Belt conveyor bearing fault diagnosis method and system based on temperature and vibration signal analysis

Abstract

This invention belongs to the field of fault diagnosis technology, specifically relating to a fault diagnosis method and system for belt conveyor bearings based on temperature and vibration signal analysis. The method includes: removing outliers and correcting baseline drift from the acquired temperature and vibration signals; optimizing variational mode decomposition using kurtosis and envelope entropy to extract fault components and generate a time-frequency map; reconstructing the map using temperature change rate-mapped weighted coefficients and performing high-frequency gain compensation; concatenating the weighted time-frequency map and a two-dimensional temperature map into a three-dimensional tensor; inputting this tensor into a residual network with coordinate attention and deformable convolutional branches; and adjusting the joint loss using the temperature energy proportion to output the diagnostic result. This invention effectively enhances the model's multimodal feature representation capability under complex and variable operating conditions by establishing a physical correlation between temperature change and high-frequency vibration, significantly improving diagnostic accuracy and generalization performance.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology. More specifically, this invention relates to a method and system for fault diagnosis of belt conveyor bearings based on temperature and vibration signal analysis. Background Technology

[0002] Bearings, as key components of belt conveyor transmission and support systems, operate under harsh environments such as heavy loads, high dust levels, and variable conditions, making them highly susceptible to wear, fatigue spalling, and other failures. Bearing failure not only leads to conveyor downtime and equipment damage but can also cause serious safety accidents and economic losses. In actual operation, the complex mechanical structure and strong background noise can mask early, subtle bearing fault characteristics. Traditional diagnostic methods often rely on single vibration signals for analysis; however, a single signal contains limited equipment status information and is highly susceptible to fluctuations in operating conditions and transmission path attenuation, resulting in high false negative and false positive rates under complex conditions. Therefore, multimodal monitoring integrating vibration and temperature signals, along with deep learning technology, has become an important development direction in the field of equipment fault diagnosis. Vibration signals can effectively detect transient impacts and high-frequency characteristics of bearings, while temperature signals can macroscopically represent frictional heat generation and long-term deterioration trends.

[0003] Currently, combining multi-sensor signal acquisition with deep learning networks for state recognition based on multi-domain feature transformation is a common research approach in this field. Chinese patent document CN120162734A discloses a method for large bearing state recognition based on dynamic interactive fusion of multi-sensor, multi-domain features. This method involves installing sensors at multiple locations on the large bearing to collect vibration signals, performing sliding window sampling on the vibration signals, and generating time-frequency maps, time-frequency grayscale maps, Gram angle field maps, and recursive graphs through multi-domain information transformation. The image data is then input into a pre-trained ResNet50 model to extract features, and graph convolutional networks and graph attention networks are constructed to perform high-order interaction and dynamic fusion of multi-domain features. Finally, fault classification is performed using a manifold space similarity metric. By utilizing multi-domain information transformation and multi-level improved graph neural network feature extraction techniques, this method can deeply explore the profound connection between bearing vibration and faults, improving the accuracy and reliability of bearing health status recognition to a certain extent.

[0004] However, the above-mentioned technical solutions can, to a certain extent, achieve the extraction of multi-domain features and the interactive fusion at the network level. However, existing technologies still have shortcomings when facing complex temperature and vibration multimodal monitoring scenarios. First, temperature and vibration signals collected on-site are often accompanied by high-amplitude outlier impacts and baseline drift. Conventional preprocessing methods cannot simultaneously preserve weak fault features and suppress strong background noise, resulting in poor quality of the underlying input data. Second, existing variational mode decomposition is mostly based on empirically setting the number of mode layers and penalty factors, which easily leads to over-decomposition, under-decomposition, or mode aliasing of signals, making it difficult to accurately extract effective fault components. Third, existing multimodal fusion mostly only involves shallow data splicing at the network channel level, failing to link macroscopic temperature change trends with microscopic high-frequency vibration features from a physical mechanism perspective. Finally, conventional residual networks lack the ability to spatially perceive and extract subtle local deformation features under different operating conditions when processing two-dimensional time-frequency maps. Furthermore, the loss function used during model training is usually statically balanced and cannot adaptively and dynamically adjust parameters according to the contribution of multimodal features in the current input samples. This results in low diagnostic accuracy and generalization performance of the network when facing associated faults and variable operating conditions. Summary of the Invention

[0005] To address the technical problem that existing technologies have failed to explore the correlation between temperature changes and high-frequency vibration characteristics, and are unable to adjust based on the multimodal characteristics of input samples, this invention provides solutions in the following aspects.

[0006] In a first aspect, the present invention provides a method for fault diagnosis of belt conveyor bearings based on temperature and vibration signal analysis, comprising: S1, acquiring vibration and temperature signals of the belt conveyor bearing; using median-cubic spline interpolation to remove outliers from the vibration signal to obtain a preprocessed vibration signal; and correcting drift of the temperature signal using differential and moving average thresholds to obtain a preprocessed temperature signal; S2, performing variational mode decomposition on the preprocessed vibration signal, with the penalty factor determined by the ratio of kurtosis to envelope entropy; progressively increasing the number of mode layers for decomposition; determining the number of mode layers when the center frequency distance between adjacent modes is less than a set threshold; and calculating the cross-correlation coefficient to filter mode components; S3, performing continuous wavelet transform on the mode components to generate a time-frequency diagram, and then... The preprocessed temperature signal is transformed into a two-dimensional temperature map through Gram angle field transformation. The temperature change rate is calculated and the weighted coefficients obtained by mapping with the hyperbolic tangent function are used to reconstruct the time-frequency map to obtain a weighted time-frequency map. When the temperature change rate exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency map. S4. The low-frequency energy map, the two-dimensional feature map of the high-frequency band, and the temperature feature map corresponding to the overall two-dimensional temperature map of the weighted time-frequency map are stitched together as three channels to obtain a three-dimensional tensor. This tensor is input into the pre-trained residual network to output the fault category. The residual block of the residual network includes parallel coordinate attention branches and deformable convolution branches. The network training adopts a loss function that combines center loss and cross-entropy loss. The balance coefficient is adjusted by the temperature channel energy ratio of the batch samples.

[0007] This invention effectively eliminates high-amplitude outliers of vibration and corrects temperature baseline drift by preprocessing methods combining median and cubic spline interpolation with difference and moving average thresholds. It avoids mode aliasing during signal decomposition by using a variational mode decomposition method that combines kurtosis and envelope entropy to determine the penalty factor. Furthermore, by utilizing temperature change rate weighting and implementing high-frequency band gain compensation, a close correlation between macroscopic temperature changes and microscopic high-frequency vibrations is established from a physical mechanism perspective. This enhances the multimodal feature representation capability of the residual network model under complex variable operating conditions, significantly improving the accuracy and generalization performance of bearing diagnosis.

[0008] Preferably, outliers are removed from the vibration signal using median-cubic spline interpolation to obtain a preprocessed vibration signal. This includes: dividing the vibration signal into non-overlapping data segments and calculating the median of the vibration amplitude within each data segment; calculating the absolute difference between the amplitude and the median of each data point within the data segment, and multiplying the median of the absolute difference sequence by a set constant as a fluctuation threshold; identifying data points with an absolute difference greater than the fluctuation threshold as impact outliers and removing them; extracting the time and amplitude of the normal data points adjacent to the removed outliers, constructing a cubic spline interpolation function, calculating the estimated amplitude at the removal location and filling it in, thereby achieving signal interpolation recovery and obtaining the preprocessed vibration signal.

[0009] This invention can more accurately identify transient impact outliers caused by environmental interference by adaptively calculating the fluctuation threshold of local data segments. It uses cubic spline interpolation for numerical filling, which not only filters out abnormal high-amplitude interference, but also fully ensures the phase continuity and smoothness of the vibration signal in the time domain waveform.

