Hotel, poor restaurant servicePosted Aug 8, 2014 on Hotels
The hotel was very nice, with a very modern room suite. Bathroom was huge and had a great rain shower and separate big deep tub. There was also a pretty nice buffet breakfast included. The service at the restaurant the first morning was great- you barely finished the last scrap from your plate and they were taking it away, However service for dinner was about the worst I've ever seen. Three of us ordered together and they brought each of our meals out one at time- so far apart that each person was pretty much through with their meal as the next person's dish came out. Then we all had to wait and wait. Finally after every other customer had left, we gave up on getting desert and were able to get the check. It was an expensive meal with 15% service added on (and the service had been close to non-existent). I signed the bill charging it to my room. We were then going to bed, having to get rested for our early morning flight, when there was a knock at the door. There stood a waitress, telling me I couldn't charge the bill to my room, because the total was about 4RMB (yes, less than a dollar) higher than the deposit they had charged to my card when I arrived. OK, I had to get dressed while she waited in the hallway, to then escort me back to the restaurant to pay the bill there with my credit card. A really bad experience during an otherwise enjoyable stay.
by A verified traveler
Posted Jun 30, 2014 on Hotels
by CindyHongKong from Hong Kong
Clean and spacious room, good servicePosted Jun 5, 2014 on Hotels
Rooms are of good size, and I got free upgrades which is always a plus. What impressed me most was when I called the concierge in the morning to enquire about distance from the hotel to the bus terminal where I can buy same day ticket to Jiuzhaigou. The young man not only told me what I asked, but after I hung up he actually called me back in two minutes to tell me that he had checked on the internet and there were only 7 bus tickets left for the time I wanted and I should buy quick before they got sold out. I was really impressed by his initiative and wish to express to him my token of thanks. I forgot to note his name but that was 7:30 am on June 4.
for Everyoneby Greg from Perth Australia
Good valuePosted May 28, 2014
Great hotel which is very well appointed and reasonably priced. Very comfortable with modern fittings to make the stay enjoyable. Would thoroughly recommend it if visiting Chengdu.
for Business Travelersby Travels tooo much
Great Modern medium size hotelPosted May 8, 2014 on Orbitz
Really nice refreshing hotel. The kind of place that makes staying in a hotel in a foreign country one of the highlight experiences. its a cool place. not the most amenities. Was not there long enough to even go to the gym, but staying there was fun and i would stay there again for sure. It's an adult hotel. I w/ not consider this property the kind of place I w/ go back to with kids.
by A verified traveler
Probably the best modern hotel in CDPosted Mar 7, 2014 on Hotels
Stayed here for 2 nites. Very modern style. Great location. Friendly staff. Tasty food. Everything is perfect for us. Will definitely stay in this hotel again if revisit Chengdu.
by A verified traveler
Posted Mar 2, 2014 on Hotels
Service on the first day was bad. Subsequent days were Better.


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Brace yourself for a more electric future. We recently announced that Ford will invest US$4.5 billion (CAD$6.54 billion as of the date of publication) into expanding and innovating our fleet of electrified vehicles over the next four years. That investment comes in addition to the funding we have already committed to cleaner and more efficient technology.
We'll be using this investment to drive new innovation in electrified vehicle technologies, like US$2.1 million (CAD$3.05 million as of the date of publication) to research better battery technologies at the University of Michigan.
What does this mean for consumers? A future with more electrified options in the Ford lineup, and even better in-vehicle technologies. We'll be adding 13 new EVs to our portfolio by 2020—meaning 40 percent of all of our nameplates around the world will be offered in electrified versions. First out of the gate next year will be a new Focus Electric, which will come with lightning-fast, 480 Volt DC charging capability that can juice up 80 per cent of the car battery's capacity in just 30 minutes, with a projected range of 160 kilometres. It will also feature technologies that will help drivers maximize vehicle efficiency.
Building Cars Around Drivers
As part of this investment, we're reimagining the design and development process altogether, shifting to focus on the driver experience, and not just the vehicle itself. We're exploring how consumers interact with vehicles, gaining insight into the cognitive, social, cultural, technological and economic nuances that impact product designs. This refocusing puts the owner's experience while driving a vehicle at the center of how we think about building it.
"This new way of working brings together marketing, research, engineering and design in a new way to create meaningful user experiences, rather than individually developing technologies and features that need to be integrated into a final product," said Raj Nair, executive vice president, Product Development. "We are using new insights from anthropologists, sociologists, economists, journalists and designers, along with traditional business techniques, to reimagine our product development process, create new experiences and make life better for millions of people."
"As both an auto and a mobility company, we at Ford are going further than just designing the product to move people from point A to point B," Nair said. "We are considering the way customers interact with our vehicles as a unified experience, looking for ways to excite and delight customers and make their lives better."
And now, getting into a Ford electrified vehicle has never been easier! With government incentives available in some provinces, the cost of buying or leasing a Ford electrified vehicle may be comparable or even less than its gas-powered counterpart. Learn more here.


