Phase-based Vibration Displacement Measurement and Modal Analysis Algorithm for Bearing Test Bench

Abstract

The present invention discloses a vibration displacement measurement and modal analysis algorithm for a bearing test bench based on phase, including: video shooting of the bearing test bench; constructing a phase pyramid model based on the Gabor filter, adding different vibration direction and different scale information, inputting the video into the phase pyramid model, and calculating phase matrices in different directions and at different scales through the Gabor filter; respectively solving the spatial and temporal axial gradient changes by the difference method, and solving the curves of the transverse and longitudinal velocities changing with time by using the outer product formula for solving the velocity vector; obtaining the changes of the transverse and longitudinal displacements of the full-field pixel points corresponding to the full-field structural points in the video at this scale with time through frequency domain integration; then decomposing the full-field displacement signal by the SVD method, decomposing the kernel function coefficients by the FDD method, and obtaining the structural natural frequencies on the singular value components by the peak-to-peak method.

Description

Technical Field

[0001] The present invention relates to the field of vision measurement methods, and particularly to a vibration displacement measurement and modal analysis algorithm based on phase for a bearing test bench. Background Art

[0002] With the continuous improvement of science and technology, in recent years, the research on bearing damage detection has been more in-depth. As the most widely used component in electromechanical equipment, the health status of bearings directly affects the normal operation of the unit. To avoid the occurrence of chain failures, it is of great significance to trace the source of faults and eliminate potential hazards in the early stage of bearing damage. Compared with the existing vibration measurement methods, most of them require wired contact measurement and can only perform local detection. If a systematic and comprehensive visual real-time monitoring system can be established, it is possible to effectively monitor the whole field and non-contact of bearings or other structures, and effectively prevent and reduce the occurrence of safety accidents. The development of real-time detection technology and equipment based on machine vision is an important line of defense and safeguard measure for structural faults.

[0003] At present, structural monitoring using machine vision means has been developed both at home and abroad. For example, digital image correlation method is used for vibration measurement, and great improvements have been made in terms of measurement accuracy and range. However, the main problems of these methods are high requirements for the feature region, non-whole field, and susceptibility to illumination conditions, which limit their application scope. Summary of the Invention

[0004] The object of the present invention is to provide a vibration displacement measurement and natural frequency extraction algorithm based on phase for a bearing test bench, so as to solve the problems of high requirements for the feature region, non-whole field, and susceptibility to illumination conditions in the existing detection methods, and at the same time extract the structural natural frequency from the displacement data of the whole field.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] The embodiment of the present application discloses a vibration displacement measurement algorithm based on phase for a bearing test bench, which sequentially includes the following steps:

[0007] Step 1: According to the vibration condition of the object to be detected, different high-speed cameras are used to photograph the whole field of the object;

[0008] Step 2: Based on the gabor filter, a directionally controllable pyramid is constructed, and at least 4 layers of pyramids are constructed for the subsequent realization of displacement measurement, including the task of solving the vibration displacement using phases of different scales and directions;

[0009] Step 3: In the task of solving the vibration displacement using phases of different scales and directions in Step 2, construct Gabor filters of different scales and directions to process the video, output corresponding groups of phase diagrams. The phase is used to solve the velocity gradient in the corresponding direction, and at the same time, the velocity gradient with respect to time is solved for each pixel point of the phase diagram to calculate the full-field velocity data that changes with time. Integrate in the frequency domain the changes in the transverse and longitudinal displacements of the full-field pixel points corresponding to the full-field structure points at this scale over time. Calculate the velocities of the vibration in the x and y directions of the full field through the following formula:

[0010]

[0011] In the formula, are the groups of phase diagrams output by Gabor filters of different scales and directions, that is, the phases of different scales and directions in the video; θ is a direction variable that can be defined artificially; r is a scale variable, that is, the layer corresponding to the controllable pyramid in the corresponding direction; u and v are the velocities of the object vibrating in the x and y directions respectively;

[0012] Step 4: Use a phase-based visual displacement measurement algorithm to obtain the full-field displacement, and then use a bearing modal analysis algorithm based on SVD for modal analysis. For the bearing modal analysis algorithm based on SVD, first use the SVD method to calculate the first K principal components of the full-field displacement, and then decompose the kernel function coefficients through the frequency domain decomposition method. Use the peak-to-peak method to obtain the structural natural frequencies on the singular value components. The formula for the frequency domain decomposition method is as follows:

[0013] p(t i ) = Φ SD q(t i ) + v(t i )

[0014] In the formula, p(t i ) is the kernel function coefficient, Φ SD is the modal shape matrix in the spatial domain, and v(t l ) is the noise generated by the measurement.