[0010] Preferably, the temperature signal is corrected for drift by differential and moving average threshold to obtain a preprocessed temperature signal, including: performing a first-order differential operation on the temperature signal and dividing it by the sampling time interval to obtain a temperature change rate sequence; calculating the arithmetic mean of the temperature change rate sequence within a sliding time window; determining that the temperature signal has baseline drift when the absolute value of the arithmetic mean within the sliding time window is greater than a set threshold and the high-frequency vibration energy within the corresponding window has not increased synchronously; extracting the arithmetic mean of the temperature data within the normal time period before drift occurs as the normal baseline; and performing a detrending operation on the temperature data after drift occurs, removing the first-order tilt component based on polynomial fitting, and smoothly splicing it back to the normal baseline to complete the drift correction of the temperature signal and obtain the preprocessed temperature signal.

[0011] This invention uses a sliding time window combined with the asynchronous rise characteristics of high-frequency vibration energy for joint judgment, which can accurately identify low-frequency baseline drift caused by sudden changes in operating conditions or sensor temperature drift. It uses historical normal baselines for translation correction, which effectively ensures the high consistency of data baseline during subsequent feature extraction.

[0012] Preferably, variational mode decomposition is performed on the preprocessed vibration signal to screen modal components, including: calculating the negative cumulative sum of the product of the probability density of the envelope sequence of the preprocessed vibration signal and its own logarithm as the envelope entropy; calculating the ratio of the fourth central moment of the amplitude of the preprocessed vibration signal to the square of the variance as the kurtosis; multiplying the ratio of the signal kurtosis to the envelope entropy plus a smoothing term by a preset constant coefficient as the penalty factor for variational mode decomposition; successively increasing the number of modal layers for decomposition, calculating the difference in center frequencies of each adjacent mode after each decomposition, stopping the increment when the ratio of the difference in center frequencies to the highest cutoff frequency of the signal is less than a set threshold, and outputting each modal component corresponding to the determined number of modal layers; calculating the normalized cross-correlation coefficient between each modal component and the preprocessed vibration signal, and retaining modal components whose normalized cross-correlation coefficient is greater than a set correlation threshold.

[0013] This invention adaptively sets the penalty factor for the decomposition algorithm by calculating the ratio of kurtosis to envelope entropy, and uses the normalized difference of the center frequencies of adjacent modes for anti-aliasing judgment. It can objectively and adaptively determine the optimal number of decomposition layers, effectively avoiding the problem of over-decomposition or under-decomposition of signals caused by manual experience in setting parameters, and thus extracting purer and more effective fault feature components.

[0014] Preferably, the temperature change rate is calculated and weighting coefficients are obtained by mapping through the hyperbolic tangent function. The weighted time-frequency graph is reconstructed using the weighting coefficients to obtain a weighted time-frequency graph. When the temperature change rate exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency graph. This includes: calculating the ratio of the preprocessed temperature signal difference between adjacent sampling times to the time interval as the temperature change rate; inputting the temperature change rate into the hyperbolic tangent function after dimensionless processing to generate the first weighting coefficient; extracting the first weighting coefficient corresponding to the current data segment as a global constant variable; multiplying the first weighting coefficient with the amplitude of each frequency band in the two-dimensional time-frequency graph matrix to obtain the weighted time-frequency graph; when the temperature change rate exceeds the set threshold, constructing a second weighting coefficient greater than 1 using the ratio of signal kurtosis to envelope entropy as the gain base; and multiplying the second weighting coefficient with the amplitude of the high-frequency band of the weighted time-frequency graph.

[0015] This invention utilizes the nonlinear translation and scaling characteristics of the hyperbolic tangent function to smoothly convert the unbounded rate of temperature change into a bounded first weighting coefficient, avoiding the numerical explosion of reconstructed features caused by extreme temperature rise; at the same time, it implements high-frequency band gain compensation through the second weighting coefficient, which greatly enhances the extremely weak high-frequency impact edge features under abnormal temperature rise and sudden change conditions, avoiding the loss of key fault information.

[0016] Preferably, the preprocessed temperature signal is transformed into a two-dimensional temperature map through Gram angle field transformation, including: obtaining the maximum and minimum values ​​of the preprocessed temperature signal sequence; mapping each data point in the temperature signal sequence to the range of -1 to 1 through min-max normalization; calculating the inverse cosine value of each data point after normalization to obtain the polar angle sequence in the polar coordinate system; calculating the sum of the polar angles corresponding to any two times in the polar angle sequence and taking the cosine value of the sum of the polar angles as the element value of the coordinate matrix corresponding to the two-dimensional map; traversing all time pairs to generate a two-dimensional matrix composed of the cosine values ​​of the sum of the polar angles as the two-dimensional temperature map.

[0017] Preferably, the low-frequency energy map, the two-dimensional feature map of the high-frequency band, and the temperature feature map corresponding to the overall two-dimensional temperature map of the weighted time-frequency map are stitched together as three channels to obtain a three-dimensional tensor, including: in the weighted time-frequency map, extracting the two-dimensional matrix of the low-frequency band portion as the R channel according to a set frequency slice threshold; extracting the two-dimensional energy matrix of the high-frequency band portion of the weighted time-frequency map, normalizing it, and resampling it to the same size as the R channel to generate a two-dimensional high-frequency feature matrix that retains the high-frequency distribution structure as the G channel; normalizing the overall two-dimensional temperature map and resampling it to the same size as the R channel to generate a two-dimensional temperature feature matrix that retains the temperature time-series correlation structure as the B channel; and stitching the R channel, G channel, and B channel in the depth dimension to generate a size-matched three-dimensional tensor.

[0018] Preferably, the residual network includes an input layer, a feature extraction sub-network, a global average pooling layer, and a fully connected output layer connected in sequence, and the feature extraction sub-network includes multiple cascaded residual blocks.

[0019] Preferably, in the joint loss function, the cross-entropy loss algorithm is used to optimize the classification boundary of different fault categories, and the center loss algorithm is used to reduce the intra-class distance of samples of the same fault category in the feature space.

[0020] Secondly, the present invention provides a belt conveyor bearing fault diagnosis system based on temperature and vibration signal analysis, including a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned belt conveyor bearing fault diagnosis method based on temperature and vibration signal analysis is implemented.

[0021] By adopting the above technical solution, the above-mentioned method for diagnosing belt conveyor bearing faults based on temperature and vibration signal analysis is generated into a computer program and stored in a memory so that it can be loaded and executed by a processor. In this way, a terminal device can be made based on the memory and the processor for convenient use.

[0022] The beneficial effects of this invention are as follows: This invention effectively filters out vibration outliers and corrects temperature drift through preprocessing methods such as median interpolation and differential thresholding. It employs variational mode decomposition based on adaptive parameters of kurtosis and envelope entropy to accurately extract fault components and avoid mode aliasing. Furthermore, this invention reconstructs the time-frequency diagram using a temperature change rate mapping weighting coefficient and implements gain compensation for the high-frequency band exceeding the threshold, thus physically linking the macroscopic temperature rise trend with microscopic high-frequency vibration, effectively enhancing the subtle fault characteristics that are easily masked under abnormal operating conditions.

[0023] Furthermore, this invention concatenates multi-band vibration features with two-dimensional temperature maps into a three-dimensional tensor, achieving strict spatial alignment of multi-modal features. The tensor is input into an improved residual network, utilizing parallel coordinate attention and deformable convolutional branches to effectively balance spatial localization of the fault area and extraction of local deformation features. In addition, the model is trained using a joint loss function dynamically adjusted by the energy proportion of the temperature channels, adaptively constraining the aggregation degree of similar features and alleviating the problem of mismatched loss weights under different operating conditions, thereby improving the accuracy and generalization performance of belt conveyor bearing fault diagnosis. Attached Figure Description

[0024] Figure 1 This is a flowchart of the belt conveyor bearing fault diagnosis method based on temperature and vibration signal analysis in this invention; Figure 2 This is a comparison diagram of the waveforms before and after vibration signal preprocessing in this invention; Figure 3This is a mapping curve of normalized temperature change rate and weighting coefficient in this invention; Figure 4 This is a bar chart comparing the diagnostic accuracy of different schemes in this invention. Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0026] This invention discloses a method for diagnosing belt conveyor bearing faults based on temperature and vibration signal analysis, referring to... Figure 1 This includes steps S1-S4: S1. Acquire temperature and vibration signals and perform preprocessing.

