# Application of Wireless Sensor Network Data Fusion Technology in Mechanical Fault Diagnosis

Authors: Xinle Zhao; Zuhui Shen; Zhisheng Jing
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In order to solve the problem that a large number of vibration signals cannot be transmitted in real time in the application of wireless sensor networks (WSNs) in mechanical fault diagnosis, a mechanical fault diagnosis method based on multilevel and hierarchical information fusion of WSNs was proposed. In this method, the cluster tree network structure is used to expand the coverage of network monitoring, and WSNs information fusion is divided into three levels: data-level fusion, feature-level fusion, and decision-level fusion. The terminal node performs data-level fusion on the original vibration information to extract feature information; the cluster-head node performs feature-level fusion on the feature information to obtain pattern recognition results; and the gateway node performs decision-level fusion on the recognition results to evaluate the running status of mechanical equipment. The results show that the slight damage fault of the bearing inner ring can be accurately diagnosed by decision-level fusion based on four groups of probability distribution functions. According to the statistics of 30 test results, the fault recognition rate is 83.3%. The method can be applied to mechanical fault diagnosis effectively.


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## Body

## 1. Introduction

Construction machinery plays a very important role in China’s manufacturing of equipment. It plays a vital role in infrastructure, mining machinery, transportation engineering, industrial production, and other industries. In the production and operation of construction machinery, it often works for a long time at full load. Traditional construction machinery is generally checked and maintained by engineers and technicians after failure. When the problem is serious, the production of enterprises is often delayed, and there are large hidden dangers to safe operation [1].The Internet of Things (IOT) is the latest development of the Internet. It is called the Internet of Things, or IOT for short. It means the Internet of everything, and it is based on RFID technology, video recognition technology, infrared sensing, global positioning technology, and laser scanner technology to install all kinds of information sensors on the device and deploy ZigBee wireless sensor network 4G or 5G network internally or externally, according to the standard agreed application protocol to achieve multiple entities for intelligent identification information exchange and measurement control [2]. An Expert System, whose full English name is Expert System, is the latest technology in contemporary artificial intelligence technology and computer technology integration development. It can focus on the knowledge and experience of domain experts, search their built-in knowledge base according to the questions raised by users, carry out artificial intelligence logic reasoning of various complex algorithms, and finally give reasonable judgement conclusions or relatively correct solutions [3]. Therefore, an expert system has incomparable advantages in the fault diagnosis of construction machinery equipment.Therefore, combining the Internet of Things technology and expert system technology, an intelligent fault diagnosis expert system for construction machinery equipment has been designed and developed. It can realize the operation of engineering machinery equipment before the failure of early and rapid warning to improve the efficiency of engineering operations, so as to ensure the maximum extent of enterprise safety production, which has very important practical significance.


## 2. Literature Review

In the field of mechanical equipment fault diagnosis in wireless sensor networks, some researchers have studied this problem. Xueyi studies online remote induction motor energy monitoring and performs intelligent data processing in WSNs instead of direct transmission of original data. Only relevant and necessary information is transmitted to upper computer users, which reduces network communication load. However, the performance and storage capacity of the sensor nodes used are limited [4]. Cao et al. [5] applied a wireless sensor network to vibration monitoring of rotating machinery equipment in a power plant, judged the similarity of vibration data in time series by a data-level fusion algorithm, and decided on the data sending strategy by a task-level fusion algorithm. To reduce the total bandwidth and energy demand, this method is only applicable to redundant data from similar sources and has great limitations [5]. Zhao et al. [6] adopt the star wireless sensor network topology, obtain monitoring signals based on Jennic JN5139 sensor nodes, carry out signal feature extraction and fault pattern recognition on terminal nodes, and only transmit recognition results to gateway nodes. The recognition results are fused on the gateway node to solve the data transmission problem to a certain extent. However, the coverage of star topology is limited, and multitasks such as signal acquisition, feature extraction, and pattern recognition on terminal nodes will lead to a heavy load on terminal nodes. All nodes used are collected independently, and the network and data transmission protocol stack adopted do not support the synchronous acquisition of vibration signals from multiple sensor nodes [6]. Wang et al. [7] adopt a tree-like network topology to obtain vibration signals based on Imote2 wireless sensor network nodes and extract quality parameters and frequency components exceeding the amplitude threshold from sensor nodes. Data fusion is performed on the data fusion node based on quality parameters, and the quality evaluation and fusion results are output. This method promotes the transmission of uncertain information about measured values between the source sensor node and the gateway node, reduces the potential attenuation of acquired or transmitted diagnostic information, and does not consider the synchronous acquisition of vibration signals [7].In order to increase the coverage of network monitoring and balance the load of sensor nodes, the author adopts a cluster tree network structure to perform hierarchical information fusion for nodes at all levels in WSNs and to evaluate the overall operating status of mechanical equipment by transmitting a small amount of characteristic information instead of a large number of original vibration signals.