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Travis: I was groped by three 'very famous' women
Dave Lee Travis has told a court "half the country would be in jail" if patting or pinching a woman's bottom was a crime in the 1970s.
And he told the jury in his sexual assault trial that during his career he had been groped by three "very famous" women, who had squeezed his manhood.
He said: "I could give you names of four women, three of whom are very famous, who have groped me - and I mean groped me.
"I don't mean touch my back or bottom, but they have put their hands down my legs and squeezed me.
"Do you want their names? I'm not going to give them to you. But it happened."
Travis, who faced a tense grilling under cross examination in the dock, told jurors at Southwark Crown Court that he was amused that prosecutors were questioning him over his sex life.
He said: "I do find it funny because you are still going down this road. It is as if you are saying that women were queuing up to sit on my knee and have sex with me and that is not the case."
Miranda Moore QC, prosecuting, replied: "You weren't really a sex symbol were you?"
Chuckling slightly Travis said: "I take that as a personal insult. I would have thought I was fair to middling."
Ms Moore QC retorted: "Your public persona was big, hairy and jokey - not a sex symbol regardless of thinking you were."
Travis conceded: "I've never said I'm a sex symbol, I doubt it. You are right. I'm a big hairy bear."
The DJ, 68, was also quizzed over claims he "jiggled" the breasts of a BBC Radio 4 Woman's Hour announcer while she was live on air in the early 1980s.
He told the court that he would have thought someone was "crazy" if they groped a woman - but said if he had it would have been a joke.
He said: "At the time if I had decided to do that it would not have been me doing an indecent thing, but it would not have been me anyway.
"If I do something I do it as a lighthearted joke. But that does not include jiggling people's breasts up and down."
I've never said I'm a sex symbol, I doubt it. You are right. I'm a big hairy bear
In an increasingly tense exchange, the DJ was asked about comments he made to police that described men touching women in the 1970s as "flirtatious".
The DJ said: "I never agreed it was OK to carry on.
"I was saying that, based on this case and the ladies who have come forwards from 1973 or 1981 or 82, and I had grabbed somebody's bottom and pinched their bottom and I was asked that by the police I would say yes - I did that."
Laughing slightly, he added: "I'm saying, why would I want to go through the pain of cross examination about this? I would own up to it.
"If patting somebody's bottom was a crime in the 1970s half the country would be in jail I suppose."
The former Top of the Pops presenter maintained he never sexually assaulted anyone but said he had been "tactile" with female fans, touching them and giving them hugs.
He said he was a victim of "a witch hunt" by women who were lying, mistaken, or even bearing a "grudge" because he did not sign autographs for them.
The court had earlier heard that when he was quizzed by police about a string of sex offences he told them: "When you are in a sweetshop you don't eat sweets."
Explaining what he meant by these words, Travis said: "In general as a personality there are invariably a lot of women around the place and it is because you don't need to go out searching for everybody."
He said he did have "consensual sex and consensual kissing" but he insisted he had never sexually assaulted anybody.
He added: "If you are in a situation of trust, you are a broadcaster it is not the thing to do to be taking advantage of women at any time.
"But what I'm saying is, I'm not an angel."
The married DJ also appeared to say that women were always the instigator when he strayed from his wife.
Asked by Ms Moore QC if he "simply gave into temptation when women offered their affections to you", Travis replied "yes".
Travis denies 13 indecent assaults and one sexual assault involving 11 woman and spanning 30 years.
The case continues.


text: I live in Cary NC( Zone 7 ). I am getting ready to lay empire zoysia sod this weekend. I was wondering if there would be any benefit to applying some organic fertilizer before I lay the sod, and raking it in? I was thinking it may activate the soil a bit. I tilled and leveled the yard this past weekend. If so, any recommendations for a good organic fertilizer? I was thinking perhaps corn meal. I also have a small bag of starter fertilizer that I was planning on spreading a day or so before I lay the sod. Thanks!


