BACKGROUND 
       [0001]    The field of the disclosure relates generally to structural health monitoring, and more specifically, to systems and methods for providing temperature compensation in structural health monitoring. 
         [0002]    Many structural health monitoring (SHM) systems operate by producing a vibration signal, for example by exciting a piezo-electric (PZT) actuator bonded to a structure, and then reading that signal with a PZT sensor bonded at a separate location. Any damage that has occurred between the two PZT transducers will change the characteristics of the transmitted signal, as compared to the characteristics of a transmitted signal where no damage has occurred between the two transducers. 
         [0003]    Many SHM algorithms work in the time domain by comparing a reference, or baseline, signal with a comparison signal that may be indicative of damage. In a properly operating SHM system, the degree of difference between the two signals is proportional to the size of damage in the structure. Examples of damage in such structures include a crack having a length or a delamination area within the structure. 
         [0004]    Although there are many ways to measure the difference between two signals, normalized RMS error is one very common measure. The RMS error is calculated by subtracting the comparison signal from the reference signal forming an error signal. Each sample of this error signal is squared and summed. The result is divided by the number of samples to get the mean square value and the square root of this value is taken. This is the Root Mean Square or RMS of the error signal. This number is then normalized by the RMS value of the reference wave. 
         [0005]    Unfortunately damage is not the only variable that can change a signal. A real world effect that strongly affects a signal is the temperature of the structure when the PZT actuator produces the signal and the PZT sensor measures the signal. One effect of temperature change is to stretch (heating) or compress (cooling) the signal with a secondary effect of distorting the shape of the signal. Due to this effect, the mean squared error between two waveforms recorded at temperatures only a few degrees apart is of the same order of magnitude as the mean squared error between waveforms recorded from a structure before and after damage. 
       BRIEF DESCRIPTION 
       [0006]    In one aspect, a method for compensating for environment induced variations in structural health monitoring application data is provided. The method includes imparting a vibration signal onto a structure at a first location, the structure at a first temperature, receiving a comparison signal at a second location of the structure, the comparison signal resulting from the vibration signal, accessing data representing a reference signal, the reference signal previously received at the second location, based on an imparted vibration at the first location, the reference signal received when the structure was at a second temperature, dividing the comparison signal and the reference signal across a plurality of time windows, performing a cross correlation between the comparison signal and the reference signal in each time window by recording an amount of time shift required to maximally correlate the comparison signal and the reference signal within each time window, performing a weighted regression on time to estimate time delay, the weights based on a relative amount of signal energy from the reference signal in each time window, to determine a relationship between time and time shift as a quadratic or higher order equation, and using the determined relationship between time and time shift of the comparison signal to reduce the effects of environment on the comparison signal. 
         [0007]    In another aspect, one or more computer-readable storage media having computer-executable instructions embodied thereon are provided, wherein when executed by at least one processor, the computer-executable instructions cause the at least one processor to receive comparison signal data relating to a vibration experienced at a location of a structure, the comparison signal data resulting from a vibration signal imparted onto the structure at a different location, the comparison signal data generated when the structure is at a first temperature, access data representing a reference signal, the reference signal previously received at the structure location, and also based on an imparted vibration at the different location, the reference signal received when the structure was at a second temperature, divide the comparison signal and the reference signal across a plurality of time windows, perform a cross correlation between the comparison and reference signals in each of the time windows by recording an amount of time shift required to maximally correlate the two signals within each time window, perform a weighted regression, the weights based on the relative amount of signal energy from the reference signal in each time window, to determine a relationship between time and time delay as a quadratic or higher order equation, and use the relationship between time and time delay to reduce the effects of environment on the comparison signal. 
         [0008]    In still another aspect, a method of compensating for temperature effects in a structural health monitoring system is provided. The method includes compensating for nonlinear phase changes in a comparison signal, as compared to a reference signal, wherein a phase shift factor is replaced with a general function, implementing a weighted regression of time shifts associated with the comparison signal across each of a plurality of time windows to determine parameters of the general function, implementing a time-shift outlier correction process onto the weighted regression, and processing the comparison signal using the general function and the parameters determined for the general function to provide output corresponding to a reduction in a stretch or a compression of the reference signal and the comparison signal. 
