Health assessment of water pumps using high-dimensional monitoring data

With the increasing depth of control equipment applications in water plants, the water plant system has become more complex. As an essential equipment in water plants, the health condition of pumps has a direct impact on the operational efficiency of water plants and plays a crucial role in determining whether the water transmission and distribution system can operate smoothly (Bayindir & Cetinceviz 2011). Ensuring that the pumps have better quality, higher reliability, and greater availability has become an urgent issue to be addressed (Luna et al. 2019).

Factors such as excessive vibration, heightened current, and abnormal magnetic flux are the main indicators of equipment malfunction and damage to vulnerable parts (Bhuiyan et al. 2022; Zhao et al. 2022). Numerous researchers have demonstrated how internal and external electrical faults generate parasitic radial forces (rotating waves) and tangential forces (pulsating torques) within induction motors, leading to a deterioration of equipment health (Tsypkin 2017). As a result, various monitoring sensors, including self-powered vibration sensors, stator vibration, stator line bar vibration, air gap, and magnetic field intensity, have been employed to monitor the operational conditions of mechanical gear systems (Li et al. 2022).

In addition to the proliferation of monitoring device sensors, there has been rapid development in various methods for assessing device health (Elsheikh et al. 2019; Ma et al. 2019). These methods can be generally classified into physics-based (or model-based), data-driven, and hybrid approaches (Li & Li 2017). Physics-based approaches aim to establish explicit mathematical models based on the fundamental physical principles that govern the underlying mechanisms of mechanical systems or their components. Computer programs have been utilized for automated simulation, aiming to replicate the reasoning and decision-making processes of experts in the field (Qian et al. 2021). However, physics-based approaches heavily rely on expert domain knowledge of physical models, making them infeasible for complex systems (Dutta et al. 2022; Pan et al. 2022).

On the other hand, machine learning techniques strive to learn the nonlinear nature of mechanical systems by treating them as black-box models (Zhao et al. 2019b; Goyal et al. 2020). Consequently, obtaining proper relationships between the inputs and outputs of machinery systems requires high-quality (less noise), highly sampled, and large-volume time-series data. Unfortunately, most industrial time-series data exhibit significant noise, posing challenges for machine learning technology in the field of equipment health assessment (Wang et al. 2019). Especially concerning industrial time-series data, fitting machine learning models becomes an issue due to the presence of sensor noise, as the numerical rank of noisy data may be far larger than the dimension of the true dynamical features (Lee et al. 2018; Zhao et al. 2019a; Cheng et al. 2020).

In summary, most existing studies on equipment health assessment have primarily focused on the development of monitoring equipment or the analysis of specific monitoring indices. However, there is a noticeable lack of research considering multiple monitoring indicators, especially when dealing with high-dimensional data (Bolón-Canedo et al. 2016). With the advancements in Internet of thing (IoT) monitoring sensor technology, there is a growing trend toward shifting from single sensors to the fusion monitoring of multiple sensors for device health monitoring. This leads to the use of high-dimensional datasets in data-driven models. Furthermore, accurately determining the exact time of equipment failure poses an inherent challenge. Much of the existing research relies on data collected in controlled experimental environments, which often suffer from insufficient volume and quality. Although some unsupervised learning methods have been utilized for abnormal state monitoring, ensuring their robustness remains a challenging task (Dai et al. 2020).

Addressing the shortcomings and challenges in existing research, this article proposes a data-driven approach as the framework for an equipment health assessment algorithm. In the data collection phase, multiple sets of diverse monitoring sensors were installed in six pumps.

To overcome the difficulties arising from massive data features, data redundancy, and long-term dependencies in the original monitoring dataset, the algorithm integrates the max-relevance and min-redundancy (mRMR) method, principal component analysis (PCA), and long short-term memory (LSTM) neural network. In the data preprocessing stage, the mRMR method is utilized to address correlation and redundancy issues among the original monitoring data. Subsequently, the PCA method is employed to reduce the dimensionality of the categorical data, aiding in the screening of important features.

Leveraging accurate data on pump failure times, this study classifies the equipment's health state based on the severity of the failures, using the post-classification fault degree as the target for the model. Finally, the LSTM method was employed to construct an association model between IoT monitoring data and device health.

