Predicting the Remaining Life of Liquid Filters from Data

In many industries, including aviation and power generation, filters remove contaminants from fluids. As fluid passes through, contaminants accumulate on the filter. Over time the filter clogs, which degrades machine performance and leads to failure.

Replacing filters at fixed intervals can cause two kinds of loss. A filter that is still usable gets discarded, or a filter that clogs before the interval ends goes unnoticed. What a plant manager needs is a number that says, “How clogged is this filter now, and how much longer can it be used?”

So, can we diagnose the condition of a filter and calculate in advance the time remaining until it clogs, using only sensor data that record the pressure and flow rate before and after the filter?

This post reads one paper that answers this question.

• Title: Data-driven health condition and RUL prognosis for liquid filtration systems
• Journal: Journal of Mechanical Science and Technology
• Year: 2021
• DOI: 10.1007/s12206-021-0323-8

The paper proposes a data-driven prognostics method for liquid filtration systems. It first defines an index that represents the health condition of the filter. It then predicts the values of that index, from the point where it starts to drop clearly to the end of life, with a recurrent neural network–based model, and uses the prediction to obtain the remaining life. The key terms used in this post are as follows.

• Remaining Useful Life (RUL): The time remaining from the time of measurement until the machine is judged to have failed.
• Condition-Based Maintenance (CBM): An approach that evaluates the condition of a system using data collected through continuous monitoring or inspection, and decides on necessary maintenance before the predicted failure.
• Prognostics and Health Management (PHM): An engineering field that aims to improve reliability and reduce maintenance costs by evaluating machine condition numerically. It is the most widely used method in CBM.
• Health Index (HI): A quantitative indicator that expresses the health condition of the whole system as a value between 0 and 1.
• Pressure drop: The difference between the upstream pressure and the downstream pressure of a filter.
• Degradation point: The point at which filter performance starts to drop clearly. The paper holds that this point must be found first in order to obtain the RUL.
• End of Life (EOL): The point at which the predicted HI reaches 0 or converges to 0.

Motivation: Filter Clogging Must Be Known in Advance as a Number Anyone Can Read

Why Filter Life Prediction Matters

The paper gives the following reasons.

• Filters support the smooth operation of many systems, so they are an important maintenance target.
• When contaminants clog a filter, machine performance degrades and failures occur. Preventive maintenance, which replaces worn parts before they clog, is therefore important to equipment managers.
• To make preventive maintenance efficient, CBM must be applied, which evaluates the current condition of the filter through real-time monitoring and predicts the RUL.
• Liquid filters are used for problems such as maintaining oil purity and resolving water shortages.

The paper divides PHM into four areas: detection, diagnosis, assessment, and prognosis. Detection finds a failure without knowing its cause, and diagnosis identifies the cause and type of the failure. Assessment judges the health condition of a machine based on its recent operation, and prognosis predicts future health condition and RUL. This paper deals with both assessing the current condition with the HI and predicting the RUL.

What Existing Research Has Not Addressed

The paper divides prognostic models into physics-based models and data-driven models. A physics-based model describes product condition with equations, using knowledge of the failures that can occur in the equipment. Its failure prognosis is more accurate than that of other models, so it suits industries where safety matters most, such as power plants and aircraft. However, it is hard to connect to real-time data, and it requires expert knowledge and many resources for each product, so it is hard to use as a general-purpose approach.

A data-driven model predicts equipment failure from collected data. As sensor technology has advanced, data can be collected in real time from products in use, and the accuracy of RUL estimation by these models is also rising. In the filter field, Skaf et al. estimated filter RUL with a condition-based prognostics method.

The paper points out three gaps.

• Research on liquid filters is scarcer than research on other types of filters.
• Most existing liquid filter studies used physics-based models. Physics-based models are costly to implement and hard to build accurately for complex systems.
• Existing prognostics studies predicted indicators that are themselves highly correlated with the system. This approach requires knowing multiple indicators, so it is hard for non-experts to understand the current condition of the system.

The paper therefore holds that research is needed that assesses condition and predicts failure with an HI.