         [0009]    The features, functions, and advantages that have been discussed can be achieved independently in various embodiments or may be combined in yet other embodiments further details of which can be seen with reference to the following description and drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a graph illustrating simulated PZT sensor data, a reference signal received from the sensor at one temperature, and a comparison signal received from the sensor at a different temperature. 
           [0011]      FIG. 2  is an illustration of the waveforms of  FIG. 1  divided into multiple time windows. 
           [0012]      FIG. 3  is a magnified illustration of a single time window from  FIG. 2 . 
           [0013]      FIG. 4  illustrates a plot of time against time-shift for a fourteen window sample of a comparison signal and a reference signal. 
           [0014]      FIG. 5  illustrates a plot of time against time-shift for the fourteen window sample of a comparison signal and a reference signal of  FIG. 4 , and further illustrates a bias in calculated phase shift when it is assumed that time delay at time zero is zero. 
           [0015]      FIG. 6  is illustrates incorporation of the intercept which leads to a removal of the bias in phase shift that is illustrated in  FIG. 5 . 
           [0016]      FIG. 7  illustrates that removal of the bias in the phase shift estimation is not enough, alone, to provide good compensation. 
           [0017]      FIG. 8  illustrates that the majority of the signal energy is contained within the fourth and fifth time windows of the fourteen widow sample. 
           [0018]      FIG. 9  illustrates the use of weighted regression for placement of the phase shift line. 
           [0019]      FIG. 10  shows, in a top graph, a wave against a reference wave with the time delay curve calculated with standard regression, and in a bottom graph, a properly compensated wave against the reference wave, the properly compensated wave generated using weighted regression. 
           [0020]      FIG. 11  illustrates a outlier produced in the tenth time window number of the fourteen window sample and how the outlier skews the resultant regression line down, away from the rest of the data points. 
           [0021]      FIG. 12  illustrates that the pattern of time delay with respect to time is strongly curved for non-homogenous structure such as composites. 
           [0022]      FIG. 13  is a flow diagram of an aircraft production and service methodology. 
           [0023]      FIG. 14  is a block diagram of an aircraft. 
           [0024]      FIG. 15  is a diagram of a data processing system. 
       
    
    
     DETAILED DESCRIPTION 
       [0025]    As stated above, the temperature of the structure when the PZT actuator produces the signal and the PZT sensor measures the signal can affect test measurements and results in a phase change of the signal with respect to the original temperature. For a given temperature change, this can be modeled as y(t)=x(t−ζt) (Equation 1), where ζ is the phase shift factor. 
         [0026]    Equation 1 can be understood better by examining  FIG. 1 , which illustrates two sets of simulated PZT sensor data taken at different temperatures. The comparison signal  10  appears to be a stretched version of the reference signal  20 . In  FIG. 1  it is clear that at the beginning, the comparison signal  10  and the reference signal  20  are nearly identical and lie directly on one another. As time passes, however, the comparison signal  10  appears to be stretching away from the reference signal  20 , with more stretching occurring as additional time passes. This stretching is commonly referred to as phase shift as measured by time delay. 
         [0027]      FIG. 2  is an illustration of the waveforms (comparison signal  10  and reference signal  20 ) of  FIG. 1  divided into multiple time windows. The amount of time delay associated with each window can be calculated. As shown in  FIG. 2 , the amount of time delay is greater in each succeeding window. 
         [0028]      FIG. 3  is a magnified illustration of a single time window  50  from  FIG. 2 . The reference signal  20  and the comparison signal  10  are magnified. The double headed arrow  60  denotes the amount of time delay in time window  50 . The amount of time it would take to shift the comparison signal  10  to make it coincident with the reference signal  20  is the measure of time delay. This calculation is done using a short time cross correlation. 
