A production line fault checking method based on regional attention learning mechanism

By synchronously acquiring signals from multiple sources and constructing a collaborative degradation factor calculation model, and dynamically adjusting the weight coefficients, the problem that traditional single-signal detection cannot adapt to complex faults is solved, and accurate assessment and effective detection of equipment status are achieved.

CN120651527BActive Publication Date: 2026-02-06湖南工商大学
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Patent Information

Application Number
CN202510835023.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-06-20
Publication Date
2026-02-06
Estimated Expiration
2045-06-20

AI Technical Summary

Technical Problem

Traditional single-signal detection is difficult to capture multiple types of composite degradation characteristics, and static weight models cannot adapt to the fluctuations in operating conditions during long-term equipment operation, resulting in decreased fault detection accuracy and frequent false alarms and missed detections.

Method used

A method based on regional attention learning mechanism is adopted to simultaneously collect low-frequency vibration signals, high-frequency acoustic emission signals and temperature time-series signals. Multidimensional feature vectors are extracted through frequency band decomposition, pulse density analysis and acceleration calculation to construct a collaborative degradation factor calculation model, and a maintenance feedback mechanism is introduced to dynamically adjust the weight coefficients.

Benefits of technology

It enables effective detection of complex faults, improves the accuracy of fault early warning and the reliability of equipment status assessment, reduces false alarm rate and false alarm rate, and improves the pertinence of equipment maintenance and production efficiency.

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Abstract

The application discloses a production line fault checking method based on a regional attention learning mechanism, relates to the technical field of production line fault checking, and synchronously collects low-frequency vibration, high-frequency acoustic emission and temperature time sequence signals, covers multidimensional fault characteristics such as mechanical wear, shaft misalignment and thermal effect abnormality, and solves the problem that traditional single signal detection is not complete. According to different signal characteristics, key abnormal characteristics are focused, redundant noise is filtered, and the effectiveness of the characteristics is improved. A collaborative degradation factor model is constructed based on health history data, the weight coefficient is dynamically adjusted through maintenance post-down rate feedback, the device working condition change is adapted, and the poor adaptability of the static model is avoided. The maintenance effect (collaborative degradation factor down rate) is quantitatively evaluated, accurate maintenance is guided, invalid maintenance is reduced, and the production line operation and maintenance efficiency is improved.
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Description

Technical Field

[0001] This invention relates to the field of production line fault inspection technology, specifically a production line fault inspection method based on a region attention learning mechanism. Background Technology

[0002] In modern industrial production, rotating equipment on the production line (such as motors, fans, and pumps) serves as the core power unit, and its operating status directly affects the stability and efficiency of the production line. Timely and accurate detection and early warning of equipment faults are crucial for avoiding unplanned downtime, reducing maintenance costs, and ensuring safe production. Traditional methods for troubleshooting production line equipment mainly rely on single-signal detection technologies, such as bearing wear detection based on vibration signals or thermal overload warnings based on temperature signals. However, with the increasing complexity of industrial equipment, equipment faults often manifest as multi-type composite deterioration (such as the coexistence of bearing wear and shaft misalignment, and the coupling of mechanical damage and thermal effects). Single-signal detection has the following significant drawbacks:

[0003] Focusing on only a single physical quantity (such as vibration energy or temperature value) makes it difficult to capture the coordinated degradation characteristics of multiple fault types, which can easily lead to missed or false diagnoses. Moreover, existing methods mostly use static weight models (such as fixed weight coefficients for vibration, acoustic emission, and temperature characteristics), which cannot adapt to the fluctuations in operating conditions (such as load changes and differences in ambient temperature and humidity) or the shift in feature distribution caused by aging during long-term operation of equipment, resulting in decreased detection accuracy after long-term use. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a production line fault inspection method based on a regional attention learning mechanism.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] This application discloses a production line fault inspection method based on a region attention learning mechanism, comprising the following steps:

[0007] Simultaneously acquire low-frequency vibration signals, high-frequency acoustic emission signals, and temperature timing signals from rotating equipment on the production line;

[0008] The low-frequency vibration signal is decomposed into frequency bands to obtain vibration feature vectors; the high-frequency acoustic emission signal is analyzed by pulse density to obtain acoustic emission feature vectors; and the temperature time series signal is processed to extract the absolute value of temperature change acceleration.

[0009] Acquire historical data on the health status of similar devices, and construct a collaborative degradation factor calculation model based on the historical data;

[0010] The vibration characteristic vector, acoustic emission characteristic vector, and absolute value of temperature change acceleration are input into the collaborative degradation factor calculation model to obtain the collaborative degradation factor.

[0011] Determine whether the collaborative degradation factor exceeds the preset warning threshold; if so, trigger a fault alarm command.

[0012] Acquire low-frequency vibration signals, high-frequency acoustic emission signals, and temperature timing data after the staff performs maintenance according to the fault alarm command;

[0013] The synergistic degradation factor was recalculated based on the newly acquired low-frequency vibration signal, high-frequency acoustic emission signal, and temperature time series data, and the rate of decrease of the synergistic degradation factor before and after maintenance was calculated.

[0014] Determine whether the rate of decline of the synergistic degradation factor is lower than a preset decline threshold. If so, adjust the model parameters of the synergistic degradation factor calculation model, and recalculate the rate of decline of the synergistic degradation factor based on the adjusted model parameters until the rate of decline exceeds the preset decline threshold, triggering the model optimization completion instruction.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] 1. By covering the three core physical characteristics of the equipment—mechanical vibration (reflecting bearing wear), acoustic emission (reflecting shaft misalignment), and thermal effects (reflecting abnormal heat dissipation)—it solves the problem that traditional single-signal detection (such as vibration only or temperature only) cannot cover complex faults.

[0017] 2. By quantifying and integrating the vibration cycle change rate, the monthly average offset of acoustic emission, and the absolute value of temperature change acceleration, a multi-dimensional assessment of short-term anomalies, long-term degradation, and thermal effect coupling of equipment is achieved.

[0018] 3. To address the shift in fault characteristics caused by equipment aging, environmental changes, or load fluctuations, a dynamic adjustment mechanism for weighting coefficients is used to ensure the accuracy of test results and maintain the precision of test results after long-term use. Attached Figure Description

[0019] The disclosure of this invention is illustrated with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. In the drawings, the same reference numerals are used to refer to the same parts. Wherein:

[0020] Figure 1 This is a flowchart of the method of the present invention;

[0021] Figure 2 This is a data flow diagram of the present invention. Detailed Implementation

[0022] It is readily understood that, based on the technical solution of this invention, those skilled in the art can propose various interchangeable structural methods and implementations without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention.