## 3. Research Method

### 3.1. WSNs’s Multilevel Hierarchical Information Fusion Fault Diagnosis Architecture

The mechanical fault diagnosis architecture of WSNs multilevel and hierarchical information fusion is shown in Figure1, which consists of a gateway node, multiple cluster-head nodes, and terminal nodes to form a cluster tree network [8]. WSN information fusion can be divided into three levels: data fusion, feature fusion, and decision fusion. The terminal node is responsible for collecting vibration signals and performing a data-level fusion of vibration information to extract feature information. The cluster-head node is responsible for performing a feature-level fusion of feature information of terminal nodes in the cluster to obtain pattern recognition results. The gateway node is responsible for the establishment, management, and maintenance of the whole WSNs, and integrates the d-S evidence theory to express the uncertainty of the identification results at the decision level. It has advantages in measurement and combination, and the artificial neural network has nonlinear processing ability, which can solve the problem of the difficult assignment of basic probability in the D-S evidence theory. At the same time, it has many similarities with WSNs in structure and function and can be well combined with WSNs [9]. Therefore, the cluster head nodes in this architecture are trained to generate the radical Basis Function (RBF) neural network classifier and perform feature-level fusion on the feature set of the terminal node hybrid domain to obtain the pattern recognition results describing the running state of mechanical equipment. Based on d-S evidence theory, the gateway node makes fusion decisions for independent diagnosis results of the cluster-head node and evaluates the overall running status of mechanical equipment.Figure 1
WSNs’s multilevel hierarchical information fusion fault diagnosis architecture.


### 3.2. Dual-Core WSNs Node Design

WSNs’ multilevel hierarchical information fusion requires strong signal processing capability and large enough sample storage space for all sensor nodes in the fusion [10]. The author designs a dual-core sensor node, which uses two independent processing and control cores to control the signal processing unit and the wireless module, respectively, and has a large capacity SD card as the main storage medium to meet the requirements of information fusion.The dual-core WSNs node design scheme is shown in Figure2. Core 1 is a low-power STM32f103 microcontroller based on the ARM cortex-m3 kernel running at 72 MHz, utilizing the processor’s excellent computing performance and excellent system response to events. It is capable of performing thumb-2 instruction sets including hardware division single-period multiplication and bit-field operations for optimal performance and code size, with 256 kB Flash space and 64 kB internal RAM, allowing the node to easily run more complex algorithms. Transplant μC/OS-II real time operating system to improve processor utilization, design real time task dynamic priority configuration to ensure real time response and efficient processing of tasks [11]. The Core 2 is an enhanced 8051 microprocessor integrated with the RADIO frequency chip TI CC2430, which supports the IEEE802.15.4 wireless communication protocol and is responsible for completing tasks such as time synchronization and data receiving and receiving in WSNs ad hoc networks.Figure 2
Dual core WSNs node.The dual-core design divides a complex task into multiple subtasks and maps them to a heterogeneous dual-core processor for coordination. It can not only enhance the overall performance of sensor nodes but also reduce the coupling between software and hardware modules, so as to meet the real time processing of node vibration signals and multitask scheduling, such as network communication, without mutual interference [12]. The two cores interact with each other in the form of command packets. When receiving a command packet or a response packet, they first go through the eight-order CRC check. If the check is correct, they perform the corresponding tasks to enhance system stability. The nodes are powered by large-capacity rechargeable lithium batteries with protective circuits.The WSNs node storage module uses an 8 GB microSD memory card as the main storage medium, and the FAT32 file system is established on the card. A large number of original vibration data and important calculation parameters are stored on the card in the form of files, which is convenient for data retrieval and management. The node with the method of dynamically allocated memory pool allocation effectively nodes to run efficiently during the execution of a more complex algorithm. A long array can be temporarily stored in the form of a file on an SD card, setting up the dynamic variables in memory space can be used to store other data needed to be immediately operation, effectively easing the node load calculation [13]. The SDIO interface of the cortex-M3 microprocessor is used to read and write microSD memory cards in 4-bit Direct Memory Access (DMA) mode, and the maximum speed can reach 1.5 MB per second, fully meeting the requirements of real-time signal processing on the storage system.An independent signal processing unit is designed on WSNs nodes to avoid the problems of high cost and high node energy consumption caused by using high-performance microprocessors. Design and develop the real-time preprocessing and common analysis functions for mechanical vibration signal analysis and optimize the algorithm to form a relatively complete set of high-efficiency and low-complexity embedded function library [14]. The structural block diagram of the embedded function library is shown in Figure 3, which includes 8 modules, including a basic mathematical function module, a statistics function module, a transformation function module, an interpolation operation function module, and a filtering function module, and the corresponding function functions of each module [15].Figure 3
Embedded function library structure block diagram.