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Search Results for "definition of success"
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Thursday April 22,
Tags #meeting, #definition of success, #slowing of failure, #rate of doing nothing, #improve
The Boss says, "The company is happy to annouce that compaired to previous years, we improved our rate of revenue decline." The Boss says, "We've been doing great since we redefined success as a slowing of failure." The Boss says, "Moving on. Who has a status report?" Wally says, "I improved my rate of doing nothing."
Wednesday January 28,
Success Is About Who You Know
Tags #success, #blame, #blaming
Wally: Success is all about who you know. I'm not successful, so apparently it doesn't help to know you. Dilbert: I"m sorry I let you down. Wally: It's as if you aren't even trying.
Tuesday June 29,
Tags #slug, #success, #energy, #fast, #fat, #stick paper, #slimy, #face
Dilbert says, "My success depends on your doing your role in a timely and energetic manner." Dilbert says, "People say you're a big, fat slug, but I have confidence in you. I'll stick this to your slimy face and hope for the best." Dilbert says, "I like to think I'm a pretty good judge of character."
Wednesday July 07,
Tags #report, #oil rigs, #explode, #medicine, #bacteria, #pharmaceuticals, #government, #share holder, #success, #lie
The Boss says, "I'm happy to report that none of our oil rigs exploded." The Boss says, "Our children's pharmaceuticals are not tainted with bacteria, and the government is not investigating our financial practices." The Boss says, "All we're doing is quietly losing share-holder value." CEO says, "I knew it would feel like success if we kept at it!"
Saturday July 24,
Tags #Advice, #death ray, #invention, #evil, #coffee maker, #disservice, #success, #garbage man
Dilbert says, "My company wants to turn my invention into a death ray. How can I stop them from succeeding?" Garbage man says, "There is one natural force that can stop any form of success. It goes by the name?" Dilbert says, "Wally?" Wally says, "How may I be of disservice?"
Friday November 19,
Tags #website, #revamp, #launch, #technology, #crash, #success, #failure
Dilbert says, "We launched our revamped website today." Dilbert says, "All of the technology we used is already obsolete and every vendor we hired is out of business." Dilbert says, "?And it just crashed." Dilbert says, "I miss the days when we had brief windows of success."
Monday June 23,
Wally: Success depends on who you know. I only know losers such as you, so thanks for nothing. Dilbert; I'm sorry I ruined your promising career. Wally: You're holding me back.
Saturday February 14,
Fifty Tips For Success
Tags #success, #secret, #obliviousness, #Advice, #career advice
Asok: A 27-year-old tech millionaire published his list of fifty things you need to do to succeed. Dilbert: In other words, he has no idea why he succeeded. Asok: Sure he does. He even has a chart of his top thirty... priorities. Okay, I hear it now.
Friday May 08,
Celebrate Failure
Tags #success, #failure, #credit, #taking credit, #reasoning, #managers
Boss: Failure is the raw material of success. From now on, I will celebrate your failures. Dilbert: Will you still be taking credit for our successes? Boss: That part stays the same. I'm only trying to increase the contrast to your failures.
Monday June 22,
Not That Invested In Your Success
Tags #work ethic, #laziness, #communication, #excuse, #excuses
Wally: I made no progress on your project because I was waiting to ask you some questions. Coworker: You could have emailed me. Or texted me. Or stopped by my desk. Wally: I"m not that invested in your success.


text:
Simen is a Norwegian photographer turned designer and entrepreneur, who currently lives and moves around in Southeast Asia. A traveler at heart, he loves to share his stories about faraway places and weekend getaways. His writing contains everything from photography tutorials to health tips and interviews.
Simen left Norway at the age of 21, and has since lived in Amsterdam, Taipei, Ho Chi Minh City, and Bali.
Simen is the founder of Nemis Clothing and PASAR FASHION ONLINE.


text:
Is rubbing your belly in front of people considered offensive?
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December 3rd, 2009, 02:28 PM
Mom at Home
homeschooling mom of 2
Join Date: Aug 2009
Location: Jersey Shore, but MI is home
Posts: 1,960
I've been rubbing mine all the time lately, mostly w/o even realizing it but also to clue people in that "hey I'm pregnant, not just fat" LOL and also because 1/2 the time lately its freaking sore from growing/stretching and pushing/rubbing on it makes it feel better. I'm also all for nursing mom's nursing anywhere they want, my IL's and DH's family were so anti nursing and expected me to usher myself and my newborn upstairs or in a back bedroom... I loved nursing her right in front of them w/o them even realizing it and then watching when they realized it's what she had been doing (just me being a bit sadistic though I suppose), but I always smile at any nursing moms I see and actually realize I have to make sure I don't stare, not to be rude or weird but just because after nusing my own DD for so long I see it as such a beautiful thing.
~ Candi
wife to Craig 5/28/2002 mom to Aliya 3/31/2004 and Liliana 4/6/2010
Mom at Home
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text:
Every week, we take an in-depth look at the three major fantasy football skill positions. On Mondays, we discuss quarterbacks. Look for running backs Wednesdays and wide receivers Thursdays.
Culpepper done for the season
The Vikings have confirmed that a disappointing year for Daunte Culpepper has ended early. A season-ending knee injury has now taken the first- or second-round pick of many fantasy teams away for the remainder of the campaign.