[0023] Application Overview

[0024] In traditional production line rotating equipment fault detection, single-signal detection techniques struggle to effectively capture multiple types of complex degradation characteristics. Vibration signal analysis focuses on monitoring wear of mechanical components, while temperature signals reflect changes in thermal effects. However, these two exhibit a non-linear correlation in scenarios where bearing wear and shaft misalignment coexist, making it impossible for single-signal detection models to accurately identify complex fault modes. Static weighted models cannot adapt to feature distribution shifts caused by load fluctuations during long-term equipment operation. For example, under high-load conditions, the correlation between vibration energy baseline drift and temperature change rate changes, resulting in a mismatch between weighting coefficients and current operating conditions. Consequently, fault detection accuracy decreases with prolonged operation.

[0025] For example, in a combined fault scenario involving motor bearing wear and cooling system performance degradation, vibration signal energy increases significantly in the initial deterioration stage, while the acceleration due to temperature change exhibits a lag response due to cooling delay. A single vibration detection model triggers an early warning before the temperature anomaly reaches the threshold, even though the actual equipment remains in a safe state, leading to an increased false alarm rate. Simultaneously, seasonal changes in ambient temperature cause fluctuations in the temperature signal baseline. The static weighted model overemphasizes the contribution of temperature characteristics under high-temperature summer conditions, masking subtle early wear features in the vibration signal and causing missed detections.

[0026] If the above problems are not addressed, false alarms and missed detections under combined fault modes will increase the frequency of unplanned downtime and raise maintenance costs. Static weighted models cannot dynamically adapt to changes in operating conditions; their detection accuracy continuously declines after long-term operation, reducing the reliability of equipment health status assessment and increasing the risk of sudden failures. In complex degradation scenarios involving the coupling of multiple physical quantities, traditional methods struggle to establish cross-modal feature correlations, affecting the accuracy of fault root cause localization, delaying the timeliness of maintenance decisions, and ultimately leading to accelerated equipment performance degradation and shortened service life.

[0027] To address the aforementioned challenges, this application first considers how to capture complex degradation characteristics through multi-source signal fusion. Traditional single-signal detection struggles to correlate the nonlinear relationship between vibration, acoustic emission, and temperature, leading to false alarms and missed detections. To resolve this, this application attempts to simultaneously acquire low-frequency vibration, high-frequency acoustic emission, and temperature time-series signals. Multi-dimensional feature vectors are extracted through frequency band decomposition, pulse density analysis, and acceleration calculation to construct cross-modal feature correlations. To address the inability of static weighted models to adapt to fluctuating operating conditions, this application introduces a maintenance feedback mechanism. After each maintenance, the feature contribution is reassessed, and weight coefficients are dynamically adjusted to ensure the model continuously matches the current equipment state. Furthermore, considering the differences in response delays of different signals in complex faults, this application proposes establishing a collaborative degradation factor benchmark based on historical health data. The overall degradation degree is quantified through weighted calculation, and a dual judgment mechanism of warning threshold and degradation rate is combined to achieve closed-loop optimization of fault detection and maintenance effectiveness verification.

[0028] In this regard, such as Figure 1 As shown, this application proposes a production line fault inspection method based on a region attention learning mechanism, including the following steps:

[0029] Simultaneously acquire low-frequency vibration signals, high-frequency acoustic emission signals, and temperature timing signals from rotating equipment on the production line;

[0030] Low-frequency vibration signals, high-frequency acoustic emission signals, and temperature time-series signals can establish a complete monitoring chain for equipment, from microscopic damage (high-frequency acoustic emission signals) to macroscopic dynamics (low-frequency vibration signals) to system thermodynamics (temperature time-series signals). High-frequency acoustic emission signals capture microscopic fracture sounds within materials, low-frequency vibration signals record the vital signs of mechanical structures, and temperature time-series signals monitor the system's energy metabolism. This combination achieves full life-cycle coverage of equipment health at a reasonable cost, avoiding early fault detection (advantage of acoustic emission) and identifying complex fault modes (multi-signal correlation). Simultaneously, temperature signals provide a safety net, making it the optimal solution for predictive maintenance of industrial equipment. Low-frequency vibration signals refer to the fundamental physical quantities used to monitor the mechanical vibration state of rotating equipment on production lines. Specifically, they can be achieved by using accelerometers to collect vibration signals from the equipment casing surface. The frequency range is typically set to 0-10kHz to cover typical mechanical fault characteristics such as bearing wear and shaft misalignment. High-frequency acoustic emission signals refer to dynamic stress wave signals that reflect damage to the internal microstructure of equipment. Specifically, they can be achieved by using resonant acoustic emission sensors to acquire signals in the 100kHz-1MHz frequency band, enabling the capture of transient events such as bearing crack propagation and lubrication failure. Temperature time-series signals refer to time-series data that continuously records temperature changes in key parts of the equipment. Specifically, they can be achieved using infrared thermometers or embedded thermocouples, and are used to monitor the thermal state of the equipment during operation.

[0031] The low-frequency vibration signal is decomposed into frequency bands to obtain a vibration feature vector; the high-frequency acoustic emission signal is analyzed by pulse density to obtain an acoustic emission feature vector; the temperature time-series signal is processed to extract the absolute value of temperature change acceleration. The vibration feature vector is a multi-dimensional feature set characterizing the vibration state of the equipment. Specifically, wavelet packet decomposition technology can be used to analyze the frequency band energy of the low-frequency vibration signal, extracting the energy proportion of each sub-frequency band to form a feature vector, which is used to quantify the degree of mechanical degradation of the equipment. The acoustic emission feature vector is a characteristic index characterizing the internal damage activity of the equipment. Specifically, pulse density statistics can be used to calculate the number of acoustic emission events exceeding a threshold per unit time, forming a feature vector reflecting the damage activity. The absolute value of temperature change acceleration refers to the absolute value of the second derivative of the temperature time-series signal. Specifically, the least squares method can be used to fit the temperature time-series curve and extract the quadratic coefficient, which is used to quantify the abnormal temperature rise rate of the equipment.