Method: Convert Pressure Drop to a 0–1 Index and Predict the Post-Degradation Segment with an LSTM

The paper describes the procedure in three sections: data preprocessing, HI definition and health stage division, and RUL calculation by HI prediction. In this post, the second section is split into HI definition and health stage division, giving four steps. Step 1 removes noisy data and reduces the large variation in pressure drop. Step 2 defines the HI, and Step 3 divides health stages with K-means clustering. Step 4 predicts the HI with three Long Short-Term Memory (LSTM) models to obtain the RUL, and validates the prediction models with metrics.

Case and Data

The analysis data are liquid filter clogging data provided by the PHMe20 Data Challenge. The experimental setup consists of the following elements.

• Pump and liquid tanks: The pump moves liquid from one tank to another.
• Damper: Prevents the pipe from expanding when pressure rises.
• Filter and pressure/flow sensors: Monitor the flow rate and pressure before and after the filter.
• Data acquisition device: Connected to a computer and records the measurements.

The suspension that was pumped through is a mixture of PEEK particles and water. PEEK particles have a density of 1.3 g/cm3, close to that of water, and a very low absorption rate of 0.1 %/24 h. A low absorption rate means the particles do not swell in water, and a density close to that of water means they stay suspended in water longer.

The data contain records from the start of filter use until failure. Six groups were formed from combinations of particle size and solid content ratio, and four experiments were run for each group. The data therefore comprise 24 files in total. In each file, the flow rate (ml/m), upstream pressure (PSI), and downstream pressure (PSI) were recorded every 0.1 seconds.

The group composition combines two particle size ranges with three solid content levels. The particle sizes are 45-53 micron and 63-75 micron, and the solid content ratios are 0.4 %, 0.425 %, and 0.45 %. Groups 1 to 3 used the small particles and groups 4 to 6 used the large particles.

The failure criterion follows that of the Data Challenge. If the pressure drop is greater than 20, the filter is considered clogged. In each group, the first three samples were used for training and the last sample for testing. For group 1, for example, 01-03 were used for training and 04 for testing.

Step 1: Noise Removal and Moving Average

• Input: Flow rate, upstream pressure, and downstream pressure for each sample (at 0.1-second intervals)
• Processing: Delete abnormal segments, compute pressure drop, apply a simple moving average
• Output: Moving Averaged Pressure Drop (MAPD) time series

The processing order is as follows.

1. Delete the initial segment right after start-up in which the flow rate is abnormally small. The paper regarded this segment as the time needed for the system to reach full operation and judged it to be noisy data.
2. Delete the segments in which the pressure drop is 20 or more. These segments are data that continued to be recorded after filter failure and are not needed for analysis.
3. Subtract the downstream pressure from the upstream pressure to obtain the pressure drop.
4. Apply a simple moving average to the pressure drop to create the MAPD.

The moving average is needed because the variation in the measurements at 0.1-second intervals was very large. If the variation is left as it is, it could be misread as the filter condition changing abruptly at nearby time points. The paper reduced the variation to improve the stability and accuracy of prediction.

MAPD(t) is the average of the pressure drop over the k+1 intervals from time t-k to t. The researchers settled on k = 6 through repeated experiments, so the average is taken over 7 intervals. Since the measurement interval is 0.1 seconds, one average collects the pressure drop over 7×0.1=0.7 seconds. An MAPD of 0 means the upstream and downstream pressures are equal and the filter is in its best condition. An MAPD of 20 means filter failure.

Step 2: Defining the Health Index

• Input: MAPD time series
• Processing: Divide by the failure criterion of 20 to convert to the 0–1 range
• Output: HI at each time point

To check filter performance degradation, it is common to use the pressure difference before and after the fluid passes through the filter. The paper therefore created an HI by converting the MAPD to a value between 0 and 1. The equation is HI(t) = 1 − MAPD(t)/20.

An HI of 1 is the optimal condition, and the point at which the HI reaches 0 or converges to 0 is the EOL. With this conversion, even non-experts who do not know the filter’s failure criterion can check the filter condition.

