CN114692831B - Method for calculating variable convolution kernel for variable resolution, storage medium - Google Patents
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Abstract
The invention discloses a method for calculating a variable convolution kernel aiming at variable resolution, wherein the time resolution and the frequency resolution of window functions in wavelet transformation are different, the time domain width and the frequency domain width of windows in a time-frequency image of the wavelet transformation are different, and the size of the convolution kernel convolved with the windows in the time-frequency image is respectively determined according to the time domain width and the frequency domain width of the windows in the time-frequency image. According to the method, the corresponding convolution kernel sizes are designed according to the time domain width and the frequency domain width of each window in the time-frequency image, the problem that objects with different scales or deformation at different positions are difficult to convolve by using convolution kernels with the same size is solved, and bearing fault diagnosis and classification can be carried out in a shorter time, so that higher precision is obtained.
Description
Technical Field
The invention relates to the technical field of convolutional neural networks, in particular to a method and a storage medium for calculating a variable convolutional kernel aiming at variable resolution.
Background
The bearing is used as one of the core components of the mechanical system and is important for the efficient, stable and reliable operation of the mechanical system. Many methods for bearing fault classification have been developed, and conventional methods for bearing fault diagnosis classification can be classified into three main categories: based on signal processing, machine learning and deep learning. The signal processing-based method requires more priori knowledge and cannot realize a diagnosis process with higher precision and automation. Machine learning-based bearing fault classification methods require more correlation techniques to extract sensitive features. The bearing fault classification based on deep learning can automatically identify the representative features of bearing faults from the original data, and reduce the dependence on technologies such as fault feature extraction and the like, so that the bearing fault classification based on deep learning becomes a mainstream technology of bearing fault diagnosis.
Meanwhile, the bearing fault diagnosis and classification method based on deep learning can be divided into three types: based on a time domain analysis method, a frequency domain analysis method and a time-frequency domain analysis method, respectively. The time domain analysis method is completely localized in the time domain and does not contain frequency domain information. The frequency domain based analysis method is completely localized in the frequency domain and does not contain time domain information. The time-frequency signal is analyzed based on the time-frequency domain analysis method, the time-frequency signal has time domain information and frequency domain information, and the wavelet transformed signal has the requirement of automatic adaptation time-frequency analysis, so that the time-frequency signal subjected to wavelet transformation is selected as a convolution neural network input to become a trend.
However, wavelet transformation is combined with the convolutional neural network, and the processed time-frequency image is input into a model of the convolutional neural network. If the receptive field of the active elements in the same convolutional neural network layer is the same size (receptive field refers to the area in the input space that affects a particular element of the network), it is not preferable for advanced convolutional neural network layers in spatial locations. It is difficult to convolve with convolution kernels of the same size because of objects of different dimensions or deformations at different locations.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a method for calculating a variable convolution kernel aiming at the variable resolution, which designs the variable convolution kernel according to the time domain width and the frequency domain width of each window in a time-frequency image and is used for solving the problem that objects with different scales or deformations at different positions are difficult to convolve with convolution kernels with the same size.
In order to achieve the above purpose, the present invention adopts the following technical scheme, including:
a method of computing a variable convolution kernel for a variable resolution, comprising the steps of;
S1, carrying out wavelet transformation on a signal to obtain a wavelet transformed time-frequency image; wherein, the time resolution and the frequency resolution of each window function in the wavelet transformation are different, and the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency image are different All different;
s2, calculating the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency image
S3, according to the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency imageRespectively determining the convolution kernel size convolved with each window in the time-frequency image;
the width of a convolution kernel convolved with a window in the time-frequency image is as follows: the time domain width delta (ψ (a,b)) of the window is rounded to a rounded value;
the convolution kernel height convolved with a window in the time-frequency image is: frequency domain width of the window And rounding the rounded values.