[0032] Historical data of similar equipment under healthy conditions are obtained, and a collaborative degradation factor calculation model is constructed based on the historical data. The collaborative degradation factor calculation model refers to a mathematical model that integrates multi-source signal features to evaluate the overall degradation degree of the equipment. Specifically, the gradient descent method can be used to optimize the weight coefficients of vibration, acoustic emission, and temperature features. Through weighted calculation, the multi-dimensional degradation coupling effect of mechanical damage, microcracks, thermal anomalies, etc. is comprehensively reflected.

[0033] The vibration characteristic vector, acoustic emission characteristic vector, and absolute value of temperature change acceleration are input into the collaborative degradation factor calculation model, and the collaborative degradation factor is obtained after weighted calculation.

[0034] Determine whether the collaborative degradation factor exceeds the preset warning threshold. If so, generate a fault alarm command. The preset warning threshold refers to the critical value of the degradation factor that triggers the fault alarm. Specifically, it can be calculated using historical data statistical methods to determine the upper limit of the distribution of degradation factors of healthy equipment, which is used to distinguish between normal fluctuations and abnormal degradation states.

[0035] Reacquire the low-frequency vibration signal, high-frequency acoustic emission signal, and temperature timing data after the staff performed maintenance according to the fault alarm command;

[0036] The synergistic degradation factor was recalculated based on the newly acquired low-frequency vibration signal, high-frequency acoustic emission signal, and temperature time series data, and the rate of decrease of the synergistic degradation factor before and after maintenance was calculated.

[0037] The system determines whether the rate of decline of the synergistic degradation factor is lower than a preset threshold. If so, it adjusts the weighting coefficients in the weighted calculation of the synergistic degradation factor and recalculates the rate of decline based on the adjusted weighting coefficients until the rate of decline exceeds the preset threshold. Post-maintenance data recalculation refers to a data closed-loop mechanism for verifying maintenance effectiveness. Specifically, it assesses maintenance effectiveness by comparing the rate of decline of degradation factors before and after maintenance, providing feedback for dynamically adjusting the weighting coefficients. Weighting coefficient adjustment refers to an adaptive process of optimizing feature weights based on maintenance effectiveness. Specifically, it employs an incremental learning algorithm to prioritize adjusting the acoustic emission feature weights, addressing the problem that traditional static weighting models cannot adapt to shifting operating conditions.

[0038] The core innovation of this application lies in constructing a multi-source signal collaborative degradation assessment system. By fusing the time-frequency characteristics of vibration, acoustic emission, and temperature signals, it breaks through the bottleneck of single-signal detection in identifying complex faults. It establishes a dynamic weight adjustment mechanism, iteratively optimizing feature weights based on maintenance effect feedback, overcoming the performance degradation problem of static models in long-term operation. It forms a closed-loop control process of detection-maintenance-verification, and quantitatively assesses the maintenance effectiveness through the degradation factor decline rate, realizing the self-optimization capability of the fault diagnosis system.

[0039] like Figure 2 The diagram shown is a data flow chart of this application; as a preferred embodiment, the solution of this application is specifically implemented as follows:

[0040] On a production line in a factory, a rotating piece of equipment was selected as the monitoring object. Vibration sensors, acoustic emission sensors, and temperature sensors were installed on this equipment to collect low-frequency vibration signals, high-frequency acoustic emission signals, and temperature time-series signals, respectively. The sampling frequencies were set to 1 kHz for the vibration signal, 100 kHz for the acoustic emission signal, and 1 Hz for the temperature signal.

[0041] The acquired low-frequency vibration signal was decomposed into 8 frequency bands using wavelet packet decomposition. The energy value of each frequency band was calculated, and the band with the highest energy value was selected as the vibration feature vector. The high-frequency acoustic emission signal was divided into time windows, with each time window being 1 ms in length. The pulse density within each time window was calculated, and the average density of the 10 time windows with the highest density values ​​was selected as the acoustic emission feature vector. The temperature time series signal was fitted with a quadratic curve, and the absolute value of the coefficient of the quadratic term was extracted as the absolute value of the temperature change acceleration.

[0042] Data on this type of equipment under normal operating conditions was extracted from historical databases, and this data was used to train a collaborative degradation factor calculation model. The model adopted a weighted summation method, with initial weights set to 0.4 for vibration characteristics, 0.4 for acoustic emission characteristics, and 0.2 for temperature characteristics.

[0043] The acquired vibration feature vector, acoustic emission feature vector, and absolute value of temperature change acceleration are input into the model to calculate the co-deterioration factor. A warning threshold of 0.8 is set; when the co-deterioration factor exceeds 0.8, the system issues a fault alarm command.

[0044] Maintenance personnel inspect and maintain the equipment according to the alarm commands. After maintenance, signals are re-acquired and the co-deterioration factor is calculated. The rate of decrease in the co-deterioration factor before and after maintenance is calculated, and an expected decrease rate threshold of 30% is set.

[0045] If the actual decrease rate is less than 30%, adjust the model weights. First, reduce the weight of acoustic emission features by 0.05 each time until it reaches 0.6 or the decrease rate meets the requirement. If it still does not meet the requirement, reduce the weight of vibration features by 0.05 each time until it reaches 0.7 or the decrease rate meets the requirement.

[0046] Through the above-described scheme, this application achieves effective detection of complex faults in rotating production line equipment. By simultaneously acquiring multi-source signals and extracting features, multi-dimensional operational status information of the equipment is captured, overcoming the limitation of single-signal detection being insufficient to identify complex faults. A collaborative degradation factor calculation model built based on historical health data enables a quantitative assessment of the overall degradation level of the equipment, improving the accuracy of fault early warning. The introduced maintenance feedback mechanism and dynamic weight adjustment method allow the detection model to continuously adapt to changes in equipment status and operating conditions, solving the problem of decreased detection accuracy after long-term use of static weight models. Through dual judgment of early warning threshold and degradation rate, a closed-loop optimization of fault detection and maintenance effectiveness verification is achieved, improving the targeting and effectiveness of equipment maintenance. This method significantly reduces the false alarm and false negative rates in complex fault scenarios, effectively reducing unplanned downtime and improving equipment reliability and production efficiency.