[0027] In an optional embodiment, vibration and temperature signals of the belt conveyor bearing are acquired. Outliers in the vibration signal are removed using a median-cubic spline interpolation method to obtain a preprocessed vibration signal. Drift in the temperature signal is corrected using a difference and moving average threshold method to obtain a preprocessed temperature signal.

[0028] Specifically, piezoelectric accelerometers and thermocouple temperature sensors deployed on the belt conveyor bearing housings synchronously acquire one-dimensional time-series raw vibration and temperature signals at a fixed sampling frequency. A fixed sliding window is set to traverse the raw vibration signal, and the absolute difference between the middle value of the window and the actual amplitude at the center point is calculated. If the absolute difference is greater than three times the standard deviation, the current data point is determined to be an outlier and is set to empty. A cubic spline interpolation algorithm is used with the sampled data on both sides of the outlier as control nodes to construct piecewise cubic polynomial equations. The solutions are then used to fill in the missing positions with smooth numerical values, and the preprocessed vibration signal is output.

[0029] For the original temperature signal, the temperature difference between sampling points at adjacent time points is calculated and divided by the corresponding sampling time interval to obtain the temperature change rate sequence. The local moving average of the temperature change rate sequence within a preset window length is calculated, and this local moving average is used as the window temperature change trend. This window temperature change trend is then compared with a preset drift threshold. When the absolute value of the temperature change trend within a certain window exceeds the preset drift threshold, and the high-frequency energy or high-frequency envelope of the vibration within the corresponding window does not increase synchronously, baseline drift is determined to exist in the temperature signal, and baseline translation correction is performed on the drifted data segment. When the temperature change rate increases and is accompanied by a synchronous increase in the high-frequency energy of the vibration, the increasing trend of the temperature change rate is retained as a possible true fault temperature rise trend and is not deleted as drift, resulting in the preprocessed temperature signal.

[0030] In some embodiments, median-cubic spline interpolation is used to remove outliers from the vibration signal to obtain a preprocessed vibration signal. Specifically, the vibration signal is divided into non-overlapping data segments, and the median of the vibration amplitude within each data segment is calculated. The absolute difference between the amplitude of each data point within a data segment and the median is calculated, and the median of the absolute difference sequence is multiplied by a set constant as a fluctuation threshold. Data points with an absolute difference greater than the fluctuation threshold are identified as impact outliers and removed. The time and amplitude of the normal data points adjacent to the removed outliers are extracted, a cubic spline interpolation function is constructed, the estimated amplitude at the removal location is calculated and filled in, and signal interpolation recovery is achieved to obtain the preprocessed vibration signal.

[0031] The original vibration signal of the conveyor belt bearing, typically sampled at 10kHz to 20kHz, is divided into fixed, non-overlapping data segments according to the time series, with the segment length N set to 1024. For each signal segment, the median amplitude M is calculated. The absolute difference sequence between each sampling point and the median amplitude M is calculated, and the median of the absolute difference sequence is taken as the absolute median difference (MAD). Based on statistical distribution principles, the fluctuation threshold is set to 4.4478 times the absolute median difference (MAD). During traversal detection, if the absolute difference of a data point is greater than the calculated fluctuation threshold, the relevant data point is determined to be a transient impact outlier caused by electromagnetic interference or sensor loosening, and the data at the location of the transient impact outlier is cleared.

[0032] After outlier removal, taking the time of outlier removal as the center, extract 3 to 5 adjacent normal data points to the left and right, respectively. For example, extract the discrete amplitudes and corresponding timestamps of the first 4 points and the last 4 points. Based on the coordinate data of 8 known reference points, a piecewise cubic polynomial algorithm that requires continuity of the first and second derivatives at each data connection point is used to construct a smooth cubic spline interpolation function that conforms to the low-frequency trend of the signal.

[0033] By substituting the time coordinates corresponding to the field points into the constructed cubic spline interpolation function, the estimated amplitude at the corresponding positions is obtained and filled in, thereby filtering out high-amplitude interference while ensuring the phase continuity of the vibration signal in the time domain waveform, and outputting a pre-processed smooth vibration signal.

[0034] Reference Figure 2 The original signal waveform exhibited an abnormal amplitude spike in the middle, while the processed signal waveform, at the same point in time, showed a smooth trend matching the surrounding waveforms, without any drastic jumps. This waveform change demonstrates that the method of using median filtering combined with cubic spline interpolation can effectively identify and remove abnormally high-amplitude outliers in the signal, and accurately fill in missing data, thereby restoring the original continuity of the signal.

[0035] In some embodiments, the temperature signal is corrected for drift by differential and moving average thresholding to obtain a preprocessed temperature signal. Specifically, a first-order differential operation is performed on the temperature signal, and the result is divided by the sampling time interval to obtain a temperature change rate sequence. The arithmetic mean of the temperature change rate sequence is calculated within a fixed-length sliding time window. When the absolute value of the arithmetic mean within the sliding time window is greater than a set threshold, and the high-frequency energy or high-frequency envelope of the vibration within the corresponding window does not increase synchronously, it is determined that the temperature signal has experienced baseline drift. The arithmetic mean of the temperature data within the normal time period before the drift occurs is extracted as the normal baseline. For the temperature data after the drift occurs, a detrending operation is performed, and the first-order skew component is removed based on polynomial fitting. The data is then smoothly spliced ​​back to the extracted normal baseline to complete the drift correction of the temperature signal and obtain the preprocessed temperature signal.

[0036] A PT100 temperature sensor is used to collect the temperature signal sequence for the conveyor belt bearing at a low frequency, performing a first-order forward differential operation (e.g., setting the sampling rate to 1Hz). The calculated difference value is divided by the sampling period to obtain the temperature change rate sequence between adjacent time points. A sliding time window with a length W of 60 sampling points and a sliding step size of 1 sampling point is set, corresponding to a time span of 60 seconds at a sampling rate of 1Hz. The arithmetic mean of the temperature change rate sequence elements within each window is calculated successively using the set sliding time window. The calculated arithmetic mean represents the overall trend of short-term temperature changes.

[0037] When the absolute value of the arithmetic mean within a certain sliding window exceeds the set environmental drift threshold (preferably set to 0.05℃ / s), and the high-frequency energy or high-frequency envelope of the vibration within the corresponding time window does not synchronously exceed the preset linkage threshold, it is determined that the current temperature signal has caused baseline drift due to a sudden change in operating conditions or sensor temperature drift, and the end of the sliding window where the drift occurred is marked as the drift start point. If the rate of temperature change exceeds the environmental drift threshold while the high-frequency energy or high-frequency envelope of the vibration increases synchronously, the temperature rise is considered as a real temperature rise trend that may be related to bearing friction heating, and the baseline translation and deletion operation is not performed. To implement the baseline drift correction operation, a normal stable time period before the drift start point that has not triggered an alarm is extracted by reverse tracing, for example, the length of the normal stable time period is set to 120 sampling points. The arithmetic mean of the original temperature data within the normal stable time period is calculated, and the result is frozen as a normal baseline constant for calibration, for example, the calculated normal baseline constant is 45.2℃.

