The traditional acoustic-based diagnosis (ABD) technique based on single-channel testing has a significant engineering value. Since its diagnosis robustness is sensitive to sound signal acquisition location, it develops slowly. To solve this problem, the 2-dimensional (2D) sound field variation near the machine is adopted for diagnosis by the near-field acoustic holography (NAH)- based fault diagnosis method with array measurement. However, its performance is limited due to the neglect of the sound field normal change information. To dig the sound field fault information further, a 2.5-dimensional (2.5D) acoustic field diagnosis method is presented in this paper and its performance compared with the 2D technology is verified by the bearing diagnostic test. Different from the 2D technique with only one source image, the 2.5D acoustic field model consists of source image, holographic sound image, and the differences between them, and its effective feature model is constructed by Gabor wavelet feature extraction and random forest feature reduction algorithm. The diagnostic effect of the 2.5D technique compared with the 2D technique increases more than 11% in the bearing diagnostic test. It provides new ideas for the development of the NAH-based fault diagnosis method, and further improves the ABD technique-based array measurement.
Fault diagnosis has great significance to support equipment for safe and reliable operation and reduce maintenance costs. When a machine works, mechanical vibration will occur by the dynamic forces within the machine. This vibration pattern changes when an initial fault starts to evolve. The vibration signals can be easily detected by different kinds of sensors mounted directly onto the machine, such as position sensors, velocity sensors, and accelerometers. Thus, vibration-based fault diagnosis has been a well-established field for the last decades, and many vibration signal analysis techniques have rapidly developed—time analysis [
As another expression of mechanical energy transmission, the sound signature also carries information about the condition of the machine. Therefore, extracting the acoustic characteristics of the machine to detect failure parts is an effective technique in fault diagnosis [
In view of the above problems, a new 2.5D sound field diagnosis technology is proposed and employed to diagnose bearing failure in this paper. It coopts the construction thoughts of the 2.5D underground tunnels seismic analysis model [
The bearing acoustic signals are measured through holographic array, and the amplitude distribution of sound pressure of the two-dimensional acoustic field at the holographic measurement position can be directly obtained. Meanwhile, NAH technology is applied to reconstruct the two-dimensional sound field information at the bearing sound source location. Then, a 2.5D sound field model with the information of normal spatial change is constructed, which is made up of source image, holographic sound image, and the difference between them. Its changed characteristics are described by the Gabor wavelet features. In addition, based on the random forest feature selection algorithm, certain valuable Gabor wavelet features are closely related to the running state of the bearing are selected. And then, the support vector machine is used for pattern classification to realize the bearing fault diagnosis. Compared with acoustic image diagnosis technology, the 2.5D acoustic field fault diagnosis technology improves the diagnosis robustness by further integrating the sound field change information of the normal dimension and further develops the ABD technology based on the array test and acoustic imaging algorithm.
The diagnosis process based on the spatial features of the 2.5D sound field is shown in Figure
Flowchart of fault diagnosis based on 2D/2.5D sound field.
Compared with the 2D acoustic image fault diagnosis procedure, the main improvements of the 2.5D acoustic field diagnosis technique are as follows: Construction of 2.5D acoustic field model: after the array measurement of the sound signals, spectrum analysis of every microphone is implemented and the acoustic pressure amplitude at the fault sensitive frequency is picked up to form the holographic sound image. Then, the NAH imaging algorithm is carried out to reconstruct the sound source image. The source image is subtracted from the holographic sound image to obtain the difference sound image, which describes the normal variation of sound field between the sound source and the array measurement position. Finally, the 2.5D acoustic field model containing spatial change information is constructed by synthesizing the three acoustic images. Effective features of 2.5D acoustic field: firstly, extract Gabor wavelet features of three acoustic images in the 2.5D acoustic field model and arrange them in order to preliminarily construct the eigenvector. Secondly, the importance of eigenvector is analyzed by using the random forest algorithm. Finally, an effective eigenvector is further constructed based on the significance effect of features on the classification results and the diagnostic efficiency.
Based on the idea of information fusion, the new ABD technology with the 2.5D sound field model enriches the sound field normal change information, whilst the random forest dimension reduction technology is adopted to retain effective information and remove redundant information, which can further improve the robustness of the diagnosis.
NAH is a hot technique in visualizing sound field and can reconstruct the mechanical sound field accurately. It collects sound pressure on the holographic-measuring surface surrounding the sound source and rebuilds the sound field on the sound source surface by means of the spatial field transformation relationship between the sound source surface and the holographic surface [
Sketch map of sound field propagation [
FFT-based NAH is a simple frequency-domain sound field reconstruction technology and is implemented in this paper. Assume the holographic plane
In the formula,
The texture information of the image can reflect the local subtle changes of the image effectively, and the diagnostic robustness of Gabor wavelet feature is verified [
Assume
In this formula,
The texture classification features of the image usually adopt mean value
In this paper, the common values 5 and 8 are, respectively, taken for
Random forest is a new machine learning method which is composed of multiple classification and regression tree (CART) and decision trees.
About 1/3 of the data which were unselected in every sampling are called out of bag (OOB). The importance of feature variables
In the formula,
SVM is a high-performance machine learning method based on structural risk minimization principle and statistical learning theory, which has been widely used in the field of pattern recognition. The key thought is to seek an optimal classification hyperplane to meet the classification requirements. Assume
In the formula,
In the identification process, the sample set is randomly sequenced for 5 times, and 3/4 of every random sorted sample is taken as the training sample and the remaining 1/4 is used as the test sample to build a 5 duplicate cross-validation sample database, and the average value of the five-time identification rate is picked up as the final recognition effect.