[0047] This application further proposes the following steps for calculating the synergistic degradation factor:

[0048] Calculate the periodic rate of change ΔEv of the vibration eigenvector Ev:

[0049] ΔEv=(Ev current -Ev weekago ) / Ev weekago ;

[0050] In the formula, Ev current Ev is the current weighted vibrational energy value. weekago This represents the vibration energy value under the same working conditions 7 days prior.

[0051] Calculate the monthly average offset ΔDa of the acoustic emission eigenvector Da:

[0052]

[0053] In the formula, Da current This is the acoustic emission feature vector for the current day. This represents the monthly average value of the acoustic emission feature vector for that month.

[0054] Weighted calculation yields the Co-deterioration factor (CDF):

[0055] CDF=α·ΔEv+β·ΔDa+γ·|ΔT′|;

[0056] In the formula, |ΔT'| is the absolute value of the acceleration due to temperature change, and α, β, and γ are the weight values ​​configured in the synergistic degradation factor calculation model.

[0057] Among them, the calculation of the week-on-week change rate ΔEv captures short-term abnormal fluctuations in vibration energy by comparing current and historical data under the same working conditions; the calculation of the monthly average deviation ΔDa identifies long-term trend deviations in acoustic emission characteristics by comparing daily data with the monthly average; the weighting coefficients α, β, and γ are pre-configured in the model and correspond to the contribution of vibration, acoustic emission, and temperature characteristics, respectively.

[0058] Specifically, when calculating the week-on-week rate of change, it is necessary to ensure that the data from 7 days ago is consistent with the current operating conditions to avoid errors introduced by differences in load or environment. The calculation of the monthly average offset should be based on the complete data of the current month, and the monthly average should be updated using the moving average method to reflect real-time changes. During the weighted calculation process, the weight coefficients of the vibration feature vector and the acoustic emission feature vector are dynamically adjusted according to the model configuration. For example, when the equipment is under high load conditions, the vibration weight coefficient can be increased to 0.4, and the acoustic emission weight coefficient can be decreased to 0.4. The absolute value of temperature change acceleration is used as a supplementary indicator, and its weight coefficient remains fixed or is finely adjusted according to preset rules. Through the above steps, the synergistic degradation factor can comprehensively characterize the degree of degradation of multiple signal features, and the configurability of the weight coefficients enhances the model's adaptability to different operating conditions.

[0059] Through the above technical solution, this application achieves comprehensive analysis of multiple signals from rotating equipment on a production line. By calculating the week-on-week rate of change of the vibration characteristic vector, the short-term trend of the equipment's vibration state is captured. By calculating the monthly average offset of the acoustic emission characteristic vector, the medium-term changes in the equipment's acoustic emission characteristics are reflected. Combined with the absolute value of temperature change acceleration, the health status of the equipment is comprehensively assessed. The weighted calculation of the synergistic degradation factor comprehensively considers information from three dimensions: vibration, acoustic emission, and temperature, improving the accuracy and reliability of fault detection. Furthermore, by configuring different signal weight values ​​in the synergistic degradation factor calculation model, this method possesses good adaptability and flexibility, and can be optimized and adjusted according to the characteristics of different types of equipment.

[0060] This application further proposes:

[0061] The weighting coefficients for adjusting the weighted calculation of the co-deterioration factor include:

[0062] Prioritize reducing the weight coefficient β of the acoustic emission eigenvector; the update formula is as follows:

[0063] β'=max(β-η·(δ th -δ),0.4);

[0064] When reducing β to the lower limit is still ineffective, the weighting coefficient α of the vibration eigenvector is reduced, and the update formula is:

[0065] α'=max(α-η·(δ th -δ),0.7);

[0066] In the formula, δ represents the rate of decrease of the synergistic degradation factor. th η is the preset descent threshold, and η is the configurable learning rate.

[0067] The weight adjustment process employs a phased strategy. First, the weight coefficient β of the acoustic emission feature vector is reduced, with a lower limit set at 0.4. If this adjustment still fails to meet the reduction rate requirement, the vibration feature vector is then reduced, with a lower limit set at 0.7. A configurable learning rate η controls the weight adjustment amplitude, with a range limited to 0.01–0.1, dynamically optimized using historical adjustment data. δ is introduced into the weight coefficient update formula. th -δ is used as an adjustment variable to correlate the magnitude of weight adjustment with the degree of deviation from the actual maintenance effect.

[0068] Acoustic emission eigenvectors can directly reflect microscopic energy release events within materials (such as crack initiation and fracture of friction micro-protrusions). These events can generate high-frequency elastic waves in the early stages of a fault, while the vibration signal may not yet show significant amplitude changes at this time. The high-frequency characteristics of acoustic emission eigenvectors make them easy to separate from mechanical vibration noise in the frequency domain. Pure fault features can be effectively extracted through high-pass filtering or wavelet packet decomposition. In contrast, vibration signals are easily affected by the equipment's fundamental frequency and harmonics, and early fault features are easily submerged. Vibration signals reflect the overall dynamic response of the equipment (such as imbalance, misalignment, loosening, etc.), but are not sensitive to local minor damage; significant vibration energy is only generated when the fault develops to a certain scale. Therefore, the weighting coefficients of the acoustic emission eigenvectors are adjusted first, followed by the weighting coefficients of the vibration eigenvectors. The essence of this adjustment method is a dynamic balance of fault sensitivity.

[0069] Early warning can be achieved by leveraging the sensitivity of acoustic emission to microscopic damage.

[0070] False alarms caused by oversensitivity can be suppressed by adjusting the weights.

[0071] While ensuring that no macroscopic faults are overlooked, the system's ability to detect minor faults is restored.

[0072] Specifically, when the rate of decrease in the co-deterioration factor fails to meet the target after maintenance operations, the reduction value of the acoustic emission eigenvector weight coefficients is calculated first. The reduction value is determined by the learning rate η and the deviation of the degradation rate δ. th The product of -δ is determined; for example, when the descent rate deviation is 0.1 and the learning rate η is 0.05, the weight coefficient is reduced by 0.005. If the updated acoustic emission weights still cannot meet the requirements even at the lower limit of 0.4, the vibration feature vector weight adjustment is initiated, using the same calculation logic but setting a different lower limit value of 0.7. This phased adjustment mechanism optimizes the model's response sensitivity to different fault characteristics by prioritizing the adjustment of acoustic emission features sensitive to pulse density, followed by the adjustment of vibration features sensitive to energy changes. For example, in the early wear stage of bearings, prioritizing the reduction of acoustic emission weight β can improve the detection capability of microcracks; while when shaft misalignment worsens, reducing vibration weight α can more effectively reflect abnormal energy fluctuations.