[0038] For subsequent real-time temperature data after baseline drift is detected, the arithmetic mean of the temperature within the current evaluation window is calculated, for example, if the drift is to 50.1℃. For the original temperature data segment after drift, a polynomial fitting-based method is used to extract and remove its first-order tilt component for detrending. The detrended data is then accumulated with a pre-frozen normal baseline constant, replacing a simple vertical translation operation and avoiding jagged edges at adjacent window seams. This baseline drift correction process reduces low-frequency background shifts caused by sensor drift or slow environmental drift, ensuring the consistency of the data baseline for subsequent diagnostic input data during long-term operation, and outputting a pre-processed temperature signal.

[0039] S2. Decompose the vibration signal and filter the modal components.

[0040] In an optional embodiment, variational mode decomposition is performed on the preprocessed vibration signal. The penalty factor for variational mode decomposition is determined by the ratio of kurtosis to envelope entropy. The signal is decomposed by successively increasing the number of mode layers. When there is a phenomenon where the center frequency distance between adjacent modes is less than a set threshold, the number of mode layers for variational mode decomposition is determined, and the cross-correlation coefficient is calculated to select the optimal modal components.

[0041] Specifically, the variational mode decomposition algorithm is executed based on the Python third-party signal processing library vmdpy. Before decomposition, the envelope of the preprocessed vibration signal is extracted, and the envelope entropy of the vibration signal is calculated using the Shannon entropy formula. The ratio of the fourth-order central moment to the squared variance of the vibration signal is calculated using statistical formulas to obtain the signal kurtosis. The calculated signal kurtosis is divided by the envelope entropy plus a smoothing term, and then multiplied by a preset scaling constant coefficient, which serves as the value of the second-order penalty factor in the variational mode decomposition algorithm.

[0042] The initial number of modal layers for decomposition is set to 2 for the first decomposition. The spectrum of each intrinsic mode function (IMF) is extracted using Fast Fourier Transform (FFT), and the center frequency of each IMF is found. The absolute difference between the center frequencies of all adjacent IMFs is calculated, and it is determined whether any absolute difference is less than a preset frequency distance threshold. If no absolute difference is found below the preset threshold, the number of modal layers is increased by 1, and the decomposition process is repeated until the center frequency distance between adjacent modes is less than the preset threshold, or the number of modal layers reaches the preset maximum number of layers. When the latest decomposition result shows that the center frequency distance between adjacent modes is less than the preset threshold, it indicates that the algorithm has over-decomposed. At this point, the iterative calculation is stopped, and the current number of modal layers minus 1 is determined as the optimal number of modal layers. If the preset maximum number of layers is reached without triggering the over-decomposition criterion, the preset maximum number of layers is used as the determined number of modal layers, and the decomposition result corresponding to the determined number of modal layers is output as the determined modal decomposition result. Subsequently, the corresponding variational mode decomposition results are re-executed or called according to the determined number of modal layers and the determined penalty factor to obtain the components of each intrinsic mode function.

[0043] The cross-correlation coefficient between each intrinsic mode function component and the preprocessed original vibration signal under the determined modal layer is calculated using the Pearson correlation coefficient algorithm. Intrinsic mode function components containing too much noise and with small correlation coefficients are removed, and components with cross-correlation coefficients greater than a set threshold are retained as the final selected modal components.

[0044] In some embodiments, variational mode decomposition is performed on the preprocessed vibration signal, and modal components are selected. Specifically, the negative cumulative sum of the probability density of the envelope sequence of the preprocessed vibration signal and the logarithmic product of the probability density of the envelope sequence itself is calculated, and the calculated negative cumulative sum is used as the envelope entropy of the vibration signal; the ratio of the fourth central moment of the amplitude of the preprocessed vibration signal to the square of the variance is calculated, and the calculated ratio is used as the kurtosis of the vibration signal; the ratio of the obtained signal kurtosis to the envelope entropy plus a smoothing term is multiplied by a preset constant coefficient as the penalty factor for variational mode decomposition; the number of modal layers in variational mode decomposition is set to an initial value, and the number of modal layers is increased sequentially. The modal components are decomposed. After each decomposition, the difference between the center frequencies of each adjacent mode is calculated. When the ratio of the calculated difference to the highest cutoff frequency of the vibration signal is less than a set threshold, the increment is stopped. The modal layer number of the previous decomposition is taken as the determined modal layer number, and each modal component corresponding to the determined modal layer number is output. The normalized cross-correlation coefficient between each modal component and the preprocessed vibration signal is calculated. The modal components with the normalized cross-correlation coefficient greater than the set correlation threshold are retained as the input modal components for subsequent continuous wavelet transform.

[0045] The preprocessed vibration signal is subjected to Hilbert transform to extract the amplitude magnitude of the analytic signal, generating an envelope sequence. The generated envelope sequence is then normalized to obtain a discrete probability density distribution sequence. Using information entropy theory, the negative summation of the products of each element in the discrete probability density distribution sequence with the natural logarithm is calculated to obtain the envelope entropy of the vibration signal. The calculated envelope entropy represents the sparsity of the periodic impact characteristics excited by the bearing fault in the sequence. Based on the time-domain statistical characteristics of the vibration signal, the fourth central moment of the signal amplitude is calculated and divided by the square of the variance to obtain the kurtosis of the vibration signal. The calculated kurtosis can objectively represent the degree of impact amplitude during the fault change stage.

[0046] The kurtosis representing the impact intensity is divided by the sum of the envelope entropy and the smoothing term. This calculated ratio is then multiplied by a value between 1500 and 2500, for example, setting the preset scaling constant to 2000, thus generating a variable as the second-order penalty factor in variational mode decomposition. During iterative optimization, the initial value of the number of modal layers K is preset to 2, and incremental decomposition tests are performed with a step size of 1. The maximum number of modal layers is then set. For example, a value between 8 and 10. After each layer of decomposition converges and updates the extracted intrinsic mode components, the center frequencies of each mode are sorted in ascending order of numerical value, and the absolute difference between the center frequencies of adjacent modes is calculated sequentially. The absolute difference of all extracted center frequencies is divided by the highest cutoff frequency of the signal determined by the Nyquist sampling theorem; for example, when the sampling frequency is 10kHz, the highest cutoff frequency is 5000Hz. When the normalized frequency difference ratio between any two adjacent modes is less than the set anti-aliasing threshold, it indicates that frequency overlap or over-decomposition has occurred. The preferred range for the anti-aliasing threshold is between 0.05 and 0.1. At this point, the algorithm forcibly terminates the incremental iteration and outputs the maximum number of layers that previously met the distribution conditions as the determined number of mode layers. If the number of mode layers reaches the preset maximum number of mode layers... If the decomposition criterion has not been triggered, then the preset maximum modal layer number will be set. The minimum modal layer number is used as the determined modal layer number; if the previous layer number is less than the preset minimum modal layer number, then the preset minimum modal layer number is used as the determined modal layer number. Subsequently, variational modal decomposition is performed based on the determined modal layer number and the determined penalty factor to obtain the candidate intrinsic modal components.

[0047] After determining the number of modal layers, the normalized cross-correlation coefficient between each intrinsic modal function component and the preprocessed vibration signal is calculated sequentially. For example, the m-th modal component and the preprocessed vibration signal can be mean-reduced separately, and the normalized correlation coefficient after mean-reduction of the two signals can be calculated. When the normalized correlation coefficient is greater than a preset correlation threshold, the corresponding modal component is considered to still retain the effective fault information in the original vibration signal, and the corresponding modal component is retained. When the normalized correlation coefficient is less than or equal to the preset correlation threshold, the corresponding modal component is considered to mainly contain noise or has a weak correlation with fault diagnosis, and the corresponding modal component is discarded. If there is no modal component with a normalized cross-correlation coefficient greater than the preset threshold, at least one modal component with the largest normalized cross-correlation coefficient is selected as the minimum input. Finally, the filtered modal components are output as input data for subsequent continuous wavelet transform to generate time-frequency maps.

[0048] S3. Generate a time-frequency diagram and apply gain compensation.