         [0029]      FIG. 4  illustrates a plot  100  of time  102  against time shift  104  for a fourteen window sample of comparison signal  10  and reference signal  20 . By performing a linear regression, time shift as a function of time can be calculated. Note that the phase shift factor ζ (per Eq. 2) has been calculated as the coefficient of t in  FIG. 4  and has the value of 0.002212. 
         [0030]    Issues in calculating the phase shift factor can occur under various adverse conditions. For example, large defects in a structure have been shown to produce erroneous estimates (e.g., outliers) of time shift in various time windows. These outliers, if left in the data set skew the estimate of the phase shift factor and therefore result in poor temperature compensation. One method to remove such outliers is to use only the first half of the waveform. A second method is to set an upper limit on the maximum values of the calculated time delay based on cross correlating adjacent (temperature-wise) baseline waveforms which are presumed to provide a basis for a clean calculation. 
         [0031]    Robust Temperature Compensation for Non-Homogenous Structures and Noisy Environments 
         [0032]    The process set forth above, as well as the described methods to remove outliers, are insufficient for providing temperature compensation in composite structures, especially when there is more than a 10 degree C. temperature change between each baseline waveform. A number of improvements have been made to in order to provide temperature compensation under more difficult conditions. These difficult conditions include large defects, large temperature differences between the two waveforms, and non-homogenous structure such as those made from composite materials. 
         [0033]    y(t)=x(t−ζt) makes the implicit assumption that the time shift at time-zero is 0.0. As shown in  FIG. 5 , making this assumption in all cases will cause a bias in the calculated phase shift and will result in inaccurate temperature compensation. One known cause of this bias is caused by hardware time delays in reporting true excitation start times. In other cases it may simply be convenient to truncate a small portion of the start of the waveform to remove corrupted signal. 
         [0034]    In any case the phase shift factor is replaced with a more general function of time, ‘t’, as follows: y(t)=x(t−ƒ(t)), with ƒ(t) being ζt+φ, where ζ represents the slope of the time delay curve and φ is the curve intercept accounting for any system biases.  FIG. 6  illustrates incorporation of the intercept which leads to a removal of the bias in phase shift. It is noted that the time against time shift line now passes through the data points. 
         [0035]    Although this method removes the bias in the phase shift estimation, it alone is not enough to provide good compensation as shown in  FIG. 7 . The reason this compensation worked so poorly is due to the important fact that each time delay data point is treated as equally important despite the fact that a minority of the points represent most of the energy in the signal. Examining  FIG. 8 , it is clear that most of the signal energy is contained within the fourth and fifth time windows. If the compensation is off in those windows, there will be a large difference in the normalized RMS error, whereas if the compensation were off in windows  1 ,  13 , and  14 , it would hardly register in the error. 
         [0036]    What is needed then is a way to emphasize data points in high energy time windows and place less emphasis on time delay data points in low energy time windows. This emphasis and reduction in emphasis is accomplished using a technique called weighted regression. Weighted regression is a technique that emphasizes some data points over others by weighting each data point with a weight ‘W’ according to some criterion. Weighted regression has the effect of replicating each data point ‘W’ times. Determining what the weights should be has a large impact on the effectiveness of this approach. 
         [0037]    In regard to the SHM application described herein, the normalized RMS values of the reference signal contained in each window are used as the weights although the comparison signal could be used instead. Using these values as weights properly rewards and penalizes each time delay data point according to its energy (importance). 
         [0038]    Using weighted regression on time to estimate time delay, with the weights based on a relative amount of signal energy from the reference signal in each time window, the new placement of the phase shift line is shown in  FIG. 9 . Note that the three most important points in terms of energy are all well above the line in the top graph  200  of  FIG. 9 . Graph  200  is compared to the bottom graph  210  of  FIG. 9  where the energy of the time windows is taken into account. It is noted how the line in graph  210  now passes through or very near each point. 
