A Data-Driven Diagnosis Scheme Based on Deep Learning toward Fault Identification of the Hydraulic Piston Pump

Abstract

The piston pump is the significant source of motive force in a hydraulic transmission system. Owing to the changeable working conditions and complex structural characteristics, multiple friction pairs in the piston pump are prone to wear and failure. An accurate fault diagnosis method is a crucial guarantee for system reliability. Deep learning provides a great insight into the intelligent exploration of machinery fault diagnosis. Hyperparameters are very important to construct an effective deep model with good performance. This research fully mines the feature component from vibration signals, and converts the failure recognition into a classification issue via establishing a deep model. Furthermore, Bayesian algorithm is introduced for hyperparameter optimization as it considers prior information. An adaptive convolutional neural network is established for typical failure pattern recognition of an axial piston pump. The proposed method can automatically complete fault classification and represents a higher accuracy by experimental verification. Typical failures of an axial piston pump are intelligently diagnosed with reduced subjectivity and preprocessing knowledge. The proposed method achieves an identification accuracy of more than 98% for five typical conditions of an axial piston pump.

1. Introduction

The hydraulic piston pump is an essential power element in the hydraulic system and can realize the transformation between mechanical energy and hydraulic energy [1,2,3]. Because of the advantages of its small size, a high power/weight ratio and easy variable adjustment, the axial piston pump has been diffusely utilized in marine, aerospace and mining equipment, under working conditions containing high efficiency and high pressure [4,5,6]. The operational process of the axial piston pump is a composite motion of rotary motion and linear motion, with multiple friction pairs and large friction amplitude. However, the construction characteristics make main friction pairs prone to failure. Moreover, it is hard to estimate the potential effects of different fault levels on the persons and the system [7,8,9]. The hiddenness and coupling of failure features augment the trouble of extraction and classification. This has led researchers to exploit and explore an effective and available approach for the fault classification of axial piston pumps.

Failure diagnosis is essentially taken as a problem of pattern classification and identification. Fault diagnosis technologies are generally segmented into three types, methods on account of signals, methods on the strength of analytical models, and methods based on knowledge [10,11,12]. Signal-based methods are to acquire the effective feature value by directly analyzing the measured signal, and make a high request for the professional basis on the signal processing. The detection signal can be described from any single perspective or a combination of multiple feature perspectives, such as frequency domain, time domain, wavelet transform, and adaptive mode decomposition. Yan et al. constructed a multi-source information fusion method and fully mined the space and time relationship of signals. By comparing with the voting and connecting, the method showed a higher accuracy for the active magnetic bearing system [13]. Kannan et al. put forward a three-module information integration means. Moreover, a weighted failure recognition based on sensor signal was researched, and the way was validated by using vibration and acoustic emission signals [14]. Under strong interference noise and strong pumping pulses, Xiao et al. proposed a fuzzy entropy-assisted singular spectral denoising means to extract failure features of bearings in a piston pump [15]. Zheng et al. put forward a modified Autogram on the base of power spectral entropy, effectively overcoming the pollution problem of vibration signals caused by Gaussian and non-Gaussian noise [16]. Considering the preventive maintenance of aeroderivative gas turbines, a diagnosis means on the strength of continuous wavelet transform (CWT) was developed for the early faults identification [17]. On this basis, Zhao et al. proposed a new feature selection means on the base of amplitude spectrum imaging by using CWT and image transformation, constructing a convolutional deep-belief network with Gaussian distribution to catch fault features of bearing [18]. By using the Teager energy operator and multipoint optimal minimum entropy deconvolution adjusted, Xiao et al. successfully extracted useful fault frequencies and achieved failure mode recognition of bearings in a hydraulic pump [19]. To determine the highly sensitive frequency band in axial piston pumps for easy identification of defective components, Zhou et al. researched a novel way on account of the tangent-hyperbolic fuzzy entropy measure [20].

