Introductory Time Series

[NegativeKurtosis]

Hello Everyone,

New member and rather new to statistics / times series problems. I am an electro - mechanical engineer by trade and am tasked with solving with what I believe to be a times series problem. I am looking for some insight as to how I might approach said problem :

I have a DAQ ( data acquisition computer system ) that monitors low voltage signals from a giant water pump motor system. The DAQ provides a new signal every 15 minutes through out the day ( hence the times series question ). I am analyzing these low voltage signals with the ( ICWT ... inverse continuous wavelet transform in Matlab). With each new update, the series changes. I expect this as I'm adding an element to a series. Specifically I am wondering how to proceed in normalizing ( or stabilizing ) the time series so that the changes in the analysis in the underlying ICWT are not so drastic. In other words, maintain the approx trend of the signal. As you can see in the attached screenshot, this particular signal fluctuates between . 6898 and .6918. Currently, I am re-analyzing the entire time series each time a new low voltage element is added to the series. This causes radical shifts in the ICWT analysis. The objective here is to 'catch electrical anomalies before they cause significant damage'. I use the words 'normalize' and 'stabilize' because I am unsure how to describe analyzing or transforming the time series to achieve this effect.

I have read a bit about stationarity, differencing, auto correlation, ARIMA, etc but am unsure if any of those processes would be appropriate here. Would appreciate any suggestions. Hope this makes sense.

Thank You,
Richard

 

[noetsi]

If you are new to statistics time series is a rough place to start. To me it is probably the most difficult area of statistics.

ARIMA is designed to forecast future values. I have never seen it used for a process change such as you are addressing. You might look at spectral analysis - an entirely different type of time series used largely by engineers and physicists. I know only that it exists To me anyhow it seems closer to what you are interested in.

Miner probably is the one who's help you need.

 

[NegativeKurtosis]

Thanks for your reply and suggestion noetsi. I have used spectral analysis but it is more useful for static signal analysis. I couldn't find any info on the site or in the FAQ about sending a message to a specific user ( Miner ). Is that possible / recommended ?

 

[Miner]

I've been watching this thread, but am not clear on what NK is trying to do, so I don't know whether frequency analysis would help.

 

[Miner]

I couldn't find any info on the site or in the FAQ about sending a message to a specific user ( Miner ). Is that possible / recommended ?

Just add @ in front of the username like @NegativeKurtosis . You should now see an alert in the upper right of your screen.

 

[NegativeKurtosis]

Thanks for your reply and suggestion noetsi. I have used spectral analysis but it is more useful for static signal analysis. I couldn't find any info on the site or in the FAQ about sending a message to a specific user ( Miner ). Is that possible / recommended ?

I've been watching this thread, but am not clear on what NK is trying to do, so I don't know whether frequency analysis would help.

Scales ( used in Wavelet analysis ) are essentially equivalent to frequencies ( commonly used by the Fourier Transform ) both methods fall under the umbrella of signal / frequency analysis. However, my question is regarding time series. Specifically the dynamic analysis of a real time system. I was just wondering if there was a method in analyzing a dynamic time series. Let me try to illustrate with the following screenshot. I removed the red voltage signal line for clarity. I also adjusted the alpha values to provide variations in the shading of the bar time graph. Note the differing heights of the bar time graph with each voltage reading. Is there a specific process / transformation that should be used in time series analysis to mitigate this effect ?

Hope this provides some clarity.
Thanks,
Richard

 

[Miner]

This is more clear. Do the voltages follow, but vary around a known transfer function [Y=f(x)]? I'm thinking of the prediction intervals around a regression line.

 

[NegativeKurtosis]

I normally determine and use IQR values to create sort of a "confidence band" around these voltages. These are based on the time interval and of course the motor voltage output characteristics as each one is different. So, to a degree, yes and no. They act as sort of a "second line of defense" in
validating whether or not any voltage spikes are anomalies or common occurrences. These also vary wildly like the bar graph because they are a function of time. Maybe I'm approaching this problem in the wrong manner ?

 

[Miner]

By definition, the IQR will only capture the middle 50% of the data. This is probably overly sensitive. What about using the whiskers as your limits?

 

[NegativeKurtosis]

I understand exactly what you're saying. The issue though isn't necessarily the "limit". It is the representation of the "limit" throughout time. Again, the IQR confidence band changes radically with time like the bar graph example. As I sit and look at this problem, I am beginning to think that it is impossible....how can you add to a time series, transform it and yet not change it radically. I have read alot of journal articles about time series and so many of them reference Arma / Arima that I'm beginning to think that that must be the way to go, even though I am not trying to predict or forecast anything. So much of this seems empirical though. I was hoping to find a solid, straight forward way to accomplish this. By the way, thanks so much for your time and input. It is enormously appreciated !

 

[Miner]

What you are attempting is similar to a control chart with control limits. However, most control charts are based on a stationary series or upon a linear trend. You might try a smoothing approach like a moving average and use that to project the limits forward by one lag.

 

[NegativeKurtosis]

I made a cursory review of control charts ( never heard of them, learned something new today : - ) ) and moving averages. Based on the changes in the bar graph between the three voltage readings, I'd have to make an approx 50 period moving average. Wouldn't that cause an enormous lag ( a 50 period lag ) in the projection / forecast process ? I understand that it would "smooth" it but wouldn't it also cause a lag ? Excuse me if this seems trivial, I don't use these processes on a daily basis .

 

[Miner]

Yes, moving averages does result in a lag. I would start much smaller, test it and increase it slowly if necessary. We are in an area where statistics is blind and experimentation is required. If I correctly understand what you are attempting to do, you want to separate the signal from the noise, so you are not overcontrolling. This is exactly what control charts were designed to do. Their use is almost entirely limited to industrial statistics, but would be applicable over a much wider area. They assume that the noise comes from a stationary process and any deviation from that is a signal that the process has changed. They were then adapted to handle a linear trend such as from tool wear. We are trying to adapt them further to a nonlinear cycle.

 

[NegativeKurtosis]

Interesting. It appears I have some research / experimentation to do. Thank you again for your continued replies, insight and time. Tremendously appreciated !!

 

[noetsi]

ARMA and ARIMA are very popular [although increasingly the field has moved past them because they are exclusively univariate for the most part]. Just because something is popular does not mean they make sense for what you are interested in.

I would stay away from ARIMA unless you want to invest a lot of time in them. They have lots and lots of gray in them.

 

[NegativeKurtosis]

Thanks noetsi. I did not feel they were appropriate for my application based on a cursory examination in the begininngin but I figured it was worth at least seeking some input from people who may use them on a regular basis. Thanks for your time and your recommendation to consult with Miner. Much appreciated.