         [0039]    Performing the temperature compensation process with this newly generated time delay line produces a very good compensated signal as is shown in  FIG. 10 . Specifically, the top graph  300  shows the poorly compensated wave  310  against a reference wave  312  with the time delay curve calculated with standard regression. The bottom graph  320  shows a properly compensated wave  330  that was generated using the regressing line generated using weighted regression. 
         [0040]    Under various adverse conditions such as non-homogenous structures such as composites, large damage sites, or large temperatures differentials, time delay data points can be calculated that don&#39;t follow the trend of other data points. These outliers can skew the regression line and lead to poor temperature compensation. For example,  FIG. 11  illustrates an outlier  350  produced in time window number  10  and how it skews the resultant regression line  352  down, away from the rest of the data points. 
         [0041]    Noting that a temperature change produces changes that are either all stretching or all compressing suggests a way to correct for these outliers. First, the time delay data point associated with highest window energy is most likely to be calculated correctly due to its very high signal to noise ratio. Deformations caused by defects or material characteristics will have the smallest overall affect on these high energy waveforms. Thus it can be established if the waveform is stretching at all points or contracting at all points. Once any stretching or contracting has been established, a short time cross correlation algorithm can be run, and run only on those signal points consistent with the observation. In other words, the comparison waveform either slides to the left to become coincident or it slides to the right. The high energy portion of the waveform determines in which direction the waveform should slide. 
         [0042]      FIG. 11  shows the point of highest correlation for a positive time delay lies close to the trend of the other points. The regression lines calculated from these corrected points provides for good temperature compensation. 
         [0043]    Non-Linear Functional Representation of Time Delay 
         [0044]    Although in homogenous structures such as aluminum the time delay is linear with respect to time, this is not always the case for non-homogenous structure such as composites. As shown in  FIG. 12 , the pattern of time delay with respect to time is strongly curved. While a linear fit using weighted regression will correctly compensate the fifth time window of  FIG. 12 , most of the rest of the waveform will be poorly compensated. One solution is to replace the ƒ(t) in y(t)=x(t−ƒ(t)) with a ƒ(t) capable of modeling nonlinear behavior. Once such formula is ƒ(t)=αt 2 +ζt+φ, which leads to y(t)=x(t−(αt 2 +ζt+φ)) which models time delay as a quadratic function of time. In one alternative of this embodiment, the formula may model as a higher order equation. 
         [0045]    Using ƒ(t)=αt 2 +ζt+φ to generate the regression curve leads to an accurate representation of the time delay data and thus a good temperature compensation obtained using y(t)=x(t−(αt 2 +ζt+φ)). 
         [0046]    The described embodiments provide temperature compensation improvements when interpreting SHM data by reducing the effects of environment on the comparison signal. For example, one improvement relates to replacing the phase shift factor 4 with a general function ƒ(t), specifically y(t)=x(t−(αt 2 +ζt+φ)). This configuration change compensates for nonlinear phase changes in nonhomogenous structures and removes time delay biases. 
         [0047]    Implementation of weighted regression using time window energy as the relative weighting function maximizes the effectiveness of the compensation by focusing on the most important sections of the signal and by eliminating a need to use the ‘first half of signal’ as described above. In addition, an implementation related to forced time delay consistency provides a robust outlier elimination process independent of the need for additional baselines. 
         [0048]    Embodiments of the disclosure may be described in the context of aircraft manufacturing and service method  600  as shown in  FIG. 13  and an aircraft  700  as shown in  FIG. 14 . During pre-production, aircraft manufacturing and service method  600  may include specification and design  602  of aircraft  700  and material procurement  604 . 
         [0049]    During production, component and subassembly manufacturing  606  and system integration  608  of aircraft  700  takes place. Thereafter, aircraft  700  may go through certification and delivery  610  in order to be placed in service  612 . While in service by a customer, aircraft  700  is scheduled for routine maintenance and service  614  (which may also include structural health monitoring (SHM), modification, reconfiguration, refurbishment, and so on). 
