HYDRAULIC SYSTEM INSTABILITY
Hydraulic test rig
Modern hydraulic systems belong to the most crucial machinery elements in various manufacture processes and running vehicles. At the same time, their structure is more complex than ever and their ability to stay operational is crucial. This can be achieved by constantly monitoring condition of the hydraulic device and eventually take appropriate steps to avoid systems downtime by either repairing or replacing critical system components.
Recently, Helwig, et al. [Helwig] provided an experiment with a complex hydraulic system [UCI] composed of multiple parts. The entire system consists of a primary working and a secondary cooling-filtration circuit that are connected by the oil tank [Helwig, UCI].
Within the hydraulic test rig, sensor data were recorded as the entire hydraulic system performed load cycles which lasted exactly 60 seconds. To monitor conditions of the overall complex system, 17 sensors constantly recording data were used. The sensors measured physical conditions like pressure, temperature, volume flow, vibrations, motor power and cooling power and the records were provided from over 2200 cycles in total. Frequency of sensor data are different for distinct sensor types – 1 Hz data come from for temperature and vibration sensors, 10 Hz from volume flow sensors and multiple 100 Hz sensors measured pressure in system components.
In their experiment, Helwig et al. also measured various target parameters reflecting system condition – „health status“ which include cooler condition, valve condition, internal pump leakage, hydraulic accumulator pressure and the overall stability of the entire system. The overall stability condition is the most important quantity describing actual state of the complex device and in this report we focus on predicting conditions (configurations of physical sensors data) that are correlated to system instability.
Fig. 1 – A selected time interval from the hydraulic test rig experiments showing input data – standardized features extracted from sensors that measured physical quantities during load cycles (colored points) and overall stability condition (black line) with values 0 – stable and 1 – unstable conditions.
Physical sensors are either 1, 10 or 100 Hz and therefore provide 60, 600 or 6000 data points per each 60-seconds cycle. During the feature engineering process, we model the problem by assigning a set of attributes to each load cycle. From the recorded sensor data, we chose to include mean value from system cycle, standard deviation within the cycle and the most prominent frequency present in one cycle data, together providing possible 51 features. From these, over 30 with non-zero correlation with the stability flag were selected.
Characteristic frequencies of all physical parameters within each cycle were calculated by fast Fourier transform (FFT) and dominant frequencies (those with highest amplitude) were weighted by their corresponding amplitude effectively providing frequency values non-zero only for oscillating parameters, like vibrations.
Predicting system instability
We tried several algorithms to predict the stability flag for the whole hydraulic system, yet very good results were provided from simple (linear) logistic regression model. Besides providing predictions, linear models also bring insight into the importance effect of individual features.
The model trained on a random subset of samples (load cycles) taken from the whole duration of the experiment reaches nearly 100 % accuracy and other performance indicators on the test set. However, testing the model on such randomly chosen cycles is too optimistic way in predicting real-life model performance since all types of examples (load cycle data and stability condition) are practically known to the model during training (because of the homogenous random split).
Much more realistic way to estimate model performance is to split the dataset into train and test set block-wise, like that, e.g. 80% of the samples that form a continuous time block will be assigned to train set and the remaining 20% of samples to test set, but also forming an uninterrupted time interval. Such split should then be performed several times, each time choosing the test set in different closed time interval. This way of splitting data into training examples and testing dataset provides better error estimate since it mimicks the situation when the model will face unknown system conditions (configurations of sensor-data values that were not typically present in the training set).
Results – random and block-wise sampling
In the table below, there are shown RESULTS of the logistic regression model trained & tested on random homogenous split samples and on 80% : 20% block-wise data split cross-validated over 5 different split positions. Performance indicators include average accuracy, precision, recall and F1-score for the unstable-conditions class.
———————————————————- Accuracy ———- Cohen’s kappa ———- Precision ——- Recall —— F1-score ———
homogenous random split 93.6% 0.86 0.92 0.90 0.91
80%-20% CV with block-wise split 79.7% 0.53 0.70 0.65 0.67
Tab – Results for anticipating hydraulic system instability conditions from datasets constructed by random data-sampling and by choosing blocks of data corresponding to uninterrupted time intervals.
The results indicate that cca. 2000 cycles are enough for training the model, which is able to successfully predict hydraulic system condition in previously unknown circumstances – configurations of physical parameters. Moreover, results from the homogenous random split (that reaches nearly full accuracy) indicate that using more examples that would come from longer time intervals of experiment would enable the model to learn even much better results.
[Helwig] Nikolai Helwig, Eliseo Pignanelli, Andreas Schatze, Condition Monitoring of a Complex Hydraulic System Using Multivariate Statistics, in Proc. I2MTC-2015 – 2015 IEEE International Instrumentation and Measurement Technology Conference, paper PPS1-39, 2015
[Schneider] Tizian Schneider, Nikolai Helwig, Andreas Schatze, Automatic feature extraction and selection for classification of cyclical time series data – Technisches Messen 84(3), 198-206, 2017