Bearing is one of the most common vulnerable and important parts of mechanical equipment; its running state affects the whole mechanical performance directly. The diagnosis of bearing state has an important engineering value. Therefore, bearing fault diagnosis has always been a research hotspot in the field of fault diagnosis. By selecting bearing as the research object, verifying the effectiveness of the new 2.5D ABD technique and its advantages over the 2D acoustic image diagnosis technology has better universality and higher engineering practical value.
In order to ensure the repeatability of the test and reduce the influence on the repeated disassembling of the parts in the test system on research results, the machinery fault simulator (MFS) test bench manufactured by SpectraQuest Inc. of the United States is adopted. At the same time, the test bench is modified based on the idea of improving signal-to-noise ratio (SNR) of the bearing and keeping load constant, and the motor bearing test bench is built. The arrangement of the motor bearing test bench and the relative position of every part are shown in Figure
Layout diagram of the motor-bearing system.
The bearing test system is shown in Figure
Bearing test rig.
In most cases, it is a gradual process for the bearing from the normal to failure, and the bearing state change of certain key components will affect the performance of the whole equipment. Based on the motor-bearing test system, bearing 1 close to the motor is assumed to be nonkey monitoring bearing, while bearing 2 far from the motor is assumed to be the key bearing under monitoring. The bearing inner ring is selected as the research object during the test, and different running states of the bearing inner ring are simulated by machining holes of different diameters in the bearing inner ring with the electric discharge machining (EDM) method, as is shown in Figure
Bearing inner-race fault by EDM.
The system is in fault state when the failure diameter of bearing 2 inner ring hole is set as
Based on the structural parameters of the test bearing ER-16K and the rotational speed of the drive shaft, the bearing inner ring fault frequency in theory is
Spectrum analysis of reference source 3 under fault conditions.
Based on the near-field sound holography technology and fault frequency, a 2.5D sound field model is constructed for every test operating condition sample and one sound field model under normal and fault conditions is randomly selected, as shown in Figure
The 2.5D sound field model obtained under experimental conditions. (a) Normal state source image; (b) fault state source image; (c) normal state holographic sound image; (d) fault state holographic sound image; (e) normal state difference sound image; (f) fault state difference sound image.
The positions of bearing 1 and bearing 2 in the source images in Figures
The 2.5D acoustic field model integrates not only more effective fault information but also a lot of redundant and invalid information. Based on the idea of information fusion, the diagnostic robustness can be only improved effectively when the amount of effective information is greater than that of the redundant information. The Gabor wavelet texture features of 80 dimensions are directly extracted from every acoustic image in the 2.5D sound field model, and the texture features of 240 dimensions are sequentially arranged on three sides. Then, the significance of Gabor wavelet texture features of each dimension is analyzed through the random forest algorithm, as shown in Figure
Feature importance of 2.5D sound field model.
As is seen in Figure
For the five sets of samples which have been randomly divided, the 2D NAH-based diagnosis technique based on single source image texture feature is adopted for diagnosis analysis and the average recognition effect is 0.844.
When using the 2.5D NAH-based diagnostic technique based on the spatial characteristics of 2.5D sound field proposed in this paper, the random forest algorithm is used to sort the importance of the features, and the feature combination is selected according to different proportions in order to build an effective sound field feature model. It means that the 240 Gabor wavelet features are ranked based on importance, and different 2.5D sound field feature models can be constructed by different numbers of the 240 features. For example, 10% denotes that the top 24 Gabor wavelet features are selected to build a feature model for diagnosis and analysis. The average identification rate of the five sets of samples varies with the proportion of the number of features, as shown in Figure
The recognition rates varying the percentile of texture features selected.
By comparing the diagnostic results of sound image and 2.5D sound field and analyzing the changes of recognition rate with the percentage of feature number in Figure The highest recognition rate of the 2.5D sound field diagnosis technology based on the spatial characteristics of the 2.5D sound field is 11.1% higher than that based on the 2D source image, indicating that the new 2.5D NAH-based diagnosis technique within integrating spatial variation information of normal sound field which is proposed in this paper has richer diagnostic information and better diagnostic efficiency. When all 240 dimensional texture features are used to build the 2.5D acoustic field model, the recognition rate is 0.888, which is 4.44% higher than the recognition rate of the sound image diagnostic technology based on 80 dimensional texture features of a single source. However, the amount of feature dimension increases by two times, indicating that the effective diagnostic information increases while the redundant information also increases. The recognition rate fluctuates with the proportion of number of valid texture features. It shows that the effective information and the redundant information increase alternately, and the best diagnosis effect can be obtained only when the two information reaches a certain balance.
The new 2.5D sound field diagnosis technique further improves the NAH-based diagnosis technology. By using the source acoustic image, holographic acoustic image, and the difference acoustic image of the two, a 2.5D acoustic field model is constructed, which integrates the acoustic field variation information at different spatial locations. Then, the spatial feature dimension is reduced based on the random forest feature selection algorithm, effective feature information is retained, redundant information is reduced, and diagnostic robustness is improved. The experimental results of the bearing show that the 2.5D sound field diagnosis technique is effective and feasible and has some advantages over the original 2D NAH-based diagnosis technology. By using the spatial variation information of sound field for diagnosis and analysis, the NAH-based diagnosis technology with array measurement is expanded and improved, further enriching the ABD technology.
The Mat data used to support the findings of this study were supplied by Junjian Hou under license and so cannot be made freely available. Requests for access to these data should be made to Junjian Hou at
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (Grant no. 51505433); Scientific and Technological Research Projects of Henan (Grant no. 172102210058); Ph.D. Early Development Program of Zhengzhou University of Light Industry (Grant no. 2014BSJJ015); and the Plan of Key Research Projects of Higher Education of Henan Province (Grant no. 16A460028).