A method and system for vibration protection of rotating machinery based on adaptive resonant neural networks

Abstract

This invention discloses a method and system for vibration protection of rotating machinery using an adaptive resonant neural network. The method includes: acquiring millisecond-level vibration acceleration signals of the rotating machinery through a distributed piezoelectric sensor array to obtain real-time operating parameters of the equipment and generate a time-to-work synchronous vibration signal stream; inputting the time-to-work synchronous vibration signal stream into a resonant neural network and dynamically generating a frequency-domain-time-varying adaptive threshold group based on the operating parameters; extracting weak impact resonance feature tensors using the multi-scale resonance kernel of the resonant neural network; projecting the weak impact resonance feature tensors onto an orthogonal fault subspace using a tensor decomposition algorithm to separate a decoupled fault feature matrix; and generating a real-time protection decision instruction set based on the comparison results between the decoupled fault feature matrix and the equipment's historical operating database. Using this invention, the detection sensitivity and positioning accuracy of weak faults under unsteady operating conditions can be improved, achieving real-time adaptive optimization of vibration protection for rotating machinery.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence technology, specifically an adaptive resonant neural network-based method and system for protecting rotating machinery from vibration. Background Technology

[0002] Rotating machinery is widely used in industry, and its operating status directly affects production safety and efficiency. Traditional vibration protection methods are mostly based on fixed thresholds or static models, which are difficult to adapt to the complex vibration characteristics under unsteady conditions, leading to missed or false alarms of early faults. In existing technologies, although frequency domain analysis methods can identify some faults, they are insufficient in capturing weak impact characteristics and transient resonant modes, and lack adaptability to operating conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for vibration protection of rotating machinery based on an adaptive resonant neural network, in order to overcome the shortcomings of the prior art, improve the detection sensitivity and positioning accuracy of minor faults under unsteady conditions, and realize real-time adaptive optimization of vibration protection for rotating machinery.

[0004] One embodiment of this application provides a method for vibration protection of rotating machinery using an adaptive resonant neural network, the method comprising:

[0005] The millisecond-level vibration acceleration signal of rotating machinery is collected by a distributed piezoelectric sensor array, and the real-time operating parameters of the equipment are obtained to generate a time-work synchronous vibration signal stream.

[0006] The time-work synchronous vibration signal stream is input into a pre-trained resonant neural network, and frequency domain-time-varying adaptive threshold group is dynamically generated in combination with working condition parameters. The threshold group includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0007] Using the multi-scale resonant kernel of the resonant neural network, nonlinear feature decoupling is performed on the vibration signal flow to extract the weak impact resonance feature tensor. The tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions.

[0008] The weak impact resonance feature tensor is projected onto the orthogonal fault subspace using the tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the energy distribution of the resonance modes of a typical fault.

[0009] Based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0010] Optionally, the step of acquiring millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, simultaneously obtaining real-time operating parameters of the equipment, and generating a time-to-work synchronous vibration signal stream includes:

[0011] Based on the geometric characteristics of the bearing housing of rotating machinery, a piezoelectric sensor array is deployed on the surface of the equipment using a spatial symmetric point placement algorithm to generate a three-dimensional sensor coordinate mapping table;

[0012] Multi-channel synchronous acquisition is triggered based on a coordinate mapping table. The original vibration signal is acquired with a preset sampling period. The rotational speed and load parameters are read in real time through the industrial bus, and the original multi-source signal stream with timestamp is output.

[0013] The original multi-source signal stream is input into an adaptive noise complete set empirical mode decomposer, and the speed fluctuation noise is separated by the operating parameters to generate a noise-reduced signal stream with decoupled operating conditions.

[0014] The noise-reduced signal stream is dynamically resampled to synchronize with the rotational speed. The sampling interval is adjusted according to the instantaneous rotational speed to output a time-to-work strictly synchronized vibration signal stream.

[0015] Optionally, the step of inputting the time-to-work synchronous vibration signal stream into a pre-trained resonant neural network and dynamically generating a frequency-domain time-varying adaptive threshold set in combination with operating parameters, wherein the threshold set includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics with changes in rotational speed, including:

[0016] The time-work strictly synchronous vibration signal stream is input into the resonant neural network, and the joint features of speed-load are extracted through the working condition coding module, and the working condition state vector is output.

[0017] The historical fault database is retrieved using the operating condition state vector as an index. The resonant frequency band energy envelope of typical faults is generated by the spectral kurtosis energy focusing algorithm, and the fault energy envelope template set is output.

[0018] The fault energy envelope template set is input into the nonlinear autoregressive predictor, and the resonance energy threshold boundary is predicted by combining the rotational speed change rate. The initial frequency domain threshold surface is then output.

[0019] The threshold surface is dynamically compressed by a time-varying gain regulator of a neural network to generate a frequency-domain time-varying adaptive threshold set.

[0020] Optionally, the multi-scale resonant kernel of the resonant neural network is used to perform nonlinear feature decoupling on the vibration signal flow and extract a weak impact resonance feature tensor. The tensor includes the transient impact component, modulation sideband component, and resonance attenuation characteristics of early faults under unsteady conditions, including:

[0021] The time-to-work strictly synchronized vibration signal stream is divided into time windows of preset length, a multi-scale wavelet resonance kernel is input, and the resonance frequency band is activated by combining the frequency domain-time-varying adaptive threshold group, and the multi-scale resonance response spectrum is output.

[0022] A fourth-order cumulant transformation is performed on the multi-scale resonance response spectrum to enhance the phase consistency of transient impact and generate an impact enhancement spectrum.

[0023] Based on the impulse enhancement spectrum, the modulation sideband energy is integrated to calculate the energy percentage within ±5 octaves of the characteristic frequency, and the sideband energy distribution matrix is ​​output.

[0024] The resonance quality factor Q is calculated using an exponential decay model fitting algorithm, and a decay characteristic parameter vector is generated.

[0025] By stacking the impact enhancement spectrum, sideband energy distribution matrix, and attenuation characteristic parameter vector along the time dimension, a three-dimensional weak impact resonance feature tensor is constructed.

[0026] Optionally, the weak impact resonance feature tensor is projected onto the orthogonal fault subspace using a tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonant mode energy distribution of a typical fault, including:

[0027] Parallel factor decomposition of the three-dimensional weak impact resonance characteristic tensor is performed to obtain the core tensor and orthogonal factor matrix, and the decomposed core tensor is output.

[0028] Construct an orthogonal basis for the fault subspace based on the fault energy envelope template set, and project the core tensor onto the basis space to generate the fault projection core tensor.

[0029] For the fault projection core tensor, the Tucker3 compression model is used to reduce the order along the feature dimension, retaining the components whose variance contribution rate is greater than the preset contribution threshold, and outputting a simplified fault feature tensor.

[0030] The fault feature tensor is simplified by dividing it into time slices, and the L2 norm of each slice in the fault subspace is calculated to generate the fault energy distribution vector.

[0031] By integrating the fault energy distribution vectors of all time slices, a decoupled fault feature matrix is ​​constructed.

[0032] Optionally, based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set. The instruction set includes fault level assessment and fault type location information, including:

[0033] The decoupled fault feature matrix is ​​compared with the historical fault database. The similarity between each column vector and the corresponding historical fault is calculated by the dynamic time warping algorithm, and the fault matching degree vector is output.

[0034] Using the fault matching degree vector as a condition, an enhanced fault sample is synthesized through a conditional generative adversarial network to generate an adversarial training sample set.

[0035] The adversarial training sample set is injected into the resonant neural network, and the resonant kernel weights are updated using an online meta-learning strategy to output the optimized resonant kernel parameters.

[0036] The fault type is located based on the elements in the fault matching degree vector that exceed the preset matching threshold. The protection level is determined by combining the energy gradient, and a real-time protection decision instruction set containing fault level assessment and fault type location information is generated.

[0037] Another embodiment of this application provides a rotating machinery vibration protection system based on an adaptive resonant neural network, the system comprising:

[0038] The acquisition module is used to acquire millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and at the same time obtain the real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream.

[0039] The input module is used to input the time-work synchronous vibration signal stream into a pre-trained resonant neural network and dynamically generate a frequency domain-time-varying adaptive threshold group in combination with the working condition parameters. The threshold group includes the resonant frequency band energy limit under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0040] The decoupling module is used to decouple the vibration signal flow nonlinearly using the multi-scale resonant kernel of the resonant neural network and extract the weak impact resonant feature tensor, wherein the tensor includes the transient impact component, modulation sideband component and resonant attenuation characteristics of the early fault under unsteady conditions.

[0041] The separation module is used to project the weak impact resonance feature tensor onto the orthogonal fault subspace using a tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault.

[0042] The generation module is used to update the resonant kernel weights of the resonant neural network through an online adversarial training mechanism based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, and generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0043] Another embodiment of this application provides a storage medium storing a computer program, wherein the computer program is configured to execute the method described in any of the preceding claims when running.

[0044] Another embodiment of this application provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method described in any of the preceding claims.

[0045] Compared with existing technologies, this invention provides a rotating machinery vibration protection method based on an adaptive resonant neural network. It acquires millisecond-level vibration acceleration signals of the rotating machinery using a distributed piezoelectric sensor array, simultaneously obtaining real-time operating parameters to generate a time-to-work synchronous vibration signal stream. This time-to-work synchronous vibration signal stream is input into a pre-trained resonant neural network, which dynamically generates a frequency-domain time-varying adaptive threshold set based on the operating parameters. The multi-scale resonant kernel of the resonant neural network is used to extract weak impact resonance feature tensors. Tensor decomposition algorithms are used to project these weak impact resonance feature tensors onto an orthogonal fault subspace, separating a decoupled fault feature matrix. Based on the comparison between the decoupled fault feature matrix and the equipment's historical operating database, a real-time protection decision instruction set is generated. This improves the detection sensitivity and location accuracy of weak faults under unsteady conditions, achieving real-time adaptive optimization of rotating machinery vibration protection. Attached Figure Description

[0046] Figure 1 A hardware structure block diagram of a computer terminal for a rotating machinery vibration protection method based on an adaptive resonant neural network, provided in an embodiment of the present invention;

[0047] Figure 2 A flowchart illustrating a method for protecting rotating machinery using an adaptive resonant neural network, provided in an embodiment of the present invention.

[0048] Figure 3 This is a schematic diagram of the structure of an adaptive resonant neural network-based vibration protection system for rotating machinery, provided in an embodiment of the present invention. Detailed Implementation

[0049] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0050] This invention first provides a method for protecting rotating machinery from vibration using an adaptive resonant neural network. This method can be applied to electronic devices, such as computer terminals, specifically ordinary computers.