An applicable mathematical model is needed for diagnosis objectives when using the model-based methods. Its applications and diagnostic results could be strongly limited, owing to the practical difficulty in establishing an accurate model. Sun et al. employed an enhanced inverse Gaussian process to analyze wear degradation and achieved residual life prediction of a piston pump [21]. The accuracy was increased by taking random factors and measurement errors into account in the establishment of the prediction model. By building a mathematical model of the intelligent hydraulic pump system, Ma et al. put forward an identification technology using a nonlinear unknown-input observer. The method could recognize common failures and provide a guide for system reliability [22]. Ying et al. constructed an improved time-varying displacement excitation model. The dynamic simulation of a pump swash plate with some defects was conducted [23]. In the research of predicting bearing defects, Zhou et al. established a sparsity measure based on entropy, and conducted envelope analysis on defects in piston pumps [24]. The research on the dynamic vibration characteristics of the multi body system of an axial piston pump has great implications for fault detection and evaluation. Ying et al. constructed a lumped-parameter model and predicted the vibration response of the rotor and separator components [25]. Tang et al. investigated the vibration characteristics of misalignment friction-mixed faults in an axial piston pump, established a rotor-bearing model, and studied the dynamic characteristic of mixed faults under different parameters. It was found that a unique frequency component may be helpful in detecting the fault [26]. Chao et al. established a physical flow loss model for flow loss coefficient of axial piston pumps under various working status, and proposed a hybrid method of model-data driven to evaluate the health conditions of axial piston pumps [27]. Moreover, Chao et al. developed a health assessment model for axial piston pumps, using density-weighted support vector data to describe and construct a dimensionless health factor to assess the working status of pumps [28]. Effective structural design can reduce fluid-related problems. Chao et al. elucidated the mechanism by which the design of a capped piston can improve the flow features of a piston pump. The results indicated that a novel design is promising. Moreover, it can efficaciously improve fluid-related problems [29].

The development of artificial intelligence promotes intelligent diagnosis methods based on knowledge [30,31,32]. The neural network is a representative of knowledge-based methods. Lan et al. researched the extreme learning machine for fault identification of slipper wear on a hydraulic pump [33]. Some adaptive-signal decomposition methods were utilized for vibration signal denoising and characteristic selection, such as wavelet decomposition, empirical mode decomposition, local mean decomposition, extreme-point symmetric mode decomposition and so on. Rapur et al. employed a support vector machine (SVM) for multi-type fault identification of centrifugal pumps on the strength of current signals and vibration signals [34]. Shi et al. conducted imbalanced fault identification of an automatic driving vehicle on account of a SVM modified by the grey wolf optimizer algorithm [35]. As further progress of machine learning and deep learning (DL) provides a broad horizon for more complex identification problems [36,37,38], a simple DL model with two hidden layers was constructed for the classification of clogging fault in the centrifugal pump. Multi-source information from pressure, acceleration and current was used for analysis and contributed to the improvement of the prediction accuracy [39]. Yang et al. applied the transfer learning strategy into failure mode recognition of rotary machinery, and verified the research way in laboratory and practice [40,41]. By introducing diverse perspectives of space, channel and sequence, a deep transfer learning framework was established for failure mode recognition of bearing under changing conditions. The method integrated a feature enhancement network and a long-short term memory for feature enhancement and targeted extraction [42]. A compound DL method was designed for failure type identification of a piston pump on account of acoustic signals and vibration signals [43]. Typical faults of four main components were studied, including piston, valve plate, slipper and return disk. The attention mechanism, residual network and transfer learning were combined to accomplish the information fusion and enhance the generalization capability under changing loadings. Chao et al. utilized the convolution neural network (CNN) to realize cavitation recognition of a hydraulic pump [44,45]. Xu et al. used residual evaluation based on cumulative sum to detect faults in electro-hydraulic controlled variable-displacement pumps [46]. Kumar et al. carried out failure recognition of a centrifugal pump on account of a CNN by extracting useful features from acoustic signals [47]. Chen et al. combined the cyclic spectral and a CNN to achieve the failure identification of bearings. Group normalization was introduced for decreasing the effects of data imbalance [48]. The method represented a strong generalization ability and advantageous precision through experimental validation. In the absence of a large number of labeled data, Dong et al. put forward an unsupervised anomaly detection method for piston pumps based on subsequence time-series clustering. Simultaneously, it can also identify weak fault data; enhancing the generalization ability of this means, under variable external loads [49]. Furthermore, intelligent optimization algorithms have been introduced for selecting the critical model hyperparameters (HPs) and broadening the direction for fault pattern recognition of an axial piston pump, such as random search, adaptive search, artificial intelligence optimization and swarm intelligence optimization [50,51,52]. Much research on intelligent fault identification of rotating machinery has been conducted and some achievements have been made, while there are still some challenges to be solved.

(1)

Due to the complex structure and hidden failure mode of an axial piston pump, it is arduous and critical to probe into a method of fault identification to ensure the stability of system.

(2)

Traditional diagnosis methods strongly rely on the specialized knowledge. Their practical applications are limited by strict requirements for signal processing and failure mechanisms.