[0073] For example, the configurable learning rate η is initially set to 0.05, and the preset descent threshold δ is... th Set it to 0.3.

[0074] The current weight coefficient of the acoustic emission eigenvector β is 0.2, and the decrease rate of the co-degradation factor CDF is 0.1. Therefore, the weight coefficient of the updated acoustic emission eigenvector is:

[0075] max[0.2-0.05*(0.3-0.1),0.4]=0.4.

[0076] If reducing the weight coefficient of the acoustic emission eigenvector to the lower limit of 0.4 is still ineffective, reduce the weight coefficient α of the vibration eigenvector.

[0077] For example, if the current weight coefficient α of the vibration eigenvector is 0.5 and the decrease rate of the co-deterioration factor CDF is 0.15, then the weight coefficient of the updated vibration eigenvector is:

[0078] max[0.5+0.05*(0.3-0.15),0.7]=0.7.

[0079] Therefore, by dynamically adjusting the weighting coefficients of acoustic emission and vibration eigenvectors, the calculation of the co-deterioration factor becomes more flexible and accurate.

[0080] Through the above technical solution, this application can dynamically adjust feature weights based on actual maintenance results, thereby improving the calculation accuracy of the co-deterioration factor. Specifically, prioritizing the reduction of the weight coefficient of the acoustic emission feature vector can more sensitively capture early minor faults in the equipment; when the acoustic emission features are insufficient to reflect the fault, the weight of the vibration feature vector is further reduced to comprehensively assess the equipment status. This adaptive weight adjustment mechanism overcomes the limitations of the fixed weight model, making the fault detection results more closely match the actual equipment status and improving the accuracy and reliability of production line fault detection.

[0081] This application further proposes:

[0082] When there are 3 consecutive maintenance cycles, δ < 0.5δ th When this occurs, temperature weighting correction is initiated, and the correction formula is as follows:

[0083] γ'=γ-λ·|ΔT'-ΔT ref |;

[0084] In the formula, λ is a configurable attenuation factor, and ΔT ref This serves as a benchmark value for the acceleration of temperature change in similar devices under healthy conditions.

[0085] The trigger condition for temperature weight correction is that the rate of decrease δ does not reach the preset threshold δ after three consecutive maintenance cycles. th Half of the value is used to determine whether intervention in the temperature parameter is needed by statistically analyzing the relationship between the number of maintenance visits and the rate of decline. In the correction formula, the attenuation factor λ controls the weight adjustment range to prevent over-adjustment; the temperature change acceleration reference value ΔT... ref Historical data from similar equipment under healthy conditions is used to ensure that the correction direction is aligned with the equipment's normal operating condition. The absolute value of temperature change acceleration ΔT' is compared to the baseline value ΔT. ref The difference reflects the degree to which the current temperature characteristics deviate from a healthy state; the larger the difference, the greater the weight adjustment.

[0086] Compared to the weighting coefficients α of the vibration characteristic vector and β of the acoustic emission characteristic vector, the temperature weight γ is adjusted after certain preconditions are met because the temperature signal has a certain lag, and equipment temperature changes need to be transmitted through physical processes such as metal heat conduction and convection heat dissipation. Furthermore, the impact of ambient temperature fluctuations (such as diurnal temperature difference and seasonal changes) on the temperature signal is much greater than that on the vibration / acoustic emission signal, and directly adjusting the weights can easily lead to misjudgments. At the same time, temperature anomalies are usually secondary effects of mechanical faults (such as bearing wear → increased friction → temperature rise), and adjusting the temperature weights may mask the true root cause of the fault. Therefore, the weighting coefficients α of the vibration characteristic vector and β of the acoustic emission characteristic vector are adjusted first to avoid affecting the determination of the true cause of the fault by adjusting the temperature weight γ.

[0087] For example: Set the configurable attenuation factor λ to 0.01. Assuming the temperature weight γ before the update is 0.2, the temperature change acceleration benchmark value ΔT for similar devices in a healthy state is... ref 0.5℃ / h 2 The current absolute value of the acceleration due to temperature change, ΔT', is 0.8℃ / h. 2 The updated temperature weights are calculated as follows:

[0088] 0.2 - 0.01 * (0.8 - 0.5) = 0.197.

[0089] Therefore, the temperature weight was appropriately reduced, thereby decreasing the impact of temperature changes on the calculation of the co-deterioration factor.

[0090] Through the above technical solution, this application can adjust the calculation model of the synergistic degradation factor by modifying the temperature weight, even when the rate of decline of the synergistic degradation factor remains low after multiple consecutive maintenance. This dynamic adjustment mechanism improves the adaptability of the fault detection model to changes in operating conditions during long-term equipment operation, avoids misjudgments caused by temperature changes, and thus improves the accuracy and reliability of production line fault detection.

[0091] This application further proposes a method for setting a configurable learning rate, including:

[0092] Statistical analysis of the historical successful adjustment count N and the total number of adjustments M;

[0093] Update according to the formula:

[0094] η'=η0·(1+log 10 (N / M));

[0095] In the formula, η0 is the initial learning rate, and the value range of constraint η' is (0.01, 0.1).

[0096] Among them, the historical number of successful adjustments N and the total number of adjustments M are used to quantify the historical experience of the learning rate adjustment effect; the update formula introduces a logarithmic function to balance the impact of the historical adjustment success rate on the learning rate, avoiding sudden changes in the learning rate η due to too few adjustments; the constraint range prevents the learning rate η from exceeding the reasonable range, ensuring the stability of the weight coefficient adjustment process.

[0097] For example, if the initial learning rate η0 is 0.05 and the historical adjustment success rate is 60%, then the updated learning rate is:

[0098] 0.05*[1+lg(0.6)]=0.039, falling within the range of 0.01~0.1. This dynamic adjustment mechanism allows the learning rate to adapt to changes based on historical adjustment effects: when the success rate is high, the learning rate η is appropriately increased to accelerate convergence; when the success rate is low, the learning rate η is decreased to avoid oscillations in the weight coefficients. Therefore, during long-term operation of the equipment, the learning rate η can automatically optimize with changes in operating conditions, improving the efficiency and stability of weight coefficient adjustment and avoiding the unreliability caused by repeated manual adjustments.