[0051] The following detailed explanation uses a computer terminal as an example. Figure 1This is a hardware structure block diagram of a computer terminal for a rotating machinery vibration protection method based on an adaptive resonant neural network, provided in an embodiment of the present invention. Figure 1 As shown, the computer device includes a processor, memory, and network interface connected via a system bus, wherein the memory may include non-volatile storage media and internal memory.

[0052] The non-volatile storage medium can store an operating system and a computer program. This computer program includes program instructions that, when executed, cause the processor to perform any adaptive resonant neural network-based method for protecting rotating machinery from vibration.

[0053] The processor provides computing and control capabilities, supporting the operation of the entire computer device.

[0054] The internal memory provides an environment for the execution of computer programs in non-volatile storage media. When the computer program is executed by the processor, it enables the processor to execute any adaptive resonant neural network method for protecting rotating machinery from vibration.

[0055] This network interface is used for network communication, such as sending assigned tasks. Those skilled in the art will understand that... Figure 1 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0056] It should be understood that the processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among these, a general-purpose processor can be a microprocessor or any conventional processor.

[0057] See Figure 2 The present invention provides a method for protecting rotating machinery from vibration using an adaptive resonant neural network, which may include the following steps:

[0058] S201 collects millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and simultaneously acquires real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream;

[0059] Specifically, based on the geometric characteristics of the bearing housing of rotating machinery, a spatial symmetric point placement algorithm can be used to deploy an array of piezoelectric sensors on the surface of the equipment to generate a three-dimensional sensor coordinate mapping table.

[0060] First, for the core vibration source of rotating machinery (such as steam turbines and centrifugal compressors)—the bearing housing—its physical structural characteristics need to be analyzed. Engineers obtain a precise geometric model of the bearing housing using a 3D laser scanner to identify key areas: the distribution surface of the bearing cap bolt holes, the mounting plane of the base, and the radial / axial force transmission paths. Based on this, a Spatial Symmetric Layout Algorithm (SSLA) is used to plan the sensor locations. This algorithm uses the centerline of the bearing housing as the axis of symmetry and calculates the optimal placement coordinates in force-sensitive areas (such as the four corners of the bearing cap and both sides of the centerline of the base), ensuring coverage of the detection blind spots for all vibration modes. For example, for a circular bearing cap with eight bolt holes, the algorithm generates eight evenly distributed points (45-degree angular intervals) and one center point, forming an "8+1" symmetrical array. Each placement coordinate includes three-dimensional values ​​of X (axial), Y (radial), and Z (vertical), with an accuracy of 0.1 millimeters (mm). All coordinate data is stored in a 3D SensorCoordinate Mapping Table (3D-SCMT), which records the unique ID of each sensor, the radius of curvature of the mounting surface, the normal vector (used to correct the measurement direction), and the offset relative to the bearing center.

[0061] During actual deployment, operators mark positioning points on the equipment surface according to the 3D-SCMT. A miniature piezoelectric sensor (PZT) is fixed using a high-temperature adhesive. Its core is a lead zirconate titanate (PZT-5H) piezoelectric ceramic sheet, approximately 10 mm × 10 mm × 2 mm in size, with a built-in charge amplifier (CA) to convert mechanical deformation into electrical signals. Each sensor is equipped with an electromagnetic shielding housing and connected to a central acquisition box via an armored cable. After deployment, a position verification process is performed: a portable vibration calibrator (such as a handheld vibrator) is used to apply a standard sinusoidal excitation (e.g., frequency 100 Hz, acceleration 1 m / s²) to a known location on the bearing housing, verifying whether the phase difference of each sensor's output signal matches the theoretical distance in the 3D-SCMT. If the deviation exceeds 5%, the position is readjusted and the mapping table is updated.

[0062] The core value of 3D-SCMT lies in providing a spatial reference for subsequent signal fusion. For example, when the signal amplitude difference between two sensors (such as ID01 and ID05) at diagonal positions on the bearing cap exceeds 20%, an off-center load fault can be identified; if high-frequency resonance occurs at the center point (ID09) while there is no response at the edge points, it suggests a local structural crack. The mapping table also associates sensor sensitivity coefficients (unit: picocoulombs per Newton pC / N) and temperature drift compensation parameters to ensure the comparability of data from different locations. The final generated 3D-SCMT is stored in JSON format for use by all subsequent modules.

[0063] Multi-channel synchronous acquisition is triggered based on a coordinate mapping table. The original vibration signal is acquired with a preset sampling period. The rotational speed and load parameters are read in real time through the industrial bus, and the original multi-source signal stream with timestamp is output.

[0064] The acquisition system uses a coordinate mapping table (3D-SCMT) as the trigger reference. The central acquisition box houses a multi-channel synchronous acquisition card (such as a 24-bit analog-to-digital converter), with each channel corresponding to a sensor ID. When the start command is issued, the acquisition card synchronously activates all channels according to the sensor serial number in the 3D-SCMT, based on a preset sampling period (Sampling Period, SP, typically 0.5 ms, corresponding to a sampling rate of 2000 Hz). The analog voltage signal (range ±10 volts V) output by the piezoelectric sensor is converted into a digital signal (resolution 0.1 mV) by the ADC after passing through an anti-aliasing filter (cutoff frequency 800 Hz). Simultaneously, the operating parameters of the equipment control system are read in real time via industrial bus (IB) such as PROFIBUS-DP (Process Field Bus-Decentralized Periphery) or EtherCAT (Ethernet for Control Automation Technology): rotational speed (RS, revolutions per minute rpm) is obtained from encoder pulse count, and load (LD, percentage %) is taken from the motor current transmitter. All data are bound to the same timestamp (Timestamp, TS, accuracy ±1 microsecond μs).

[0065] Synchronization assurance relies on hardware design: the acquisition card is equipped with a Complex Programmable Logic Device (CPLD), using a quartz crystal oscillator (frequency stability ±1 / 1 million ppm) as the clock source to generate a Global Sampling Pulse (GSP). The CPLD simultaneously monitors the Data Ready Signal (DRS) of the industrial bus. When the DRS is valid, it latches the current rotational speed and load value and associates them with the vibration signal frame at the same timestamp. For example, at a certain moment TS=163000000μs, channels 1-9 acquire 9 vibration waveforms (each channel with 1024 points), simultaneously recording RS=3000rpm and LD=80%. This data is packaged into a Raw Multi-source Signal Stream (RMSSS), with a data structure including timestamps, sensor ID arrays, vibration data matrices, and operating parameter structures.

[0066] To prevent data loss, a dual-buffering storage strategy is employed: the first second of data is temporarily stored in high-speed Static Random-Access Memory (SRAM), and then transferred to a Solid-State Drive (SSD). Real-time performance of RMSSS is achieved through a Circular Data Queue (CDQ), with a configurable queue depth (default 10 seconds). When the vibration protection system requests data, the CDQ outputs the latest data packet with a timestamp. Strict synchronization between operating parameters and vibration signals (deviation <10μs) is fundamental to subsequent time-operation synchronization analysis, such as accurately correlating speed fluctuations with vibration spectrum shifts.

[0067] The original multi-source signal stream is input into an adaptive noise complete set empirical mode decomposer, and the speed fluctuation noise is separated by the operating parameters to generate a noise-reduced signal stream with decoupled operating conditions.

[0068] The original multi-source signal stream (RMSSS) is first input to the Adaptive Noise Complete Ensemble Empirical Mode Decomposition (ANCEEMD). This decomposition algorithm is an improvement on Empirical Mode Decomposition (EMD), and its core steps are as follows:

[0069] Noise injection: Multiple sets of white Gaussian noise (WGN, with an amplitude of 20% of the signal standard deviation) are added to the original vibration signal.

[0070] Multi-round decomposition: Perform EMD on each noisy signal to decompose it into a set of Intrinsic Mode Functions (IMFs) representing different frequency components.

[0071] Ensemble averaging: Averaging IMFs with the same index to eliminate the influence of noise.

[0072] This process introduces a special operating condition parameter guidance mechanism: the theoretical frequency (RF = RS / 60 Hz) is calculated using the rotational speed (RS), and the components related to RF (such as the 1st to 5th harmonics of RF) are marked in the IMF screening.

[0073] Speed ​​fluctuation noise separation is a key innovation. The system extracts the instantaneous rotational speed curve (IRSC) from operating parameters and calculates the rotational speed rate (RSR, revolutions per square second in r / s²) through numerical differentiation. When the RSR exceeds a threshold (e.g., 50 r / s²), the equipment is determined to be in a transient acceleration / deceleration condition. At this time, ANCEEMD activates dynamic noise suppression mode.

[0074] During the IMF reconstruction phase, components associated with RF (labeled as "speed noise") are automatically removed.

[0075] Wavelet Threshold Denoising (WTD) was performed on the remaining IMFs, using the sym8 wavelet basis, and the threshold was adaptively adjusted according to the rotational speed fluctuation amplitude.

[0076] For example, when the rotational speed suddenly drops from 3000 rpm to 2500 rpm, the RF drops from 50 Hz to 41.67 Hz. The algorithm will reduce the IMF energy of the 50 ± 2 Hz frequency band to zero, while retaining the bearing fault characteristic frequency band (such as the outer ring fault frequency of 123 Hz).

[0077] Output a decoupled, denoised signal stream (OD-DSS). This stream retains the original timestamps, but the vibration data is replaced with the denoised waveforms. Verification example: During the startup phase of a wind turbine (speed 0→3600rpm), the fault impact in the original signal was overwhelmed by speed fluctuations (SNR = -5dB). After processing with ANCEEMD, the speed noise energy was reduced by 90%, and the fault impact SNR was improved to 15dB. The OD-DSS is stored in HDF5 format and includes the channel ID, timestamp, denoised waveform, and index of removed noise components (used for fault diagnosis backtracking).

[0078] The noise-reduced signal stream is dynamically resampled to synchronize with the rotational speed. The sampling interval is adjusted according to the instantaneous rotational speed to output a time-to-work strictly synchronized vibration signal stream.

[0079] Synchronous Dynamic Resampling (RSDR) aims to eliminate signal distortion under variable speed conditions. The system extracts a timestamp sequence from the noise-reduced signal stream (OD-DSS) and combines it with the instantaneous rotational speed (IRS) from the operating parameters to calculate the instantaneous rotation angle (IRA) corresponding to each sampling point. The calculation formula is: IRA_k = IRA_{k-1} + 2π × (IRS_k + IRS_{k-1}) × Δt / 120. Where Δt is the sampling interval (0.5ms), and IRS_k is the rotational speed (rpm) at point k. This formula converts equal-time interval sampling into equal-angle interval sampling (Angle-Domain Sampling, ADS).

