Research on Performance Degradation Assessment and Abnormal Health Status Detection of Quayside Crane Lifting Gearbox Based on Information Fusion

Abstract

In order to solve the problems of subjectivity in the extraction of traditional degradation features and incomplete degradation information contained in a single sensor signal, a performance degradation assessment and abnormal health status detection method based on information fusion for the quayside crane lifting gearbox is proposed. Firstly, the correlation between the vibration and temperature of the gearbox is analyzed; secondly, the Convolutional Neural Network (CNN) and entropy degradation features from the full fault cycle vibration and temperature data of the lifting gearbox are extracted respectively; then, the final degradation indicators of the vibration and temperature data are obtained, respectively, through feature optimization, and the fusion degradation indicator is obtained by combining the two indicators; finally, the performance degradation assessment and abnormal health status detection of the gearbox are carried out. The effectiveness and superiority of the proposed method in the performance degradation evaluation of the gearbox are verified by comparison, and the proposed method can identify the initial degradation point of the gearbox earlier than the method based on the single vibration degradation index and the method based on the fusion of the traditional vibration degradation feature and the temperature entropy degradation feature.

1. Introduction

With the development of economic globalization, all major ports are equipped with quayside container cranes that can load and unload containers efficiently. However, the quayside cranes are faced with problems such as long continuous working times, bad working environments, and frequent start and stop, etc. With the accumulation of service time, the risk of failure will increase significantly. It will affect daily work and cause huge economic losses and even casualties when the failure occurs [1]. Therefore, effective real-time monitoring of the quayside crane, analysis of potential failure risks during operation, timely and accurate health diagnosis, and the development of targeted maintenance plans are of great practical significance for avoiding huge accidents caused by sudden failures, improving the safety and reliability of the quayside crane, and improving the health management and intelligent operation and maintenance level of the enterprise.

Health diagnosis technology has been paid more and more attention with the continuous development of mechanical equipment. Health diagnosis can be divided into fault pattern recognition and performance degradation assessment, and most current studies are biased toward fault pattern recognition [2]. This type of research is a passive maintenance model, focusing on the diagnosis of the fault category at a certain point in time, that is, posterior maintenance, in which the failure has already occurred and has consequences, and the diagnosis becomes a “death certificate” [3]. Performance degradation assessment is an active maintenance mode, focusing on the measurement of the degree of performance degradation in the whole life cycle of machinery and equipment, that is, predictive maintenance, which can timely and accurately provide an effective “treatment plan” and early warning of failure. In the process of long-term service of mechanical equipment, the performance gradually declines from the health state until serious failure occurs [4]. The main steps of performance degradation assessment technology include data acquisition and processing, degradation feature extraction, degradation assessment model construction, and performance degradation state assessment [5]. Current studies on performance degradation evaluation focus on components such as bearings and gears, which use the life cycle data obtained from accelerated life experiments under stable output conditions to verify the validity, while the laboratory environment is superior and interference is less, which is different from the data collected in the field [6]. As an important transmission component of the lifting mechanism of the quayside crane, the gearbox works in a state of unstable load change for a long time, the working environment is harsh, and there are many interferences, which leads to the state degradation stage which is not necessarily as obvious as the laboratory data.

Health diagnosis technology can be divided into the model-based approach, knowledge-based approach, and data-driven approach. Model-based methods use the physical equations and models of the system for fault diagnosis, including techniques based on mathematical models, state estimation, and system identification [7]. The knowledge-based approach utilizes expert systems, rule bases, and expertise for fault diagnosis. These methods rely on the knowledge and experience of domain experts [8]. Nowadays, mechanical equipment is becoming more complex, making it difficult to establish accurate physical models, and the operation of the equipment will generate a large amount of monitoring data. The data-driven approach is not limited to accurate physical models and expert knowledge and can be used to assess the performance degradation of equipment based on monitoring data. As an effective data feature extraction tool, deep learning abstracts the original data layer by layer to a more accurate feature scale through the deep neural network structure, to extract key features that reflect the characteristics of the data [9]. Compared with traditional feature extraction methods, deep learning-based methods have the characteristics of automatic feature extraction without a lot of prior knowledge and expert experience, so it is favored by most scholars.