[0049] In an optional embodiment, a continuous wavelet transform is performed on the selected modal components to generate a time-frequency map. The preprocessed temperature signal is then transformed into a two-dimensional temperature map using a Gram angle field transform. The rate of temperature change is calculated and weighting coefficients are obtained through hyperbolic tangent function mapping. The time-frequency map is reconstructed using the weighting coefficients to obtain a weighted time-frequency map. When the rate of temperature change exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency map.

[0050] Specifically, a continuous wavelet transform algorithm is employed, using the complex Morlet wavelet as the mother wavelet function to perform time-frequency domain mapping on each modal component. The wavelet coefficient matrix is ​​calculated, and its absolute value is taken, followed by extremum normalization. Corresponding elements of the coefficient matrices of all components are added and fused to generate a basic time-frequency map containing full-band information.

[0051] The Gram angle field transform algorithm is used to scale the preprocessed temperature signal to the range of -1 to 1, and then maps it to an angle sequence in polar coordinates using an inverse cosine function. The cosine matrix of the sum of the polar angles at each time step is calculated to generate a time-fidelity two-dimensional temperature map. The Gram angle field transform algorithm is a method for converting a one-dimensional time series into a two-dimensional image. It primarily involves mapping the sequence to a polar coordinate system and then calculating the cosine of the sum of the polar angles at different time points to form a two-dimensional matrix that preserves the temporal relationship.

[0052] The temperature change rate of the preprocessed temperature signal in the current batch is calculated for adjacent sampling times, and dimensionless processing is performed using a preset reference temperature rise rate. The dimensionless temperature change rate is input into the hyperbolic tangent function and mapped to a weighting coefficient. This weighting coefficient corresponding to the current data segment is extracted as a global constant variable. This global constant variable is then multiplied by a scalar multiplication of all frequency band amplitudes in the basic two-dimensional time-frequency plot matrix to complete feature reconstruction and output the weighted time-frequency plot.

[0053] A logical decision branch is established. When the detected temperature change rate exceeds a pre-set safety threshold, a high-frequency pixel matrix located in the upper half of the weighted time-frequency graph is extracted using a slicing operation along the vertical axis (frequency axis). A compensation gain coefficient greater than 1 is constructed based on the calculated kurtosis and envelope entropy. The high-frequency pixel matrix is ​​then traversed, and each pixel is multiplied by the constructed compensation gain coefficient to enhance the subtle high-frequency impact edge features under abnormal operating conditions of sudden temperature changes.

[0054] In some embodiments, the temperature change rate is calculated and weighting coefficients are obtained by mapping using a hyperbolic tangent function. The weighted time-frequency graph is then reconstructed using these weighting coefficients to obtain a weighted time-frequency graph. When the temperature change rate exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency graph. Specifically, the ratio of the difference between the preprocessed temperature signals at adjacent sampling times to the time interval is calculated, and this ratio is used as the temperature change rate. The temperature change rate is dimensionless and then input into the hyperbolic tangent function. After linear translation and scaling, a first weighting coefficient ranging from 0.5 to 1.5 is generated. The first weighting coefficient corresponding to the current data segment is extracted as a global constant variable. This global first weighting coefficient is multiplied uniformly with the amplitude of each frequency band in the two-dimensional time-frequency graph matrix to obtain the weighted time-frequency graph. When the temperature change rate exceeds the set threshold, a second weighting coefficient greater than 1 is constructed using the ratio of signal kurtosis to envelope entropy as the gain base. The second weighting coefficient is multiplied with the high-frequency band amplitude of the weighted time-frequency graph to achieve gain compensation for the high-frequency band energy.

[0055] For multi-source fusion diagnostic scenarios, the difference in preprocessed temperature amplitudes at adjacent sampling points is calculated, and this difference is divided by a fixed sampling period, such as 1s or 5s, to obtain the temperature change rate representing the real-time temperature rise trend. Using a historically measured limit temperature rise rate of the conveyor belt bearing, such as 0.5℃ / s, as a reference base, the currently calculated temperature change rate is divided to achieve dimensionless processing. The calculated dimensionless value is then input as an independent variable into the hyperbolic tangent function for S-shaped compression mapping. Based on the translation and scaling principle of the hyperbolic tangent function, linear coordinate translation and amplitude scaling are performed using a formula to generate a first weighting coefficient with values ​​ranging from 0.5 to 1.5. The formula is as follows:

[0056] in, The first weighting coefficient; The temperature change rate after dimensionless processing.

[0057] Reference Figure 3 The smooth curve in the figure illustrates a non-linear transition trend in the weighting coefficients as the normalized rate of temperature change changes. When the normalized rate of temperature change is near the origin, the curve slope is steepest, indicating extreme sensitivity to temperature variations. Conversely, as the normalized rate of temperature change extends towards its extreme values, the curve slope gradually decreases, and the weighting coefficients approach their upper and lower limits, achieving a smooth saturation compression effect. This non-linear mapping trend demonstrates that the mapping method can smoothly and effectively convert unbounded temperature change rates into bounded weighting coefficients, avoiding the explosion of feature values ​​caused by extreme temperature changes, while preserving the modulating effect of the temperature rise trend on the reconstructed features.

[0058] When processing the two-dimensional time-frequency graph matrix generated by continuous wavelet transform, the first weighting coefficient within the corresponding period of the current vibration data segment is extracted along the time axis of the two-dimensional time-frequency graph matrix. This first weighting coefficient is used as a global constant variable representing the low-frequency temperature trend. The vertical frequency band amplitude vectors of all frequency scales contained in the two-dimensional time-frequency graph matrix are uniformly multiplied by this global first weighting coefficient. In this way, the micro-energy distribution of the vibration signal is enhanced or suppressed through the macroscopic representation of low-frequency temperature rise, and the signal reconstruction is completed to obtain the weighted time-frequency graph. Based on the obtained weighted time-frequency graph, when the monitored real-time temperature change rate suddenly exceeds the preset wear warning threshold, the wear warning threshold is preferably set to 0.2℃ / s. The kurtosis and envelope entropy of the vibration signal calculated in the previous stage are extracted. The ratio of the vibration signal kurtosis to the envelope entropy is used as the gain base, and an additional weight adjustment factor, such as 0.1, plus an offset constant of 1, is added to construct a second weighting coefficient whose value is always greater than 1. The constructed second weighting coefficient is usually between 1.2 and 2.

[0059] Based on prior knowledge of the frequency band distribution of early bearing failures, the boundaries are defined in the weighted time-frequency graph according to the frequency axis. For example, high-frequency band matrix blocks above 2000Hz are extracted, and all time-frequency elements in the extracted high-frequency blocks are multiplied point-to-point by the constructed second weighting coefficient.

[0060] In some embodiments, the preprocessed temperature signal is transformed into a two-dimensional temperature map through Gram angle field transformation. Specifically, the maximum and minimum values ​​of the preprocessed temperature signal sequence are obtained, and each data point in the preprocessed temperature signal sequence is mapped to the range of -1 to 1 through min-max normalization; the inverse cosine value of each data point after normalization is calculated to obtain the polar angle sequence in polar coordinates; the sum of the polar angles corresponding to any two times in the obtained polar angle sequence is calculated, and the cosine value of the sum of the polar angles is obtained. The calculated cosine value is used as the element value of the coordinate matrix corresponding to the two-dimensional map; all time pairs are traversed to generate a two-dimensional matrix composed of the cosine values ​​of the sum of the polar angles, and the generated two-dimensional matrix is ​​used as the two-dimensional temperature map.