[0080] The resampling process uses cubic spline interpolation (CSI):

[0081] Set the target angle interval (e.g., 0.5 degrees, corresponding to 720 points per revolution).

[0082] A mapping relationship between non-uniform time signals and uniform angle signals is established based on the IRA sequence.

[0083] The vibration amplitude is interpolated at the target angle point using the CSI algorithm.

[0084] For example, when the rotational speed is reduced from 3000 rpm to 2500 rpm, the signal at the original fixed sampling rate of 2000 Hz will exhibit spectral ambiguity; after resampling, with 720 points fixed per revolution, the bearing fault characteristic frequency (such as the outer ring fault frequency at 3.57 times the rotational frequency) maintains a constant spectral position in the angular domain.

[0085] Output a Time-Operation Strictly Synchronized Vibration Signal Stream (TOS-SVSS). This signal stream contains:

[0086] Angular domain waveform: Vibration data at equal angular intervals (0.5 degrees), with the length varying with rotational speed (each frame contains data from multiple rotations at high speeds).

[0087] Synchronization condition labels: absolute timestamp of the start point of each frame, average rotational speed, and load value.

[0088] Resampling metadata: Interpolation error estimate (typically <0.1%).

[0089] The final data is stored in a three-dimensional array of "time-angle-amplitude" to ensure that the fault characteristic frequency and rotational speed are strictly linearly related in subsequent analysis, thus overcoming the problem of spectrum leakage under variable speed conditions.

[0090] This method first achieves high-precision vibration signal acquisition through a spatially optimized piezoelectric sensor array. Combined with operating parameters such as rotational speed and load obtained from an industrial bus, signal processing techniques are used to eliminate interference from speed fluctuations, ultimately generating a multi-source signal stream that is strictly synchronized with the operating conditions. This synchronization mechanism ensures the timing accuracy of subsequent analysis, solving the problem of signal distortion caused by changes in operating conditions in traditional vibration monitoring, and providing high-fidelity input data for fault diagnosis. The time-operation synchronization characteristic allows the fault characteristics analyzed later to accurately correspond to the equipment's operating status.

[0091] S202, the time-work synchronous vibration signal stream is input into a pre-trained resonant neural network, and frequency domain-time-varying adaptive threshold group is dynamically generated in combination with working condition parameters. The threshold group includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0092] Specifically, the time-work strictly synchronous vibration signal stream can be input into the resonant neural network, and the joint features of speed and load can be extracted through the working condition coding module to output the working condition state vector;

[0093] Signal Stream Preprocessing and Operating Condition Feature Extraction

[0094] The Time-Work Synchronized Vibration SignalStream (TW-SVSS) contains millisecond-level vibration acceleration signals and real-time equipment operating parameters (such as rotational speed (RPM) and load percentage (LOAD_PCT)). This signal stream is first input into the Operating Condition Encoding Module (OCEM) of the resonant neural network. The OCEM has a built-in multi-layer feature fusion structure: the first layer uses a rotational speed-load joint encoder (RLJE) to normalize the rotational speed value (unit: revolutions per minute) and the load value (unit: percentage) to the 0-1 range (e.g., 5000 RPM is normalized to 0.5, and 80% load is normalized to 0.8). The second layer calculates the nonlinear interaction features between speed and load through a Condition Feature Cross Layer (CFCL), such as generating a joint feature factor J_FACTOR = (NORM_RPM * 0.7) + (NORM_LOAD * 0.3) + (NORM_RPM^2 * 0.2) (where NORM_RPM is the normalized speed and NORM_LOAD is the normalized load). The third layer uses a Temporal Sliding Window Integrator (TSWI) to perform a moving average on the joint features of 10 consecutive sampling points to eliminate instantaneous fluctuation noise. The final output is an 8-dimensional Operating Condition State Vector (OCSV), where the vector elements represent joint features such as the mean speed, mean load, speed change gradient, load change gradient, and speed-load covariance.

[0095] Dynamic feature weight allocation

[0096] The generation process of the operating condition state vector (OCSV) incorporates an Adaptive Feature Weighting Mechanism (AFWM). This mechanism presets a feature weight template (WT) based on the equipment type (e.g., centrifugal compressor / gearbox). For example, for a speed-sensitive compressor, the weight of the speed mean feature is set to 0.4, and the weight of the load mean feature is set to 0.2; while for a load-sensitive gearbox, the weight of the load mean feature is increased to 0.5. The weight allocation is dynamically adjusted through a learnable parameter matrix to ensure that the OCSV accurately represents the essential characteristics of the current operating condition. Simultaneously, OCEM integrates an Abnormal Condition Interceptor (ACI). When a speed change rate exceeding 200 revolutions per second or a load fluctuation exceeding 15% is detected, a feature recalibration process is triggered to prevent invalid features from contaminating subsequent analyses.

[0097] Vector output correlated with historical data

[0098] The generated operating condition vector (OCSV) is accompanied by a timestamp and operating condition label (such as "high speed light load" and "low speed heavy load"), and is stored in real time to the Equipment Operation History Database (EOHD). The database uses a Condition Cluster Index (CCI) to group similar operating conditions (OCSVs with an Euclidean distance less than 0.1) into the same cluster, providing an efficient query path for subsequent historical fault database retrieval. Thus, the OCSV, as a digital fingerprint of operating conditions, lays the foundation for threshold generation.

[0099] The historical fault database is retrieved using the operating condition state vector as an index. The resonant frequency band energy envelope of typical faults is generated by the spectral kurtosis energy focusing algorithm, and the fault energy envelope template set is output.

[0100] Intelligent search of historical fault database

[0101] Using the operating condition vector (OCSV) as the index key (IK), a nearest neighbor search is performed in the Historical Fault Library (HFL). HFL stores tens of thousands of historical fault cases, each containing the OCSV at the time of the fault, vibration spectrum data, and a fault type label (e.g., bearing inner ring crack, gear tooth breakage). The retrieval employs an Approximate Nearest Neighbor (ANN) algorithm, setting a similarity threshold of SIM_THRES=0.85 (cosine similarity), and returns the 20 most matching historical fault datasets. For example, if the current OCSV has a similarity of 0.92 with the case "bearing inner ring fault - high-speed condition," then the vibration spectrum of that case is prioritized.

[0102] Spectral kurtosis energy focusing processing

[0103] The retrieved historical fault vibration data were processed using the Spectral Kurtosis Energy Focusing Algorithm (SKEFA). This algorithm is executed in three steps:

[0104] Multi-scale spectral kurtosis calculation: Within the 1kHz~10kHz frequency band, sub-bands are divided with a step size of 50Hz, and the kurtosis value KURT_BAND (characterizing the steepness of the impact component) of each sub-band is calculated.

[0105] Energy envelope extraction: For sub-bands with kurtosis values ​​greater than the preset threshold KURT_THRES=3.5 (empirical value), Hilbert Transform Envelope Demodulation (HTED) is used to extract the resonant band envelope signal.

[0106] Envelope normalization and template formation: The envelope signal is normalized to the [0,1] interval according to the total energy to generate a normalized energy envelope curve (NEEC). Each curve is marked with its center frequency (e.g., 4500Hz) and bandwidth (e.g., ±200Hz).

[0107] Template set construction and working condition adaptation

[0108] Integrate NEEC curves from all matching failure cases and aggregate them by failure type:

[0109] Bearing failure category: includes envelope templates for inner ring, outer ring, and rolling element failures, with center frequencies concentrated in the high-frequency range (>5kHz).

[0110] Gear faults: Envelope templates including broken teeth and pitting, characterized by sideband clusters (dominant frequency ± meshing frequency).

[0111] The final output is a Fault Energy Envelope Template Set (FEETS). Each template includes a fault type identifier, resonant frequency band range (F_MIN, F_MAX), energy envelope extreme point sequence (PEAK_SEQ), and operating condition fit score (CAS, range 0~1). For example, the template "BPFO_5000RPM" represents the bearing outer ring fault envelope at 5000 rpm, and its CAS=0.93 indicates a high degree of match with the current operating condition.

[0112] The fault energy envelope template set is input into the nonlinear autoregressive predictor, and the resonance energy threshold boundary is predicted by combining the rotational speed change rate. The initial frequency domain threshold surface is then output.

[0113] Nonlinear autoregressive modeling

[0114] The Nonlinear Autoregressive Predictor (NARP) uses a Long Short-Term Memory (LSTM) network as its core, and its input layer receives two key data streams:

[0115] The energy envelope extreme point sequence PEAK_SEQ (historical energy trend) in the fault energy envelope template set FEETS.

[0116] Real-time speed change rate (RPM Change Rate, RPM_CR, unit: revolutions per minute / second).

[0117] The network structure consists of three LSTM layers (128 neurons each) and one fully connected output layer. During training, envelope data with working condition labels from a historical fault database are used, and the objective function is to minimize the root mean square error (RMSE) between the predicted energy envelope and the true envelope.

[0118] Dynamic threshold boundary prediction

[0119] For each fault template, NARP performs rolling prediction:

[0120] Short-term prediction: Using the most recent 10 PEAK_SEQ values ​​as the initial state, combined with the current rotational speed change rate RPM_CR (e.g., +50 rpm), the evolution trajectory of the energy envelope within the next 3 seconds is predicted (Predicted Envelope Trajectory, PET).

[0121] Threshold boundary generation: A dynamic margin (DM) is superimposed on the PET (Predicted Threshold) parameter. DM is a linear mapping of the absolute value of the rate of change of rotational speed, |RPM_CR|: DM = BASE_MARGIN + K * |RPM_CR|. Where BASE_MARGIN = 0.1 (base margin), and K = 0.002 (sensitivity coefficient). For example, when |RPM_CR| = 100, DM = 0.1 + 0.2 = 0.3, indicating that the threshold boundary is 30% wider than the predicted envelope.

[0122] Frequency domain threshold surface construction

[0123] By integrating the prediction results of all fault templates, a three-dimensional Initial Frequency Domain Threshold Surface (IFDTS) is constructed:

[0124] X-axis: Frequency (1kHz~10kHz, resolution 50Hz).

[0125] Y-axis: Fault types (such as bearing inner ring, broken gear teeth, etc., 10 categories).

[0126] Z-axis: Energy threshold (range 0~1).

[0127] The curved data is stored as a tensor structure, where each element THRESHOLD[freq][fault_type] represents the energy upper limit for a specific frequency and a specific fault type. For example, THRESHOLD

[4500] [BPFI] = 0.85 means that at a frequency of 4500Hz, the energy threshold for a bearing inner ring fault is set to 0.85.

