Time varying correlation: suggestion

[serbring]

Hi,

I made some measurements in a vehicle and I have one output signal (i.e. force in a vehicle component) and many input signals which few are digital (discrete only 2 values are possible) and others are anolog (continuous variables).Here you can see the output signal and two of the many input signals I have. As you can see all the signals are non stationary and the two plotted input signals lead to big oscillations in the output signals (e.g. at 460s when the input 1 signal changes from 0 to 1 or between 540s and 560s where there input2 oscillates and the same does the output signal).

I need to know for each big change in the output signal which input signal or group of input signals have generated it. My first idea was to compute the time-varying correlation between the force signal and all the input signals and by checking the instants where the correlation coefficients are high, thus I will be able to identify which input signals have lead to a locally big change of the output signal. At first, I used the moving window approach (i.e. fixed window size) and I used the Pearson's coefficient to evaluate the correlation. But as you can see , the correlation is strongly non linear especially with digital signals and windows size heavily affects the correlation values. Then I switched to the distance correlation coefficient, but the results slightly improved in less evident correlations. I tried with this basic method because I'm new in this topic, but probably more advanced ones exist, which they better detect relevantcorrelations. Which method would you suggest me to further improve the correlation detection? Any suggestions is appreciated.
Thanks

 

[mmwave]

Thank you for sharing your research and question. I would suggest using a more advanced method for identifying correlations between your input and output signals. One method that may be helpful is called dynamic time warping (DTW). DTW is a technique that can measure the similarity between two time series signals, even if they have different lengths or are non-stationary. It is commonly used in fields such as speech recognition and bioinformatics, but it can also be applied to your situation.

Another approach you could consider is using a machine learning algorithm, such as a neural network, to identify correlations between the input and output signals. This would involve training the algorithm on your data and then using it to predict which input signals are most likely to lead to big changes in the output signal. This method may require more data and expertise, but it could potentially provide more accurate results.

In addition to using these methods, it may also be helpful to consider the physical relationships between the input and output signals. For example, if you have knowledge of the system and its components, you may be able to identify which input signals would have the most influence on the output signal.

I hope this helps and good luck with your research!