The key features of the algorithm proposed in this article are summarized as follows:

• 1.

  Data preprocessing stage: The algorithm takes into account the complexity of variables in the original dataset and automatically categorizes the data. To eliminate redundant variables, the mRMR method, which considers nonlinear correlation between variables, is used.

• 2.

  Training set generation stage: The algorithm marks the time before an abnormality occurs in the equipment as an abnormality. By learning data-driven models, the algorithm predicts the equipment health degree, rather than diagnosing in real time, which reserves sufficient time for equipment maintenance.

• 3.

  Accurate classification labels: The presence of dedicated maintenance personnel facilitated the prompt and precise identification of abnormal operating conditions in the six pumps. The time of failure was further validated through video surveillance installed in the pump station.

The process of water pump health assessment is outlined as follows. First, the mRMR method is employed to partition the original data, followed by the implementation of the PCA method to reduce the dimensionality of the partitioned data. Second, the pump's maintenance records are utilized to annotate its health index. Finally, the preprocessed data are input into an LSTM neural network to establish the correlation between the feature set and health states. This approach effectively achieves the objective of evaluating the pump's health index.

Figure 1 depicts the flowchart for the water pump health assessment.

To address this issue, the mRMR method is employed, which calculates the correlation between feature subsets and categories based on the mean of the information gain of each feature and category. It uses the sum of mutual information between features and features and then divides it by the square of the number of features in the subset as the feature–feature redundancy. This approach considers not only the correlation between features and categorical variables but also the correlation between features and features.

Given the total features X of the original monitoring data, the mRMR algorithm aims to find the subset of features S containing of features. Via the incremental search method to find the near-optimal features, it starts by randomly selecting a feature as the feature set Sm-1 and find the mth feature from the remaining features X – Sm-1. The feature is selected to maximize Ø(.):

Continuously subloop is formed, and when Ø(.) is lower than the set threshold, the feature search is stopped, a remaining feature is randomly selected to generate a new feature set, and all the features in the feature set X are finally categorized.

The main goal of the dimensionality reduction phase is to make the feature dimension smaller while minimizing information loss. For a sample matrix, the number of new features is reduced to less than the number of original features by replacing and reducing the features (Jollife & Cadima 2016).

When there are multiple features, the covariance matrix is used to represent the correlation between multiple features. The PCA algorithm is constructed with the goal of linear independence between new features, i.e., the covariance between new features is 0. The essence is to make the covariance matrix of the new features a diagonal matrix, with the diagonal elements as the variance of the new features and the off-diagonal elements as 0, indicating that the covariance between the new features is 0 and the corresponding feature vectors are orthogonal.

According to the historical monitoring data and the maintenance records of the equipment, the health status is divided into four different status levels, namely, no fault, fault in 30 min, minor fault, and downtime fault, and assigned values of [0,1,2,3], as shown in Table 1.

The LSTM model is commonly employed in the analysis of time-series data and is proficient in predicting continuous values for regression tasks. By associating specific numerical values with the health condition of the devices, we are able to effectively categorize them into distinct classes based on the predefined threshold or criteria. This transformation allows us to leverage classification techniques and tools to analyze and predict the health status of devices, enabling more accurate and efficient assessment compared to traditional evaluation methods. To facilitate this transformation from the conventional LSTM model to a classification problem, we introduced an additional fully connected layer tailored to accommodate the number of categories, followed by the utilization of the Softmax function. The number of neurons in this fully connected layer should be equal to the number of classification categories.

Following the fully connected layer, the Softmax function is employed. The Softmax function transforms the output into a vector that represents a probability distribution, ensuring that the probabilities of all categories sum up to 1. The function is shown as follows:

Through this computation, the Softmax function can transform the original values into numerical values representing relative probabilities, where larger values correspond to higher probabilities.

Consequently, through the application of the Softmax function to the output of an LSTM model, a probability distribution that represents the various classes can be obtained. The class with the highest probability can then be selected, enabling effective classification.

During model training, the loss is calculated using labeled data, and backpropagation is employed to update the model parameters accordingly. This iterative process aims to optimize the model and improve its classification performance.