[0128] The threshold surface is dynamically compressed by a time-varying gain regulator of a neural network to generate a frequency-domain time-varying adaptive threshold set.

[0129] Time-varying gain regulator design

[0130] The Time-Varying Gain Regulator (TVGR) is a dedicated module in resonant neural networks, consisting of two parts:

[0131] The Condition Sensitivity Analysis Unit (CSAU) receives the Condition State Vector (OCSV) and outputs the Gain Base Value (GAIN_BASE) (0.8~1.2). For example, under high-speed conditions (>8000 rpm), the Gain Base Value is 1.1, which improves threshold sensitivity.

[0132] Transient Impact Detection Unit (TIDU): Real-time monitoring of the peak-to-peak value (PPV) of the vibration signal. When the PPV exceeds 150% of the baseline value, a suppression coefficient SUPP_FACTOR = 0.7 is generated to prevent false triggering.

[0133] Threshold surface dynamic compression

[0134] Perform compression on the initial frequency domain threshold surface IFDTS: Adjusted threshold = original threshold × GAIN_BASE × SUPP_FACTOR.

[0135] Frequency dimension compression: Apply an additional 0.9 times attenuation factor to the high-frequency band (>7kHz) (high-frequency noise suppression).

[0136] Differentiated handling for fault types: For faults that develop rapidly (such as bearing cracks), the compression rate is reduced by 10% (i.e., the threshold is relaxed by 10%); for faults that change slowly (such as gear wear), the compression rate is increased by 10% (the threshold is tightened by 10%).

[0137] The compression process employs a Parallel Channel Processing Architecture (PCPA), with 10 fault-type channels operating independently to ensure real-time performance.

[0138] Adaptive threshold group generation

[0139] The final output is a Frequency-Time Adaptive Threshold Set (FTATS), whose core features include:

[0140] Nonlinear adaptive: The threshold changes exponentially with rotational speed. For example, for every 1000 rpm increase in rotational speed, the bearing failure threshold increases by 5%, and the gear failure threshold increases by 3%.

[0141] Multi-mode coverage: Includes independent threshold subgroups for 5 typical failure modes, each subgroup containing:

[0142] Resonance frequency band energy limits (e.g., energy in the [4200Hz, 4800Hz] range and an upper limit of 0.75);

[0143] Transient impact counting threshold (e.g., the number of impacts exceeding 5g per second ≤ 3 times);

[0144] Sideband energy ratio threshold (e.g., the energy ratio of the main frequency ± 2 times the meshing frequency ≤ 40%).

[0145] Dynamic update mechanism: The threshold group is refreshed every 200 milliseconds based on the latest operating condition status vector (OCSV) to ensure real-time synchronization with the equipment's operating status. The threshold group is output in JSON format for subsequent use by the fault feature decoupling module.

[0146] By performing in-depth analysis of the synchronization signal flow using a resonant neural network, and combining historical fault databases with real-time operating parameters, a frequency threshold curve that dynamically varies non-linearly with rotational speed is generated. These thresholds can adapt to the normal range of vibration energy under different operating conditions of the equipment, overcoming the limitations of fixed thresholds and significantly improving the fault detection sensitivity under unsteady conditions. The dynamic threshold set provides a precise criterion for the identification of early, subtle faults.

[0147] S203, using the multi-scale resonant kernel of the resonant neural network, nonlinear feature decoupling is performed on the vibration signal flow to extract the weak impact resonance feature tensor, wherein the tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions.

[0148] Specifically, the time-to-work strictly synchronized vibration signal stream can be divided into time windows of preset length, input with a multi-scale wavelet resonance kernel, and combined with a frequency domain-time-varying adaptive threshold group to activate the resonance frequency band and output a multi-scale resonance response spectrum.

[0149] Time window segmentation and signal preprocessing

[0150] The Time-Work Synchronized Vibration Signal Stream (TW-SVSS) received by the system is a signal with equal angular intervals after dynamic resampling at rotational speed. First, based on the typical fault characteristic frequency range of rotating machinery (e.g., bearing fault frequencies are often distributed between 0.1 and 5 times the rotational speed), a preset time window (e.g., a window length of 100 milliseconds, corresponding to covering 3–5 revolutions at low speeds and tens of revolutions at high speeds) is set. A sliding window mechanism (10 millisecond step) is used to segment the signal stream to ensure that fault impact events are not truncated. The signal within each time window needs to be zero-mean normalized (ZMN) to eliminate DC offset; simultaneously, it is weighted using a Hanning window (HW) function to reduce spectral leakage. The preprocessed signal window is bound to the current operating parameters (e.g., rotational speed 3000 rpm, load 80%) to form a standardized input unit.

[0151] Band Activation of Multiscale Wavelet Resonance Nuclei

[0152] The Multi-Scale Wavelet Resonance Kernel (MS-WRK) consists of a set of parallel complex Morlet wavelet transform layers, each corresponding to a specific center frequency (e.g., 500 Hz, 2000 Hz, 5000 Hz) and bandwidth (Q value range 5–50). The core innovation lies in combining a Frequency-Time Adaptive Threshold Set (F-TATS): for example, when the rotational speed increases from 3000 rpm to 3500 rpm, the threshold corresponding to "bearing outer race fault" in F-TATS nonlinearly increases from 0.15 g² / Hz to 0.22 g² / Hz in the 4000 Hz band. MS-WRK activates the resonant band through the following process:

[0153] Threshold triggering: Calculate the instantaneous energy (IE) at each wavelet scale. If the energy at a certain scale at time point t exceeds the dynamic threshold of the corresponding fault mode in F-TATS (e.g., >0.18g² / Hz for the 4000 Hz band), then mark that scale as "active".

[0154] Frequency band association: Based on the preset fault-frequency band mapping table (e.g., associating gear meshing faults with 2–4 times the meshing frequency), only the frequency bands in the activated scale that are related to potential faults in the current operating condition are retained.

[0155] Resonance enhancement: Apply Q-factor adaptive amplification (Q value decreases as rotational speed increases) to the active frequency band to suppress background noise and enhance fault resonance response.

[0156] Multiscale resonance response spectrum generation

[0157] For each activation scale, a Hilbert Transform (HT) is performed to extract the envelope signal, and then a Short-Time Fourier Transform (STFT) is used to generate a time-spectrum matrix (1 ms time resolution, 10 Hz frequency resolution). The time-spectrums of all activation scales are superimposed by frequency band to form a Multi-Scale Resonance Response Spectrum (MS-RRS). This spectrum has a three-dimensional data structure: a time axis (100 points within a 100 ms window), a frequency axis (0–10 kHz divided into 1000 lines), and an energy axis (unit: g² / Hz). For example, when a sudden change in rotational speed is detected, the MS-RRS exhibits a resonance peak lasting 20 ms in the 4250 Hz band with an energy of 0.25 g² / Hz, which is significantly higher than the background noise of 0.08 g² / Hz.

[0158] A fourth-order cumulant transformation is performed on the multi-scale resonance response spectrum to enhance the phase consistency of transient impact and generate an impact enhancement spectrum.

[0159] Physical meaning and calculation of fourth-order cumulants

[0160] The Fourth-Order Cumulant Transform (FOCT) is used to distinguish between Gaussian noise and non-Gaussian impulse signals. Traditional power spectra (second-order statistics) cannot characterize phase information, while the fourth-order cumulant can capture the higher-order nonlinear characteristics of a signal. For each frequency point f in the MS-RRS... k (e.g., 4250 Hz), calculate the fourth-order cumulant of the vibration signal x(t) within a sub-window with a length of 20 milliseconds by sliding along the time axis:

[0161] Mathematical definition implementation: The actual calculation uses a simplified algorithm—first calculate the kurtosis (KUR) of the sub-window signal, and then obtain the normalized cumulative amount (C4>0 indicates pulse characteristics) according to the formula C4=KUR-3. For example, under normal operating conditions, C4≈-0.2, but when the bearing peels off and generates a transient impact, C4 suddenly increases to 2.5.

[0162] Phase consistency enhancement: By comparing the cumulative phase angle (PA) of adjacent sub-windows, if the PA difference of three consecutive sub-windows is less than 15 degrees, it is determined to be a phase-consistent continuous impact (such as crack propagation); otherwise, it is random noise.

[0163] Enhancement and fusion of impact components

[0164] Design the Impact Enhancement Function (IEF):

[0165] Weighting: A weight matrix W(f,t) is generated based on the C4 value. When C4 > 1.0, W = 1 + tanh(C4); otherwise, W = 0. For example, when C4 = 2.5, W ≈ 1.99, significantly strengthening the impact region.

[0166] Spectral fusion: The weight matrix W is element-wise multiplied with the original MS-RRS (Hadamard product) to obtain the preliminary enhanced spectrum. Further, the Coherent Averaging Technique (CAT) is introduced: impact events within the same fault cycle (e.g., a 10-millisecond fault cycle for the bearing outer race) are time-aligned and superimposed, improving the signal-to-noise ratio by 3–5 dB.

[0167] Structured output of shock enhancement spectrum

[0168] The Impact-Enhanced Spectrum (IES) is a two-dimensional time-frequency matrix (time × frequency), with two additional key feature layers:

[0169] Impact marking layer: The impact points with C4>1.5 and consistent phase are identified by a binary matrix (e.g., marked as 1 at t=35 milliseconds and f=4250 Hz).

[0170] Impact strength layer: Stores normalized impact energy values ​​(range 0–1.0). Ultimately, the IES replaces the original MS-RRS in subsequent processes, improving the signal-to-noise ratio of its transient impact components by approximately 8 dB, laying the foundation for sideband analysis.

[0171] Based on the impulse enhancement spectrum, the modulation sideband energy is integrated to calculate the energy percentage within ±5 octaves of the characteristic frequency, and the sideband energy distribution matrix is ​​output.

[0172] Physical mechanism and feature extraction of modulation sidebands

[0173] The impact of rotating machinery failures (such as bearing raceway damage) modulates the equipment's natural frequency, forming modulation sidebands (MSBs) centered on the characteristic frequency (CF, such as the bearing outer ring failure frequency of 107 Hz). Methods for locating the CF in IES:

[0174] Operating condition correlation: Based on the current speed (3000 rpm = 50 Hz) and bearing geometry parameters (number of rollers 8), the theoretical CF is calculated to be 50 × 0.4 × 8 = 160 Hz (outer ring failure).

[0175] Peak search: Scan the IES in the low-frequency band of 0–500 Hz to find the point of maximum energy (e.g., actual CF = 158 Hz). Define an analysis bandwidth of ±5 octaves centered on CF: lower limit 158 / 32 ≈ 4.9 Hz, upper limit 158 ​​× 32 = 5056 Hz.