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GraphicRiver 3 Handcrafted Delicious Badges 3415129
Category: Web Element | Comment: ( 0 )
GraphicRiver 3 Handcrafted Delicious Badges 3415129
Web Element \ Badges & Stickers
Sweets \ Stickers \ Offer \ Special \ Textured \ Vector \ Yellow \ Vintage \ Shape
Web Element - 3 Handcrafted Delicious Badges 3415129 by zhumai @ GraphicRiver
Web Element \ Badges & Stickers
Graphics Files Included: Photoshop PSD; High Resolution: No; Layered: Yes; Minimum Adobe CS Version: CS6; Pixel Dimensions: 590x1210.
A nice collection of 3 Handcrafted Delicious Badges will suit great for your website, special offers or brochures.
You'll find full layered PSD file, 3 badges in PNG and text file with font's links.
If you want to customize badges, please, write me an e-mail ( [email protected] ).
- Full Photoshop shapes layers
- All text editable
- Well organized layers
- Free Google web fonts
I've used Google web fonts.
Noticia Text
Classic Pricing Tables; Price Tags; Christmas Gingerbreads; Travel Icons.
Keywords: badge, badges, brown, candy, cupcake, delicious, handcrafted, handmade, paper, price, retro, special offer, stickers, sweets, textured, vector shape, vintage, yellow.


text:
One woman's journey through life with invisible illnesses:
EDS (Ehlers-Danlos Syndrome, Hypermobility Type)
PoTS (Postural Tachycardia Syndrome)
LPHS (Loin Pain-Hematuria Syndrome)
Bipolar Disorder (Type II)
PTSD (Post-Traumatic Stress Disorder)
EDS (Ehlers-Danlos Syndrome, Hypermobility Type)
Wednesday, March 31, 2010
March 2010 Update
much love,
2 comments:
- Sweet Disorder Photography and Design said...
Yea! I'm glad you're still around! :)
I'm so sorry to hear about all you've been going through. EDS & POTS makes regular hardships so much harder. The last several months I started going through a divorce, and lost my little girl that I raised from ages 1-3. And, of course, my body decides it's time to be worse than ever. I totally understand you not writing! I hope things get better for you. Lots of love-
- April 1, 2010 at 9:09 AM
- Vegan Danielle Davis said...
@Jenn - Thank you so much for your sweet comment. I am glad to see that you are still around too! It is always so nice to see your comments - reminds me that there are others out there who are going through the same thing and I really am inspired at how we all persevere! I am sorry to hear about your divorce and your little girl. I am sure that is hard on top of the 'normal' hardships you endure. Please keep me posted and leave comments as you have time and are feeling up to it! I look forward to them! Much love and bendy hugs! xo
- April 17, 2010 at 7:17 PM


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Written on: 18/06/2005 by nick2004 (1 review written)
Good Points
Fast processor, nice dedicated 64mb graphics from ATI, Large harddrive, Four usb ports, Infrared (I like that because I can transfer to my mobile!) and a nice large screen.
Bad Points
Quite a short battery life, but I didn't buy this notebook for portability, more of a second PC really and you could always purchase a second battery as backup for on the go computing.
General Comments
Great quality/workmanship together with a fast processor and a dedicated 64mb graphics card from ATI make this notebook look great!
More than enough space with the 60 gigabyte harddrive,four usb ports to connect all your peripherals and the option to upgrade the memory or hard-drive make this notebook well worth the investment. Recommended!
As rated by our community of reviewers
" I mean for the price this laptop is okay but the sound is really ba... " Read More
Written by haleyrangers
" Remember not to include your name or names of staff members. Go in ... " Read More
" MSI GL72 17.3" Laptop i7 GTX 960M 16GB RAM 1000GB 128GB SSD " Read More
Written by AndrewWrob
" Recommendable for Average Use " Read More
Written by Lauren5
" Acer rubbish " Read More


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Posted by elliemae1 on 3/12/2017, 4:47 pm, in reply to "Re: US Rider - SO DUMB!"
Edited by elliemae1 on 3/12/2017, 4:50 pm
US Rider has done fine for me before, but this time I found out about their, "one service order at a time", policy.
So they wouldn't tell the dispatcher a boost AND Maybe a tow if the boost didn't work.
I'm working up the chain of command having quite the conversation, including in writing, about this with them. They're the ones who had to pay the dispatcher twice, not me.
Illegetimi non carborundum.
« Back to index | View thread »


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Bayview Limousine Service provided excellent, prompt and professional transfers for my VIP doctors and colleagues last week.
I regularly use Limousine Company's all across th...
All reviews seem positive
Limo rentals in the Seattle, WA area
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