By incorporating this modification, the LSTM model can be effectively repurposed to address classification challenges, allowing for the generation of probability distributions for different classes. Consequently, the class with the highest assigned probability can be selected to determine the category of interest.

Vibration, magnetic flux, temperature, noise, and electric current are monitored in the motor bearing, near-end motor bearing, and far-end motor bearing of the pump. The monitoring sensor is programmed to trigger data collection every hour, capturing measurements continuously for a duration of 10 s during each sampling event. This periodic and consistent sampling scheme guarantees the collection of representative observations at regular intervals throughout the monitoring process. The interpolation method is used to solve the problem of low monitoring frequency of some monitoring indicators. The monitoring principle of monitoring indicators is presented in Table 3. The detailed monitoring indicators are shown in Table 4.

Our monitoring sensor collected data from October 2022 to June 2023. The initial time of pump failure was reported by onsite maintenance personnel, and the accurate time was confirmed through video surveillance. Given the voluminous quantity of raw data, we employed undersampling techniques on the dataset. To mitigate the potential risk of data leakage, we performed a rigorous time-based partitioning of our training and testing sets, as outlined in Table 5.

The classification of the monitoring indicators presented in Table 4 is accomplished by utilizing the mRMR method as described above under section ‘mRMR’. The threshold value for Ø(.) is set at 0.25. Table 6 shows the classification of the 26 monitoring indicators into four distinct categories.

Applying the PCA method as described above under section ‘PCA’, the four categories of monitoring indicators are individually subjected to dimensionality reduction, with the target dimension set to 2. Taking several pumps as examples, Figure 5 illustrates the data after dimensionality reduction for monitoring indicators during select time intervals.

The LSTM model was trained using the methods outlined above under ‘Methods’ section. The evaluation of the model's classification prediction performance was conducted using the accuracy metric, which calculates the ratio of correctly predicted samples to the total number of samples in the testing dataset. On the validation set, the prediction accuracy was found to be 99.1%.

Considering the presence of data imbalance in our dataset, where the majority of instances indicate normal pump operation, we employed a confusion matrix to assess the performance of our model across various classification targets. Figure 6 portrays the confusion matrix, elucidating the predictive outcomes across various health states.

Based on the results, it can be observed that the proposed method presented in this study achieves the highest level of accuracy among the compared models. The comparative analysis of the algorithmic models reveals that LR exhibits the poorest performance due to the high dimensionality of the dataset, which causes the linear model to underperform. SVM performs relatively worse than RNN due to its simplistic model structure, which is typically only suitable for a restricted and fixed set of features. Comparatively, LSTM performs slightly better than RNN as the gate function integrated into the LSTM architecture allows it to effectively capture long-term dependencies, which is a challenge for RNNs. Moreover, LSTM can automatically learn meaningful features from the original signal without requiring feature engineering.

The analysis of the results before and after applying the data dimensionality reduction method shows that the prediction accuracy significantly improves after dimensionality reduction using the mRMR-PCA method proposed in this article. The dataset used in this study is high dimensional and of large volume, and employing the dimensionality reduction technique helps in eliminating unnecessary and redundant features, thereby reducing the impact of noise and enhancing the model's accuracy and generalization ability.

This article presents a method for assessing the health status of water pumps by fusing and analyzing multiple monitoring and sensing indicators. The proposed approach involves classifying the monitoring data using the mRMR method, reducing the dimensionality of the classified data using PCA, and inputting the processed data into an LSTM neural network to evaluate the health status of the pump. The effectiveness of the proposed algorithm is demonstrated through experiments conducted on six groups of pumps at the Xiasha Pumping Station in Hangzhou. The performance of the proposed method is compared with that of LR, SVM, RNN, and other algorithms. The experimental results show that the proposed algorithm has the highest accuracy for identifying the health status of pumps. Moreover, the proposed method can reduce the number of features in the dataset, leading to a reduction in computation and storage space. In addition, it can respond promptly to abnormal situations during the pump health status assessment process.

However, due to the limited number of samples, we only collected operational data from six pumps. Although our proposed method showed good performance on the collected dataset, the generalizability of this method to a wider range of diverse pumps remains uncertain. Further collection of additional sample data is necessary, and it is also the direction for our future work.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.