[0176] Sideband energy integration algorithm

[0177] Modulation Sideband Energy Integration (MSEI) is performed in three steps:

[0178] Bandpass filtering: IES sub-spectrums were extracted in the range of 4.9–5056 Hz using a 128th order FIR filter.

[0179] Spectrum segmentation: Based on CF=158 Hz, multiple sub-bands are divided:

[0180] Center band: CF ± 1 octave (79–316 Hz)

[0181] First sideband: CF ± (1–2) octaves (39.5–79 Hz and 316–632 Hz)

[0182] Second to fifth order sidebands and so on

[0183] Energy percentage calculation: Calculate the energy integral E for each sub-band k. k Calculate its proportion of total energy R k =E k / ∑E. For example, under normal conditions, the proportion of secondary sidebands is R2≈15%, while under fault conditions, R2 rises to 35%.

[0184] Construction of sideband energy distribution matrix

[0185] The Sideband Energy Distribution Matrix (SEDM) is a two-dimensional structure (time window number × sideband level), where each element stores the energy percentage R of the corresponding time window and sideband level. k Key processing:

[0186] Time alignment: Each 100-millisecond window outputs a row vector [R1,R2,...,R5] (5 sideband layers).

[0187] Fault feature encoding: For example, when a gear has a partial tooth breakage, SEDM shows that the proportion of the secondary sideband R2 suddenly increases to 42%, and fluctuates periodically over time (the period is equal to the gear rotation period). This matrix directly characterizes the fault modulation intensity and mode.

[0188] The resonance quality factor Q is calculated using an exponential decay model fitting algorithm, and a decay characteristic parameter vector is generated.

[0189] Establishment of a physical model for resonant attenuation

[0190] The resonant decay characteristics excited by fault impacts are quantified by the quality factor (QF), which physically represents the number of cycles required for the resonant energy to decay to 1 / e. For each marker impact event in the IES (e.g., the 4250 Hz resonance peak at t=35 ms):

[0191] Time-domain waveform extraction: Extract the impact decay segment (e.g., 50 milliseconds after impact) from the original vibration signal.

[0192] Model selection: The Exponential Decay Model (EDM) is adopted: A(t)=A0e^(-πf0t / Q), where A0 is the initial amplitude, f0 is the resonant frequency (4250 Hz), and Q is the parameter to be solved.

[0193] Q-value fitting algorithm implementation

[0194] The Exponential Decay Model Fitting Algorithm (EDM-FA) consists of three stages:

[0195] Envelope extraction: The envelope A(t) is obtained by performing a Hilbert transform on the attenuated signal.

[0196] Initial value estimation: Calculate the time t1 when the amplitude decays to 37% (i.e., 1 / e), and obtain the initial estimate from Q_est=πf0t1 (for example, Q_est≈267 when t1=0.02 seconds).

[0197] Nonlinear optimization: Starting with Q_est, minimize the error function ∑[A(t)-A0e^(-πf0t / Q)]² using the Levenberg-Marquardt algorithm (LMA). The iteration terminates when the relative error is <0.1% (e.g., Q=253.6 at the end).

[0198] Attenuation characteristic parameter vector generation

[0199] The Decay Characteristic Parameter Vector (DCPV) contains three key parameters:

[0200] The main parameter Q value directly characterizes the resonance persistence (Q>300 indicates minor damage, Q<150 indicates severe cracking).

[0201] Goodness-of-fit R²: Evaluates the reliability of the model (requires R² > 0.85).

[0202] Attenuation asymmetry: Calculate the ratio of rise time to decay time (normal ≈ 0.3, fault > 1.0).

[0203] Each impact event generates a set of parameters, arranged into a vector in chronological order. For example, if 3 impacts are detected within a 100-millisecond window, the DCPV is [Q1,R²1,Asym1, Q2,R²2,Asym2, Q3,R²3,Asym3].

[0204] By stacking the impact enhancement spectrum, sideband energy distribution matrix, and attenuation characteristic parameter vector along the time dimension, a three-dimensional weak impact resonance feature tensor is constructed.

[0205] Data structure alignment and standardization

[0206] To integrate features from multiple sources, a unified time reference is required:

[0207] Time axis alignment: Divide the 100-millisecond window into 10 time slices (TS) at 10-millisecond intervals.

[0208] Feature resampling:

[0209] IES downsamples to 10 milliseconds / frame (each frame contains 1000 frequency points);

[0210] SEDM is averaged over time slices (one sideband distribution vector per slice).

[0211] In DCPV, parameters are assigned to the most recent time slice.

[0212] 3D Tensor Construction Process

[0213] The 3D Weak-Impact Resonance Feature Tensor (3D-WIRFT) is constructed in the following hierarchy:

[0214] First dimension (timeline): 10 time slices (TS1 to TS) 10 ).

[0215] Second dimension (feature axis): 1005 feature channels in total.

[0216] Channels 1–1000: IES frequency energy values ​​(0–10 kHz);

[0217] Channels 1001–1005: Percentage of the 5 sidebands in SEDM;

[0218] Channels 1006–1008: Q value, R², and Asym of DCPV.

[0219] The third dimension (sample axis): multiple consecutive time windows stacked together (e.g., generating 6 tensors per minute).

[0220] Example: Channel 1001 of TS5 stores the average proportion of secondary sidebands within 5 milliseconds, R2=0.38, and channel 1006 stores Q=210.

[0221] The engineering significance and advantages of tensors

[0222] This tensor achieves spatiotemporal correlation of three key features for the first time:

[0223] Complementary fault sensitivity: IES captures high-frequency resonance (sensitive to micro-damage), SEDM reveals modulation patterns (indicating local faults), and DCPV quantifies the degree of damage.

[0224] Anti-interference capability: When speed fluctuations cause sudden changes in energy in the IES, the Q value stability of the DCPV can distinguish between real faults and operating condition disturbances.

[0225] Supports tensor decomposition: provides structured input for subsequent fault subspace projection, such as separating the "bearing inner ring fault" feature subspace through Tucker decomposition.

[0226] A multi-scale resonant kernel is used to separate minute impact components with fault characteristics from complex vibration signals. Time-frequency analysis is then used to extract a three-dimensional feature tensor containing transient impacts, sideband modulation, and resonant attenuation, fully preserving the typical characteristic patterns of early faults. This achieves holographic extraction of weak fault features and solves the problem of traditional methods struggling to capture early fault features in strong noise environments. The three-dimensional tensor structure provides a rich information carrier for subsequent fault separation.

[0227] S204, The weak impact resonance feature tensor is projected onto the orthogonal fault subspace through the tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault.

[0228] Specifically, the three-dimensional weak impact resonance feature tensor can be decomposed in parallel to obtain the core tensor and orthogonal factor matrix, and the decomposed core tensor can be output.

[0229] The system receives a three-dimensional weak impact resonance feature tensor (dimensions: number of time windows × number of feature types × number of frequency bands) generated by the previous stage. This tensor is a comprehensive data structure containing impact enhancement spectra, sideband energy distribution matrices, and attenuation characteristic parameters within multiple time segments. To extract the implicit fault features, the system invokes a parallel factorization algorithm (PARAFAC). This algorithm treats the three-dimensional tensor as a superposition of multiple rank tensors and iteratively optimizes the orthogonal factor matrices in three directions (corresponding to time, feature, and frequency band dimensions, respectively) and a low-rank core tensor using alternating least squares (ALS). The core tensor is much smaller than the original tensor (e.g., the original tensor size is 1000×30×50, while the core tensor can be compressed to 10×10×10), but it retains the core correlation patterns of the original data. The decomposition process is executed in parallel on a distributed computing cluster: First, the original tensor is partitioned along the time dimension (e.g., every 100 time windows form a block) and distributed to different computing nodes; each node independently calculates the local factor matrix, and then the master node synchronously updates the global orthogonal factor matrix using a global consensus algorithm (e.g., ADMM - Alternating Direction Multiplier Method). The iteration termination condition is set to a residual change rate of less than 0.1% or a maximum number of iterations of 50.

[0230] In each ALS iteration, the system sequentially fixes two factor matrices and optimizes a third matrix. For example, when optimizing the time factor matrix: the three-dimensional tensor is expanded into a two-dimensional matrix along the time dimension (size: number of time windows × (number of features × number of frequency bands)), and least-squares fitting is performed with the Kronecker product of the feature-frequency band factor matrix. The updated time factor matrix needs to be Gram-Schmidt orthogonalized to ensure that the column vectors are orthogonal. When optimizing the feature factor matrix: the tensor is expanded along the feature dimension (size: number of features × (number of time windows × number of frequency bands)), and the fitting and update are performed similarly. The optimization of the frequency band factor matrix adopts the same logic. The core tensor is calculated by projection after all factor matrices are updated: the original tensor and the transpose of the three factor matrices are contracted. This process requires special handling of data mutations under non-steady-state conditions: a robust weighting function is introduced to assign low weights to data points with very large residuals (such as periods of sudden strong noise interference) to reduce their interference with the decomposition results.

[0231] After decomposition, the system outputs three orthogonal factor matrices (time factor matrix U, feature factor matrix V, and frequency band factor matrix W) and a core tensor G. The core tensor G is the key output; the value of each element represents the coupling strength of the three dimensional factors under a specific combination. For example, a high value at position (3,5,2) in the core tensor indicates a strong correlation between the third time mode, the fifth feature mode, and the second frequency band mode, potentially corresponding to the resonance mode of a specific fault. The system stores the core tensor G in a cache and attaches a decomposition quality report (including fitting residuals, iteration count, and orthogonality test indicators) for subsequent steps. Simultaneously, the factor matrices are used for real-time visualization: the time factor matrix can be mapped to a time-series curve of the equipment's operating status, the feature factor matrix displays the weight distribution of various resonance features, and the frequency band factor matrix generates a heatmap of the fault-sensitive frequency band.

[0232] Construct an orthogonal basis for the fault subspace based on the fault energy envelope template set, and project the core tensor onto the basis space to generate the fault projection core tensor.

[0233] The fault energy envelope template set is generated from a historical fault database and contains resonant frequency band energy distribution templates for typical faults (such as bearing inner ring spalling, gear tooth breakage, and rotor imbalance) under standard operating conditions. Each template is a vector (length = number of frequency bands) describing the energy intensity characteristics of the fault in each frequency band. The system first orthogonalizes these templates: the Gram-Schmidt orthogonalization algorithm is used to transform the template vector set into pairwise orthogonal vector bases. For example, the bearing inner ring fault template vector V_bearing and the gear fault template V_gear, after orthogonalization, yield new basis vectors V'_bearing and V'_gear, satisfying the dot product V'_bearing·V'_gear=0. After all fault templates are processed, an orthogonal basis matrix B (size: number of frequency bands × number of fault types) is formed. The space spanned by its column vectors is the fault subspace, which is decoupled from noise and normal vibration modes.