### 3.3. Realization of WSNs Information Fusion Fault Diagnosis Method

Due to the limited computing resources and energy of WSNs nodes, the complexity of algorithms needs to be considered in information fusion processing. Time complexity and space complexity are two important characteristics of algorithm complexity as well as two important characteristics for measuring software power consumption, so the author uses these two characteristics to measure the complexity of the node fusion algorithm at all levels. Time complexity is mainly measured byOs in terms of algorithm average time complexity. The measurement of spatial complexity Ss mainly includes three aspects: the space used by the problem itself, the space used by the program itself, and the space used by dynamic variables [16]. The space used by the problem itself has nothing to do with the algorithm, and the space occupied by the program code has little influence on the spatial complexity of the algorithm, so it is not discussed here, but the memory occupied by the dynamic variables of the measurement algorithm.


#### 3.3.1. WSNs Data-Level Fusion of Terminal Nodes

When mechanical equipment fails, the amplitude and probability distribution of vibration signals will change, and the corresponding spectral components and the amplitude of different spectral peaks will also change. By constructing some quantitative characteristic statistical indexes of mechanical equipment vibration signals in the time domain or frequency domain, the characteristic statistical indexes of various fault modes of mechanical equipment can be represented in the data-level fusion of WSNs nodes and finally selected according to the following criteria: calculate requirements, classification performance, feature domains (time domain, frequency domain, etc.), and the optimal number of features [17]. D feature statistical indexes were selected to form feature sets and used to construct a d-dimensional feature space x∈Rd.Taking the feature extraction of data with a len of 2048 points as an example, the time complexity of node extraction of the statistical index of each time domain feature isO (1), and the memory space occupied by the data involved in the operation is 4 × len bytes. During the fast Fourier transform, the original vibration signals and characteristic information obtained by the 24 kB node are stored in the SD card in the form of files to save the memory space dynamically opened for the sample input array and transform output array.


#### 3.3.2. WSNs Cluster-Head Node Feature-level Fusion

The cluster-head node receives the feature information sent by the terminal node in the cluster and performs feature-level fusion as a sample [18]. The algorithm flow is shown in Figure 4.Figure 4
Cluster-head node feature-level fusion algorithm flow.During the neural network training, ｈ training samples are randomly selected as the clustering centercii=1,2,…,h, and the Euclidean distance between the input training samples xp and the center ci. Assign xp to each cluster set of input samples Ωpp=1,2,…,P, calculate the average value of training samples in each cluster set Ωp, and get the new cluster center ci. If the new cluster center ci does not change, get the final base function center ci of the RBF neural network; otherwise, regroup according to the nearest neighbour rule to get the new cluster center ci. The Gaussian function was selected as the basis function to solve the variance σi. The calculation formula is shown in formula (1) [19]. The weights w between the hidden layer and the output layer are modified by the supervised learning algorithm. The clustering center ci, variance σi and weights w of the trained neural network are saved in file form on the SD card of the cluster-head node.(1)σi=cmax2h,cmax is the maximum distance between the selected centers.The cluster-head node receives the test samples of the terminal nodes in the cluster and determines whether the neural network classifier is generated first. If not, the training sample set on its SD card is read for training to generate the neural network classifier. Otherwise, the neural network parameters in the corresponding files of the SD card are directly read and the test samples are fused at the feature level, and the basic probability assignment (BPA) of each pattern to be identified is obtained by using the neural network generalization ability. Since D-S theory requires the sum of probability distribution functions of each evidence body to be 1, the probability distribution function is normalized by the output results of the neural network, and the following formula (2) is obtained [20]:(2)mBi=yBi∑i=1NyBi,yBi is the output result of the neural network classifier; Bii,2,…,N indicates the fault of i type. N is the number of fault types to be identified; the probability distribution function myBi is used to further the decision-level fusion.The time complexity of each function isO(1) in the process of generating a neural network classifier for cluster head node training, and the size of the memory space dynamically allocated to it is determined by the specific size of the network classifier. The training samples and test samples obtained by nodes are stored on SD cards in the form of files. The neural network is used to manage the data in the test stage through the file system, and the memory call strategy is designed to reduce the memory pressure of nodes. The embedded function library is loaded when the node application is written to realize the neural network learning and testing better so that the cluster-head node can realize the feature-level fusion [21].