[0099] By setting a range of values, the learning rate η is prevented from being too large or too small, ensuring the stability and effectiveness of the weight adjustment process. This adaptive mechanism improves the adaptability of the collaborative degradation factor calculation model to different equipment and operating conditions, enhancing the accuracy and reliability of fault detection.

[0100] This application further proposes a method for setting a preset descent threshold, including:

[0101] The mean μ and standard deviation σ of the decline rate of the Co-deterioration factor CDF in historical maintenance records were statistically analyzed.

[0102] Calculate the preset descent threshold δ using the following formula:

[0103] δ = max(0.25, μ-2σ).

[0104] The degradation rate data in historical maintenance records is accumulated through long-term maintenance operations and covers the actual maintenance effects under different equipment conditions and operating conditions. The mean degradation rate μ reflects the average improvement of the synergistic degradation factor (CDF) by maintenance operations, and the standard deviation σ characterizes the dispersion of the degradation rate data.

[0105] δ = max(0.25, μ-2σ) calculates the lower limit of the threshold by combining the mean of the decline rate μ and the standard deviation σ, ensuring that the threshold is not lower than the benchmark value of 0.25, avoiding the threshold being too low due to data fluctuations, and preventing the threshold from being excessively reduced when the mean decline rate is too low due to equipment aging or abnormal operating conditions.

[0106] For example, when the mean rate of decline is 0.4 and the standard deviation is 0.1, 0.4 - 2 * 0.1 = 0.2, and 0.25 is taken as the final threshold.

[0107] This threshold setting method ensures that the triggering conditions for weight adjustments after maintenance are neither too lenient nor too strict, balancing the timeliness and accuracy of maintenance operations.

[0108] Through the above technical solution, this application can dynamically adjust the preset threshold for descent based on historical maintenance data, improving the rationality and adaptability of the threshold setting. This avoids misjudgments that may result from manually fixing the threshold, while also considering the long-term changing trends of equipment operating status, making fault detection and maintenance effectiveness evaluation more accurate and reliable. Furthermore, by introducing statistical methods, the impact of outliers on threshold setting is reduced, improving the robustness of the system.

[0109] This application further proposes the following process for obtaining vibration feature vectors:

[0110] Wavelet packet decomposition is performed on the low-frequency vibration signal to obtain multiple sub-frequency band signals;

[0111] Calculate the daily energy change rate of each sub-band signal and select the sub-band with the largest change rate as the target sub-band;

[0112] The vibration feature vector is generated by multiplying the energy value of the target sub-frequency band by a preset weighting coefficient.

[0113] Among them, wavelet packet decomposition uses a multi-scale analysis method to decompose the low-frequency vibration signal into different frequency bands; the daily energy change rate is obtained by calculating the ratio of the current daily energy to the previous working day's energy; the target sub-frequency band selection is based on a dynamic sorting mechanism of energy change rate; and the preset weight coefficients are preset according to the sensitivity of different frequency bands to faults in historical data.

[0114] Specifically, the low-frequency vibration signal is divided into multiple sub-bands using wavelet packet decomposition, each covering a specific frequency range. For each sub-band, its daily energy change rate is calculated, reflecting the energy fluctuation of the equipment's operating status between adjacent working days. By comparing the daily energy change rates of all sub-bands, the sub-band with the largest change rate is selected as the target sub-band, corresponding to the frequency characteristic of the most significant current equipment degradation. The energy value of the target sub-band is multiplied by a preset weighting coefficient to generate a vibration feature vector. The weighting coefficient is determined by analyzing the correlation between energy changes in different frequency bands and fault occurrence in historical fault data. This method enhances the characterization ability of vibration features for early degradation by dynamically selecting the frequency band with the most significant energy changes, avoiding the feature omission problem that may occur with fixed frequency band decomposition.

[0115] As a preferred embodiment, the solution of this application is specifically implemented as follows:

[0116] Wavelet packet decomposition was performed on the low-frequency vibration signal to obtain multiple sub-frequency band signals. Specifically, the 0-1000Hz low-frequency vibration signal was decomposed into 32 sub-frequency band signals using the db4 wavelet basis with 5 levels of wavelet packet decomposition.

[0117] The daily energy change rate of each sub-band signal is calculated, and the sub-band with the largest change rate is selected as the target sub-band. Further, the average energy value of each sub-band signal over 24 hours is calculated and compared with the average energy value of the same period on the previous day to obtain the daily energy change rate. The sub-band with the largest daily energy change rate is then selected as the target sub-band.

[0118] The vibration feature vector is generated by multiplying the energy value of the target sub-frequency band by a preset weighting coefficient. The preset weighting coefficient can be set to 0.8, and the vibration feature vector is obtained by multiplying the energy value of the target sub-frequency band by this coefficient.

[0119] Through the above technical solution, this application can effectively extract the most sensitive frequency band features in low-frequency vibration signals and capture the vibration energy changes caused by equipment degradation. Multi-scale analysis of the vibration signal is achieved through wavelet packet decomposition, and selecting the sub-frequency band with the largest rate of change as the target sub-frequency band allows focusing on the most significant degradation features. Multiplying the energy value of the target sub-frequency band by a preset weighting coefficient highlights the contribution of key features. The resulting vibration feature vector accurately reflects the changes in the equipment's vibration state, providing reliable input for subsequent calculation of the collaborative degradation factor.

[0120] This application further proposes the following process for obtaining acoustic emission feature vectors:

[0121] The high-frequency acoustic emission signal is divided into multiple pulse sequences according to a time window;

[0122] Calculate the standard deviation of pulse density within each time window, and select the pulse cluster time period where the standard deviation exceeds a preset threshold;

[0123] The average density of the pulse cluster during the time period is used as the acoustic emission feature vector.

[0124] The length of the time window is a configurable parameter, ranging from 5 to 30 seconds, to accommodate the pulse signal periodicity characteristics of different devices. The standard deviation of pulse density is calculated by statistically analyzing the fluctuation in the number of pulses per unit time within each time window. Pulse clusters with a standard deviation exceeding a preset threshold indicate significant density changes within that period, potentially corresponding to abnormal equipment impact events. The density mean of pulse cluster periods is calculated by removing low-density noise periods and retaining the statistical mean of high-density pulse clusters, making the acoustic emission feature vector more focused on valid fault signals.

