What is the relationship between EGT, Fuel Flow, N1, N2 and Air Temperature?
I am not really sure what sort of engine failures you want to predict, but ECTM is usually used to detect things such as;


Worn air seals
Blade tip wear (compressors and turbines)
Compressor fouling
Eroded blades and turbine nozzle guides


These hardware issues cause changes in the “state variables”;


N1 (LPC) compressor efficiency 
N2 (HPC) compressor efficiency 
N2 (HPT) turbine efficiency 
N1 (LPT) turbine efficiency 


These changes in component efficiency then result in changes of the engine parameters;


N1 rpm
N2 rpm
Fuel flow
Exhaust gas temp
etc.


By detecting changes in the measurements, ECTM aims to tell you which module (LPC, HPC, HPT, or LPT) has degraded. Usually, it’s not possible to say why the efficiency has decreased (i.e. you can’t tell if it’s erosion of the blade leading edge, or worn blade tips), you can only tell which module is affected.

But the relationship you want between changes of efficiency and the measured parameters, is very complex. For that step, you need a performance simulation program, to give sufficient accuracy if you are actually going to apply the approach to data from a real engine. Otherwise, all one can say is, when an engine degrades, fuel flow, temperature, and rpms will go up. And they go up for most (or all) of the faults above. So, unless you know how much they change for each fault, you can’t tell which module has degraded. Then, your method is just saying “the engine has degraded” (not so useful), rather than why (and, only the LPC needs a repair, for example, which is cheaper and quicker than an HPC repair, because it requires a lot more disassembly).

But, if all you want to do is test an approach in theory, you could just make up the increase in each parameter, it doesn’t have to be accurate, because it’s just a mathematical example, you are not going to apply it to an actual engine, so the predicted effects of degradation don’t need to match reality closely. Just make up 4 different patterns of degradation;


degraded LPC: 50 rpm N1 increase, 200 rpm N2 increase, 5% inc in fuel flow, 200 deg inc in EGT
degraded HPC: 100 rpm N1 inc., 200 rpm N2 inc, 7% in in fuel flow, 150 deg inc in EGT


etc...

Then, create multiple examples of each fault by add a random amount of noise to each parameter, say &lt; or up to 1% of full scale value (and you can make full scale up as well, let’s say, N1 = 8,500 rpm, N2 = 12,250 rpm, fuel flow = 3.2 lb/s, EGT = 650 deg C.)

Now, you have examples with noise, of known faults. See how well your method can correctly find the faults....

Sure, it’s a little crude, but if you can’t get hold of a performance simulation program that lets you change the efficiency of the modules to generate the degraded fault behaviour, at least it lets you do something. You can play around with the numbers, and see what size enables you to detect a fault, and what size does it start to get confused/ wrong.