#### 3.3.3. Decision-Level Fusion of WSNs Gateway Nodes

The cluster-head node uses an RBF neural network classifier to recognize the characteristic information of terminal nodes in the cluster, and the probability distribution function of each pattern is obtained as an evidence body. The gateway node uses D-S theory synthesis rules to fuse the probability distribution functions of multiple evidence bodies at the decision level, and the principle is as follows [22]. Θ is set as the recognition frame, a defined function m:2Θ⟶0,1, called the mass function, satisfies mφ=0 (φ is the empty set), ΣmA=1A∈2Θ and mA 为 2Θ is called the probability distribution function of, mA is the basic probability number of proposition 2Θ, so mA is called Dempster’s synthesis rule of finite A. The Dempster composition rule of a limited number of Θ, and m1, m2,…, mn on the identification framework is:(3)m1⊕m2⊕⋯⊕mnA=∑A1∩A2∩⋯∩An=Am1A1m2A2…mnAn1−k,k is the uncertainty of evidence.(4)k=∑A1∩A2∩⋯∩An=φm1A1m2A2…mnAn.The gateway node fused the probability distribution functions of multiple evidence bodies into a new set of probability distribution functions, and the fused functions were used as the decision-making basis to obtain the overall running state of mechanical equipment.


## 3.1. WSNs’s Multilevel Hierarchical Information Fusion Fault Diagnosis Architecture

The mechanical fault diagnosis architecture of WSNs multilevel and hierarchical information fusion is shown in Figure1, which consists of a gateway node, multiple cluster-head nodes, and terminal nodes to form a cluster tree network [8]. WSN information fusion can be divided into three levels: data fusion, feature fusion, and decision fusion. The terminal node is responsible for collecting vibration signals and performing a data-level fusion of vibration information to extract feature information. The cluster-head node is responsible for performing a feature-level fusion of feature information of terminal nodes in the cluster to obtain pattern recognition results. The gateway node is responsible for the establishment, management, and maintenance of the whole WSNs, and integrates the d-S evidence theory to express the uncertainty of the identification results at the decision level. It has advantages in measurement and combination, and the artificial neural network has nonlinear processing ability, which can solve the problem of the difficult assignment of basic probability in the D-S evidence theory. At the same time, it has many similarities with WSNs in structure and function and can be well combined with WSNs [9]. Therefore, the cluster head nodes in this architecture are trained to generate the radical Basis Function (RBF) neural network classifier and perform feature-level fusion on the feature set of the terminal node hybrid domain to obtain the pattern recognition results describing the running state of mechanical equipment. Based on d-S evidence theory, the gateway node makes fusion decisions for independent diagnosis results of the cluster-head node and evaluates the overall running status of mechanical equipment.Figure 1
WSNs’s multilevel hierarchical information fusion fault diagnosis architecture.