[0061] For a preprocessed one-dimensional time-temperature signal sequence of length N, for example, setting N to 224 to accommodate the fixed input size requirements of the subsequent deep residual network, a global search is performed to obtain the maximum and minimum values ​​of the data within the truncated sequence. Based on the min-max normalization principle in signal processing, a mapping formula is applied for calculation. That is, the amplitude of the current data point is subtracted from the minimum value, divided by the difference between the maximum and minimum values, multiplied by 2, and subtracted by 1. This linearly stretches and maps all data points in the original one-dimensional temperature sequence so that they lie within the closed interval from -1 to 1. When the maximum and minimum values ​​are equal, the normalization result is set to 0 to avoid a denominator of 0 during calculation.

[0062] For each data point in the mapped sequence, the normalized amplitude in the one-dimensional Cartesian coordinate system is converted into an angular representation in the polar coordinate system, resulting in a polar angle time series limited to the range of 0 to π radians. The temporal order of the temperature series is preserved through the row and column indices of the matrix. For polar angle sequences of the same length 224, the index points of any two moments in the sequence are set as... And index point set And all times are iterated through integers from 1 to 224, and the time is... Corresponding polar angle and time The corresponding polar angles are added together, and the cosine value of the sum of the polar angles is calculated.

[0063] Construct an empty matrix container with length and width N. Iterate through all time index pairs of the original polar angle sequence using nested loop logic, filling each pair with the calculated cosine value until the row number is reached. , column number is The two-dimensional space corresponds to the interior of the coordinate matrix elements. The generated 224×224 inner product operation symmetric matrix fully encodes the correlation of the one-dimensional temperature sequence at different time spans. The generated inner product operation symmetric matrix is ​​output as a two-dimensional intuitive image feature of deep learning, namely a two-dimensional temperature map.

[0064] S4. Construct a three-dimensional tensor and perform fault diagnosis.

[0065] In an optional embodiment, the low-frequency energy map, the high-frequency band two-dimensional feature map, and the temperature feature map corresponding to the two-dimensional temperature map of the weighted time-frequency map are concatenated as three channels to obtain a three-dimensional tensor. The three-dimensional tensor is input into a pre-trained residual network to output fault categories. The residual blocks of the residual network include parallel coordinate attention branches and deformable convolution branches. During network training, a loss function combining center loss and cross-entropy loss is used. The balance coefficient of the combined loss function is adjusted by the energy proportion of the temperature channels in the batch samples.

[0066] Specifically, the weighted time-frequency map is segmented along its frequency axis according to a set frequency slicing threshold. A two-dimensional low-frequency band matrix is ​​extracted from the lower half of the low-frequency region and resampled to a set resolution to generate a low-frequency energy map matrix. The two-dimensional amplitude matrix of the time-frequency region in the upper half is retained, and after normalization and resampling, a two-dimensional high-frequency feature map matrix is ​​generated. Simultaneously, the two-dimensional temperature map is normalized and resampled to generate a temperature feature map matrix with the same dimensions as the low-frequency energy map matrix and the two-dimensional high-frequency feature map matrix.

[0067] Using deep learning's tensor concatenation operation, low-frequency energy maps, high-frequency feature maps, and temperature feature maps are stacked and fused sequentially along the depth channel dimension to obtain a standard 3D tensor. An 18-layer residual network model is built using the PyTorch deep learning framework. ImageNet pre-trained weights corresponding to the size-matching layers in the standard residual network backbone are loaded. The newly added coordinate attention layer, offset convolutional layer, and deformable convolutional layer are initialized and trained. Parallel coordinate attention and deformable convolutional branches are constructed within the residual block; the coordinate attention branch extracts weight features with spatial orientation awareness; the deformable convolutional branch adjusts the convolution sampling position based on the learned offset and extracts local deformation features. The output features of the two branches are element-wise added and fused after matching the number of channels and spatial dimensions, then added to the input features of the residual block via a shortcut connection and processed by an activation function before being output.

[0068] During the network training phase, the forward propagation terminus includes a joint loss function combining cross-entropy loss and center loss algorithms. Cross-entropy loss optimizes the classification boundaries for different fault categories, while center loss reduces the intra-class distance between samples of the same fault category in the feature space. Before calculating the energy proportion of the temperature channel, the three channels are normalized to the same scale. The ratio of the sum of squared pixels of the third temperature channel to the total sum of squared pixels of all three channels in the current batch input tensor is calculated and used as the adjustment weight for the center loss term. This joint loss function guides the backpropagation update of the network parameters.

[0069] In some embodiments, the low-frequency energy map, the high-frequency band two-dimensional feature map, and the temperature feature map corresponding to the two-dimensional temperature map of the weighted time-frequency map are stitched together as three channels to obtain a three-dimensional tensor, which is then input into the residual network to output the fault category. Specifically, in the weighted time-frequency graph, a two-dimensional matrix of the low-frequency band is extracted as the R channel according to a set frequency slice threshold; a two-dimensional energy matrix of the high-frequency band is extracted from the weighted time-frequency graph, and the extracted two-dimensional energy matrix of the high-frequency band is normalized and resampled to the same size as the R channel to generate a two-dimensional high-frequency feature matrix that retains the high-frequency distribution structure, which is used as the G channel; the two-dimensional temperature graph is normalized as a whole and resampled to the same size as the R channel to generate a two-dimensional temperature feature matrix that retains the temperature time-series correlation structure, which is used as the B channel; the R channel, G channel, and B channel are concatenated in the depth dimension to generate a size-matched three-dimensional tensor; the three-dimensional tensor is input into a residual network, which includes an input layer, a feature extraction sub-network, a global average pooling layer, and a fully connected output layer connected in sequence. The feature extraction sub-network includes multiple cascaded residual blocks containing parallel coordinate attention branches and deformable convolution branches. Each residual block also includes an identity mapping or size-matched shortcut connection connected to the input features. After processing by the residual network, the fault diagnosis result of the conveyor belt bearing is output.

[0070] Assume the initial pixel resolution of the input weighted time-frequency image is 256×224 along both the time and frequency axes. Based on the set bearing rotor fundamental frequency and the frequency slicing threshold corresponding to the main outer race fault frequency range, for example, specifying a frequency truncation limit of 1000Hz, a matrix slicing operation is performed on the weighted time-frequency image. The time-frequency two-dimensional energy matrix blocks covered by the low-frequency band are extracted and uniformly resampled to the standard network input size of 224×224 using a bilinear interpolation algorithm. This image, containing the core information of frequency conversion amplitude modulation, is used as the red R channel of the pseudo-color image.

[0071] For the high-frequency band remnants above the slice threshold, a two-dimensional amplitude distribution matrix of the high-frequency band on the time and frequency axes is retained. The two-dimensional amplitude distribution matrix is ​​normalized and uniformly resampled to a size of 224×224 using a bilinear interpolation algorithm, thereby generating a two-dimensional high-frequency feature matrix that can characterize the high-frequency impact energy distribution, fault characteristic frequencies, harmonics, and harmonic structures, which serves as the green G channel of the image.

[0072] Simultaneously, the previously generated 224×224 two-dimensional Gram-field temperature map was normalized. When sizes were inconsistent, it was resampled to 224×224 using bilinear interpolation to generate a two-dimensional temperature-time feature matrix, which served as the blue B channel of the image.

[0073] By concatenating R, G, and B channels with the same spatial size along the depth dimension, a standard input data structure with a spatial size of 224×224 and 3 channels is constructed. Before inputting this data into the network, the standard input data structure can be converted into a channel-first format.

[0074] The feature extraction subnetwork comprises multiple cascaded residual blocks, each containing two parallel branches: a coordinate attention branch and a deformable convolution branch. The residual blocks preserve shortcut connections from the input features to the output. The coordinate attention branch performs one-dimensional global average pooling along the height and width directions of the feature map, extracting spatial orientation features in the horizontal and vertical directions. The feature maps from these two directions are concatenated and input into a shared two-dimensional convolutional layer to generate an intermediate feature map. This intermediate feature map is then segmented along the spatial dimension and mapped to horizontal and vertical attention weights, respectively. The horizontal and vertical attention weights are multiplied with the original feature map to obtain an enhanced feature map. The deformable convolution branch contains multiple deformable convolutional layers. Additional offset convolutional layers learn the spatial two-dimensional offset of each sampling point on the feature map. Based on this two-dimensional offset, the receptive field of the convolutional kernel is adjusted, and deformation features are extracted. The enhanced feature map output from the coordinate attention branch and the deformable feature map output from the deformable convolution branch are added and fused element by element. The fused feature is then added element by element to the input feature of the residual block and processed by an activation function before being output to the next residual block.