Wang et al. reviewed and summarized the health indicators of bearings and gears based on vibration signals [10]. Huang et al. verified the disturbance removal ability of Nuisance Attribute Projection (NAP) in feature space by using vibration signals of rolling bearings under different working conditions and studied the influence of the application sequence of Ranking Mutual Information (RMI) and NAP on the bearing performance degradation index [11]. Lv et al. proposed a new degradation feature extraction method, and considering the completeness of samples, logistic regression and SVDD models were used, respectively, to evaluate bearing performance degradation [12]. It can be seen that most existing performance degradation assessment studies rely on vibration signals, but the fault mechanism of mechanical equipment is complex and diverse, and different faults may produce similar fault states. If single sensor data are used for degradation assessment, the extracted degradation index may not be able to better reflect the degradation process. Therefore, the research on multisource information fusion methods is of great significance. On the one hand, there is a clear correlation between the vibration and temperature of the gearbox: the greater the vibration, the more heat generated, and the higher the temperature. On the other hand, there is also a correlation between entropy and temperature: temperature is the driving force for heat transfer, and heat transfer leads to changes in entropy, so the entropy feature in the temperature signal can be extracted as a degradation indicator. However, the performance degradation evaluation based on the fusion of vibration and temperature signals is rarely studied, especially in large port machinery such as the quayside crane.

In conclusion, this paper first analyzes the correlation between vibration and temperature of the gearbox, then extracts the CNN degradation feature from the full fault cycle vibration data and the entropy degradation feature from the full fault cycle temperature data of the lifting gearbox, and then carries out feature optimization on the extracted high-dimensional degradation feature set to obtain the final degradation index of the vibration and temperature data, respectively; finally, the fusion degradation index is used to evaluate the performance degradation and detect the abnormal health status of the gearbox. Figure 1 shows the whole frame of the proposed method.

The subsequent sections of this article are structured as follows. The related theoretical backgrounds of correlation analysis of vibration and temperature of the gearbox, CNN, Support Vector Data Description (SVDD) model, and Chebyshev Inequality are introduced in Section 2. In Section 3, the full fault cycle data of the quayside crane lifting gearbox are used to verify the proposed method. Finally, Section 4 presents conclusions and future work.

2. Related Work

2.1. Correlation Analysis of Vibration and Temperature of the Gearbox

The gearbox produces vibration $vib$ under the action of load $Z$, $vib$ as $Z$ increases, the temperature $T$ of the gearbox rises at the same time; therefore, there is a proportional relationship: $T\propto vib\propto Z$ [13]. Vibration generated by gearbox operation is a process of energy loss, and the thermal process of the gearbox includes heat production and heat dissipation. The main sources of heat production include friction heat $Q_f$ generated between mechanical components, elastic energy consumption heat $Q_e$ generated by mechanical components themselves, and inertia energy consumption heat $Q_i$; the main forms of heat dissipation include heat dissipation $Q_{air}$ on the surface of the gearbox and heat absorption $Q_{oil}$ of the lubricating oil inside the gearbox. The temperature change of the gearbox per unit of time $\Delta T$ can be obtained by the difference between heat production $Q_1$ and heat dissipation $Q_2$ as:

$$\left\{\begin{array}{l}{Q}_1=Q_f+Q_e+Q_i\hfill \\ Q_2=Q_{air}+Q_{oil}\hfill \\ \Delta T=Q_1-Q_2\hfill \end{array}\right.$$

(1)

When the gearbox vibrates, there will be relative motion between the mechanical components, resulting in friction heat as:

$$Q_f=f_v\cdot F_v\cdot dt$$

(2)

Among them, $f_v$ is the amount of heat generated by friction per unit of time, $F_v$ is the magnitude of vibration, and $dt$ is the time interval.

When the gearbox vibrates, it will also cause elastic deformation of the mechanical parts, resulting in elastic energy consumption heat as:

$$Q_e=k_e\cdot F_v^2\cdot dt$$

(3)

Here, $k_e$ is the amount of heat consumed per unit of vibration energy.

Mechanical components are also subject to inertia, resulting in inertial energy consumption heat as:

$$Q_i=k_i\cdot a^2\cdot dt$$

(4)

Among them, $k_i$ is the amount of heat consumed per unit of acceleration energy, and $a$ is the vibration acceleration.

Temperature change inside the gearbox is expressed as:

$$\Delta T=\frac{Q_f+Q_e+Q_i}{c\cdot m}$$

(5)

where $c$ is the total heat capacity of the internal mechanical components, and $m$ is the total mass of the internal mechanical parts. The above formula can become:

$$\Delta T=\frac{f_v\cdot F_v\cdot dt+k_e\cdot F_v^2\cdot dt+k_i\cdot a^2\cdot dt}{c\cdot m}$$

(6)

$$\Delta T=\frac{k_{e}dt}{cm}{F}_v^2+\frac{f_{v}dt}{cm}{F}_v+\frac{k_i{a}^{2}dt}{cm}$$

(7)

In summary, the vibration of the gearbox generates heat, making the temperature rise, and the greater the vibration, the higher the temperature, so there is an obvious correlation between them, which provides a theoretical basis for the fusion of the vibration and temperature signals of the gearbox.