In step S2, the time domain width delta (ψ (a,b)) and the frequency domain width of the window in the time-frequency imageThe calculation mode of (2) is as follows:
Δ(ψ(a,b))＝|a|Δ(ψ)
wherein a is the scale of wavelet transformation, and b is the displacement of wavelet transformation; a is not equal to 0, b is any real number;
ψ represents the wavelet transform function when a=1, b=0; A form after Fourier transform is carried out on the psi; delta (ψ) is the time domain width of the wavelet transform of a=1, b=0; Frequency domain width of wavelet transform of a=1, b=0;
Phi (a,b) denotes a wavelet transform function of scale a and displacement b; A form of a Fourier transform of psi (a,b); delta (psi (a,b)) is the time domain width of the wavelet transform with a scale of a and a displacement of b; The frequency domain width of the wavelet transformation with the scale of a and the displacement of b;
Due to delta (psi (a,b)) and frequency domain width of window in time-frequency image Is a constant value, i.e
The calculation mode of the scale a of the wavelet transformation is as follows:
Wherein F c is the wavelet center frequency, T s is the sampling time, and F a is the actual frequency;
And delta (psi) and The calculation mode of (a) is as follows:
Wherein w 0 and gamma are constants and positive values; t is a time variable; w is the frequency domain variation; i represents an imaginary symbol;
Therefore, the time domain width Δ (ψ (a,b)) and the frequency domain width of each window of the time-frequency image are obtained Is a value of (2).
In step S3, in the deep layer of the convolutional neural network, the tensor convolved by the convolution kernel is convolved by using ResNet modules.
The signals are bearing fault signals, wavelet transformation is carried out on the bearing fault signals, and a time-frequency image of wavelet transformation of the bearing fault signals is obtained; performing feature recognition on the time-frequency image of the wavelet transformation of the bearing fault signal by utilizing a convolutional neural network, so as to classify bearing faults; the convolution kernel in the convolution neural network is a variable convolution kernel, namely the convolution kernel which is convolved with each window in the time-frequency image is different in size; and solving the convolution kernel size convolved with each window in the time-frequency image by adopting the method of the steps S1-S3.
The invention also provides a storage medium for calculating a variable convolution kernel for a variable resolution, the storage medium storing a computer program comprising program instructions which, when executed by a processor, cause the processor to perform the method of claim 1 or 2 or 3.
The invention has the advantages that:
(1) The algorithm can design the corresponding convolution kernel size according to the time domain width and the frequency domain width of each window in the time-frequency image, solves the problem that the objects with different scales or deformation at different positions are difficult to convolve by using the convolution kernels with the same size, and enables the bearing fault classification diagnosis to be carried out in a shorter time to obtain higher precision.
(2) The prior art aims to solve the problem that objects with different scales or deformation at different positions are difficult to convolve with convolution kernels with the same size, and mainly improves the convolution shape, the design of weights and the like. However, since previous designs of convolution shapes and weights are image-based, no consideration is given to designing a variable convolution kernel from the time-frequency image aspect of the wavelet transform. However, the variable convolution kernel is designed from the aspect of wavelet transformed time-frequency images, specifically, the variable convolution kernel is designed according to the time domain width and the frequency domain width of each window in the time-frequency images, and bearing fault diagnosis and classification can be carried out in a shorter time, so that higher precision is obtained.
(3) According to the invention, a correlation module of ResNet is embedded in a designed variable convolution kernel method to extract texture and detail information of bearing faults, a larger variable convolution kernel is used for extracting the characteristic change of the most original texture detail in a shallow layer, and then a ResNet module is used for respectively convoluting tensors of the bearing faults after the variable convolution kernel convolution in a deep layer, so that the characteristic correlation in a larger local range is prevented from being lost, and satisfactory bearing fault diagnosis classification prediction performance is obtained.
Drawings
FIG. 1 is a flow chart of a method of designing a variable convolution kernel in accordance with the present invention.
Fig. 2 is a schematic diagram of a time-frequency image window of a wavelet transform.
Fig. 3 is a schematic diagram of variable convolution kernels of different sizes designed for time-frequency images.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In this embodiment, UT6818 mechanical vibration analysis and fault simulation experiment table is used to collect bearing fault diagnosis classification data. The test bed mainly comprises an engine, a belt, a bearing seat, an acceleration sensor and a bearing part. The acceleration sensor is arranged on the bearing seat, and the speed of the bearing is controlled by the three-phase motor through the elastic coupling.
Data set collection was performed using UT6818 mechanical vibration analysis and fault simulation test stand. The PC end is connected with the acceleration sensor to collect bearing vibration signals, and vibration signals are collected at a sampling frequency of 51200 Hz. Seven of the bearing failures were collected, including one bearing health no failure condition and six bearing crack failure conditions.