[0125] Specifically, the high-frequency acoustic emission signal is first divided into continuous time windows of fixed length, for example, every 10 seconds. The number of pulses per second is counted within each window, forming a pulse density sequence. The standard deviation of this sequence is calculated; if the standard deviation exceeds a preset threshold (e.g., 0.8), the window is determined to be a pulse cluster period. The density mean of all selected pulse cluster periods is calculated using a weighted average, where the weights can be dynamically adjusted based on the period length or density peak value. This method effectively suppresses background noise interference by screening for highly volatile periods and extracting their density mean, enabling the acoustic emission feature vector to reflect the sudden high-frequency energy release caused by internal equipment failures such as wear and cracks, thereby improving the detection sensitivity and anti-interference capability of the collaborative degradation factor calculation model.

[0126] Through the above technical solution, this application can effectively identify transient abnormal pulse clusters in high-frequency acoustic emission signals, eliminate conventional steady-state noise interference, and accurately capture sudden stress wave signals released by mechanical damage in equipment. This method enhances the sensitivity of acoustic emission feature vectors to local degradation features through dynamic segmentation and statistical screening mechanisms, thereby improving the ability of collaborative degradation factors to characterize complex faults and avoiding feature extraction bias caused by uneven pulse signal distribution.

[0127] This application further proposes the following process for extracting the absolute value of temperature change acceleration:

[0128] A quadratic curve is fitted to the temperature time series signal in hourly units;

[0129] The coefficients of the quadratic term of the conic section are extracted as the acceleration values ​​of temperature change, thus obtaining the absolute value of the acceleration of temperature change.

[0130] As a preferred embodiment, the solution of this application is implemented as follows: In the temperature time-series signal processing, the continuously collected temperature data of the production line equipment is divided into processing units by hour. Within each processing unit, the least squares method is used to perform a quadratic polynomial fitting on the temperature data points to obtain a form such as: T(t) = at 2 The equation for the curve is +bt+c. The absolute value of the quadratic coefficient 'a' is extracted as the acceleration of temperature change. When the temperature series shows an accelerating upward or downward trend, the absolute value of this coefficient will increase significantly. For example, in the scenario of abnormal bearing friction, the absolute value of the quadratic coefficient of the temperature curve may increase from 0.03℃ / h under normal operating conditions. 2 The temperature suddenly increased to 0.15℃ / h 2 The absolute value of the temperature change acceleration generated therefrom is input into the collaborative degradation factor calculation model for weighted calculation.

[0131] Through the above technical solution, this application effectively solves the technical deficiency of traditional temperature monitoring methods that only focus on the absolute value of temperature and ignore the dynamic characteristics of the changing trend. By mathematically representing the coefficient of the quadratic term, the acceleration characteristics of temperature changes can be accurately captured, avoiding misjudgments caused by slow fluctuations in ambient temperature. This technical approach makes the contribution of the temperature signal in the co-deterioration factor strongly correlated with the actual degree of equipment degradation, especially in the detection of abnormal thermal effects in the early stage of failure, significantly improving the characterization ability of complex fault characteristics.

[0132] This application further proposes a method for constructing a collaborative degradation factor calculation model based on historical data, including the following steps:

[0133] Acquire historical data on the health status of multiple devices of the same type;

[0134] Extract vibration feature vectors, acoustic emission feature vectors, and absolute values ​​of acceleration due to temperature change;

[0135] The weighting coefficients of vibration eigenvectors, acoustic emission eigenvectors, and absolute values ​​of temperature change acceleration in the model are optimized using the gradient descent method until the weighted co-deterioration factor approaches 0.

[0136] In this process, historical data acquisition must cover the entire lifecycle operation data of multiple devices in a healthy state to ensure data diversity; feature vector extraction must use the same algorithm as real-time detection to ensure the consistency of model input features; gradient descent method takes the minimization of the co-deterioration factor as the objective function, and adjusts the weight coefficients iteratively to make the model output approach the baseline value of the healthy state.

[0137] Specifically, the model first extracts vibration feature vectors, acoustic emission feature vectors, and absolute values ​​of temperature change acceleration from historical operating data of multiple similar devices, using these as training samples. Then, the weight coefficients of each feature are initialized, and the error between the output value of the co-deterioration factor under the current weights and the baseline value of the healthy state is calculated using a gradient descent algorithm. The weight coefficients are then updated based on backpropagation of the error. For example, if the initial weight coefficient of the vibration feature vector is 0.3, it may be adjusted to 0.28 during gradient descent to reduce the error. This process iterates until the weighted calculation result of the co-deterioration factor stably approaches 0, indicating that the model has learned the optimal weight combination of each feature under healthy conditions. The model established in this way can dynamically adapt to the differences in feature distribution among different devices, improving long-term detection accuracy.

[0138] As a preferred embodiment, the specific implementation of this application is as follows: In an industrial motor health status monitoring scenario, historical operating data of multiple motors of the same model are collected, including vibration signals, acoustic emission signals, and temperature time-series signals. First, wavelet packet decomposition is performed on the vibration signals to extract the target sub-frequency band with the largest daily energy change rate in each sub-frequency band as the vibration feature vector; the acoustic emission signals are segmented by time windows, and time periods with pulse density standard deviations exceeding a preset threshold are selected, and their density mean is calculated as the acoustic emission feature vector; the temperature signals are fitted with a quadratic curve, and the absolute value of the quadratic term coefficient is extracted as the temperature change acceleration feature. Subsequently, a collaborative degradation factor calculation model with initial weight coefficients of 0.33 is constructed. Based on the health status data, the weight coefficients are iteratively adjusted using the gradient descent method. In each iteration, the mean square error of the collaborative degradation factor under the current weights relative to zero is calculated, and the weight coefficients are updated by backpropagation until the mean square error of 100 consecutive iterations is less than 0.001 and the change amplitude of the weight coefficients is less than 0.005, at which point the optimization is terminated, and a stable model with a vibration weight of 0.28, an acoustic emission weight of 0.51, and a temperature weight of 0.21 is finally obtained.