2.2. CNN

CNN is a kind of feedforward neural network with convolutional computation and depth structure, which has been widely used in image processing, natural language processing, fault diagnosis, and other fields in recent years. Zhong et al. proposed a gas turbine fault diagnosis method based on CNN transfer learning and confirmed that the proposed method has good fault diagnosis ability under the condition of small samples [14]. In order to overcome the problem of low diagnosis efficiency in the existing mechanical intelligent fault diagnosis research based on deep transfer learning, which mainly considers the stable speed scenario, Cao et al. proposed an unsupervised domain-shared CNN for efficient fault transfer diagnosis of machines from stable speed to time-varying speed [15]. Zheng et al. conducted a research study on weak fault diagnosis of rolling bearings based on two-dimensional CNN images, converting one-dimensional time series of bearing vibration signals into images, which can effectively identify the degradation of the inner ring, outer ring, and rolling element [16]. The structure of CNN includes the input layer, hidden layer, and output layer, and the hidden layer includes the convolution layer, pooling layer, and fully connected layer [17].

2.2.1. Convolutional Layer

The convolutional layer extracts the features related to the classification object through the weight backpropagation of the convolutional kernel, and more advanced features can be extracted by increasing the number of convolutional layers, which can be expressed as:

$$x_j^l=f\left({\displaystyle \sum _{i\in M_j}{x}_i^{l-1}⊛k_{ij}^l+b_j^l}\right)$$

(8)

Among them, $⊛$ is the convolution operator, $x_i$ is the $i$-th input mapping, $k$ is the $S\times S$ convolution kernel, $b_j$ is additive bias, $M_j$ is a feature map of the convolution layer, $l$ is layer $l$ in the network, and the convolution result is passed to the activation function $f$.

2.2.2. Pooling Layer

The pooling layer can reduce the feature dimension and speed up network training and calculate the average or maximum convolution features in adjacent neurons in the previous convolution layer. Figure 2 shows the implementation principle of the maximum pooling layer.

2.2.3. Fully Connected Layer

The fully connected layer is usually at the tail of the neural network to classify the features, and the output of the fully connected layer can be expressed as:

$$O=f^{\prime }\left({\displaystyle \sum _{j=1}^d{x}_j^F{\omega }_j+b_j}\right)$$

(9)

Here, $O$ is the output value, $x_j^F$ is the $j$ neuron in the fully connected layer, ${\omega }_j$ is the weight of $O$ and $x_j^F$, $b_j$ is the deviation from $O$, and $f\prime$ is the activation function of the fully connected layer.

2.3. SVDD

SVDD is based on the Support Vector Machine (SVM), which has the advantages of fast fitting speed, high classification accuracy, and good robustness under small samples. SVDD uses normal sample data to build a hypersphere to classify test samples. This method is practical and can deal with the problem of the lack of failure samples. Xia et al. proposed a fault diagnosis method based on SVDD for the irregularity of planetary gear fault characteristics of a helicopter main reducer [18]. In order to solve the problem of how to add unknown faults to the fault pattern library for adaptive updating of the fault diagnosis model when new unknown faults are identified, Xu et al. proposed an unknown fault identification method based on PSO-SVDD [19]. The principle of SVDD follows below.

Suppose the normal state sample is $\left\{x_i,i=1,2,\dots ,N\right\}$, SVDD uses a nonlinear mapping to map it into a high-dimensional feature space, denoted by $\left\{\phi \left(x_i\right),i=1,2,\dots ,N\right\}$. A minimum hypersphere is constructed in a high-dimensional space to cover all or most of the state samples. The center of the hypersphere is $a$, the radius is $R$, and the samples inside and outside the sphere are target and anomaly samples, respectively [20]. The hypersphere radius $R$ is equal to the distance between the center of the sphere and the support vector $x_{sv}$, expressed as:

$$\begin{gathered} R^2=\Vert \phi \left(x_{sv}\right)-a{\Vert }^2=K\left(x_{sv},x_{sv}\right)- \\ 2{\displaystyle \sum _{i=1}^N{\alpha }_{i}K\left(x_i,x_{sv}\right)+{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\alpha }_i{\alpha }_{j}K\left(x_i,x_j\right)}}} \end{gathered}$$