Here is a calculation example. If the MAPD is 0, HI = 1 − 0/20 = 1, and if the MAPD is 20, HI = 1 − 20/20 = 0. Conversely, the MAPD can be recovered from an HI value. The threshold HI of 0.929286 for group 1, which appears in Step 3, corresponds to an MAPD of (1 − 0.929286)×20 = 1.41428 PSI.

Step 3: Dividing Health Stages with K-Means Clustering

• Input: HI time series for each sample
• Processing: Determine the number of clusters with the elbow method and perform K-means clustering
• Output: Three health stages (healthy, transitional, unhealthy) and the HI at the degradation point (threshold)

Right after the system starts operating, the change in HI is small. It is difficult to estimate the RUL accurately while performance has not declined. In fact, most HI values were concentrated in the healthy or transitional stage. The paper therefore divided the health stages first and then found the degradation point at which the filter stops operating normally.

The processing order is as follows.

1. Increase the number of clusters K from 1 and compute the Sum of Squared Error (SSE). The SSE is computed from the distances between cluster centers and the data belonging to those clusters.
2. Find the elbow point, where the SSE decreases rapidly and then barely changes afterward. The K at that point is the optimal number of clusters.
3. Perform K-means clustering with the chosen K. K-means clustering is a method that creates a set number of clusters and assigns each data point to the nearest cluster.
4. Set the boundary between the transitional stage and the unhealthy stage as the degradation point, and take the HI at this point as the threshold.

K-means clustering is a method often used in PHM to divide health stages. Examples include a study that divided the health stages of bearings into four clusters and a study that distinguished the health stages of anemometers.

In the case study, as K increased, the rate of change in SSE was 74.9 % and 13.8 % up to K = 3. After that, the rate of change stayed below 5 %. K = 3 therefore became the elbow point. Because the elbow point was 3 for all the experimental data, the number of clusters was fixed at 3. The three health stages are healthy, transitional, and unhealthy.

The threshold for each group differed depending on particle size. For the 45-53 micron groups (groups 1 to 3), the thresholds were 0.929286, 0.928482, and 0.925179. For the 63-75 micron groups (groups 4 to 6), they were 0.852947, 0.850569, and 0.847221. Converting the threshold of group 6 back to MAPD gives (1 − 0.847221)×20 = 3.05558 PSI.

Step 4: HI Prediction and RUL Calculation with an LSTM

• Input: HI sequence of the previous 30 time points
• Processing: Predict the HI of the next time point with an LSTM, then feed the prediction back into the input and repeat
• Output: Predicted HI curve, predicted EOL, RUL, and four performance metrics

The LSTM is derived from the Recurrent Neural Network (RNN), which is often used for time series prediction. When an RNN uses earlier information after a long time, its learning ability drops sharply. The LSTM remedies this problem by adding a cell state. The layers and operations inside the cell selectively accept input information, so information can be retained or modified even in long sequences.

The processing order is as follows.

1. The input is the HI of the previous 30 time points including the current time t, that is, [HI(t−29), …, HI(t)]. The output is the HI of the next time point, HI(t+1).
2. If all values in the input sequence are lower than the threshold, the filter is judged to have entered the unhealthy stage and prediction begins.
3. The last prediction result is fed back into the input. The next input is [HI(t−28), …, HI(t), HI(t+1)] and the output is HI(t+2).
4. The point at which the predicted HI reaches 0 is taken as the EOL, and the RUL is obtained from the difference from the prediction start time.

The RUL equation is RUL(t_n) = t_EOL − t_n. Here t_EOL is the EOL time and t_n is the measurement time. Prediction starts in the unhealthy stage because it is difficult to predict the RUL while the filter is operating normally.

Prediction performance was evaluated with four metrics.

• Root Mean Square Error (RMSE): The standard deviation of the prediction error. The differences between actual and predicted values are squared and averaged, and then the square root is taken.
• Normalized RMSE (nRMSE): The RMSE divided by the mean of the actual values. It makes it possible to compare models by aligning their units.
• Mean Absolute Error (MAE): The mean of the absolute values of the differences between predicted and actual values. It gives equal weight to all differences.
• Mean Arctangent Absolute Percentage Error (MAAPE): The mean of the arctangent applied to the ratio of error to the actual value.