[0234] The key operation for projecting the core tensor G onto the fault subspace is tensor-matrix product. Specifically, for the frequency band dimension (3rd order) of the core tensor, it is condensed by the transpose of the orthogonal basis matrix B of the fault subspace. Mathematically, this is equivalent to multiplying each frequency band slice matrix of the core tensor G by B^T. For example, if the core tensor G is 10×10×10 and B is 50×8 (assuming 8 fault types), then the projected core tensor G_proj (size: 10×10×8) is obtained. The significance of this operation is to map the frequency band pattern of the original core tensor to the fault feature space: the value of the k-th fault dimension in G_proj represents the degree of matching between the current data and the k-th fault template. The projection process uses block-based computation optimization: the core tensor is divided into sub-blocks (e.g., 2×2×10) along the time-feature plane, and each sub-block is multiplied by B^T in parallel by the GPU, and then concatenated to form the complete G_proj.

[0235] After projection, energy normalization is required: the Frobenius norm of G_proj in each fault dimension (i.e., the square root of the sum of squares of all elements) is calculated, and this norm is scaled to a level consistent with the energy of the historical fault template. For example, if the norm of G_proj in the "bearing inner ring fault" dimension is detected to be 1.5 for a certain period, while the standard value of the historical template is 1.0, then all elements in that dimension are divided by 1.5. This operation eliminates the absolute energy difference caused by operating condition fluctuations and preserves the relative patterns of fault characteristics. The final generated fault projection core tensor G_proj has a clear physical meaning: its third dimension (the original frequency band dimension) is compressed into a fault type dimension, and each element G_proj(i,j,k) represents the resonant energy correlation strength between the i-th time pattern, the j-th feature pattern, and the k-th type of fault.

[0236] For the fault projection core tensor, the Tucker3 compression model is used to reduce the order along the feature dimension, retaining the components whose variance contribution rate is greater than the preset contribution threshold, and outputting a simplified fault feature tensor.

[0237] The fault projection core tensor G_proj (size example: 10×10×8) still contains redundant information and needs further compression. The system adopts the Tucker3 compression model (a form of higher-order singular value decomposition), focusing on reducing the order along the feature dimension (second order). First, matrix expansion is performed along the feature dimension: G_proj is rearranged into a two-dimensional matrix M (size: number of feature patterns × (number of time patterns × number of fault types)). Truncated Singular Value Decomposition (TSVD) is performed on matrix M: the singular value decomposition of M is calculated, resulting in the left singular matrix U, singular value vector S, and right singular matrix V. Principal components are selected according to a preset variance contribution rate threshold (e.g., 95%): the proportion of the squares of the singular values ​​to the total sum of squares is accumulated from largest to smallest. When the cumulative contribution rate first exceeds 95%, the corresponding first r singular values ​​and left / right singular vectors are retained.

[0238] Suppose we retain the first r principal components (e.g., r=5), then the truncated left singular matrix U_r (size: original number of feature patterns × r) is the new factor matrix of the feature dimension. The compressed feature dimension is reduced from 10 dimensions to 5 dimensions. To maintain the tensor structure, we need to reconstruct the simplified fault feature tensor G_compact: perform a third-order tensor product operation on the truncated factor matrix U_r, the original time factor matrix (uncompressed), and the original fault type factor matrix. Specifically, we first construct a smaller core tensor (size: number of time patterns × r × number of fault types), whose elements are determined by the projection of the original core tensor onto the selected principal components; then we reassemble this core tensor with the three factor matrices (time dimension, feature dimension, fault dimension) according to the Tucker model. Finally, G_compact has a size of 10×5×8, and the feature dimension is compressed from 10 dimensions to 5 dimensions, but retains more than 95% of the original information.

[0239] The system performs interpretability verification on the order reduction results:

[0240] Principal Component Analysis: Examines the physical meaning of the r principal components retained in the feature dimension. For example, the first principal component might correspond to "impact intensity," and the second principal component might correspond to "modulation depth."

[0241] Residual monitoring: Calculate the relative error (Frobenius norm ratio) of the tensors before and after compression, and trigger an alarm when it exceeds 5%.

[0242] Fault sensitivity test: Inject simulated fault data to verify that G_compact significantly improves the response in the target fault dimension.

[0243] The validated simplified fault feature tensor G_compact will be input into the downstream processing module. The system will simultaneously generate a reduction report, including the variance contribution rate of each principal component, a key feature interpretation table, and compression error indices.

[0244] The fault feature tensor is simplified by dividing it into time slices, and the L2 norm of each slice in the fault subspace is calculated to generate the fault energy distribution vector.

[0245] The simplified fault feature tensor G_compact (size: number of time patterns × number of principal components × number of fault types) is divided into time slices along the time dimension (first order). Each time slice is a two-dimensional matrix (size: 1 × number of principal components × number of fault types), corresponding to the feature-fault distribution under a specific time pattern. For example, if there are 10 time patterns, it is divided into 10 independent time slice matrices S_t (t=1,2,...,10). Each matrix S_t has a size of 5×8 (5 principal components, 8 fault types), and its physical meaning is: the distribution of coupling strength between each type of fault and each principal component under a specific time pattern.

[0246] For each time-slice matrix S_t, calculate its L2 norm (L2-Norm) in the fault subspace. This operation consists of two steps:

[0247] Extracting vectors by fault type: Extract each column from matrix S_t (i.e., the 5-dimensional feature vector V_k corresponding to the k-th type of fault).

[0248] Calculate the vector norm: Calculate the L2 norm for each V_k. This value characterizes the combined energy intensity of the k-th type of fault in the current time mode.

[0249] For example, if the bearing fault vector within a certain time slice is [0.8, 0.4, 0.3, 0.1, 0.05], then the L2 norm = The higher this value, the more significant the resonant energy of the fault is in the current time period.

[0250] The L2 norm of all fault types within a single time slice is normalized: each ||V_k||² is divided by the maximum value of all fault norms within that time slice. For example, if the norms for 8 fault types are [0.94, 0.21, 0.07, ..., 0.33], and the maximum value is 0.94, then the normalized bearing fault value is 1.0, and other faults are scaled proportionally. The normalized value generates a fault energy distribution vector E_t (length = number of fault types) for that time slice. The elements of vector E_t range from [0,1], intuitively reflecting the relative energy proportion of each fault type. All computations are performed in parallel on the GPU using tensor processing libraries (such as TensorFlow's tf.norm function), and 10 time slices can be completed within 1 millisecond.

[0251] By integrating the fault energy distribution vectors of all time slices, a decoupled fault feature matrix is ​​constructed.

[0252] The system has generated fault energy distribution vectors E_1, E_2, ..., E_10 corresponding to 10 time slices (each vector has a length of 8). The integration operation involves stacking these vectors in chronological order into a matrix: using time pattern as the row index and fault type as the column index, constructing a two-dimensional matrix M (size: number of time patterns × number of fault types). For example:

[0253] Line 1 (E1): [Bearing failure = 0.98, Gear failure = 0.15, ..., Imbalance = 0.02];

[0254] Line 2 (E2): [Bearing failure = 0.85, Gear failure = 0.31, ..., Imbalance = 0.11]; ...

[0255] Line 10 (E) 10 ): [Bearing failure = 0.07, Gear failure = 0.92, ..., Imbalance = 0.33].

[0256] This matrix M is the decoupling fault characteristic matrix, and its physical meaning is clear:

[0257] Direction of movement: Reflects the evolution of fault energy over time (e.g., startup, steady state, shutdown phases).

[0258] Column direction: Independently characterize the energy distribution of each type of fault in the entire time domain (e.g., the bearing fault column shows its activity in each time period).

[0259] To improve the robustness of the matrix under operating conditions, a time-dimensional smoothing process is added: a moving average filter (window width = 3 time points) is applied to each column of matrix M (i.e., the time series of a single type of fault). For example, the original data of the bearing fault column [0.98, 0.85, 0.77, ..., 0.07] is updated to (0.98+0.85+0.77) / 3≈0.87 after filtering. This operation suppresses numerical fluctuations caused by instantaneous disturbances and highlights the true trend of fault energy changes. Simultaneously, a confidence index is generated: the variance of each matrix element is calculated; elements with a variance below 0.01 are marked as high confidence (green), and those above 0.05 are marked as requiring review (red).

[0260] The final output decoupling fault feature matrix has two core values:

[0261] Fault type localization: Each column corresponds to an independent energy distribution for a type of fault. For example, the maximum value in column 1 appears in time slices 5-7, which, combined with the rotational speed information, can be identified as a bearing fault under high-speed conditions.

[0262] Multi-fault decoupling capability: Orthogonality strength between matrix column vectors ≥ 0.85 (verified by historical data), ensuring that gear fault alarms will not be falsely triggered when bearing fault energy increases.

[0263] This matrix is ​​directly input into the online adversarial training module to drive protection decision generation. The system synchronously stores matrix snapshots and associated time-condition tags for updating the historical fault database.

[0264] Tensor decomposition is used to project mixed fault features onto a pre-constructed orthogonal fault subspace, thereby decoupling the energy distribution of different fault modes. Each decoupled feature vector corresponds to the resonance characteristics of a typical fault, solving the feature aliasing problem in multi-fault coupling and providing independent feature representations for accurate fault classification. Orthogonal projection ensures that the analysis of each fault mode does not interfere with each other.

[0265] S205, based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0266] Specifically, the decoupled fault feature matrix can be compared with the historical fault database, and the similarity between each column vector and the corresponding historical fault can be calculated by the dynamic time warping algorithm to output the fault matching degree vector.

[0267] Construction and comparison mechanism of historical fault database

[0268] The Historical Fault Database (HFD) stores decoupled fault feature matrix (DFFM) samples of various typical faults throughout the entire lifecycle of rotating machinery. Each DFFM sample contains three key dimensions: fault type label (e.g., bearing inner ring crack, gear tooth breakage), operating condition parameters (e.g., speed 2000 rpm, load 50%), and timestamp sequence. When the real-time generated decoupled fault feature matrix (current DFFM) is input into the comparison module, the system first searches the HFD for historical samples within the operating condition similarity threshold (OCST) range based on the current speed (e.g., 1850 rpm) and load (e.g., 45%). For example, if the OCST is set to ±5% speed deviation and ±10% load deviation, then historical DFFM sample sets with speeds between 1750-1940 rpm and loads between 40.5%-49.5% are selected to form the candidate matching library (CML).