(10)

where $K\left(\cdot ,\cdot \right)$ is the kernel function, and ${\alpha }_i$ and ${\alpha }_j$ are the Lagrange coefficients. The distance $D$ between any sample $z$ and the center of the hypersphere can be expressed as:

$$\begin{gathered} D^2=K\left(z,z\right)- \\ 2{\displaystyle \sum _{i=1}^N{\alpha }_{i}K\left(z,x_i\right)+{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\alpha }_i{\alpha }_{j}K\left(x_i,x_j\right)}}} \end{gathered}$$

(11)

It can be analyzed whether the samples are located inside or outside the hypersphere, or on the boundary, by comparing the values of $D$ and $R$. $D>R$ indicates that the samples are located outside the hypersphere, which are anomaly samples. $D<R$ means that the samples are located in the hypersphere, which are target samples.

2.4. Chebyshev Inequality

The degradation index of mechanical equipment under normal operation is a random variable with definite expectations and standard deviation. To calculate its boundary value when an anomaly occurs, Chebyshev Inequality is used [21]. For a random variable $X$, if it has a finite expected value $\mu$ and a finite nonzero standard deviation $\sigma$, then for any real number $k$ greater than zero, the following formula holds:

$$P\left(\left|X-\mu \right|\ge k\sigma \right)\le \frac{1}{k^2}$$

(12)

By definition, the probability that a random variable falls outside of $k$ standard deviations from the mean is less than or equal to $1/k^2$, that is, for random variables that follow any distribution, most of their values will be concentrated in the region around the population mean. According to Chebyshev Inequality, the abnormal threshold of mechanical equipment performance degradation index DI can be set as:

$$P\left(\left|X_{DI}-{\mu }_{DI}\right|\ge k{\sigma }_{DI}\right)\le \frac{1}{k^2}$$

(13)

where $X_{DI}$ is the value of DI, ${\mu }_{DI}$ is the expected value of DI, ${\sigma }_{DI}$ is the standard deviation of DI, and $k$ is any positive number. When $k$ is given 32, the probability that the value of the degradation index DI will be 32 standard deviations from the mean is less than or equal to 1/1024 (i.e., about 0.1%). In other words, more than or equal to 99.9% of the degradation index value falls in the interval $\left[{\mu }_{DI}-32{\sigma }_{DI},{\mu }_{DI}+32{\sigma }_{DI}\right]$. Therefore, set the health status exception threshold as:

$$Threshold={\mu }_{DI}+32{\sigma }_{DI}$$

(14)

3. Experimental Verification

3.1. Data Preparation

The validity of the proposed method was verified by the full fault cycle data of the quayside crane lifting gearbox. The quayside crane lifting gearbox was taken as the research object, and the data were obtained from the NetCMAS (Net Crane Monitoring & Assessment System) online status monitoring platform of a wharf quayside crane in Shanghai. The framework and software interface of the system are shown in Figure 3a,b. The NetCMAS system was equipped with vibration and temperature sensors in the lifting mechanism. The structure of the lifting mechanism and the arrangement of measuring points are shown in Figure 3c,d. The field sensor layout is shown in Figure 4, and the name of the measuring points and the corresponding channel are shown in

Table 1. Name of measuring points and corresponding channel.

	Measuring Point Number	Measuring Point Name	Channel
1	HGH1V	Radial vibration signal of gearbox	24
2	HGH1A	Axial vibration signal of gearbox	25
3	HGH1W	Left temperature signal of gearbox	26
4	HGH2W	Right temperature signal of gearbox	27

.

The experimental object of this paper was a lifting gearbox on a quayside crane in a wharf in Shanghai. The PCB608A11 vibration sensor and PT100 temperature sensor were installed on the right end of the high-speed shaft of the lifting gearbox. The NetCMAS system was used for data acquisition and condition monitoring. The sampling frequency of the acquisition system was 2500 Hz, the sampling time was 0.8 s, and the sampling interval was 10 s. Considering the large volume of condition monitoring data, the system did not store all vibration and temperature data. For the vibration signal, the system collected and converted the vibration signal into the effective value of the vibration speed (i.e., vibration severity) to store; for the temperature signal, the system collected and calculated the average value of 2000 temperature data to store. After the installation of the system and sensor, the online monitoring of the vibration and temperature data of the gearbox was started.