(3)

The selection of model hyperparameters in common deep models depends greatly on the professional experience. There are some deficiencies for present manual adjustment and intelligent algorithms based on search and evolution.

Therefore, key contributions in the research are described as follows:

(1)

To precisely conduct fault pattern recognition of a hydraulic pump, the wear failure mechanisms of key friction pairs are investigated and explored, considering a change of wear levels and different operation conditions.

(2)

This research acquires vibration signals via non-destructive condition monitoring. It lays a foundation for the extraction of useful fault characteristics.

(3)

Eliminating some complex signal processing procedures in traditional methods; feature extraction and classification are combined in the deep model to implement the typical failure mode recognition of a piston pump. Bayesian optimization algorithm (BOA) is employed for model parameter optimization.

The remaining part of this research is organized as follows. Section 2 describes the primary theoretical background of CNN and BOA. Section 3 illustrates the flowchart and steps of the proposed diagnosis means; the means are based on a CNN optimized by BOA. In Section 4, an experimental setup and the signal acquisition are detailed. In Section 5, verification results of the diagnosis means are discussed and compared with other means. Finally, in Section 6, some conclusions are obtained.

2. Brief Theory

2.1. Convolutional Neural Network

Three obvious shortcomings can be observed when the images with large scale are processed with a common fully connected neural network. Frist, expanding the image as a vector can result in a loss of spatial information. Second, too many parameters make the model training hard and lead to an overfitting problem. CNN can overcome the above issues owing to its local connection, weight sharing and subsampling. CNN is known as a potent tool for image processing and video analysis [53,54,55]. A complete CNN can be constructed by overlaying the following structural layers, input layer, convolutional layer (CL), rectified linear-unit layer (ReLU), pooling layer, fully connected layer (FC) and output layer.

As the core layer in a CNN, CL generates most of the computation in the network and conducts feature extraction. Pooling is also a significant operation and can reduce the feature image and the dimension. Detailed operations of CL and pooling can be referred to relative researches [56,57,58].

2.2. Bayesian Optimization Algorithm

The automatic selection of HPs is essential in constructing machine learning models [59,60,61]. Some intelligent algorithms have been introduced for adaptive learning of HPs, such as particle swarm optimization and genetic algorithm. Different from other methods, BOA involves the prior knowledge of parameters into the analysis of posterior distribution [62,63,64]. BOA represents strong robustness and fast convergence.

Gaussian process (GP) and fetch function are two critical functions in BOA. The optimization objective is to search for combinations of HPs which can optimize the model performance. GP facilitates statistics and can be standardized. The subset of a multivariate Gaussian distribution is still a multivariate Gaussian distribution. Owing to the advantages of GP in figuring out nonlinear problems, it is employed to fit the objective function by fully using the previous information.

A multivariate Gaussian distribution is described as [65]:

$$F\left(g_{1:k}\right)~NOR(m(g_{1:k}),c^{\theta }(g_{1:k},g_{1:k}))$$

(1)

among them, $F$ represents a smooth function, the finite input set can be denoted by $g_{1:k}^{}$, ${m(g_{1:k})}_j={m(g_j)}_{}$ denotes the mean vector, and ${c^{\theta }(g_{1:k},g_{1:k})}_{ji}=c^{\theta }(g_j,g_i)$ can be parameterized by $\theta$ and represents the covariance matrix.

Gaussian distribution has two statistics, mean value and variance of samples. It is necessary to choose whether the next point has a higher mean or a higher variance to balance exploitation. Acquisition function can be a guide for sampling. There are numerous acquisition functions, including the methods based on improvement or entropy, and some compound methods. Expected improvement (EI) is an effective and simple improvement-based strategy, allowing for easier computation and fewer parameters distinct from improved probability and upper confidence. The computational formula of EI can be represented by [60]:

$${\alpha }_{EI}(D;\sigma ,s)=E[\mathrm{Max}(0,f(D)-f(D^{\ast }))]$$

(2)

where, $s$ represents a data acquisition, $f(D^{\ast })$ denotes the present best solution, and $f(D)$ should be maximized wherever possible.

When combining GP, EI can be described as:

$${\alpha }_{EI}(D;\sigma ,s)={\beta }_t(D;\theta ,s)[x\mathsf{\Phi }(x)+\varphi (x)]$$

(3)

among them, $x=\frac{{\mu }_t(D;\sigma ,s)-f(D^{\ast })}{\beta (D;\sigma ,s)}$, $\beta$ denotes $\beta$-sub-Gaussian noise, $\varphi$ represents probability density function of normal distribution, and $\mathsf{\Phi }$ denotes the cumulative distribution function.