The method for calculating the variable convolution kernel for the variable resolution is specifically as follows:
S1, extracting signals of bearing vibration signals, and performing wavelet transformation on the extracted bearing fault signals to obtain time-frequency images of wavelet transformation of the bearing fault signals. In this embodiment, gabor transformation is performed on the bearing fault time domain signal to obtain a time-frequency image.
As shown in fig. 2, in a time-frequency image, the vertical axis is frequency, the horizontal axis is time, the low frequency corresponds to a larger time window, the high frequency corresponds to a larger frequency window, and the width and height of the variable convolution kernel correspond to the time resolution and frequency resolution of the window function in wavelet transform, so when calculating the variable convolution kernel for the variable resolution, it is necessary to calculate the time domain width Δ (ψ (a,b)) and the frequency domain width of each window in the time-frequency image
S2, calculating the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency image
Δ(ψ(a,b))＝|a|Δ(ψ)
Wherein a is the scale of wavelet transformation, and b is the displacement of wavelet transformation; a is not equal to 0, b is any real number;
ψ represents the wavelet transform function when a=1, b=0; A form after Fourier transform is carried out on the psi; delta (ψ) is the time domain width of the wavelet transform of a=1, b=0; Frequency domain width of wavelet transform of a=1, b=0;
Phi (a,b) denotes a wavelet transform function of scale a and displacement b; A form of a Fourier transform of psi (a,b); delta (psi (a,b)) is the time domain width of the wavelet transform with a scale of a and a displacement of b; The frequency domain width of the wavelet transformation with the scale of a and the displacement of b;
due to delta (phi (a,b)) and frequency domain width of each window in the time-frequency image Is a constant value, i.e
In this embodiment, the Gabor transform is known as:
the calculation formula of the scale a of the wavelet transformation is as follows:
Wherein F c is the wavelet center frequency, T s is the sampling time, and F a is the actual frequency;
And delta (psi) and The calculation mode of (a) is as follows:
Wherein w 0 and gamma are constants and positive values; the Gabor function is a complex-valued sine function windowed by a gaussian function centered at the origin, whose fourier transform is a gaussian function centered at w=w 0, and although the Gabor function does not satisfy the allowable condition in a strict sense, if γ is sufficiently large, it approximately satisfies the condition;
t is a time variable; w is the frequency domain variation; i represents an imaginary symbol;
Therefore, the time domain width delta (psi (a,b)) and the frequency domain width of each window of the time-frequency image can be obtained Is a value of (2).
S3, according to the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency imageRespectively determining the convolution kernel size convolved with each window in the time-frequency image;
the width of a convolution kernel convolved with a window in the time-frequency image is as follows: the time domain width delta (ψ (a,b)) of the window is rounded to a rounded value;
the convolution kernel height convolved with a window in the time-frequency image is: frequency domain width of the window And rounding the rounded values.
In this embodiment, the bearing failure time domain signal is made into a 128×128 pixel time-frequency image by continuous Gabor transformation, and the time domain width Δ (ψ (a,b)) and the frequency domain width of each window in the time-frequency image are obtained by calculationThe window in the time-frequency image has a time-domain width delta (phi (a,b)) that is (9, ++ infinity), frequency domain width of window in time-frequency imageThe value of (3) varies in the interval of (0, 6×10 -2). If the time domain width delta (phi (a,b)) and the frequency domain width of the window in the time-frequency image are according toIt is not practical to set the size of the convolution kernel to 1:1, so the invention selects the rounded value of the time domain width delta (psi (a,b)) of the window in the time-frequency image as the convolution kernel width for convolution with the window; selecting window frequency domain width in time-frequency imageThe rounded value is then rounded off as the convolution kernel height that is convolved with the window.
As shown in fig. 3, for each window in the time-frequency image shown in fig. 2, several different-sized variable convolution kernels are designed, and the variable convolution kernels of different sizes and the image are convolved at different frequency values of the time-frequency image.
It is crucial to determine the variable convolution check for the entire model for these several different sizes. The number of kinds of the variable convolution kernels is determined, so that the bearing fault classification effect is better and the time is shorter.