After online status monitoring over 3 years, the 24-channel measuring point of the high-speed shaft of the lifting gearbox gave an alarm. The roller bearing failure was found in the form of roller wear after shutdown maintenance, and the on-site inspection situation is shown in Figure 5. Then, the gearbox returned to normal work after the replacement of new parts. Therefore, the full fault cycle data of the lifting gearbox were collected by the system.

The data collected in the field contained a lot of nonworking state data, noise, and outliers, which needed to be preprocessed to enhance their value density. The data preprocessing is shown in Figure 6: (1) Remove nonworking state data: Figure 6a shows the data sequence corresponding to the vibration and temperature signal, in which the data circled in green are the nonworking state data. At this time, the gearbox is in the shutdown state, but the sensors are still collecting data. The amplitude of the collected vibration data is basically close to 0, which is not meaningful for the research, so these data should be removed; (2) Removal of background noise: Background noise is caused by the influence of other mechanisms in the surrounding environment, which will cause a certain deviation of the vibration signal. In this paper, the envelope method was adopted to remove background noise. The removal of background noise of the vibration signal is shown in Figure 6b; (3) Elimination of outliers: The data in this paper were collected in real time, so it is inevitable that there will be data interference. Such interference data need to be eliminated, otherwise, the quality of data mining will be affected. The efficiency and accuracy of data mining can be improved by judging outliers as measurement errors and eliminating them. The processing of vibration and temperature signals to eliminate outliers is shown in Figure 6c,d.

After the signal cleaning process, the full fault cycle vibration and temperature data of the lifting gearbox were obtained. The vibration signal of channel 24 and the temperature signal of channel 27 were selected as the data basis, and the full fault cycle data are shown in Figure 7.

Through the analysis of Figure 7, it can be found that, with the continuous degradation of the performance of the gearbox, the amplitude of the vibration load spectrum showed a trend of increasing overall, and then began to decrease after the repair. At the same time, the load spectrum sequence contained a large number of impact components, which reflected the characteristics of the periodic lifting operation of the quayside crane. However, it is difficult to accurately analyze the process of performance degradation and judge the early degradation point simply based on the original load spectrum, so it is necessary to construct a degradation index.

3.2. Degradation Feature Extraction

In order to facilitate the degradation feature extraction and subsequent performance degradation assessment and anomaly detection of the full fault cycle data, the data were divided into 1090 data groups, with 10,240 data points in each group.

It is well known that Softmax was the activation function of the last layer in the deep learning network for the generation of probability values. However, the CNN-based method of vibration signal degradation feature extraction, which was proposed in this paper, did not go through the activation function and directly extracted the data after passing through the last fully connected layer to obtain the degraded feature dataset. The time-series features of the full fault cycle vibration data, which can capture the dynamic change, periodic pattern, and trend information of the data, were extracted by using the CNN network.

The full fault cycle vibration data of the lifting gearbox were divided into a training set and a test set according to the ratio of 7:3. Then, the training set was labeled and imported into the CNN model for training. The network structure and specific parameters of CNN are shown in

Table 2. The network structure and specific parameters of CNN.

Network Structure	Specific Parameters
Input layer	128 × 80 Matrix
Convolutional layer 1	kernel_size: 5 × 5 kernel_number: 4
Max-pooling layer 1	pool_size: 2 × 2
Convolutional layer 2	kernel_size: 5 × 5 kernel_number: 8
Max-pooling layer 2	pool_size: 2 × 2
Convolutional layer 3	kernel_size: 5 × 5 kernel_number: 16
Max-pooling layer 3	pool_size: 2 × 2
Convolutional layer 4	kernel_size: 5 × 5 kernel_number: 32
Max-pooling layer 4	pool_size: 2 × 2
Activation function	ReLU
Dropout	0.25
Fully connected layer 1	728 × 1 one-dimensional vector
Fully connected layer 2	256 × 1 one-dimensional vector
Fully connected layer 3	128 × 1 one-dimensional vector
Fully connected layer 4	64 × 1 one-dimensional vector
Fully connected layer 5	10 × 1 one-dimensional vector

. The CNN network structure consisted of one input layer, four convolutional layers, four max-pooling layers, and five fully connected layers.