There is a reason for using MAAPE. The commonly used Mean Absolute Percentage Error (MAPE) cannot be computed when the actual value is 0. When the actual value is smaller than 1, it yields values that approach infinity. All actual HI values in this study were smaller than 1, so MAAPE was used.

Variants and Scenarios: Three LSTM Architectures and Hyperparameters

The paper compared the LSTM in three architectures.

• Vanilla LSTM: A basic LSTM consisting of a single layer
• Stacked LSTM: An LSTM built by stacking multiple layers
• Bidirectional LSTM: An LSTM that learns in both the forward and backward directions

All three architectures are mainly used for failure prognosis in PHM. The paper introduces two prior studies as examples: one that predicted the RUL of aircraft propulsion engines with a bidirectional LSTM, and one that predicted the RUL of fuel cells with a stacked LSTM.

Training settings were adjusted by group and model. The activation function was Elu, the batch size was 1, and the optimizer was Adam. The researchers determined the hyperparameters by grid search. Grid search sets a range for each hyperparameter, specifies values at regular intervals within that range, and selects the values that gave the best experimental result. The final settings are as follows.

• Learning rate: 0.001 for all groups and models
• Epochs: one of 150, 162, or 210
• Dropout: 0 or 0.1
• Hidden nodes: 32 for vanilla in all groups; 60, 64, and 32 for bidirectional

Results: The Bidirectional LSTM Led Slightly on Average, but a Clear Winner Is Hard to Declare

Comparison by Data Group

The HI prediction errors of the three models were compared using the test sample of each group. The paper summarized that the vanilla LSTM performed best in groups 1, 4, and 5, and the bidirectional LSTM performed best in groups 2, 3, and 6.

In group 1, the results differed by metric. RMSE (3.189) and MAE (2.428) were lowest for the vanilla model. However, for MAAPE the bidirectional model (7.231) was lower than the vanilla model (9.464).

The bidirectional LSTM varied greatly by group. In groups 2 and 6, its RMSE (unit: %) was the lowest, at 1.134 and 1.294. In contrast, in groups 4 and 5 it was 4.712 and 4.100, the highest among the three models. The same holds for MAAPE. In group 4, the vanilla model had 3.764 and the bidirectional model had 10.375. No single model was always ahead across all groups.

Comparison of Average Performance of the Three Models

The paper averaged the metrics across groups for each model and compared again. The average RMSE was 3.073 for vanilla and 2.997 for bidirectional.

The bidirectional LSTM was lowest on three metrics: RMSE, nRMSE, and MAAPE. Only for MAE was vanilla (2.394) lower than bidirectional (2.462). Based on this average comparison, the paper concluded that the bidirectional LSTM has the highest prediction accuracy.

The difference between the two models is not large. The difference in average RMSE is 3.073 − 2.997 = 0.076. By group, the vanilla model was ahead in 3 groups. There is also only one test sample per group. The source contains no examination of whether this difference is statistically significant. Therefore, all that can be said is that the bidirectional model was slightly ahead on the average metrics, and it is hard to declare a winner between the two models.

The stacked LSTM had the highest average on all four metrics among the three models. That is, on this data the stacked LSTM had the largest average error.

Predicted RUL and Actual RUL

The last comparison is between the EOL obtained from HI prediction and the actual EOL. The paper presented the HI prediction curves of the three models for samples 04 and 36. Based on these graphs, the paper stated that the difference between the actual EOL and the predicted EOL is not large. It therefore considered the actual RUL, obtained from the degradation point, and the predicted RUL to be similar.

The paper also presented a case in which the RUL was calculated by predicting sample 04 with the vanilla LSTM. However, there is no table in the source that gives the EOL and RUL errors as numbers in units of time. The answer to this post’s question, “Can the remaining time be calculated in advance?”, therefore stays at the level of checking against graphs. Quantitative validation of RUL accuracy is lacking, and only the HI prediction metrics are confirmed numerically.

