Research on mechanical vibration monitoring based on wireless sensor network and sparse Bayes

The wireless monitoring system platform designed in this subject can be applied to the vibration monitoring of rotating machinery equipment and can even be widely applied to the vibration monitoring of other types of equipment through simple upgrades. The monitoring nodes in the system platform are used to obtain device status information. To intuitively understand the operating status of the device, the acquired device status information must also be read and displayed [14].

This requires the use of wireless networks to achieve data transmission and host computer software to display monitoring information. Through the design and analysis of the platform, the overall structure of the system is mainly composed of three parts: wireless sensor network monitoring node, wireless sensor network monitoring base station, and wireless sensor network host computer monitoring software. The structure diagram of a single wireless star network monitoring hardware platform is shown in Fig. 1.

The monitoring node installed on the rotating machine obtains the operating information of the rotating machine and transmits it to the base station node using radio frequency communication. The base station node uses Ethernet to transmit the received operating information to the monitoring host for visual monitoring [15]. The upper computer in the upper computer monitoring software is the data center of the entire hardware system. The base station node can receive the control commands of the upper computer software and then send it to the target monitoring node through radio frequency communication. The user can also observe the entire monitoring area intuitively through the monitoring host monitoring data and analyze the data through the computer to understand the running status of rotating machinery [16].

The wireless vibration monitoring network uses a star network structure, which includes a network center and multiple network nodes. The wireless sensor network monitoring base station is the network center, and the wireless sensor network monitoring node is the network node to form the first-level wireless star network structure [17]. The second-level star network structure is networked by wire. It uses the monitoring host as the network center and the wireless sensor network monitoring base station as the node. The system transmits the monitoring data to the host computer through a two-level star network structure combining wireless and wired. The structure diagram of the improved wireless sensor network monitoring hardware is shown in Fig. 2.

The signal type studied in this paper is the vibration signal of rotating machinery, which is a typical one-dimensional signal. Generally, the actual one-dimensional engineering signals have obvious aggregation characteristics in the sparse signals in the transform domain, so it is reasonable to use the block sparse structure model to describe the vibration signals of rotating machinery [28, 29]. The block structure of the signal can be expressed as a series of non-overlapping coefficient blocks. Different vibration signals were analyzed to verify the block sparse characteristics of the vibration signals, and a preliminary exploration was made for the combination of vibration signals and compression sensing of rotating machinery. In this section, the vibration signal with a load of 2hp, normal type, and three faults is selected at 800 points each [30]. The original signal has a very complex waveform in the time domain, but it has an obvious block sparse structure in the frequency domain, and when a fault exists, the larger coefficients are concentrated in the middle-frequency band. The signal has block sparse characteristics in the frequency domain and is related to the bearing vibration principle. 0 to 2000 Hz can be regarded as a low-frequency band. The low-frequency band mainly includes the ripple error of the bearing processing surface, the frequency of vibration caused by the assembly position error, and the characteristic frequency of the fault [31, 32].

In the low-frequency band, the original vibration signal is particularly susceptible to noise interference, and the energy is very low. 2000 Hz to 4000 Hz can be regarded as an intermediate-frequency band. When the bearing fails, the signal energy in the mid-band is very high. This is mainly due to the existence of a bearing surface failure. When the bearing rotates past a failure point, it will cause an impact. The impulse signal is very short in time, and the spectrum range is particularly wide [33, 34]. The inherent vibration frequency of the bearing is generally within the frequency range of the fault impact signal. Therefore, the impact signal will cause the resonance of the bearing, which is very strong. When the bearing is fault-free, the resonance will not be excited because there is no impact signal, so the normal signal has almost no energy in the middle-frequency band. High-frequency band above 4000 kHz usually contains the high-frequency band spectrum caused by fault impact and may also contain some high-frequency noise, usually the energy is the lowest [35].

Bayesian algorithm is one of the commonly used algorithms in machine learning, mainly used for classification problems [36]. It mainly refers to that under the given conditions of the training data set, first, based on the assumption of the conditional independence of the feature variables, the joint probability distribution of input and output is obtained [37]. Then, based on this model, the input instance features are used to find the maximum posterior probability output using Bayes’ theorem.