[0139] Through the above technical solution, this application effectively solves the defect that the traditional static weight model cannot adapt to the long-term operating characteristics of equipment. Through the gradient optimization process of historical health data, the collaborative degradation factor is made to stably approach the zero value benchmark under normal operating conditions of the equipment, which significantly improves the robustness of multi-source signal fusion detection, avoids false alarms caused by operating condition fluctuations or sensor drift, and provides an adaptive weight configuration mechanism for individual differences of different equipment.

[0140] The technical scope of this invention is not limited to the content described above. Those skilled in the art can make various modifications and variations to the above embodiments without departing from the technical concept of this invention, and all such modifications and variations should fall within the protection scope of this invention.

Claims

1. A production line fault checking method based on a regional attention learning mechanism, characterized in that: The method comprises the following steps: Synchronously collecting low-frequency vibration signals, high-frequency acoustic emission signals and temperature time series signals of a production line rotating equipment; Band-decomposing the low-frequency vibration signals to obtain a vibration feature vector; and performing pulse density analysis on the high-frequency acoustic emission signals to obtain an acoustic emission feature vector; Performing data processing on the temperature time series signals to extract an absolute value of temperature change acceleration; Obtaining historical data of the same type of equipment in a healthy state, and constructing a collaborative degradation factor calculation model based on the historical data; Inputting the vibration feature vector, the acoustic emission feature vector and the absolute value of temperature change acceleration into the collaborative degradation factor calculation model to obtain a collaborative degradation factor; Judging whether the collaborative degradation factor exceeds a preset warning threshold, and triggering a fault alarm instruction if yes; Obtaining low-frequency vibration signals, high-frequency acoustic emission signals and temperature time series data after maintenance by a worker according to the fault alarm instruction; Recomputing the collaborative degradation factor according to the reobtained low-frequency vibration signals, high-frequency acoustic emission signals and temperature time series data, and calculating a decline rate of the collaborative degradation factor before and after maintenance; Judging whether the decline rate of the collaborative degradation factor is lower than a preset decline threshold, adjusting model parameters of the collaborative degradation factor calculation model if yes, recomputing the decline rate of the collaborative degradation factor based on the adjusted model parameters, and triggering a model optimization completion instruction until the decline rate exceeds the preset decline threshold. The collaborative degradation factor calculation model obtains a collaborative degradation factor, which comprises: Calculating a week-to-week change rate ΔEv of the vibration feature vector Ev: acquiring a current weighted vibration energy value Ev current , the vibration energy value Ev of the same working condition 7 days ago weekago ; Weekly change rate ΔEv = (Ev current - Ev weekago ) / Ev weekago ; Calculating a monthly average value offset ΔDa of the acoustic emission feature vector Da: Acquiring an acoustic emission feature vector Da of the current day current a monthly average of the acoustic emission feature vectors of the month a monthly average offset Obtaining the collaborative degradation factor CDF through weighted calculation: CDF = α·ΔEv + β·ΔDa + γ·|ΔT'|; In the formula, |ΔT'| is the absolute value of temperature change acceleration, and α, β and γ are weight values configured in the collaborative degradation factor calculation model.

2. The method of claim 1, wherein the method further comprises: The weight coefficients in the adjustment of the collaborative degradation factor weighted calculation comprise: The weight coefficient β of the acoustic emission feature vector is preferentially reduced, and the update formula is: β' = max(β - η - (δ th - δ), 0.4); When β is reduced to the lower limit and still ineffective, the weight coefficient α of the vibration feature vector is reduced, and the update formula is: a' = max(a - η-(δ th - δ), 0.7); In the formula, δ is the degradation rate of the synergy degradation factor, δ th is a preset degradation threshold, and η is a configurable learning rate.

3. The method of claim 2, wherein the method further comprises: The weight coefficients in the adjustment of the collaborative degradation factor weighted calculation further comprise: When maintaining for 3 times continuously, δ < 0.5δ th When the temperature weight correction is started, the correction formula is: Y' = Y - l • |AT' - AT ref |; where λ is a configurable attenuation factor, ΔT ref is the acceleration of temperature change of the same type of equipment in the healthy state. γ is a temperature weight configured for the absolute value of temperature change acceleration |ΔT'| in the collaborative degradation factor calculation model, and γ' is a corrected temperature weight.

4. The method of claim 2, wherein the method further comprises: The setting of the learning rate η comprises: Statistics of the number of historical adjustment successes N and the total number of adjustments M; Updating according to the formula: η' = η0- (1 + log 10 (N / M)); In the formula, η0 is an initial learning rate, and the value range of η' is constrained to be (0.01, 0.1).

5. The method of claim 1, wherein: The setting of the preset decline threshold comprises: Statistics of the mean value μ and the standard deviation σ of the decline rate of the collaborative degradation factor CDF in the historical maintenance records; Calculating the preset decline threshold δ according to the following formula: δ = max(0.25, μ - 2σ).

6. The method of claim 1, wherein: The obtaining process of the vibration feature vector comprises: Wavelet packet decomposing the low-frequency vibration signals to obtain a plurality of sub-band signals; Calculating the daily energy change rate of each sub-band signal, and selecting the sub-band with the largest change rate as a target sub-band; Multiply the energy value of the target sub-band by a preset weight coefficient to generate the vibration feature vector.

7. The method of claim 1, wherein: The process of obtaining the acoustic emission feature vector is: Divide the high-frequency acoustic emission signal into multiple pulse sequences according to time windows; Calculate the standard deviation of the pulse density in each time window, and select the pulse cluster period whose standard deviation exceeds a preset threshold; Take the density average of the pulse cluster period as the acoustic emission feature vector.

8. The method of claim 1, wherein: The process of extracting the absolute value of the temperature change acceleration is: Fit a quadratic curve of the temperature time series according to an hour unit; Extract the quadratic term coefficient of the quadratic curve as the temperature change acceleration value to obtain the absolute value of the temperature change acceleration.

9. The method of claim 1, wherein: The process of constructing the collaborative degradation factor calculation model based on historical data includes: Obtain historical data of multiple same-type devices in a healthy state; Extract the vibration feature vector, acoustic emission feature vector, and absolute value of the temperature change acceleration; Optimize the weight coefficients of the vibration feature vector, acoustic emission feature vector, and absolute value of the temperature change acceleration in the model through the gradient descent method until the collaborative degradation factor calculated by weighting approaches 0.

Citation Information

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