In this embodiment, based on 128×128 pixels of the time-frequency image, the number of classes of the variable convolution kernels selected by the three groups of experiments is 3, 7, and 15, respectively, in the first group of experiments, as shown in fig. 3, 3 variable convolution kernels with different sizes are selected, the time-frequency image is divided into 3 blocks, each block of image has a size of 64×128, wherein the height is 64, the width is 128, and the overlapping pixels are 32. In a second set of experiments, 7 variable convolution kernels of different sizes were selected, the time-frequency image was divided into 7 blocks, each of 32×128, and the overlapping pixels were 16. In a third group of experiments, 15 variable convolution kernels with different sizes are selected, the time-frequency image is divided into 15 blocks, the size of each block of image is 16 multiplied by 128, and the overlapped pixels are 8.
Experiments were performed according to the above selections, defining 150 epochs, with a training rate of 0.01, and Adam was selected as the optimizer. Dropout is used and set to 0.5 for reducing the overfit and the loss function chooses cross entropy loss. The experimental results of these three sets of variable convolution kernels of different types, classification accuracy and model calculation time are shown in table 1. From the experimental data in table 1, the corresponding accuracy in the first set is highest and the time taken for model calculation is least. This is because, when the time-frequency image is divided into more blocks by pixel, not only the complexity of the model but also the calculation time is increased. And in order to avoid losing the edge information of the blocks, the image is valued by overlapping pixels, but at the same time, some data redundancy is caused. Thus we selected the first set of 3 variable convolution kernels of different sizes as the variable convolution kernels for this experiment.
TABLE 1
| Classification accuracy | Calculation time(s) | |
| First group of | 99.89±0.03 | 2292.14 |
| Second group of | 99.30±0.09 | 8832.70 |
| Third group of | 99.15±0.21 | 8994.31 |
In the invention, the characteristic change extraction of the most original texture detail is carried out by using a larger variable convolution kernel in the shallow layer, and then the tensor after convolution by the convolution kernel is respectively convolved by using a ResNet module in the deep layer, so that the characteristic correlation in a larger local range is avoided. For example, the total number of layers is five, then the first two layers may be defined as shallow layers and the second two layers as deep layers.
And carrying out continuous Gabor wavelet transformation on the bearing fault time domain signal to obtain a time-frequency image, and dividing the time-frequency image into a plurality of blocks according to pixel values, wherein in order to avoid that the edge of a divided image block possibly loses part information, the pixel block part needs to be repeatedly divided, namely pixel points are overlapped. The width and the height of the corresponding variable convolution kernels are calculated according to the method of the invention, and then, the convolution kernels with different sizes and the different image blocks are respectively convolved. Padding (padding) of different sizes is then used depending on the variable convolution kernel size. And then, carrying out convolution on tensors of the deep layer after the tensors are subjected to convolution by using ResNet modules through variable convolution kernels, and obtaining a plurality of three-dimensional tensors after carrying out convolution operation through a plurality of small convolution kernels. Generating the three-dimensional tensor to obtain a two-dimensional tensor with the same value in a certain dimension, splicing the two-dimensional tensors in the same dimension to obtain a two-dimensional tensor map, finally, passing the spliced two-dimensional tensor map through two full-connection layers, and finally outputting the spliced two-dimensional tensor map to be the category required by the user.
In order to evaluate the convolutional neural network based on the invention, the collected data sets of seven fault categories are subjected to experiments, the average performance of five continuous experiments is adopted as an experimental result, and the classification precision and the calculation time of the convolutional neural network are compared with the following four prior arts:
Depth Residual Shrink Network (DRSN): DRSN the use of a residual network, self-attention network and soft thresholding, respectively, reduce the training difficulty of convolutional neural networks, weight the channels of the feature map and reduce the noise of the signal.
Dynamic convolution (DynamicConv): dynamicConv dynamically aggregate multiple parallel convolution kernels according to the associated attention, increasing model complexity without increasing the depth and width of the network.
Depth residual learning (ResNet) 18): resNet18 the network layer becomes a function to learn about the layer input residual function, enabling training of deeper convolutional neural networks.
Visual geometry group (VGG-19): VGG-19 trains and tests pictures over whole pictures and multiple scales using a minimum 3 x 3 convolution kernel size and minimum spacing, improving classification accuracy.