Let x be the input n-dimensional feature variable, and set \(y \in \{ c_{1} ,c_{2} , \ldots ,c_{n} \}\) as input, X is a random variable on the input space, and Y is a random variable on the output space. The joint probability distribution of X and Y is P (X, Y), and P (X, Y) independently and identically generates the training data set.

Then, from the Bayesian formula:

Naive Bayes has constructed conditional independence for conditional probability, namely:

The probability \(p (y = 1|x, \theta )\) represents the probability that y belongs to 1 given the characteristic variable x, and \(h_{\theta } \left( x \right) = p(y = 1|x,\theta )\), then there are models:

in which \(\theta = \{ \theta_{0} ,\theta_{1} , \ldots \theta_{p} \}\) represents the coefficient value corresponding to each feature, θ value. It can be obtained by solving the maximum likelihood estimation function. Assuming that each sample in the data set is independent of each other, the likelihood function is:

The basic formula of the Naive Bayes algorithm is shown in Eq. (6), and its meaning is the probability of the output category A given the instance Y.

In practical applications, when classifying feature instances, we select the final category with the largest probability value, which can be formalized as Eq. (7).

In order to verify the reliability of the parameters of the mechanical vibration monitoring technology in actual use, we have organized various types of system tests. In the case that the function meets the business, the system also needs to meet the requirements of performance indicators such as response speed and server concurrent affordability. This system uses the Siege framework to perform performance tests and uses Noah to monitor various performance indicators. Figure 5 shows the response speed performance results of mechanical vibration monitoring technology. Figure 6 shows the results of server concurrency tolerance in mechanical vibration monitoring technology.

In the process of system performance testing, the two indicators of system response time and packet loss rate are used to test the concurrent performance of the system and the performance of responding to customers. Limited to the network environment and server performance have a greater impact on performance indicators, the network environment during the test is selected as the internal network, and the server is a stand-alone server with a brand-new system and a cluster with two stand-alone servers.

In the previous chapter, in addition to introducing the concept of block sparse structure, several reconstruction algorithms using signal block structure were mentioned, including group LASSO, block OMP, group BP, etc. This group of experiments compares the reconstruction performance of sparse Bayes and other block-based sparse structure algorithms. The experimental signal is the bearing outer ring fault signal. During the experiment, except for the sparse Bayesian algorithm, other reconstruction algorithms need to set very complicated prior conditions, which will not be discussed in detail. Figure 7 shows a comparison of original signal and reconstructed signal quality with a compression rate of 30%, and Fig. 8 shows a comparison of original signal and reconstructed signal quality with a compression rate of 50%.

It can be seen from Figs. 7 and 8 that the size of the original signal and the compression ratio has a very small impact on the reconstruction performance and can be ignored, and it can be considered that the sparse Bayesian algorithm is insensitive to the signal block structure. This is the advantage of this algorithm compared to other reconstruction algorithms based on block sparse structure. Before performing calculations, other types of algorithms must first set the block size that matches the signal type, otherwise the reconstruction error will be very large. However, the block structure information of the signal may be unknown in the actual signal processing, and only the sparse Bayesian algorithm can still reconstruct the signal with high accuracy without knowing the block structure of the signal.

Through the above experimental results, it can be observed that the four reconstruction algorithms based on fast sparse structure have no advantage, and even the reconstruction effect is even worse. This problem can be analyzed from two perspectives. First of all, although the energy of the signal has obvious concentration characteristics, it is not an ideal block structure, and there are still many small coefficients at other locations, and four reconstruction algorithms based on block sparse structure use simulation in a noise-free environment. Signal experiments are not good for actual complex signal processing. Secondly, these four kinds of block structure reconstruction algorithms require many prior conditions. Each reconstruction parameter setting needs to conform to the signal characteristics; obviously, the structure of the signal is different. This leads to a very large difference between the two transform domain reconstructed signals. In short, relying too much on the prior conditions will make the algorithm based on the sparse structure of the signal block inferior to the traditional algorithm in practical applications. Through a large number of experiments, the reconstruction performance of the block sparse Bayesian learning method and the existing reconstruction algorithm is compared. In addition, the denoising effect of block sparse Bayesian learning framework is studied. When studying the influence of the signal block structure on the reconstruction algorithm, an important conclusion is drawn through experiments, that is, the influence of the signal block structure on the block sparse Bayesian learning algorithm is negligible, which brings us new enlightenment.