[0015] Preferably, in the above-mentioned phase-based bearing test bench vibration displacement measurement algorithm, the camera is a high-speed camera, and the frame rate is 2 times or more of the frequency to be measured.

[0016] Preferably, in the above-mentioned phase-based bearing test bench vibration displacement measurement algorithm, the filter for constructing the direction controllable pyramid is a Gabor filter that can extract texture features at different directions and scales. The video data is sent into the filter for processing and calculating phase information.

[0017] Preferably, in the above-mentioned vibration displacement measurement algorithm for the bearing test bench based on phase, different directions of phase information need to be substituted into the outer product formula for solving the velocity vector, and the phase information is used to solve the velocity by the formula and integrated to obtain the displacement.

[0018] Correspondingly, a vibration mode analysis algorithm for the bearing test bench based on phase is also disclosed. The SVD algorithm reduces the dimension of the displacement data obtained in claim 1. The three-dimensional phase signal needs to be rearranged into a two-dimensional signal in advance, with each time frame being a vector, and the two-dimensional signal is dimensionally reduced.

[0019] Preferably, in the above-mentioned vibration mode analysis algorithm for the bearing test bench based on phase, the SVD method adopted by the bearing mode analysis algorithm is an improved SVD method. The two-dimensional signal is decomposed to obtain the kernel function coefficients, and FDD is performed on the kernel function coefficients. Finally, the structural natural frequency can be obtained by the peak-to-peak method.

[0020] Compared with the prior art, the present invention first selects a side that is easy to photograph and relatively close to the damaged part according to the structural conditions of the component to be measured. Considering the vibration characteristics of the bearing, the frame rate set by the camera should be as high as possible, preferably higher than twice the first-order mode. Then, according to the size of each frame of the picture, it is determined which layer of data in the pyramid to obtain. While fully considering the memory required for calculation and the running time, the robustness of the result is ensured. Then, the outer product formula of the velocity vector is established, the velocity gradients in different directions of the phase diagram are obtained, and the vibration velocity is solved and integrated using the velocity gradient of the phase. Thus, the vibration displacement data of the whole field is obtained. Finally, the dimension of the whole-field displacement data is reduced. The dimension can be determined by calculating the similarity by comparing the recombined picture with the original picture. Then, FDD analysis is performed on the dimension-reduced data.

[0021] The invention abandons the traditional processing method based on Lagrangian angles, considers each pixel point as an object from the Euler perspective, and gives full play to the advantages of the displacement information contained in the phase information and less influence by illumination.

[0022] The present invention does not require marked points, is easy to implement. At the same time, the video captured by the camera is the vibration signal, realizing full-field and non-contact measurement.

[0023] The present invention uses the vibration information of all pixel points for modal identification, thus greatly improving the accuracy of identification. Description of the Drawings

[0024] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0025] Figure 1 The figure shows the flow chart of the full-field displacement measurement and frequency extraction algorithm for the vibration of the bearing test bench based on phase in the embodiment of the present invention;

[0026] Figure 2 The figure shows the system block diagram of the detection device adopted in the embodiment of the present invention;

[0027] Figure 3 The figure shows the principle block diagram of visual displacement measurement in the embodiment of the present invention;

[0028] Figure 4 The figure shows the principle block diagram of bearing modal identification in the embodiment of the present invention. Detailed implementation manners

[0029] The following will describe in detail the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0030] As Figure 1 shown, the system of the present invention uses a high-speed camera with the model: Photron FASTCAM Mini AX200, the image resolution is 1024×1024, the camera frame rate is 4000fps, a 120W LED lighting lamp is selected as the structured light source, and the vibration video is saved in the computer.