The CNN architecture details used in this paper: each group of data was a 10,240 × 1 one-dimensional vector, which was transformed into a 128 × 80 matrix and input into the CNN network, where the number of channels was 1. Firstly, through the first convolutional layer, whose convolution kernel size was 5 × 5, the number of convolution kernels was 4, and the output dimension of this layer was 128 × 80 × 4. Then, through the first max-pooling layer with the size of the pooling window 2 × 2, the output dimension of this layer was 64 × 40 × 4. After the pooling layer, a “ReLU” activation function was introduced to add nonlinear characteristics, and the 0.25 dropout was introduced to prevent overfitting. Similarly, after the second convolutional layer and the second max-pooling layer, the output dimension was 32 × 20 × 8, after the third convolutional layer and the third max-pooling layer, the output dimension was 16 × 10 × 16, after the fourth convolutional layer and the fourth max-pooling layer, the output dimension was 8 × 5 × 32. Finally, after five fully connected layers, it became a 10 × 1 one-dimensional vector.

After 30 iterations, the accuracy rate reached 100%, and the loss function value was small close to zero, and remained stable, indicating that the network had been trained to convergence. The high-dimensional degenerate feature set was obtained after the trained network model was used to extract the feature of the full fault cycle vibration data, as shown in Figure 8.

Temperature and entropy are two important concepts in thermodynamics, and they are closely related. Temperature is a measure of the average thermal motion of molecules, atoms, or particles in an object or system, reflecting the speed and energy distribution of molecular motion within the object. Entropy is a measure of the disorder or randomness in a system. In thermodynamics and information theory, entropy is used to quantify the randomness or uncertainty of a system. A higher entropy value indicates a greater degree of disorder in the system [22].

When the temperature of an object increases, the average thermal motion of molecules increases, resulting in greater randomness and disorder in the system, leading to an increase in entropy. The second law of thermodynamics states that the change in entropy $\Delta S$ is proportional to the reciprocal of the amount of heat transferred $Q$ and inversely proportional to the temperature $T$. This relationship can be expressed as $\Delta S=Q/T$. This means that, for a fixed entropy change $\Delta S$, temperature changes affect the amount of heat absorbed or released by the system. In summary, temperature and entropy are closely related. An increase in temperature leads to an increase in entropy, and temperature changes affect the entropy change.

Entropy features, including sample entropy, approximate entropy, fuzzy entropy, and LMCD entropy, were extracted from the full fault cycle temperature data, which were taken as the high-dimensional degradation feature set of the temperature signals, as shown in Figure 9.

As shown in Figure 8 and Figure 9, it can be seen that these degradation features had a corresponding changing trend with the degradation of the gearbox performance state. However, these degradation features had obvious fluctuations, which will affect the accuracy of the subsequent performance degradation assessment and abnormal health status detection of the gearbox. Also, there were redundancy and coupling between the features in the high-dimensional degenerate feature set. Therefore, it is necessary to carry out feature optimization to effectively remove the volatility of the degenerate feature curve and reduce the redundancy of the degenerate feature vector.

3.3. Degradation Feature Optimization

Research on the optimization of degradation features, the methods of smoothing degradation features based on sliding-window-normal distribution fitting, and reducing degradation features based on Principal Component Analysis (PCA) were proposed, respectively.

3.3.1. Degenerate Feature Smoothing

Aiming at the fluctuation phenomenon of the degenerate feature curve, a degenerate feature smoothing method based on sliding-window–normal distribution fitting was proposed. The process of this method is shown in Figure 10.

Figure 11a shows a degradation feature sequence of the vibration signal. The histogram was used to analyze the distribution characteristics of samples, as shown in Figure 11b, showing normal distribution. The probability distribution of feature sequences was plotted, as shown in Figure 11c, and the curve was approximately a straight line. The results indicate that the distribution of degenerate feature sequences in the sliding window can be fitted with normal distribution. Setting the sliding window width $w=10$, step size $s=1$, and the sliding window diagram is shown in Figure 12. Then, the extracted degradation features were smoothed, and the results are shown in Figure 13. It can be seen that the fluctuation in the degradation feature curve can be filtered out, and the interference can be reduced by smoothing treatment so that it can more accurately reflect the main trend of the performance degradation process of the lifting gearbox.

3.3.2. Degenerate Feature Reduction

An effective feature reduction method was needed to effectively reduce the redundancy between high-dimensional degenerate features [23]. Manifold Learning can fuse feature information and reduce dimension, but it has high computational complexity and poor robustness compared to PCA [24]. Therefore, considering the simplicity and stability of the calculation, PCA was selected for feature dimension reduction in this paper, and the feature reduction process is shown in Figure 14. The final degradation index $D_V$ of full fault cycle vibration data and the final degradation index $D_T$ of full fault cycle temperature data were obtained after reduction, as shown in Figure 15.

