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I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on some sensors output. In the system, all these sensor readings form a signal which is constantly compared with a model and in the end create a remainder signal. In case of a sensor failure, the remainder signal violates pre-defined thresholds and raise an alarm.

For the system analysis, I use superposition law, meaning that except one, all inputs are considered zero and a step signal is propagated through the system. Here the step signal represents a sensor failure. With various approximations, I am able to get the corresponding transfer functions. That way, I can justify the system performance. However, this has raised lots of ambiguities. I am asked to justify and optimize the system performance (with the simultaneous consideration of all inputs) through time or frequency analysis. The result can be a frequency response or a mathematical equation or other system performance representations.

My questions: Since I am dealing with a relatively complex, nonlinear system, is there any way to analyze and optimize its performance with the simultaneous consideration of all inputs/sensor readings? Is there some good literature that I can study this topic from?

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    $\begingroup$ The general way to represent a nonlinear system that is also "dynamic", in that it also has memory of the past, is wirh Volterra series. But it's a big mess. $\endgroup$ Aug 18 '21 at 17:45
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If superposition works, then independent mode/component extraction is of interest. Synchrosqueezing is well-suited for this task. Extracted features can ten be fed to an anomaly detection system - optionally with Gaussianization.

Other methods can be applied to the extracted components as if they were individual signals, so the described approach is expansive and flexible.

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