[0075] By employing a parallel network structure, the coordinate attention branch can focus on preserving the directional and positional relationships of fault energy regions in the time-frequency map. The deformable convolution branch can focus on adapting to the local shifts and morphological changes of fault texture in the time-frequency map under different rotational speeds, loads, and temperature rise conditions. The fusion of features extracted by the two parallel branches avoids the phenomenon of premature suppression of another type of feature by the previous processing stage in the serial structure. This is beneficial for simultaneously preserving global spatial orientation information and local deformation information, thereby enhancing the network's ability to represent features of early weak faults and samples under varying operating conditions.

[0076] The high-dimensional features extracted by the feature extraction sub-network are reduced to a one-dimensional feature vector through a global average pooling layer and then input to the fully connected output layer. The fully connected output layer, based on the classification probability mapping principle in machine learning, maps the one-dimensional feature vector to the probability distribution of various fault states using a normalized exponential function. The probability is calculated as follows:

[0077] in, For prediction of the first The probability of a fault state; For the fully connected output layer The output value of each node; For the fully connected output layer The output value of each node; exp is an exponential function with the natural constant as its base; This represents the total number of fault state categories.

[0078] During the network training phase, the cross-entropy loss is calculated based on the output of the classification function Softmax and the true class labels of the samples. Cross-entropy loss is used to constrain the classification boundary between different fault categories. Simultaneously, a one-dimensional feature vector is extracted from the output of the global average pooling layer, and the distance between this one-dimensional feature vector and the feature center corresponding to the true category is calculated to form the center loss. The center loss is used to reduce the intra-class dispersion of samples of the same fault category in the feature space.

[0079] Before calculating the joint loss, the R, G, and B channels of the input 3D tensor are normalized to the same scale, and the sum of squared pixels for each of the three channels in the batch samples is calculated separately. The sum of squared pixels for the B channel (temperature channel) is divided by the sum of the sums of squared pixels for the three channels to obtain the energy proportion of the temperature channel. Based on the principles of energy conservation and feature weighting, the calculation method for the energy proportion of the temperature channel is as follows:

[0080] in, This represents the energy percentage of the temperature channel. These are the pixel values ​​of the two-dimensional temperature feature matrix; These are the pixel values ​​of the low-frequency energy map matrix; These are the pixel values ​​of a two-dimensional high-frequency feature matrix; This is the summation operator; To prevent smooth terms with a denominator of zero.

[0081] Using the calculated energy proportion of the temperature channel as the balance coefficient of the central loss term, a joint loss function is constructed. Based on the idea of ​​loss weighted optimization, the calculation method of the joint loss function is as follows:

[0082] in, For the joint loss function; Cross-entropy loss; The preset center loss base weights; The percentage of temperature channel energy in the batch of samples; Loss centered on the center.

[0083] Backpropagation is performed using a joint loss function to update the parameters of the residual network backbone, coordinate attention parameters, deformable convolution offset parameters, and fully connected layer parameters. This allows the model to adaptively enhance the aggregation constraint of intra-class features based on the contribution of temperature features while learning the classification boundary. When the energy proportion of temperature channels in a batch of samples is high, the constraint of the center loss is strengthened to compress the feature dispersion of similar fault samples; when the energy proportion of temperature channels is low, the constraint of the center loss is weakened, allowing the model to primarily rely on cross-entropy loss to learn the classification boundary of vibration time-frequency. This adaptive adjustment method can alleviate the problem of constraint mismatch of fixed loss weights under different operating conditions, improving the stability and generalization ability of model training.

[0084] After completing all training, the 3D tensor corresponding to the sample to be diagnosed is input into the trained residual network, and only forward propagation and softmax calculation of classification probability are performed. The class with the highest predicted probability is selected as the output result to obtain the fault diagnosis result of the conveyor belt bearing.

[0085] The ablation experiment used publicly available bearing test datasets combined with actual belt conveyor operating temperature sequences collected from a heavy industry enterprise to construct a multi-source synchronous diagnostic sample library. The experiment included five state labels: normal state, inner race fault, outer race fault, rolling element fault, and combined fault. The data partitioning strategy was to allocate 80% of the total samples to the training set and 20% to the test set. The model training employed the Adam adaptive moment estimation optimization algorithm, with an initial learning rate of 0.001, a mini-batch size of 32 samples, and a maximum of 100 iterations. The experimental baseline scheme was set as follows: inputting only a single vibration signal with an unweighted time-frequency plot into a conventional residual network, designated as Model 1; retaining complete feature processing but using a conventional residual network, designated as Model 2; retaining an improved residual network but inputting only a single feature, designated as Model 3; and a complete scheme combining all methods, designated as Model 4.

[0086] Based on the experimental results, Model 1 achieved an average diagnostic accuracy of 84.5% on the test set, with a false negative rate of 11.2% for early, minor faults. Model 2, by utilizing temperature-weighted high-frequency gain compensation and a three-channel tensor construction mechanism, improved the accuracy to 93.8% and reduced the false negative rate to 4.1%. Model 3, relying solely on an improved network with parallel coordinate attention and deformable convolution branches, achieved an accuracy of 89.2%. Model 4, representing the complete technical solution, performed best, achieving an accuracy of 98.6% on the test set. The number of iterations required to reduce the overall false negative rate to 0.5% and for the model to converge to a stable state was reduced from 75 iterations for Model 1 to 42 iterations.

[0087] Reference Figure 4The height of the bars exhibits a gradually increasing, step-like trend as the model scheme evolves. Model 1 has the lowest bar height, while the bars of Model 2 and Model 3 are both higher than those of Model 1, with Model 4 reaching the highest. The fact that Model 2's bars are higher than Model 1's demonstrates that the introduction of temperature-driven high-frequency band energy gain compensation and the multi-modal three-channel splicing strategy helps reduce background noise and the masking effect of sudden changes in operating conditions on weak high-frequency fault features. The fact that Model 3's bars are higher than Model 1's demonstrates that the parallel coordinate attention branch and deformable convolution branch can simultaneously address fault region localization and local deformation feature extraction, effectively improving the network's feature extraction capability. Model 4 has the highest bar size among all experimental models. This comparison proves that combining the multimodal feature processing scheme with the improved residual network and adjusting the balance coefficient of the central loss based on the energy proportion of the temperature channel can adaptively adjust the aggregation constraints of similar data within the feature space, alleviate the mismatch problem of fixed loss weights under different working conditions, thereby enhancing the overall expressive power of multi-source heterogeneous features and ultimately improving the stability of model training and the accuracy of diagnosis.

[0088] This invention also discloses a belt conveyor bearing fault diagnosis system based on temperature and vibration signal analysis, including a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement the belt conveyor bearing fault diagnosis method based on temperature and vibration signal analysis according to this invention.

[0089] The system also includes other components well known to those skilled in the art, such as communication buses and communication interfaces, the settings and functions of which are known in the art and will not be described in detail here.