When taking stochastic noise into account, noisy EI can be represented by:

$${\alpha }_{EI}(D;\sigma ,s)=\beta (D;\sigma ,s)[t\mathsf{\Phi }(t)+\varphi (t)]$$

(4)

among them, $t=\frac{{\mu }_t(D;\sigma ,s)-\mu ({\theta }^{\ast })}{\beta (D;\sigma ,s)}$, the best expected values can be calculated from mean results and denoted as $\mu ({\sigma }^{\ast })$.

3. Diagnosis Method

3.1. Structure of CNN

According to the practical request of typical fault pattern recognition of axial piston pump, the traditional AlexNet (T-AlexNet) is improved and shown in Figure 1.

(1)

The input size of the model is re-sized into 224 × 224 with data conversion technology.

(2)

The enhanced CNN model is composed of five CLs and three max pooling layers. The subsampling of 3 × 3 is used for the reduction of parameters and dimension.

(3)

Dropout is employed in the FC layer to reduce the structural risks of the network by randomly zeroing the partial weight or output of the hidden layer.

(4)

The structure factors of the network model are updated on account of the back-propagated gradient. The loss function value of the cross entropy is minimized and the learning of the network model is sped up.

(5)

The Adam algorithm presents the greatest performance. It combines momentum and RMSprop algorithm, and uses an adaptive learning rate and momentum to expedite the convergence of the model. Furthermore, Adam shows advantages in dealing with non-stationary problems with noise and sparse gradient. Therefore, Adam is selected in the improved AlexNet model.

(6)

Considering that the state category of the pre-diagnosed axial piston pump is five, the output layer is set as five. Softmax function is used in the classification stage.

Figure 1. Structure of the improved CNN model.

Figure 1. Structure of the improved CNN model.

3.2. Proposed Diagnosis Method

By introducing BOA for learning HPs, an adaptive diagnosis method is constructed. Four main steps are carried out, data acquisition, signal transformation, parameter optimization and the application of the method. The detailed implementation is as follows:

(1)

Data acquisition: time-series data are measured using a vibration acceleration sensor. The sensor output signal is collected by the virtual instrument NI card and data acquisition system, which is sent to the computer for analysis and processing.

(2)

Signal transformation: original vibration signals are converted into images via CWT. The two-dimensional images are taken as the input of the diagnosis model.

(3)

BOA: preset main HPs for a CNN according to T-AlexNet. The objective is to seek for the HP groups which can achieve the optimal model performance. The new HP set is gained based on the acquisition function. The types and range of HPs are determined before optimization. The relationship between the model performance and HP is fitted by employing GP.

(4)

The modified CNN model called B-AlexNet is used for automatic fault pattern recognition of an axial piston pump. The intelligence is reflected by the automatic selection of HP, and integrates feature extraction and identification.

4. Experimental Bench

The fault simulation experiments are conducted in a swash plate plunger pump, as displayed in Figure 2. The test stand mainly contains a drive motor and a piston pump. We chose a sampling frequency of 10 kHz and performed experiments of signal collection in Yanshan University.

Vibration signal is monitored by using a piezoelectric accelerometer. The type of accelerometer is YD72-D and directly installed in the end cover of the pump. The frequency ranges from 1 Hz to 18 kHz and the test range is 10,000 ms⁻². The signal acquisition is completed using a multifunctional data acquisition card with USB-6221. The sample rate is 250 ks/s and the updated rate is 833 ks/s. Four faulty conditions and a normal condition are investigated in the experiment, namely, swash plate wear (xp), slipper wear (hx), loose slipper failure (sx), central spring wear (th) and no observable fault (zc). Four defects are usually caused by friction and wear between friction pairs. The large gap between the ball socket sink and plunger ball head could lead to a loose slipper. Swash plate wear and slipper ablation could be generated by metal contact friction between the swash plate and slipper. The center spring could be worn or broken to keep contact with the seal and squeezing returning plate. Moreover, the defects in the major friction pairs will result in a great impact and loss. Five types of pressures and different fault levels of the three failures are analyzed.

5. Results and Discussion

5.1. Input Data

The CWT time-frequency distributions of vibration signals are shown in Figure 3. The dataset is constructed based on the transformed time-frequency images. Each fault consists of 1200 samples. The dataset contains 6000 images with the size of 256 × 256, which are resized into 224 × 224, and the random horizontal flip is carried out. Train sample makes up 70%, and the 30% is intended to be test sample. As for each faulty condition, the frequency presents some changes with time. The characteristics visually demonstrated in different conditions are too similar to be identified, especially for swash plate wear and central spring wear. In this case, it is impossible to accurately judge the various fault conditions of the piston pump via manual observation. It is significant to exploit an intelligent means to find out the effective characteristics for fault pattern recognition of an axial piston pump.

