How to use sensor data in an analysis?

[#1]

In the chemical process industry a lot of sensor data is captured (flows, levels, pressures, temperatures etc). This data can be described as time series non-stationary. Looking at a typical pattern, one might find a trend pattern (without seasonality or little = summer/winter or day/night) particular when looking at monotonic evolutions (such as fouling). But often the candidate features don't exhibit a trend pattern (unless the feature is used by the operator to compensate). if you have a plant issue that can be described by a certain measurement, the question often arrises: which other (set of) variable(s) caused this? Most analysis tools, for example PCA/LDA/Random forest, rely on stationary data. I want to avoid trying to create a state space model to compensate for non-stationary situations. Alternatively I could perform a double exponential smoothing, but that is only usable if I have a clear trend.

My question is: how to transform this data in such a way that I can use it for analysis such as PCA for example (and not using wavelet PCA)?

Thanks!

[#2]

Do you have access to JMP Pro? The scenario you describe is tailor made for using the Functional Data Explorer platform and associated modeling capabilities. Here's a link to a presentation given by my former (I'm retired) colleague Tom Donelly on this very topic: Modeling Streamed Sensor Data 

[#3]

Unfortunately I don't have JMP Pro

[#4]

I am assuming that you are asking how to transform multivariate time series data so you can analyze using PCA stated as on this wiki page Principal component analysis .

The analysis expects that the data are sampled from a P-dimensional random variable, and there are N samples. To the analysis, the order of samples does NOT matter, or in another word it does not care. In your example, it won't care stationary or not. Meanwhile, it won't stop you from supplying such data, in which the order of samples has a meaning. And it won't be irrelevant if one decides to ignore the order and look at the data from a different angle. Try throwing the raw data in and see what you may discover, or what inspiration you may get from the result. The main application of PCA is dimension reduction, e.g. reducing from P-dimensional data to a Q-dimensional data, where Q is much smaller than P. By that, you are already transforming your data to suit your needs, if that makes sense. In addition, you did not mention that you had tried differencing. Maybe you should try that and see whether that transformation means anything to you.