[0090] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for fault diagnosis of belt conveyor bearings based on temperature and vibration signal analysis, characterized in that, include: S1. Collect vibration and temperature signals from the belt conveyor bearings. For the vibration signal, use median-cubic spline interpolation to remove outliers, obtaining a preprocessed vibration signal. For the temperature signal, correct drift using difference and moving average thresholding, obtaining a preprocessed temperature signal. S2. Perform variational mode decomposition on the preprocessed vibration signal. The penalty factor is determined by the ratio of kurtosis to envelope entropy. Decomposition is performed by progressively increasing the number of mode layers. When the center frequency distance between adjacent modes is less than a set threshold, the number of mode layers is determined. Calculate the cross-correlation coefficient to filter modal components. S3. Perform continuous wavelet transform on the modal components to generate a time-frequency graph. Transform the preprocessed temperature signal using Gram angle field transform. The temperature map is converted into a two-dimensional temperature map. The rate of temperature change is calculated, and the weighted coefficients obtained by mapping with the hyperbolic tangent function are used to reconstruct the time-frequency map to obtain a weighted time-frequency map. When the rate of temperature change exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency map. S4. The low-frequency energy map, the two-dimensional feature map of the high-frequency band, and the temperature feature map corresponding to the overall two-dimensional temperature map of the weighted time-frequency map are stitched together as three channels to obtain a three-dimensional tensor. This tensor is input into the pre-trained residual network to output the fault category. The residual block of the residual network includes parallel coordinate attention branches and deformable convolution branches. The network training adopts a loss function that combines center loss and cross-entropy loss. The balance coefficient is adjusted by the energy ratio of the temperature channels of the batch samples.

2. The belt conveyor bearing fault diagnosis method based on temperature vibration signal analysis according to claim 1, characterized in that, Outliers are removed from the vibration signal using a combination of median and cubic spline interpolation to obtain a preprocessed vibration signal. This process includes: dividing the vibration signal into non-overlapping data segments and calculating the median of the vibration amplitude within each data segment; calculating the absolute difference between the amplitude and the median of each data point within the data segment, and multiplying the median of the absolute difference sequence by a set constant as a fluctuation threshold; identifying data points with an absolute difference greater than the fluctuation threshold as impact outliers and removing them; extracting the time and amplitude of the normal data points adjacent to the removed outliers, constructing a cubic spline interpolation function, calculating the estimated amplitude at the removal location and filling it in, thus achieving signal interpolation recovery and obtaining the preprocessed vibration signal.

3. The belt conveyor bearing fault diagnosis method based on temperature vibration signal analysis according to claim 1, characterized in that, The temperature signal is corrected for drift by differential and moving average thresholding to obtain a preprocessed temperature signal. This includes: performing a first-order differential operation on the temperature signal and dividing it by the sampling time interval to obtain a temperature change rate sequence; calculating the arithmetic mean of the temperature change rate sequence within a sliding time window; determining that the temperature signal has baseline drift when the absolute value of the arithmetic mean within the sliding time window is greater than a set threshold and the high-frequency vibration energy within the corresponding window has not increased synchronously; extracting the arithmetic mean of the temperature data within the normal time period before drift occurs as the normal baseline; and performing a detrending operation on the temperature data after drift occurs, removing the first-order tilt component based on polynomial fitting, and smoothly splicing it back to the normal baseline to complete the drift correction of the temperature signal and obtain the preprocessed temperature signal.

4. The belt conveyor bearing fault diagnosis method based on thermal vibration signal analysis according to claim 1, characterized in that, Variational mode decomposition (VMD) is performed on the preprocessed vibration signal to screen modal components. This includes: calculating the negative sum of the product of the probability density of the preprocessed vibration signal envelope sequence and its own logarithm as the envelope entropy; calculating the ratio of the fourth central moment of the preprocessed vibration signal amplitude to the square of the variance as the kurtosis; multiplying the ratio of the signal kurtosis to the envelope entropy plus a smoothing term by a preset constant coefficient as the penalty factor for variational mode decomposition; progressively increasing the number of modal layers for decomposition, calculating the difference in center frequencies between adjacent modes after each decomposition, stopping the increment when the ratio of the difference in center frequencies to the highest cutoff frequency of the signal is less than a set threshold, and outputting each modal component corresponding to the determined number of modal layers; calculating the normalized cross-correlation coefficient between each modal component and the preprocessed vibration signal, and retaining modal components whose normalized cross-correlation coefficient is greater than a set correlation threshold.

5. The method for fault diagnosis of a belt conveyor bearing based on thermal vibration signal analysis according to claim 1, characterized in that, The temperature change rate is calculated and weighting coefficients are obtained by mapping using the hyperbolic tangent function. The weighted time-frequency graph is reconstructed using the weighting coefficients to obtain a weighted time-frequency graph. When the temperature change rate exceeds a set threshold, gain compensation is applied to the high-frequency band of the weighted time-frequency graph. This includes: calculating the ratio of the preprocessed temperature signal difference between adjacent sampling times to the time interval as the temperature change rate; inputting the dimensionless temperature change rate into the hyperbolic tangent function to generate the first weighting coefficient; extracting the first weighting coefficient corresponding to the current data segment as a global constant variable; multiplying the first weighting coefficient with the amplitude of each frequency band in the two-dimensional time-frequency graph matrix to obtain the weighted time-frequency graph; when the temperature change rate exceeds the set threshold, constructing a second weighting coefficient greater than 1 using the ratio of signal kurtosis to envelope entropy as the gain base; and multiplying the second weighting coefficient with the amplitude of the high-frequency band of the weighted time-frequency graph.

6. The belt conveyor bearing fault diagnosis method based on thermal vibration signal analysis according to claim 1, characterized in that, The preprocessed temperature signal is transformed into a two-dimensional temperature map through Gram angle field transformation, including: obtaining the maximum and minimum values ​​of the preprocessed temperature signal sequence; mapping each data point in the temperature signal sequence to the range of -1 to 1 through min-max normalization; calculating the inverse cosine value of each data point after normalization to obtain the polar angle sequence in the polar coordinate system; calculating the sum of the polar angles corresponding to any two times in the polar angle sequence and taking the cosine value of the sum of the polar angles as the element value of the coordinate matrix corresponding to the two-dimensional map; traversing all time pairs to generate a two-dimensional matrix composed of the cosine values ​​of the sum of the polar angles as the two-dimensional temperature map.

7. The belt conveyor bearing fault diagnosis method based on thermal vibration signal analysis according to claim 1, characterized in that, The low-frequency energy map, high-frequency band two-dimensional feature map, and overall temperature feature map of the weighted time-frequency map are stitched together as three channels to obtain a three-dimensional tensor. This includes: in the weighted time-frequency map, extracting the two-dimensional matrix of the low-frequency band portion as the R channel according to a set frequency slice threshold; extracting the two-dimensional energy matrix of the high-frequency band portion of the weighted time-frequency map, normalizing it, and resampling it to the same size as the R channel to generate a two-dimensional high-frequency feature matrix that retains the high-frequency distribution structure as the G channel; normalizing the entire two-dimensional temperature map and resampling it to the same size as the R channel to generate a two-dimensional temperature feature matrix that retains the temperature time-series correlation structure as the B channel; and stitching the R channel, G channel, and B channel in the depth dimension to generate a size-matched three-dimensional tensor.

8. The belt conveyor bearing fault diagnosis method based on thermal vibration signal analysis according to claim 1, characterized in that, The residual network consists of an input layer, a feature extraction sub-network, a global average pooling layer, and a fully connected output layer connected in sequence. The feature extraction sub-network consists of multiple cascaded residual blocks.

9. The belt conveyor bearing fault diagnosis method based on thermal vibration signal analysis according to claim 1, characterized in that, In the joint loss function, the cross-entropy loss algorithm is used to optimize the classification boundary of different fault categories, and the center loss algorithm is used to reduce the intra-class distance of samples of the same fault category in the feature space.

10. A belt conveyor bearing fault diagnosis system based on temperature and vibration signal analysis, characterized in that, include: A processor and a memory, wherein the memory stores computer program instructions that, when executed by the processor, implement the belt conveyor bearing fault diagnosis method based on temperature and vibration signal analysis according to any one of claims 1-9.

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