## 3.2. Dual-Core WSNs Node Design

WSNs’ multilevel hierarchical information fusion requires strong signal processing capability and large enough sample storage space for all sensor nodes in the fusion [10]. The author designs a dual-core sensor node, which uses two independent processing and control cores to control the signal processing unit and the wireless module, respectively, and has a large capacity SD card as the main storage medium to meet the requirements of information fusion.The dual-core WSNs node design scheme is shown in Figure2. Core 1 is a low-power STM32f103 microcontroller based on the ARM cortex-m3 kernel running at 72 MHz, utilizing the processor’s excellent computing performance and excellent system response to events. It is capable of performing thumb-2 instruction sets including hardware division single-period multiplication and bit-field operations for optimal performance and code size, with 256 kB Flash space and 64 kB internal RAM, allowing the node to easily run more complex algorithms. Transplant μC/OS-II real time operating system to improve processor utilization, design real time task dynamic priority configuration to ensure real time response and efficient processing of tasks [11]. The Core 2 is an enhanced 8051 microprocessor integrated with the RADIO frequency chip TI CC2430, which supports the IEEE802.15.4 wireless communication protocol and is responsible for completing tasks such as time synchronization and data receiving and receiving in WSNs ad hoc networks.Figure 2
Dual core WSNs node.The dual-core design divides a complex task into multiple subtasks and maps them to a heterogeneous dual-core processor for coordination. It can not only enhance the overall performance of sensor nodes but also reduce the coupling between software and hardware modules, so as to meet the real time processing of node vibration signals and multitask scheduling, such as network communication, without mutual interference [12]. The two cores interact with each other in the form of command packets. When receiving a command packet or a response packet, they first go through the eight-order CRC check. If the check is correct, they perform the corresponding tasks to enhance system stability. The nodes are powered by large-capacity rechargeable lithium batteries with protective circuits.The WSNs node storage module uses an 8 GB microSD memory card as the main storage medium, and the FAT32 file system is established on the card. A large number of original vibration data and important calculation parameters are stored on the card in the form of files, which is convenient for data retrieval and management. The node with the method of dynamically allocated memory pool allocation effectively nodes to run efficiently during the execution of a more complex algorithm. A long array can be temporarily stored in the form of a file on an SD card, setting up the dynamic variables in memory space can be used to store other data needed to be immediately operation, effectively easing the node load calculation [13]. The SDIO interface of the cortex-M3 microprocessor is used to read and write microSD memory cards in 4-bit Direct Memory Access (DMA) mode, and the maximum speed can reach 1.5 MB per second, fully meeting the requirements of real-time signal processing on the storage system.An independent signal processing unit is designed on WSNs nodes to avoid the problems of high cost and high node energy consumption caused by using high-performance microprocessors. Design and develop the real-time preprocessing and common analysis functions for mechanical vibration signal analysis and optimize the algorithm to form a relatively complete set of high-efficiency and low-complexity embedded function library [14]. The structural block diagram of the embedded function library is shown in Figure 3, which includes 8 modules, including a basic mathematical function module, a statistics function module, a transformation function module, an interpolation operation function module, and a filtering function module, and the corresponding function functions of each module [15].Figure 3
Embedded function library structure block diagram.


## 3.3. Realization of WSNs Information Fusion Fault Diagnosis Method

Due to the limited computing resources and energy of WSNs nodes, the complexity of algorithms needs to be considered in information fusion processing. Time complexity and space complexity are two important characteristics of algorithm complexity as well as two important characteristics for measuring software power consumption, so the author uses these two characteristics to measure the complexity of the node fusion algorithm at all levels. Time complexity is mainly measured byOs in terms of algorithm average time complexity. The measurement of spatial complexity Ss mainly includes three aspects: the space used by the problem itself, the space used by the program itself, and the space used by dynamic variables [16]. The space used by the problem itself has nothing to do with the algorithm, and the space occupied by the program code has little influence on the spatial complexity of the algorithm, so it is not discussed here, but the memory occupied by the dynamic variables of the measurement algorithm.


### 3.3.1. WSNs Data-Level Fusion of Terminal Nodes

When mechanical equipment fails, the amplitude and probability distribution of vibration signals will change, and the corresponding spectral components and the amplitude of different spectral peaks will also change. By constructing some quantitative characteristic statistical indexes of mechanical equipment vibration signals in the time domain or frequency domain, the characteristic statistical indexes of various fault modes of mechanical equipment can be represented in the data-level fusion of WSNs nodes and finally selected according to the following criteria: calculate requirements, classification performance, feature domains (time domain, frequency domain, etc.), and the optimal number of features [17]. D feature statistical indexes were selected to form feature sets and used to construct a d-dimensional feature space x∈Rd.Taking the feature extraction of data with a len of 2048 points as an example, the time complexity of node extraction of the statistical index of each time domain feature isO (1), and the memory space occupied by the data involved in the operation is 4 × len bytes. During the fast Fourier transform, the original vibration signals and characteristic information obtained by the 24 kB node are stored in the SD card in the form of files to save the memory space dynamically opened for the sample input array and transform output array.