[0269] Similarity calculation using dynamic time warping algorithm

[0270] For each column vector of the current DFFM (each column independently represents the resonant mode energy distribution of a fault), the system matches historical column vectors of the same type of fault in CML. Since fault characteristics may exhibit temporal scaling (e.g., differences in impact duration), a Dynamic Time Warping (DTW) algorithm is used to calculate similarity. DTW constructs a cost matrix (CM) between the current vector (length N) and historical vectors (length M), searching for the optimal warping path (WP) that minimizes the cumulative distance. Key parameters include:

[0271] Local Distance Metric (LDM): Calculates the energy difference at corresponding time points using Euclidean distance (ED).

[0272] Warping Window (WW): Limits the time axis scaling range, set to 20% of the vector length (e.g., when N=100, WW=20 time points).

[0273] The final output is the Warped Path Cumulative Distance (WPCD), which is normalized to a similarity score (0-100%). For example, the WPCD of the current bearing inner race fault vector and historical samples is 35, and the normalized similarity is 82%.

[0274] Logic for generating fault matching degree vector

[0275] For the current DFFM's K column vectors (K being the total number of system-defined fault types), calculate the average similarity between each vector and the top-3 historical samples of the same fault type in CML, generating a K-dimensional Fault Match Degree Vector (FMDV). For example:

[0276] Column 1 (Bearing inner ring failure): Similarity with 3 historical samples was 82%, 79%, and 85% → average 82%;

[0277] Column 2 (Gear tooth breakage): Similarity 76%, 81%, 74% → Average 77%; ...

[0278] The vector element FMDV_i (i=1,2,...,K) represents the real-time matching confidence of the i-th type of fault, which is used for subsequent decision-making.

[0279] Using the fault matching degree vector as a condition, an enhanced fault sample is synthesized through a conditional generative adversarial network to generate an adversarial training sample set.

[0280] Architecture design of conditional generative adversarial networks

[0281] A Conditional Generative Adversarial Network (CGAN) consists of a generator (G) and a discriminator (D). Its innovation lies in using FMDV as conditional input. The generator G receives two inputs:

[0282] Random Noise Vector (RNV): A Gaussian distributed random number with dimension 100 (mean 0, variance 1).

[0283] Fault Matching Degree Vector (FMDV): K-dimensional real-time matching degree data.

[0284] The generator synthesizes a forged feature column vector (FFCV) using a 5-layer fully connected network (512-256-128-64-K neurons). The discriminator D receives real historical samples or forged samples and, in conjunction with the FFCV conditions, outputs a probability of authenticity (0-1).

[0285] Enhanced Fault Sample Synthesis Strategy

[0286] For fault types in FMDV where the matching degree is lower than the Sample Enhancement Threshold (SET, e.g., 70%), the synthesis process is initiated. Taking a broken gear tooth fault as an example (FMDV_2=77%):

[0287] The generator G takes RNV and FMDV as input and outputs a fake gear tooth breakage feature vector FFCV_2.

[0288] The feature boundary constraint (FBC) ensures that the energy distribution of FFCV_2 is within ±3 standard deviations of historical samples, thus avoiding the generation of invalid data.

[0289] An Operating Condition Disturbance Factor (OCDF) is added to FFCV_2, such as simulating ±2% speed fluctuations, to enhance sample diversity. The final result is an enhanced vector with the same dimensions as the real sample.

[0290] Methods for constructing adversarial training sample sets

[0291] The generated augmented vectors are inserted into the original DFFM according to the fault type, replacing the corresponding column vectors to form the Augmented Fault Feature Matrix (AFFM). For example, the column vector of broken gear teeth in the original DFFM is replaced with the synthesized FFCV_2.

[0292] The remaining columns retain real-time data.

[0293] Each AFFM is bound to a fault type label to form an Adversarial Training Sample (ATS). 5-10 ATSs are generated for each type of low-match fault, and finally packaged into an Adversarial Training Sample Set (ATSS) for subsequent network updates.

[0294] The adversarial training sample set is injected into the resonant neural network, and the resonant kernel weights are updated using an online meta-learning strategy to output the optimized resonant kernel parameters.

[0295] Dual update mechanism of resonant neural networks

[0296] The multi-scale resonance kernel (MRK) of a resonance neural network (RNN) is the core of feature extraction. The update process employs a two-branch structure:

[0297] Main branch: Processes real-time vibration signal streams and performs protection decisions (weight freezing).

[0298] Update branch: Inject ATSS samples and start weight update (weights are adjustable).

[0299] Gradient Isolation Technique (GIT) ensures that training traffic does not affect real-time tasks, and update latency is controlled within 50 milliseconds (ms).

[0300] Adaptive optimization of online meta-learning

[0301] The Online Meta-Learning Strategy (OMLS) consists of two loops: an inner loop and an outer loop.

[0302] Inner Loop: Perform small-step gradient descent (learning rate 0.001) on the update branch using a single ATS sample (such as a broken tooth of a gear AFFM) to generate temporary weights.

[0303] Outer Loop: Calculates the loss of the temporary weights on the ATSS validation set (20% of the samples), and backpropagates to update the meta-parameters (MP), including the base learning rate and gradient direction.

[0304] The key optimizer uses Adaptive Moment Estimation (Adam) with parameters β1=0.9 (first-order moment decay rate) and β2=0.999 (second-order moment decay rate).

[0305] Incremental update of resonant kernel weights

[0306] For the weight matrix of MRK (such as convolutional kernel weights and fully connected layer weights), an incremental smooth transfer (IST) strategy is adopted:

[0307] Calculate the difference matrix (DWM) between the new weights of the updated branch and the original weights.

[0308] Apply a Gaussian Decay Filter (GDF) to the DWM to suppress abrupt weight changes (e.g., weight differences with a standard deviation > 0.1 are attenuated by 50%).

[0309] The filtered DWM is then added to the main branch weights with a scaling factor (e.g., 0.3) to achieve incremental updates. The final output is the optimized resonance kernel parameters (ORKP).

[0310] The fault type is located based on the elements in the fault matching degree vector that exceed the preset matching threshold. The protection level is determined by combining the energy gradient, and a real-time protection decision instruction set containing fault level assessment and fault type location information is generated.

[0311] Threshold determination logic for fault type localization

[0312] Set a fault match threshold (FMT, e.g., 80%) and a persistence confirmation period (PCP, e.g., 5 consecutive time windows). When an element FMDV_i in FMDV consistently exceeds FMT (e.g., bearing inner race fault FMDV_1 = 82% and ≥ 80% for 5 consecutive times), fault localization is triggered.

[0313] Type positioning: Index i corresponds to the fault type (e.g., i=1 indicates a fault in the inner ring of the bearing).

[0314] Position mapping: Based on the sensor array coordinates (e.g., the energy is highest near sensor 3), output the physical position (e.g., "drive end bearing").

[0315] If multiple types of faults exceed the threshold simultaneously, the primary fault will be locked according to the Maximum Match Degree Priority (MMDP) principle.

[0316] Energy gradient analysis method for protection level

[0317] The energy gradient (EG) is calculated by decoupling the temporal variation of the fault characteristic matrix:

[0318] Extract the most recent 10 time window data (e.g., from time T-9 to time T) from the fault location column vector.

[0319] Calculate the L2 norm difference (ΔE) between adjacent time windows to generate an energy change sequence.

[0320] The linear slope (SV) fitted to the ΔE sequence, in units of energy per minute.

[0321] Protection Level (PL) is classified by slope:

[0322] SV<0.1 → Level 1 (Observation, Yellow Alert);

[0323] 0.1 ≤ SV<0.3 → Level 2 (load reduction, orange alarm);

[0324] SV ≥ 0.3 → Level 3 (Emergency Stop, Red Order).

[0325] Generation and output of real-time protection decision instruction sets

[0326] Integrate fault location and protection level to generate a structured real-time protection decision instruction set:

[0327] {

[0328] Fault Type: Crack in the inner ring of the drive-end bearing

[0329] Location reliability: 82%,

[0330] Protection Level: 2

[0331] Command content: ["Speed ​​reduced to 1500 rpm", "Load reduced to 30%"],

[0332] Energy gradient: 0.21

[0333] "Timestamp": "2025-04-11 14:23:05.876"

[0334] }

[0335] The instruction set is sent to the equipment control system via an industrial real-time bus (such as EtherCAT), which simultaneously triggers the audible and visual alarms of the human-machine interface (HMI) and generates maintenance work orders.

[0336] The system intelligently compares real-time extracted fault features with historical databases and continuously optimizes network parameters through adversarial training, ultimately outputting a complete protection decision that includes fault type, location, and severity. The system possesses online self-learning capabilities, achieving closed-loop processing from feature extraction to protection decision-making. Its adaptive capabilities ensure continuous optimization of the diagnostic model. Multi-dimensional protection commands provide precise action guidelines for equipment maintenance.

[0337] As can be seen, by collecting millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array and simultaneously acquiring real-time operating parameters of the equipment, a time-to-work synchronous vibration signal stream is generated. This time-to-work synchronous vibration signal stream is then input into a pre-trained resonant neural network, which dynamically generates a frequency-domain time-varying adaptive threshold group based on the operating parameters. The multi-scale resonant kernel of the resonant neural network is used to extract weak impact resonance feature tensors. Tensor decomposition algorithms are then used to project these weak impact resonance feature tensors onto an orthogonal fault subspace, separating the decoupled fault feature matrix. Based on the comparison between the decoupled fault feature matrix and the equipment's historical operating database, a real-time protection decision instruction set is generated. This improves the detection sensitivity and positioning accuracy of weak faults under unsteady conditions, achieving real-time adaptive optimization of vibration protection for rotating machinery.

[0338] Another embodiment of the present invention provides a rotating machinery vibration protection system based on an adaptive resonant neural network, see [link to relevant documentation]. Figure 3 The system may include:

[0339] The acquisition module 301 is used to acquire millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and at the same time obtain real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream.

[0340] The input module 302 is used to input the time-work synchronous vibration signal stream into a pre-trained resonant neural network and dynamically generate a frequency domain-time-varying adaptive threshold group in combination with the working condition parameters. The threshold group includes the resonant frequency band energy limit under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0341] The decoupling module 303 is used to decouple the vibration signal flow nonlinearly using the multi-scale resonant kernel of the resonant neural network and extract the weak impact resonant feature tensor, wherein the tensor includes the transient impact component, modulation sideband component and resonant attenuation characteristics of the early fault under unsteady conditions.

[0342] The separation module 304 is used to project the weak impact resonance feature tensor onto the orthogonal fault subspace through a tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault.