The comparative results are shown in table 2 below:
TABLE 2
The invention designs a new variable convolution kernel, and determines the size and the type of the convolution kernel, which is used for classifying bearing faults. The method can determine the number of the variable convolution kernels to realize the optimal solution of the bearing fault classification. And combining the variable convolution kernel with ResNet related modules in the convolutional neural network to extract texture and detail information of the bearing fault. Thus, satisfactory bearing failure classification prediction performance can be obtained.
In addition to the methods described above, embodiments of the invention may also be a computer program product comprising computer program instructions which, when executed by a processor, cause the processor to perform the steps in the decision making method according to various embodiments of the invention described in this specification.
The computer program product may write program code for performing operations of embodiments of the present invention in any combination of one or more programming languages, including an object oriented programming language such as Java, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device, partly on a remote computing device, or entirely on the remote computing device or server.
Furthermore, embodiments of the present invention may also be a computer-readable storage medium, having stored thereon computer program instructions, which when executed by a processor, cause the processor to perform the steps in the decision-making method according to various embodiments of the present invention described in the methods of the present specification.
The computer readable storage medium may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may include, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples (a non-exhaustive list) of the readable storage medium would include the following: an electrical connection having one or more wires, a portable disk, a hard disk, random Access Memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention, and any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
Claims (4)
1. A method of computing a variable convolution kernel for a variable resolution, comprising the steps of;
s1, carrying out wavelet transformation on a signal to obtain a wavelet transformed time-frequency image; wherein, the time resolution and the frequency resolution of each window function in the wavelet transformation are different, and the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency image are different All different;
S2, calculating the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency image
S3, according to the time domain width delta (psi (a,b)) and the frequency domain width of each window in the time-frequency imageRespectively determining the convolution kernel size convolved with each window in the time-frequency image;
The width of a convolution kernel convolved with a window in the time-frequency image is as follows: the time domain width delta (ψ (a,b)) of the window is rounded to a rounded value;
the convolution kernel height convolved with a window in the time-frequency image is: frequency domain width of the window Rounding the rounded value;
Time domain width delta (psi (a,b)) and frequency domain width of window in time-frequency image The calculation mode of (2) is as follows:
Δ(ψ(a,b))＝|a|Δ(ψ)
wherein a is the scale of wavelet transformation, and b is the displacement of wavelet transformation; a is not equal to 0, b is any real number;
ψ represents the wavelet transform function when a=1, b=0; A form after Fourier transform is carried out on the psi; delta (ψ) is the time domain width of the wavelet transform of a=1, b=0; Frequency domain width of wavelet transform of a=1, b=0;
Phi (a,b) denotes a wavelet transform function of scale a and displacement b; A form of a Fourier transform of psi (a,b); delta (psi (a,b)) is the time domain width of the wavelet transform with a scale of a and a displacement of b; The frequency domain width of the wavelet transformation with the scale of a and the displacement of b;
Due to delta (psi (a,b)) and frequency domain width of window in time-frequency image Is a constant value, i.e
The calculation mode of the scale a of the wavelet transformation is as follows:
Wherein F c is the wavelet center frequency, T s is the sampling time, and F a is the actual frequency;
And delta (psi) and The calculation mode of (a) is as follows:
Wherein w 0 and gamma are constants and positive values; t is a time variable; w is the frequency domain variation; i represents an imaginary symbol;
Therefore, the time domain width Δ (ψ (a,b)) and the frequency domain width of each window of the time-frequency image are obtained Is a value of (2).
2. The method of claim 1, wherein in step S3, the tensor convolved with the convolution kernel is convolved in a deep layer of the convolutional neural network using a ResNet module.
3. The method for calculating a variable convolution kernel for a variable resolution according to any one of claims 1-2, wherein the signal is a bearing fault signal, and the bearing fault signal is subjected to wavelet transform to obtain a time-frequency image of the wavelet transform of the bearing fault signal; performing feature recognition on the time-frequency image of the wavelet transformation of the bearing fault signal by utilizing a convolutional neural network, so as to classify bearing faults; the convolution kernel in the convolution neural network is a variable convolution kernel, namely the convolution kernel which is convolved with each window in the time-frequency image is different in size; and solving the convolution kernel size convolved with each window in the time-frequency image by adopting the method of the steps S1-S3.
4. A storage medium for calculating a variable convolution kernel for a variable resolution, characterized in that the storage medium stores a computer program comprising program instructions which, when executed by a processor, cause the processor to perform the method of claim 1 or 2.
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