[0031] Establishment of the phase pyramid and estimation of displacement:

[0032] The steerable pyramid has non-oriented, real-valued high- and low-pass coefficients, which describe the residual signal components not captured by the band-pass filter. The frequency-domain transfer function B in the oriented band of the controllable pyramid ω，θ is a scaled and rotated copy of a basic filter, indexed by scale ω and direction θ. Applying these transfer functions to the discrete Fourier transform of the image I decomposes it into different spatial frequency bands S ω，θ。Each filter isolates a continuous region of the frequency domain and thus has a local spatial impulse response. The resulting spatial bands are localized in space, scale, and direction. The transfer function of the steerable pyramid contains only the positive frequencies of the corresponding real steerable pyramid filters. That is,

[0033] 2 cos(ωx) = e iωx + e -iωx The response of is e iωx , so the concepts of amplitude and phase exist. In the frequency domain, the process of building and reconstructing the pyramid is carried out in the frequency domain, and the image can be reconstructed from the sum of the sub-bands of the pyramid at all scales and directions. The process of building the pyramid is expressed as follows:

[0034]

[0035] where, and are for image reconstruction at all scales and directions in the pyramid,

[0036] The phase-based method uses a steerable pyramid and allows us to measure local motion. A two-dimensional image changes over time f((x, y) + δ(t)), where δ(t) is the displacement function. The displaced image contour f((x, y) + δ(t)) is written as a sum of complex sinusoids,

[0037]

[0038] where each band corresponds to a single frequency ω. Starting from Equation 2, the band with frequency ω is a complex sinusoid

[0039]

[0040] Similar to traditional orthogonal wavelet decomposition, the steerable pyramid is implemented by recursively splitting an image into a set of oriented sub-bands and a low-pass residual band. The filters used in this transform are polarity separable in the Fourier domain, where they can be represented as follows,

[0041]

[0042] The radial and circumferential parts can be expressed as follows,

[0043]

[0044]

[0045] Unlike traditional orthogonal wavelet decomposition, subsampling does not produce aliasing artifacts because the support of the low-pass filter L(r, θ) complies with the Nyquist sampling criterion. The recursive process is initialized by dividing the input image into low-pass and high-pass parts using the following filters:

[0046]

[0047]

[0048] The velocity gradient with respect to time is solved for each pixel point of each phase diagram to calculate the full-field displacement data varying with time. The velocities of the full-field vibrations in the x and y directions are calculated by the following formula:

[0049]

[0050] where are the groups of phase diagrams output by Gabor filters of different scales and directions, i.e., the phases of different scales and directions in the video; θ is a direction variable that can be defined manually; r is a scale variable, i.e., the layer corresponding to the controllable pyramid in the corresponding direction; and u and v are the velocities of the object vibrating in the x and y directions, respectively.

[0051]

[0052]

[0053] The velocity between the i-th frame and the first frame of all phase points is calculated, and a displacement signal is given in a timely manner. The signal-to-noise ratio of this signal is improved by spatially locally weighted averaging the displacement signal using the local amplitude as the weight. The displacement signal is converted to millimeters by multiplying by the length of an object in the scene divided by the number of pixels it spans. This conversion between pixels and millimeters of displacement depends on the depth of the object in the scene and is constant for objects of the same depth, assuming no significant lens distortion. In summary, each individual image of the video is processed by a spatial filter to obtain a spatially local phase signal sorted in time, which can represent the displacement signal of the moving object in the video. The result of the above processing is the displacement signal at all points in the image.

[0054] To adapt to the SVD method, the displacement field is rearranged into a vector where m is n1×n2, representing the total number of measurement points. Then, the overall displacement maps at N different time frames are combined in a matrix in

[0055] K = {k 1 , k 2 , …, k i , …, k N}

[0056] wherein, is a column vector corresponding to k(t k ). Then, delete the average value of

[0057]

[0058] from the dataset. where K is a matrix composed of different column vectors, and can be expressed by the factorization of SVD as

[0059]

[0060] where and are two unitary matrices, and the superscript T represents the transpose operator, is a diagonal matrix with non - negative singular values in descending order. To improve the robustness of the estimation of U k , we use the following equation to replace equation

[0061]

[0062] where is a square diagonal matrix. As is well - known, can be represented by several of the largest singular values to represent the low - rank

[0063]

[0064] where, represents the kernel function vector. Each column of U i is a kernel function vector, and the number of kernel functions can be determined by measuring the correlation coefficient between the constructed displacement map and the original map. Using the calculated U i , the kernel function coefficients of all displacement maps can be calculated

[0065]

[0066] where, represents the kernel function coefficient, which can be used to effectively determine the natural frequency within the shape descriptor (SD) domain. Using the estimated , the natural frequency and mode shape of the SD domain can be easily estimated by using the frequency - domain decomposition method.