### 3.3.2. WSNs Cluster-Head Node Feature-level Fusion

The cluster-head node receives the feature information sent by the terminal node in the cluster and performs feature-level fusion as a sample [18]. The algorithm flow is shown in Figure 4.Figure 4
Cluster-head node feature-level fusion algorithm flow.During the neural network training, ｈ training samples are randomly selected as the clustering centercii=1,2,…,h, and the Euclidean distance between the input training samples xp and the center ci. Assign xp to each cluster set of input samples Ωpp=1,2,…,P, calculate the average value of training samples in each cluster set Ωp, and get the new cluster center ci. If the new cluster center ci does not change, get the final base function center ci of the RBF neural network; otherwise, regroup according to the nearest neighbour rule to get the new cluster center ci. The Gaussian function was selected as the basis function to solve the variance σi. The calculation formula is shown in formula (1) [19]. The weights w between the hidden layer and the output layer are modified by the supervised learning algorithm. The clustering center ci, variance σi and weights w of the trained neural network are saved in file form on the SD card of the cluster-head node.(1)σi=cmax2h,cmax is the maximum distance between the selected centers.The cluster-head node receives the test samples of the terminal nodes in the cluster and determines whether the neural network classifier is generated first. If not, the training sample set on its SD card is read for training to generate the neural network classifier. Otherwise, the neural network parameters in the corresponding files of the SD card are directly read and the test samples are fused at the feature level, and the basic probability assignment (BPA) of each pattern to be identified is obtained by using the neural network generalization ability. Since D-S theory requires the sum of probability distribution functions of each evidence body to be 1, the probability distribution function is normalized by the output results of the neural network, and the following formula (2) is obtained [20]:(2)mBi=yBi∑i=1NyBi,yBi is the output result of the neural network classifier; Bii,2,…,N indicates the fault of i type. N is the number of fault types to be identified; the probability distribution function myBi is used to further the decision-level fusion.The time complexity of each function isO(1) in the process of generating a neural network classifier for cluster head node training, and the size of the memory space dynamically allocated to it is determined by the specific size of the network classifier. The training samples and test samples obtained by nodes are stored on SD cards in the form of files. The neural network is used to manage the data in the test stage through the file system, and the memory call strategy is designed to reduce the memory pressure of nodes. The embedded function library is loaded when the node application is written to realize the neural network learning and testing better so that the cluster-head node can realize the feature-level fusion [21].


### 3.3.3. Decision-Level Fusion of WSNs Gateway Nodes

The cluster-head node uses an RBF neural network classifier to recognize the characteristic information of terminal nodes in the cluster, and the probability distribution function of each pattern is obtained as an evidence body. The gateway node uses D-S theory synthesis rules to fuse the probability distribution functions of multiple evidence bodies at the decision level, and the principle is as follows [22]. Θ is set as the recognition frame, a defined function m:2Θ⟶0,1, called the mass function, satisfies mφ=0 (φ is the empty set), ΣmA=1A∈2Θ and mA 为 2Θ is called the probability distribution function of, mA is the basic probability number of proposition 2Θ, so mA is called Dempster’s synthesis rule of finite A. The Dempster composition rule of a limited number of Θ, and m1, m2,…, mn on the identification framework is:(3)m1⊕m2⊕⋯⊕mnA=∑A1∩A2∩⋯∩An=Am1A1m2A2…mnAn1−k,k is the uncertainty of evidence.(4)k=∑A1∩A2∩⋯∩An=φm1A1m2A2…mnAn.The gateway node fused the probability distribution functions of multiple evidence bodies into a new set of probability distribution functions, and the fused functions were used as the decision-making basis to obtain the overall running state of mechanical equipment.