         [0050]    Each of the processes of aircraft manufacturing and service method  600  may be performed or carried out by a system integrator, a third party, and/or an operator (e.g., a customer). For the purposes of this description, a system integrator may include, without limitation, any number of aircraft manufacturers and major-system subcontractors; a third party may include, for example, without limitation, any number of venders, subcontractors, and suppliers; and an operator may be an airline, leasing company, military entity, service organization, and so on. 
         [0051]    As shown in  FIG. 14 , aircraft  700  produced by aircraft manufacturing and service method  600  may include airframe  702  with a plurality of systems  704  and interior  706 . Examples of systems  704  include one or more of propulsion system  708 , electrical system  710 , hydraulic system  712 , and environmental system  714 . Any number of other systems may be included in this example. Although an aerospace example is shown, the principles of the disclosure may be applied to other industries, such as the automotive industry. 
         [0052]    Apparatus and methods embodied herein may be employed during any one or more of the stages of aircraft manufacturing and service method  600 . For example, without limitation, components or subassemblies corresponding to component and subassembly manufacturing  606  may be fabricated or manufactured in a manner similar to components or subassemblies produced while aircraft  200  is in service. 
         [0053]    Also, one or more apparatus embodiments, method embodiments, or a combination thereof may be utilized during component and subassembly manufacturing  606  and system integration  608 , for example, without limitation, by substantially expediting assembly of or reducing the cost of aircraft  700 . Similarly, one or more of apparatus embodiments, method embodiments, or a combination thereof may be utilized while aircraft  700  is in service, for example, without limitation, to maintenance and service  614  may be used during system integration  608  and/or maintenance and service  614  to determine whether parts may be connected and/or mated to each other. 
         [0054]    The description of the different advantageous embodiments has been presented for purposes of illustration and description, and is not intended to be exhaustive or limited to the embodiments in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. Further, different advantageous embodiments may provide different advantages as compared to other advantageous embodiments. The embodiment or embodiments selected are chosen and described in order to best explain the principles of the embodiments, the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated. 
         [0055]    Turning now to  FIG. 15 , a diagram of a data processing system is depicted in accordance with an illustrative embodiment. In this illustrative example, data processing system  800  includes communications fabric  802 , which provides communications between processor unit  804 , memory  806 , persistent storage  808 , communications unit  810 , input/output (I/O) unit  812 , and display  814 . 
         [0056]    Processor unit  804  serves to execute instructions for software that may be loaded into memory  806 . Processor unit  804  may be a set of one or more processors or may be a multi-processor core, depending on the particular implementation. Further, processor unit  804  may be implemented using one or more heterogeneous processor systems in which a main processor is present with secondary processors on a single chip. As another illustrative example, processor unit  804  may be a symmetric multi-processor system containing multiple processors of the same type. 
         [0057]    Memory  806  and persistent storage  808  are examples of storage devices. A storage device is any piece of hardware that is capable of storing information either on a temporary basis and/or a permanent basis. Memory  806 , in these examples, may be, for example, without limitation, a random access memory or any other suitable volatile or non-volatile storage device. Persistent storage  808  may take various forms depending on the particular implementation. For example, without limitation, persistent storage  808  may contain one or more components or devices. For example, persistent storage  808  may be a hard drive, a flash memory, a rewritable optical disk, a rewritable magnetic tape, or some combination of the above. The media used by persistent storage  808  also may be removable. For example, without limitation, a removable hard drive may be used for persistent storage  808 . 
         [0058]    Communications unit  810 , in these examples, provides for communications with other data processing systems or devices. In these examples, communications unit  810  is a network interface card. Communications unit  810  may provide communications through the use of either or both physical and wireless communication links. 
         [0059]    Input/output unit  812  allows for input and output of data with other devices that may be connected to data processing system  800 . For example, without limitation, input/output unit  812  may provide a connection for user input through a keyboard and mouse. Further, input/output unit  812  may send output to a printer. Display  814  provides a mechanism to display information to a user. 