Significance and Limitations

What Changes

• Condition diagnosis and RUL prognosis of liquid filters were performed with a sensor data–based model rather than a physics-based model.
• An HI was defined by converting the moving averaged pressure drop to a 0–1 range. The filter condition can be read as a single value without interpreting multiple indicators separately.
• The degradation point was found with K-means clustering and the elbow method, and the HI at that point was used as the threshold for starting prediction.
• Vanilla, stacked, and bidirectional LSTMs were compared with four metrics, and the bidirectional LSTM was slightly ahead on the average metrics.
• Validation was carried out only on a single experimental setup using a suspension of PEEK particles and water, but the authors consider the approach applicable to various types of liquid filters because the data they used contain only the characteristics of general liquid filters.

Value for Practitioners

Switching from fixed-interval replacement to condition-based maintenance requires two bases for judgment. One is “Should we start preparing for replacement now?” and the other is “How long can it hold out?” The procedure in this paper gives a number for each of the two questions.

The HI and the threshold answer the first question. When the HI falls below the threshold and enters the unhealthy stage, replacement preparation begins from that point. The RUL, measured up to the point where the predicted HI reaches 0, answers the second question. The sensors needed are pressure before and after the filter and flow rate. Of these, the pressure difference across the filter is a value commonly used to check filter performance degradation.

The HI can be read by non-experts. A value near 1 is good and a value near 0 is failure. Equipment staff can judge the condition without memorizing the pressure drop criterion of 20.

Value for Researchers

• It shows the rationale for using MAAPE instead of MAPE in prediction problems where actual HI values are smaller than 1.
• It offers a design reference that links health stage division and RUL prediction in one procedure. The healthy segment is excluded from the prediction target, and prediction starts from the unhealthy stage.
• The result that the performance of the three LSTM architectures differed by data group is a reason to examine model selection group by group.
• Because public data (the PHMe20 Data Challenge) were used, comparison with other models on the same data is possible.

Limitations Stated by the Paper

The paper states one limitation of its own. It is what the conclusion gives as a direction for future research.

• This study used only a data-driven model. A hybrid model combining a physics-based model and a data-driven model could advance HI and RUL prognosis for liquid filters.

Conditions for Application, in the Author’s View

The following are not contents of the paper but conditions the author adds with practical application in mind.

• Data recorded all the way to failure are needed. This study trained on experimental data recorded from the start of use until failure. If a site has been replacing filters before they clog, training data must be collected separately.
• The test results came from one sample per group. At sites with more varied operating conditions, more samples should be added and the method validated again.
• The experiments used a suspension made of PEEK particles and water. For filters that remove oil or other contaminants, the clogging pattern could differ.
• The threshold differed by particle size. It was 0.929286, 0.928482, and 0.925179 for the 45-53 micron groups, and 0.852947, 0.850569, and 0.847221 for the 63-75 micron groups. If contaminant conditions change, the threshold must be obtained again.
• Prediction starts only after the filter has entered the unhealthy stage. If the lead time for procuring replacement parts is long, first check whether the time remaining after entering the unhealthy stage is longer than that lead time.
• The failure criterion of 20 is a value set by the Data Challenge. For your own equipment, use a clogging criterion suited to the manufacturer’s or operating standards.

What to Try Right Away

• Compute the pressure drop from the pressure records before and after the filter, and build the MAPD as a moving average of the previous 7 values. Divide by your own equipment’s clogging criterion to calculate HI = 1 − MAPD/criterion, and plot it together with the replacement history.
• For an HI time series recorded until failure, increase K from 1, compute the SSE, and find the elbow point. Check the boundaries between the healthy, transitional, and unhealthy stages, and record the HI at which the unhealthy stage begins as the threshold.
• In the segment below the threshold, train an LSTM that predicts the next HI from the previous 30 HI values. Start with the vanilla LSTM, compute RMSE, MAE, and MAAPE on the test sample, and compare with the bidirectional LSTM.