## 3.3.1. WSNs Data-Level Fusion of Terminal Nodes

When mechanical equipment fails, the amplitude and probability distribution of vibration signals will change, and the corresponding spectral components and the amplitude of different spectral peaks will also change. By constructing some quantitative characteristic statistical indexes of mechanical equipment vibration signals in the time domain or frequency domain, the characteristic statistical indexes of various fault modes of mechanical equipment can be represented in the data-level fusion of WSNs nodes and finally selected according to the following criteria: calculate requirements, classification performance, feature domains (time domain, frequency domain, etc.), and the optimal number of features [17]. D feature statistical indexes were selected to form feature sets and used to construct a d-dimensional feature space x∈Rd.Taking the feature extraction of data with a len of 2048 points as an example, the time complexity of node extraction of the statistical index of each time domain feature isO (1), and the memory space occupied by the data involved in the operation is 4 × len bytes. During the fast Fourier transform, the original vibration signals and characteristic information obtained by the 24 kB node are stored in the SD card in the form of files to save the memory space dynamically opened for the sample input array and transform output array.


## 3.3.2. WSNs Cluster-Head Node Feature-level Fusion

The cluster-head node receives the feature information sent by the terminal node in the cluster and performs feature-level fusion as a sample [18]. The algorithm flow is shown in Figure 4.Figure 4
Cluster-head node feature-level fusion algorithm flow.During the neural network training, ｈ training samples are randomly selected as the clustering centercii=1,2,…,h, and the Euclidean distance between the input training samples xp and the center ci. Assign xp to each cluster set of input samples Ωpp=1,2,…,P, calculate the average value of training samples in each cluster set Ωp, and get the new cluster center ci. If the new cluster center ci does not change, get the final base function center ci of the RBF neural network; otherwise, regroup according to the nearest neighbour rule to get the new cluster center ci. The Gaussian function was selected as the basis function to solve the variance σi. The calculation formula is shown in formula (1) [19]. The weights w between the hidden layer and the output layer are modified by the supervised learning algorithm. The clustering center ci, variance σi and weights w of the trained neural network are saved in file form on the SD card of the cluster-head node.(1)σi=cmax2h,cmax is the maximum distance between the selected centers.The cluster-head node receives the test samples of the terminal nodes in the cluster and determines whether the neural network classifier is generated first. If not, the training sample set on its SD card is read for training to generate the neural network classifier. Otherwise, the neural network parameters in the corresponding files of the SD card are directly read and the test samples are fused at the feature level, and the basic probability assignment (BPA) of each pattern to be identified is obtained by using the neural network generalization ability. Since D-S theory requires the sum of probability distribution functions of each evidence body to be 1, the probability distribution function is normalized by the output results of the neural network, and the following formula (2) is obtained [20]:(2)mBi=yBi∑i=1NyBi,yBi is the output result of the neural network classifier; Bii,2,…,N indicates the fault of i type. N is the number of fault types to be identified; the probability distribution function myBi is used to further the decision-level fusion.The time complexity of each function isO(1) in the process of generating a neural network classifier for cluster head node training, and the size of the memory space dynamically allocated to it is determined by the specific size of the network classifier. The training samples and test samples obtained by nodes are stored on SD cards in the form of files. The neural network is used to manage the data in the test stage through the file system, and the memory call strategy is designed to reduce the memory pressure of nodes. The embedded function library is loaded when the node application is written to realize the neural network learning and testing better so that the cluster-head node can realize the feature-level fusion [21].


## 3.3.3. Decision-Level Fusion of WSNs Gateway Nodes

The cluster-head node uses an RBF neural network classifier to recognize the characteristic information of terminal nodes in the cluster, and the probability distribution function of each pattern is obtained as an evidence body. The gateway node uses D-S theory synthesis rules to fuse the probability distribution functions of multiple evidence bodies at the decision level, and the principle is as follows [22]. Θ is set as the recognition frame, a defined function m:2Θ⟶0,1, called the mass function, satisfies mφ=0 (φ is the empty set), ΣmA=1A∈2Θ and mA 为 2Θ is called the probability distribution function of, mA is the basic probability number of proposition 2Θ, so mA is called Dempster’s synthesis rule of finite A. The Dempster composition rule of a limited number of Θ, and m1, m2,…, mn on the identification framework is:(3)m1⊕m2⊕⋯⊕mnA=∑A1∩A2∩⋯∩An=Am1A1m2A2…mnAn1−k,k is the uncertainty of evidence.(4)k=∑A1∩A2∩⋯∩An=φm1A1m2A2…mnAn.The gateway node fused the probability distribution functions of multiple evidence bodies into a new set of probability distribution functions, and the fused functions were used as the decision-making basis to obtain the overall running state of mechanical equipment.