         [0060]    Instructions for the operating system and applications or programs are located on persistent storage  808 . These instructions may be loaded into memory  806  for execution by processor unit  804 . The processes of the different embodiments may be performed by processor unit  804  using computer implemented instructions, which may be located in a memory, such as memory  806 . These instructions are referred to as program code, computer usable program code, or computer readable program code that may be read and executed by a processor in processor unit  804 . The program code in the different embodiments may be embodied on different physical or tangible computer readable media, such as memory  806  or persistent storage  808 . 
         [0061]    Program code  816  is located in a functional form on computer readable media  818  that is selectively removable and may be loaded onto or transferred to data processing system  800  for execution by processor unit  804 . Program code  816  and computer readable media  818  form computer program product  820  in these examples. In one example, computer readable media  818  may be in a tangible form, such as, for example, an optical or magnetic disc that is inserted or placed into a drive or other device that is part of persistent storage  808  for transfer onto a storage device, such as a hard drive that is part of persistent storage  808 . In a tangible form, computer readable media  818  also may take the form of a persistent storage, such as a hard drive, a thumb drive, or a flash memory that is connected to data processing system  800 . The tangible form of computer readable media  818  is also referred to as computer recordable storage media. In some instances, computer readable media  818  may not be removable. 
         [0062]    Alternatively, program code  816  may be transferred to data processing system  800  from computer readable media  818  through a communications link to communications unit  810  and/or through a connection to input/output unit  812 . The communications link and/or the connection may be physical or wireless in the illustrative examples. The computer readable media also may take the form of non-tangible media, such as communications links or wireless transmissions containing the program code. 
         [0063]    In some illustrative embodiments, program code  816  may be downloaded over a network to persistent storage  808  from another device or data processing system for use within data processing system  800 . For instance, program code stored in a computer readable storage medium in a server data processing system may be downloaded over a network from the server to data processing system  800 . The data processing system providing program code  816  may be a server computer, a client computer, or some other device capable of storing and transmitting program code  816 . 
         [0064]    The different components illustrated for data processing system  800  are not meant to provide architectural limitations to the manner in which different embodiments may be implemented. The different illustrative embodiments may be implemented in a data processing system including components in addition to or in place of those illustrated for data processing system  800 . Other components shown in  FIG. 8  can be varied from the illustrative examples shown. 
         [0065]    As one example, a storage device in data processing system  800  is any hardware apparatus that may store data. Memory  806 , persistent storage  808  and computer readable media  818  are examples of storage devices in a tangible form. 
         [0066]    In another example, a bus system may be used to implement communications fabric  802  and may be comprised of one or more buses, such as a system bus or an input/output bus. Of course, the bus system may be implemented using any suitable type of architecture that provides for a transfer of data between different components or devices attached to the bus system. Additionally, a communications unit may include one or more devices used to transmit and receive data, such as a modem or a network adapter. Further, a memory may be, for example, without limitation, memory  806  or a cache such as that found in an interface and memory controller hub that may be present in communications fabric  802 . 
         [0067]    This written description uses examples to disclose various embodiments, which include the best mode, to enable any person skilled in the art to practice those embodiments, including making and using any devices or systems and performing any incorporated methods. The patentable scope is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.
A method for compensating for environment induced variations in structural health monitoring data is described. The method includes imparting a vibration onto a structure first location, the structure at a first temperature, receiving a comparison signal resulting from the vibration at a second location, accessing data representing a reference signal previously received at the second location, based on vibration at the first location, the reference signal received when the structure was at a second temperature, dividing the signals across multiple time windows, performing a cross correlation between the signals in each window to maximally correlate the signals within each window, performing a weighted regression on time to estimate time shift, the weights based on reference signal energy in each window, to determine a relationship between time and time shift, and using the relationship between time and time shift of the comparison signal to reduce the effects of environment on the comparison signal.