[0343] The generation module 305 is used to update the resonant kernel weights of the resonant neural network through an online adversarial training mechanism based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, and generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0344] This invention also provides a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any of the above method embodiments when running.

[0345] Specifically, in this embodiment, the storage medium can be configured to store a computer program for performing the following steps:

[0346] S201 collects millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and simultaneously acquires real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream;

[0347] S202, the time-work synchronous vibration signal stream is input into a pre-trained resonant neural network, and frequency domain-time-varying adaptive threshold group is dynamically generated in combination with working condition parameters. The threshold group includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0348] S203, using the multi-scale resonant kernel of the resonant neural network, nonlinear feature decoupling is performed on the vibration signal flow to extract the weak impact resonance feature tensor, wherein the tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions.

[0349] S204, The weak impact resonance feature tensor is projected onto the orthogonal fault subspace through the tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault.

[0350] S205, based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0351] This invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the steps in any of the above method embodiments.

[0352] Specifically, the aforementioned electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the aforementioned processor, and the input / output device is connected to the aforementioned processor.

[0353] Specifically, in this embodiment, the processor can be configured to perform the following steps via a computer program:

[0354] S201 collects millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and simultaneously acquires real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream;

[0355] S202, the time-work synchronous vibration signal stream is input into a pre-trained resonant neural network, and frequency domain-time-varying adaptive threshold group is dynamically generated in combination with working condition parameters. The threshold group includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes.

[0356] S203, using the multi-scale resonant kernel of the resonant neural network, nonlinear feature decoupling is performed on the vibration signal flow to extract the weak impact resonance feature tensor, wherein the tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions.

[0357] S204, The weak impact resonance feature tensor is projected onto the orthogonal fault subspace through the tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault.

[0358] S205, based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

[0359] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A method for vibration protection of rotating machinery using an adaptive resonant neural network, characterized in that, The method includes: The millisecond-level vibration acceleration signal of rotating machinery is collected by a distributed piezoelectric sensor array, and the real-time operating parameters of the equipment are obtained to generate a time-work synchronous vibration signal stream. The time-work synchronous vibration signal stream is input into an adaptive resonance neural network, and frequency domain-time-varying adaptive threshold group is dynamically generated in combination with working condition parameters. The threshold group includes the resonance frequency band energy limit under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes. The multi-scale wavelet resonance kernel of the adaptive resonance neural network is used to decouple the vibration signal flow nonlinearly and extract the weak impact resonance feature tensor. The tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions. The multi-scale wavelet resonance kernel is composed of a set of parallel complex Morlet wavelet transform layers, each layer corresponding to a specific center frequency and bandwidth. The weak impact resonance feature tensor is projected onto the orthogonal fault subspace using the tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the energy distribution of the resonance modes of a typical fault. Based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the adaptive resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

2. The method according to claim 1, characterized in that, The process of acquiring millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, simultaneously obtaining real-time operating parameters of the equipment, and generating a time-to-work synchronous vibration signal stream includes: Based on the geometric characteristics of the bearing housing of rotating machinery, a piezoelectric sensor array is deployed on the surface of the equipment using a spatial symmetric point placement algorithm to generate a three-dimensional sensor coordinate mapping table; Multi-channel synchronous acquisition is triggered based on a coordinate mapping table. The original vibration signal is acquired with a preset sampling period. The rotational speed and load parameters are read in real time through the industrial bus, and the original multi-source signal stream with timestamp is output. The original multi-source signal stream is input into an adaptive noise complete set empirical mode decomposer, and the speed fluctuation noise is separated by the operating parameters to generate a noise-reduced signal stream with decoupled operating conditions. The noise-reduced signal stream is dynamically resampled to synchronize with the rotational speed. The sampling interval is adjusted according to the instantaneous rotational speed to output a time-to-work strictly synchronized vibration signal stream.

3. The method according to claim 2, characterized in that, The process involves inputting the time-to-work synchronous vibration signal stream into an adaptive resonant neural network, and dynamically generating a frequency-domain time-varying adaptive threshold set based on operating parameters. This threshold set includes resonant frequency band energy limits under different fault modes and exhibits nonlinear adaptive characteristics with varying rotational speed, including: The time-work strictly synchronous vibration signal stream is input into the adaptive resonance neural network, and the joint features of speed and load are extracted through the working condition coding module to output the working condition state vector. The historical fault database is retrieved using the operating condition state vector as an index. The resonant frequency band energy envelope of typical faults is generated by the spectral kurtosis energy focusing algorithm, and the fault energy envelope template set is output. The fault energy envelope template set is input into the nonlinear autoregressive predictor, and the resonance energy threshold boundary is predicted by combining the rotational speed change rate, and the initial frequency domain threshold surface is output. The threshold surface is dynamically compressed by a time-varying gain regulator of a neural network to generate a frequency-domain time-varying adaptive threshold set.

4. The method according to claim 3, characterized in that, The method utilizes the multi-scale wavelet resonance kernel of the adaptive resonance neural network to perform nonlinear feature decoupling on the vibration signal flow and extract a weak impact resonance feature tensor. This tensor includes the transient impact component, modulation sideband component, and resonance attenuation characteristics of early faults under unsteady conditions, including: The time-to-work strictly synchronized vibration signal stream is divided into time windows of preset length, a multi-scale wavelet resonance kernel is input, and the resonance frequency band is activated by combining the frequency domain-time-varying adaptive threshold group, and the multi-scale resonance response spectrum is output. A fourth-order cumulant transformation is performed on the multi-scale resonance response spectrum to enhance the phase consistency of transient impact and generate an impact enhancement spectrum. Based on the impulse enhancement spectrum, the modulation sideband energy is integrated to calculate the energy percentage within ±5 octaves of the characteristic frequency, and the sideband energy distribution matrix is ​​output. The resonance quality factor Q is calculated using an exponential decay model fitting algorithm, and a decay characteristic parameter vector is generated. By stacking the impact enhancement spectrum, sideband energy distribution matrix, and attenuation characteristic parameter vector along the time dimension, a three-dimensional weak impact resonance feature tensor is constructed.

5. The method according to claim 4, characterized in that, The weak impact resonance feature tensor is projected onto the orthogonal fault subspace using a tensor decomposition algorithm to separate the decoupled fault feature matrix. Each column of this matrix independently represents the resonant mode energy distribution of a typical fault, including: Parallel factor decomposition of the three-dimensional weak impact resonance characteristic tensor is performed to obtain the core tensor and orthogonal factor matrix, and the decomposed core tensor is output. Construct an orthogonal basis for the fault subspace based on the fault energy envelope template set, and project the core tensor onto the basis space to generate the fault projection core tensor. For the fault projection core tensor, the Tucker3 compression model is used to reduce the order along the feature dimension, retaining the components whose variance contribution rate is greater than the preset contribution threshold, and outputting a simplified fault feature tensor. The fault feature tensor is simplified by dividing it into time slices, and the L2 norm of each slice in the fault subspace is calculated to generate the fault energy distribution vector. By integrating the fault energy distribution vectors of all time slices, a decoupled fault feature matrix is ​​constructed.

6. The method according to claim 5, characterized in that, Based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, the resonant kernel weights of the adaptive resonant neural network are updated through an online adversarial training mechanism to generate a real-time protection decision instruction set. This instruction set includes fault level assessment and fault type location information, including: The decoupled fault feature matrix is ​​compared with the historical fault database. The similarity between each column vector and the corresponding historical fault is calculated by the dynamic time warping algorithm, and the fault matching degree vector is output. Using the fault matching degree vector as a condition, an enhanced fault sample is synthesized through a conditional generative adversarial network to generate an adversarial training sample set. The adversarial training sample set is injected into the adaptive resonant neural network, and the resonant kernel weights are updated using an online meta-learning strategy to output the optimized resonant kernel parameters. The fault type is located based on the elements in the fault matching degree vector that exceed the preset matching threshold. The protection level is determined by combining the energy gradient, and a real-time protection decision instruction set containing fault level assessment and fault type location information is generated.

7. A rotating machinery vibration protection system based on an adaptive resonant neural network, characterized in that, The system includes: The acquisition module is used to acquire millisecond-level vibration acceleration signals of rotating machinery through a distributed piezoelectric sensor array, and at the same time obtain real-time operating parameters of the equipment to generate a time-work synchronous vibration signal stream. The input module is used to input the time-work synchronous vibration signal stream into the adaptive resonance neural network and dynamically generate a frequency domain-time-varying adaptive threshold group in combination with the working condition parameters. The threshold group includes the resonant frequency band energy limit under different fault modes and exhibits nonlinear adaptive characteristics as the rotational speed changes. The decoupling module is used to decouple the vibration signal flow nonlinearly using the multi-scale wavelet resonance kernel of the adaptive resonance neural network and extract the weak impact resonance feature tensor. The tensor includes the transient impact component, modulation sideband component and resonance attenuation characteristics of the early fault under unsteady conditions. The multi-scale wavelet resonance kernel is composed of a set of parallel complex Morlet wavelet transform layers, each layer corresponding to a specific center frequency and bandwidth. The separation module is used to project the weak impact resonance feature tensor onto the orthogonal fault subspace using a tensor decomposition algorithm to separate the decoupled fault feature matrix, wherein each column of the matrix independently represents the resonance mode energy distribution of a typical fault. The generation module is used to update the resonant kernel weights of the adaptive resonant neural network through an online adversarial training mechanism based on the comparison results between the decoupled fault feature matrix and the equipment operation history database, and generate a real-time protection decision instruction set, wherein the instruction set includes fault level assessment and fault type location information.

8. The system according to claim 7, characterized in that, The acquisition module is specifically used for: Based on the geometric characteristics of the bearing housing of rotating machinery, a piezoelectric sensor array is deployed on the surface of the equipment using a spatial symmetric point placement algorithm to generate a three-dimensional sensor coordinate mapping table; Multi-channel synchronous acquisition is triggered based on a coordinate mapping table. The original vibration signal is acquired with a preset sampling period. The rotational speed and load parameters are read in real time through the industrial bus, and the original multi-source signal stream with timestamp is output. The original multi-source signal stream is input into an adaptive noise complete set empirical mode decomposer, and the speed fluctuation noise is separated by the operating parameters to generate a noise-reduced signal stream with decoupled operating conditions. The noise-reduced signal stream is dynamically resampled to synchronize with the rotational speed. The sampling interval is adjusted according to the instantaneous rotational speed to output a time-to-work strictly synchronized vibration signal stream.

9. A storage medium, characterized in that, The storage medium stores a computer program, wherein the computer program is configured to execute the method of any one of claims 1-6 when it is run.

10. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the method of any one of claims 1-6.

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