Unevenly spaced time-series forecasting and anomaly detection for an industrial usecase

Question

I am currently working on a PhD project for a car manufacturing company, which basically consists of creating a predictive maintenance application for the machines that are currently used to fill the air conditioning circuits of vehicles. In essence, each cycle consists of two phases designed to perform checks on the circuit followed by a last one in which the corresponding refrigerant gas is charged. Specifically, in a first phase the circuit is pressurized in order to detect leaks from inside to outside the circuit, in a second phase a vacuum is exerted on the circuit in order to detect leaks from the outside to the inside, and finally, if no leak is detected, the circuit is filled. Regarding the data collected, for each of the phases different readings are taken of the pressure reached inside the circuit, except for the gas loading phase:

• First phase (pressurization): A total of three pressure readings are taken at different times (pressurization, stabilization and control).
• Second phase (vacuum): A total of 4 readings are taken at different time instants (release of the circuit pressure to the atmospheric one, vacuum, vacuum stabilization and control).
• Third phase (charge): Grams of gas charged in the circuit.

The following figure shows the typical theoretical curve of a filling cycle with the three aforementioned phases.

As for the data, the following table presents a small sample of them:

Production Number	Type of Vehicle	Type of Engine	Pres (bar)	PresStab (bar)	PresCtrl (bar)	Patm (bar)	Vacuum (mbar)	VacuumEst (mbar)	VacuumCtrl (mbar)	Cycle Timestamp	Cycle Result
1	1	1	12,31	12,31	12,31	0	0,7	4	0,4	01/05/2021 0:50	OK
2	1	2	12,32	12,31	12,31	0	0,7	4,1	0,4	01/05/2021 0:55	OK
3	2	3	12,32	12,32	12,31	0	2,3	12,4	1,3	01/05/2021 0:58	OK
4	1	1	12,32	12,31	12,31	0	0,7	3,9	0,5	01/05/2021 1:01	OK
5	2	4	12,32	12,32	12,31	0	2	11,7	1,1	01/05/2021 1:04	OK
6	3	4	12,32	12,31	12,31	0	0,9	5,2	0,8	30/03/2021 10:45	OK
7	3	1	12,32	12,31	12,31	0	0,9	5,2	0,8	30/03/2021 10:48	OK
8	3	5	0	0	0	0	0	0	0	26/03/2021 8:29	NOK
9	2	5	0	0	0	0	0	0	0	25/03/2021 23:31	NOK
10	3	6	12,25	12,24	12,23	0	100	0	0	14/05/2019 11:33	NOK
11	1	4	12,21	0	0	0	0	0	0	11/04/2019 13:01	NOK
…	…	…	…	…	…	…	…	…	…	…	…

The objective proposed to me is to model and monitor these variables so that, following a predictive maintenance strategy, it is possible to predict their trends and detect possible anomalies in real time, allowing to anticipate failures in the pressurization of the machines or in the pump in charge of the vacuum. With regard to the results of the cycles, it is worth mentioning that only those NOKs associated with the filling console have been taken into account, discarding the cycles that have been NOKs because the vehicle circuit itself had defects (leaks, bad connections, etc.). In any case, it is to be noted that the factory does not fully trust the assigned NOK labels... so maybe it would be better to just consider the OK samples...

As far as I understand, these data constitute time series, a completely new field for me. I have some experience in supervised and unsupervised classification problems using classical machine learning algorithms, as well as in computer vision using deep learning, but none with respect to time series. One of the problems I have encountered is that the classical techniques for dealing with these types of data, such as ARIMA and its variants are only valid for equispaced time series. However, this does not apply to my case because of the industrial context from which it comes: the machine is not filling continuously, there are line stops, breaks, vacations, maintenance stops, etc.

Can anyone guide me on the way to go? Does anyone know the techniques that can be applied to this type of time series? I would appreciate any kind of help, idea or suggestion, because although I thought it would not be so complicated and that the modeling of the time series was in a very mature state, the truth is that I am quite lost. I believe that in order to apply the classical techniques, one option would be to summarize the data in new time intervals (hourly, for example), although this is not an alternative with which I feel very comfortable.

Thank you so much in advance.

Answer 1

Time-series data can be modeled without time-series models. The most trivial example is to just ignore time completely - a model independent of time. Many simple anomalies can be detected in this manner, usually called "global" anomalies.

But time-aware / time-dependent models can also be constructed by treating time as just another feature in the input vector. One can for example use a continious numeric representation, like the number of seconds, hours or days since a particular point in time. The point in time can be a generic time reference, like 1970-01-01 (Unix timestamps), or something more meaningful for your application, like production date of the requipment, or last maintenance/replacement etc. If one has cyclical patterns (seasonality) or trends, it can be useful to decompose time into components that have different time bases. For example time-of-day, day/week-of-year, year. Might not be relevant for machine monitoring though.

One task formulation for predictive maintenance is to predict time-until-failure. This can be treated as a standard regression problem, with time as one of the inputs. For simple scenarios with very smooth degradations a linear regression can work well, or one can use non-linear regressors such as RandomForest. In this formulation, each time-point is predicted independently. But one can run predictions for each instance over time, and then combine their predictions. What one wants to see is that as failure gets closer, predictions have less and less spread.