3.3.3. Information Fusion

Information fusion was a process of cognition, synthesis, and judgment of a variety of data, and the data involved in fusion often had the characteristics of being multisource, heterogeneous, and incomplete [25]. According to different fusion levels, information fusion can be divided into data layer fusion, feature layer fusion, and decision layer fusion [26].

The final degradation feature indexes $D_V$ and $D_T$ of vibration and temperature signals were obtained after the degradation feature extraction and optimization of the full fault cycle data of the quayside crane lifting gearbox. The fusion degradation index $\left[D_V,D_T\right]$ of the lifting gearbox was obtained by using the feature layer fusion in information fusion. Then, the fusion degradation index was used to evaluate the performance degradation and detect the abnormal health status of the quayside crane lifting gearbox.

3.4. Performance Degradation Evaluation of the Lifting Gearbox

Degradation feature extraction and degradation model construction were two key steps in performance degradation evaluation. The SVDD model did not require any prior knowledge and can achieve a quantitative evaluation of performance degradation degree when only normal state data were available. This paper constructed an SVDD model to evaluate performance degradation in full consideration of the actual situation that the state sample completeness of the gearbox was poor, and the method flow is shown in Figure 16.

The key steps of the performance degradation evaluation of the lifting gearbox based on the SVDD model were the following.

Step 1: The degradation feature extraction, optimization, and fusion of the vibration and temperature data in the healthy state were carried out to obtain the fusion degradation index $\left[D_V,D_T\right]$, which was used as the training sample.

Step 2: The SVDD hypersphere model was established when the training sample was input into the SVDD model for training, and the minimum hypersphere center $a$ and radius $R$ under normal conditions were obtained.

Step 3: The fusion degradation index was obtained by performing the same processing on the full fault cycle data, which were input into the trained SVDD hypersphere model. The distance $d$ between each test sample and the hypersphere center was calculated, which was used as the health index CV to complete the performance degradation assessment of the lifting gearbox.

The core idea of the SVDD method was to find a minimal hypersphere containing all or most of the target samples in the high-dimensional feature space through nonlinear mapping and try to make the target samples in the minimal hypersphere. The SVDD model was constructed by determining the kernel function parameter $s$ and penalty factor $C$. The value of $s$ was related to the fine degree of sample division: The smaller the value of $s$, the more complex the curve in the low-dimensional space, which tried to distinguish each sample from other samples, and was prone to overfitting; The larger the value of $s$, the data cannot be separated, and underfitting may occur. The value of $C$ weighed the empirical risk and structural risk: The greater the value of $C$, the smaller the empirical risk, the greater the structural risk, and the easier to overfit [27]. Based on this, the Gaussian kernel function was selected, setting $s=0.1,C=1$, and fusion degradation index $\left[D_V,D_T\right]$ was used to evaluate the performance degradation of the lifting gearbox based on SVDD, and the result is shown in Figure 17.

As illustrated in Figure 17, the overall change trend of the CV curve conformed to the law of the performance degradation of the gearbox and showed obvious stages. Before Group 210, the CV value was maintained near 0, at which time the gearbox was in a healthy state; in Group 210 to 770, the CV value began to rise and fluctuated within [0.05, 0.35], at which time the gearbox began to degenerate; since Group 771, the CV value rapidly rose to the interval [0.5, 0.75], the gearbox failed at this time; in the vicinity of Group 867, the gearbox was repaired and reoperated normally, and the CV value gradually decreased to near 0 and returned to a healthy state.

The SVDD performance degradation evaluation method based on a single vibration degradation index (Method A1) was compared to verify the superiority of the proposed fusion method (Proposed Method A), and the result is shown in Figure 18. The comparison results of the two methods are shown in

Table 3. Comparison of the two methods.

	Degradation Feature	Health Stage	Degradation Stage	Failure Stage	After-Maintenance Stage
Method A1	$D_V$	[1, 213]	[214, 775]	[776, 868]	[869, end]
Proposed Method A	$\left[D_V,D_T\right]$	[1, 209]	[210, 770]	[771, 866]	[867, end]

. The results indicate that the state division of the CV curve obtained by the two performance degradation evaluation methods was basically the same. However, due to the small amplitude range of the evaluation results of Method A1, the interval was likely to be fuzzy during the status division, resulting in the difference of critical groups between different states.

3.5. Abnormal Health Status Detection of the Lifting Gearbox

The first 200 samples of CV value of the lifting gearbox were selected as the health samples, and the mean and standard deviation were calculated. The abnormal threshold of the gearbox health status was calculated by Equation (14), which was $Threshold=0.0158$. The status was abnormal when the value of the CV curve was greater than the threshold. The result is shown in Figure 19. Through the analysis of Figure 19, it can be found that the CV value of Group 210 was greater than $Threshold$, at which time the health status of the gearbox was abnormal and the performance began to degenerate.