5.2. Hyperparameter Optimization

The following HPs are preset in BOA. The measure of import is 224 × 224, activation function is ReLU, and max polling is for subsampling. Ten crucial HPs are to be amended, including learning rate (LR), batch size (BS), epoch, the convolutional kernel number of the first CL (KN-CL1), the convolutional kernel number of the second CL (KN-CL2), the kernel size of the first CL (KS-CL1), the size of the second CL (KS-CL2), dropout rate, and the quantity of neurons in the first and second FC layer (NN-FC1, NN-FC2). The detailed parameter and optimized results are revealed in

Table 1. Hyperparameter range of BOA.

No.	Name	Range	Optimization Results
1	LR	[0.0001, 0.01]	0.00019
2	BS	[24, 56]	35
3	Epoch	[20, 50]	45
4	KS-CL1	[5, 9]	7
5	KS-CL2	[3, 7]	7
6	KN-CL1	[30, 60]	42
7	KN-CL2	[80, 140]	91
8	NN-FC1	[1000, 1600]	1231
9	NN-FC2	[400, 800]	650
10	Dropout	[0.1, 0.9]	0.67

.

The iteration is presented in Figure 4. Fast convergence of B-AlexNet can be seen by using BOA. The accuracy is more than 98% in 20 iterations. The model converges in 40 iterations and obtains a precision of 98.5%. In addition, neurons of FC 1 and FC 1 by BOA are far less than those by manual tuning. It can be validated that B-AlexNet achieves a higher classification performance. Moreover, parameters and the computation complexity are remarkably reduced.

5.3. Fault Identification Results

The B-AlexNet is validated by using optimized results. Figure 5 presents changes of training loss and accuracy with epochs. The B-AlexNet represents excellent convergence and stability.

The confuse matrix is displayed in Figure 6. M-AlexNet denotes AlexNet with manual tuning. B-AlexNet and M-AlexNet could identify more correct samples for five conditions compared with T-AlexNet. The identification of sx and th is visibly increased. The classification results of different models are displayed in

Table 2. Classification accuracy of each type.

Type	B-AlexNet	M-AlexNet	T-AlexNet
zc	100.0	100.0	100.0
xp	100.0	100.0	99.7
sx	96.7	96.9	95.8
hx	99.7	99.4	99.7
th	96.9	96.1	93.2

. B-AlexNet presents a higher precision for the five types.

The feature learning of B-AlexNet is visualized by t-distributed stochastic neighbor embedding (t-SNE) and is displayed in Figure 7. The features in the initial input layer are mixed together. Features gradually present a single cluster as a type of condition. Moreover, the five types can be clearly identified through the feature extraction and conversion of different layers. Useful characteristics in time-frequency images are gained by B-AlexNet. And then, the typical fault pattern identification of the axial piston pump is automatically completed.

6. Conclusions

Hydraulic piston pumps are known as the power heart of significant electromechanical-hydraulic equipment. This article takes a hydraulic axial piston pump as the research object. A data-driven diagnosis scheme, based on deep learning, is researched for the typical fault identification of the piston pump. Some valuable results are obtained as follows.

(1)

Based on the traditional AlexNet, an improved CNN called B-AlexNet is constructed for the intelligent defect identification of an axial piston pump.

(2)

Bayesian algorithm is adopted for the adaptive learning of model hyperparameters. The objective function on the performance of improved CNN is modeled with a Gaussian process. An improvement-based strategy, named noisy expected improvement, is filtered as the acquisition function.

(3)

The diagnosis performances of B-AlexNet are verified by experiments in an axial piston pump test bench. B-AlexNet achieves an accuracy of more than 98% for five conditions to be diagnosed. Moreover, the identification for central spring wear is remarkably enhanced compared to the traditional AlexNet.

(4)

Potential features in time-frequency images of vibration signals are adaptively acquired. The feature distribution after dimensionality reduction presents a great clustering effect. Typical failures of an axial piston pump are intelligently diagnosed with a reduced subjectivity and preprocessing knowledge.

In the future, the method proposed in this article can be further extended to the fault classification and identification based on pressure signals and acoustic signals, so as to do some in-depth research on multi-source information fusion. Moreover, the network structure and key parameters can be further optimized according to different research objects to improve the diagnostic accuracy and efficiency.