## 4. Interpretation of Result

The gearbox fault simulation test bench consists of a monopole reduced gearbox speed regulating motor, magnetic powder brake WSNs node, and MEMS acceleration sensor ADXL001, etc. The motor drive speed is 1.2 kr per minute and the sampling frequency is 10 kHz. Two fault types of simulated gearbox: a. Gear root damage of drive input end;b. Damage to the inner ring of the bearing at the driving input end. Where: number of teeth of the gearbox, z1=55, z2=75, modulus m=5, bearing model N205.Four terminal nodes (numbered 1, 2, 3, 4), two cluster-head nodes (numbered 5, 6), and one gateway node are arranged near the driver input terminal bearing seat and output terminal bearing seat to form a cluster tree network. In order to reduce the computation complexity of nodes, the time domain characteristic statistical indexes such as the amplitude of root variance and root-mean-square value and the frequency domain characteristic statistical indexes such as the mean frequency standard deviation frequency were used to characterize the gearbox operation state. For the vibration signals in normal state and two fault states, the terminal node constructs 40 groups of characteristic information samples with 2048 consecutive sampling values as one unit in time order, and the total number of samples is 120 groups. Cluster-head nodes receive 120 groups of samples from terminal nodes and input RBF neural network for network learning to generate a fault diagnosis classifier in order to reduce the network learning pressure of cluster head nodes [23], the training target error was set to 0.05. The number of neurons in the neural network input layer is determined by the characteristic dimension of 5. Set the number of neurons in the hidden layer as 3 and 1 bias neuron to consider the three operating states of the gearbox, and set the number of neurons in the design output layer as 3, namely the normal state of tooth root damage and bearing inner ring damage. The corresponding outputs are denoted as [1, 0, 0], and [0, 0], [0, 0, 1] respectively.The damaged running state of the inner ring of the bearing at the driving input end was selected as the unknown state for the neural network test. Meanwhile, the terminal nodes in the cluster constructed a group of characteristic information samples for the running state of the gearbox. The cluster head node reads the corresponding neural network classifier parameters from the SD card and inputs the feature information samples into the classifier to obtain the probability distribution function for the recognition pattern. Gateway nodes use the D-S fusion decision theory to make integrated decisions on the bodies of evidence. The fused function is used as a decision basis to identify the fault type. 30 groups of tests were conducted respectively, and the results of probability allocation and fusion decision of one group of tests are shown in Figure5. (a) A1, (b) A2, (c) A3 respectively represent the normal state of bearing root damage and bearing inner ring damage [24]. m represents the probability distribution function (D-S fusion: mA1=0.0000, mA2=0.0049, mA3=0.9951).Figure 5
Probability distribution and fusion decision result of unknown state of gearbox. (a)mA1. (b)mA2. (c)mA3.
(a)(b)(c)It can be seen that no. 3 and no. 4 nodes do not support mild damage to the bearing of the inner ring obviously, so no. 3 or No. 4 nodes can only be used to identify the operating state of the gearbox. Because the fault characteristics of slight damage to the bearing inner ring are very weak, and the sensor measuring points of no. 3 and No. 4 nodes are far away from the fault source due to the signal propagation path and other reasons, no. 3 and No. 4 nodes have not completely touched the corresponding fault characteristic signals. Based on the probability distribution function of the four groups, the decision-level fusion was carried out, and the slight damage fault of the bearing inner ring was accurately diagnosed. The results of 30 groups were statistically analyzed, and the fault recognition rate was 83.3%.


## 5. Conclusion

A mechanical fault diagnosis method based on multilevel hierarchical information fusion in wireless sensor networks is proposed. Compared with the star network structure, the network monitoring coverage of the adopted cluster tree network structure is larger. The dual-core WSNs nodes are designed to meet the requirements of the fault diagnosis architecture of WSNs with multilevel and hierarchical information fusion. Multilevel hierarchical information fusion is used to distribute computing tasks to nodes at all levels and effectively balance the computing load of sensor nodes. By transmitting a small amount of characteristic information to replace a large number of original vibration signals, the total amount of network data transmission is reduced, network bandwidth is saved, and network energy consumption is reduced, which provides a new idea for WSNs application in mechanical equipment fault diagnosis.



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*Source: 5707210-2022-09-22.xml*