[0067] p(t k ) = φ SD q(t k ) + v(t k )

[0068] where, For P i a column of, 1 ≤ k ≤ N, indicating the SD domain, in the modal shape matrix, representing the dynamic response of the modal coordinates, indicating the influence of measurement noise. In the case where v(t) and Φ SD q(t k ) are uncorrelated, the resulting covariance matrix is

[0069]

[0070] where τ = 0, 1, 2... represents the time delay, and the power spectral density matrix is calculated using the fast Fourier transform,

[0071]

[0072] where the superscript H is the Hermitian transpose. Through singular value decomposition, the resonance frequency is the peak frequency in the singular value spectrum.

[0073] The well-known techniques in the art involved in the present invention are not elaborated in detail.

[0074] This embodiment is only an exemplary illustration of the present patent and does not limit its protection scope. Those skilled in the art can also make local changes to it. As long as it does not exceed the spirit of the present patent, it is regarded as an equivalent replacement of the present patent and is within the protection scope of the present patent.

Claims

1. A vibration displacement measurement algorithm for a bearing test bench based on phase, characterized in that, it successively includes the following steps: Step 1: According to the vibration condition of the object to be detected, different high-speed cameras are used to photograph the whole field of the object; Step 2: A directionally controllable pyramid is constructed based on the gabor filter, and at least 4 layers of pyramids are constructed for the subsequent realization of displacement measurement, including the task of solving the vibration displacement using phases of different scales and directions; Step 3: In the task of solving the vibration displacement using phases of different scales and directions in Step 2, gabor filters of different scales and directions are constructed to process the video, and the corresponding groups of phase diagrams are output. The phase is solved by calculating the velocity gradient in the corresponding direction, and at the same time, the velocity gradient with respect to time is solved for each pixel point of the phase diagram to calculate the full-field velocity data varying with time. The lateral and longitudinal displacements of the full-field structure points corresponding to the full-field pixels of the video at this scale varying with time are integrated in the frequency domain, and the velocities of the full-field vibration in the x and y directions are calculated by the following formula: In the formula, are groups of phase diagrams output by Gabor filters of different scales and directions, that is, the phases of different scales and directions in the video; θ is a direction variable that can be defined artificially; r is a scale variable, that is, the layer corresponding to the direction-controllable pyramid; u and v are the velocities of the object vibrating in the x and y directions respectively; Step 4: The full-field displacement is obtained using a phase-based visual displacement measurement algorithm, and then modal analysis is performed using a bearing modal analysis algorithm based on SVD. For the bearing modal analysis algorithm based on SVD, first, the first K principal components of the full-field displacement are calculated using the SVD method, and then the kernel function coefficients are decomposed by the frequency domain decomposition method. The structural natural frequency on the singular value component is obtained using the peak-to-peak method. The formula for the frequency domain decomposition method is as follows: p(t i ) = Φ SD q(t i ) + v(t t ) where, p(t i ) is the kernel function coefficient, Φ SD is the modal vibration mode matrix in the spatial domain, and v(t i ) is the noise generated by measurement.

2. The vibration displacement measurement algorithm for a bearing test bench based on phase according to claim 1, characterized in that, the camera is a high-speed camera, and the frame rate is 2 times or more of the frequency to be measured.

3. The vibration displacement measurement algorithm for a bearing test bench based on phase according to claim 1, characterized in that, the filter for constructing the directionally controllable pyramid is a gabor filter that can extract texture features at different directions and scales, and the video data is sent into the filter for processing and calculating phase information.

4. The vibration displacement measurement algorithm for a bearing test bench based on phase according to claim 1, characterized in that, in the outer product formula for solving the velocity vector, the phase information in different directions needs to be substituted respectively, and the phase information is used to solve the velocity by the formula and integrated to obtain the displacement.

5. A vibration modal analysis algorithm for a bearing test bench based on phase, characterized in that, for the SVD algorithm to reduce the dimension of the displacement data obtained in claim 1, the three-dimensional phase signal needs to be rearranged into a two-dimensional signal in advance, with each time frame being a vector, and the two-dimensional signal is reduced in dimension.

6. The vibration modal analysis algorithm for a bearing test bench based on phase according to claim 5, characterized in that, the SVD method adopted by the bearing modal analysis algorithm is an improved SVD method. The two-dimensional signal is decomposed to obtain the kernel function coefficients, and FDD is performed on the kernel function coefficients. Finally, the structural natural frequency can be obtained using the peak-to-peak method.

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