The health state anomaly detection method based on a single vibration degradation feature (Method B1) was compared in order to verify the superiority of the proposed method (Proposed Method B). The result is shown in Figure 20, and the initial degradation point appeared in Group 214. The results show that the method based on the fusion degradation index can identify the initial degradation point of the gearbox earlier than the method based on the single vibration degradation index, which was conducive to the early fault diagnosis and analysis of the gearbox.

The vibration degradation features of the proposed fusion degradation index in this paper were extracted by CNN. For comparison, the traditional degradation features of vibration were extracted and fused with the same temperature entropy degradation features to obtain the degradation indicator (Method B2). The specific process was as follows: (1) The time-domain statistical features of vibration signals were extracted, including peak-to-peak value, mean value, variance, standard deviation, and effective value; (2) The 3-layer wavelet packet decomposition of vibration signals was carried out to obtain 8 wavelet bands, and the wavelet scale entropy of each sub-band was calculated; (3) The above features were used as the high-dimensional degradation feature set of the full fault cycle vibration data; (4) The final degradation index $D_{V1}$ of the vibration signal was obtained by optimizing the features of the high-dimensional degradation feature set; (5) Fusion degradation index $\left[D_{V1},D_T\right]$ was obtained by fusing $D_{V1}$ with the same final degradation index $D_T$ of the temperature signal; (6) Finally, performance degradation assessment and abnormal health status detection based on SVDD were carried out. The result is shown in Figure 21, and the initial degradation point appeared in Group 212. The comparison results of the three methods are shown in

Table 4. Comparison of the three methods.

	Degradation Feature	Health Stage	Initial Degradation Point
Method B1	$D_V$	[1, 213]	214
Method B2	$\left[D_{V1},D_T\right]$	[1, 211]	212
Proposed Method B	$\left[D_V,D_T\right]$	[1, 209]	210

.

As illustrated in Table 4, the initial degradation point of the lifting gearbox identified by the Proposed Method B was Group 210, Group 214 for Method B1, and Group 212 for Method B2. The results show that: (1) The degradation information implied by the signal collected by a single sensor was not comprehensive, which led to poor effect in degradation assessment and degradation point identification so that the initial degradation point identification effect using the fusion degradation index was better than that of the single sensor signal. (2) There were subjective and incomplete problems in the extraction of traditional degradation features of vibration signals, but CNN can train and extract features containing rich information of the gearbox independently, which made it effective in performance degradation assessment and degradation point identification. Therefore, the proposed fusion method was better than the traditional fusion method in identifying the initial degradation point.

4. Conclusions

In this paper, a method of performance degradation assessment and abnormal health state detection of the quayside crane lifting gearbox based on the fusion of vibration CNN degradation feature and temperature entropy degradation feature is proposed. The following conclusions can be reached through the verification of the lifting gearbox full fault cycle data:

(1)

Performance degradation evaluation of the lifting gearbox: The results of SVDD performance degradation evaluation using the fusion degradation index indicate that the CV curve of the health index presents obvious stages, which can better track the evolution process of the performance state of the lifting gearbox over time, and the degradation evaluation effect is better than that based on the single vibration degradation index. It shows that the method proposed in this paper is suitable for the performance degradation state assessment of mechanical equipment, and it has application value in the health management and intelligent operation and maintenance of mechanical equipment.

(2)

Abnormal health status detection of the lifting gearbox: The proposed method based on fusion degradation index is four groups earlier than the method based on the single vibration degradation index, and two groups earlier than the method based on the fusion of traditional vibration degradation features and temperature entropy degradation features in initial degradation point identification through the comparison of three different methods. The results show that the feature extraction method based on deep learning can solve the problem of subjectivity in the traditional feature extraction method, and the multisensor information fusion method can improve the problem of incomplete degradation information in the method based on single sensor information. Meanwhile, the fusion method presented in this paper has reference significance for the early fault diagnosis and analysis of mechanical equipment.

In the present work, CNN was used to extract the degradation features of the full fault cycle vibration data of the lifting gearbox. Although it has the advantage of automatic feature extraction, the extracted features cannot represent the actual physical meaning as the traditional degraded features, because the CNN feature extraction is encapsulated. Therefore, the interpretability of CNN feature extraction will be further studied in the future.