Vibration measurement information enhancement method based on fusion data

Abstract

The invention discloses a vibration measurement information enhancement method based on fusion data, and relates to the technical field of vibration measurement information enhancement. Edge nodes splice reasoning probability, frozen layer activation statistics, weak spectrum gradient direction and frozen layer gradient variance to generate a multi-source confidence tensor, and a heat peak list is formed through adaptive time-frequency kernel mapping; the information is uploaded after being subjected to redundancy elimination screening; a central node distributes domain credibility to each domain and then constructs a global heat map by adopting self-attention weight fusion heat peaks, and links hierarchy, frequency bands, links and working condition nodes in a mechanism attribution map network to calculate a causal path; and an attribution result triggers a strategy rule engine to select a corresponding maintenance script or a network self-checking instruction, and the maintenance script or the network self-checking instruction is pushed to a monitoring large screen, a mobile terminal and a mail in a unified message packet format along with a global heat map and a reason link, so that display and explanation of weak fault abnormity and operation and maintenance instruction closed loop are completed.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration measurement information enhancement, and in particular to a vibration measurement information enhancement method based on fused data. Background Art

[0002] In the context of the Industrial Internet, equipment health management is rapidly shifting from offline spot inspections to continuous perception and intelligent decision-making models enabled by edge-cloud collaboration. High-frequency vibration, acoustic emission, and current signals can be transmitted from field collectors to edge nodes within milliseconds, enabling soft real-time fault detection through local inference. This avoids bandwidth and latency bottlenecks caused by transmitting all raw waveforms back to the data center. As industrial assets are deployed across regions, companies are increasingly integrating multi-factory nodes into global diagnostic models through federated or distributed learning frameworks to share fault knowledge, reduce training costs, and comply with data sovereignty regulations. Furthermore, edge computing is shifting fault diagnosis from a single-point model to a heterogeneous multi-domain model. Each device has independent hardware, load, and environmental conditions, resulting in weak and dispersed spectral signatures for similar faults under different operating conditions. To maintain diagnostic accuracy, the system must perform energy normalization and time baseline alignment on the device side. It then relies on gradient compression, secure aggregation, and covariance alignment to address cross-domain representation differences. Finally, continuous monitoring and dynamic fine-tuning are used to mitigate performance degradation caused by data drift. However, existing industrial platforms mostly focus on one aspect: either they emphasize compression and encryption but ignore the significance of weak fault spectra, or they emphasize high-level fine-tuning but lack a fusion framework for hierarchical freezing and explanatory visualization. When deployed in multiple factories, they often encounter the dual dilemma of "model drift" and "surge in false alarms."

[0003] A solution is proposed to the core technical problem that "cross-domain weak fault diagnosis systems are difficult to operate in a stable, explainable and privacy-compliant closed loop under conditions of continuous distribution drift."

[0004] Specifically, due to the differences in equipment operating conditions, sensor accuracy, and network quality in each factory, the gradients and features uploaded to the central node have covariance differences and high-order phase-amplitude coupling differences in statistical distribution. If the central end only performs simple averaging or fixed threshold monitoring, weak fault spectra will be masked by high-energy channels when the global model is aggregated, resulting in the omission of hidden dangers such as early cracks, howling, or insulation aging. Once the hidden danger evolves into a strong fault, it will lead to unplanned downtime or even personal safety accidents, and cause subsequent models to produce catastrophic forgetting driven by extreme values.

[0005] At the same time, traditional plaintext feature alignment solutions expose sensitive enterprise data in multi-domain environments, violating compliance requirements such as GDPR. Furthermore, full model retraining cannot meet real-time requirements under high-frequency production cycles. Therefore, this paper provides a method for enhancing vibration information based on fused data. Summary of the Invention

[0006] (1) Technical problems solved In response to the shortcomings of the existing technology, the present invention provides a vibration information enhancement method based on fused data, which can complete feature statistical alignment in the encrypted state, strengthen weak spectral lines through self-supervision on the edge side, maintain the model steady state through dynamic freezing and high-level fine-tuning on the center side, and finally push the abnormality confidence to the overall system of the operation and maintenance interface in the form of visual heat maps and cause links, so as to ensure that weak cross-factory faults are reliably captured in the embryonic stage and the remedial measures are clear and timely, avoiding the consequences of false alarms, missed alarms and data leakage, thereby solving the technical problems recorded in the background technology.

[0007] (2) Technical solution To achieve the above objectives, the present invention is implemented through the following technical solutions: The vibration information enhancement method based on fused data includes preprocessing the source signal at each device edge node, generating a unified feature tensor, compressing it with a contrast encoder, and then using elliptic curve homomorphic encryption to form a gradient summary and upload it to the central node; The central node performs dense outer product and debiasing operations on each encrypted gradient summary, uses Riemann distance and weighted Karcher mean to obtain the global central covariance, compresses it into a domain adaptation matrix and sends it to the edge node; After the edge node receives the adaptation matrix, the time-frequency fusion network is recalibrated by progressive stitching of high-order tensors, differential weight shrinkage, and spectral gated gradient weighting, and spectral suppression is used to enhance the significance of weak spectral lines. Each edge node compresses and generates feature prototypes, exchanges them bidirectionally, and verifies security through salt value curve coupling. After verifying the cross-domain deep representation synchronization, a global consistency check is performed. The central node continuously monitors the spectral weighted comprehensive index, calculates the Riemann incremental distance to generate a dynamic threshold; when the spectral weighted comprehensive index exceeds the threshold, it freezes the low- and middle-level parameters, increases the high-level learning rate, and allows for fine-tuning of the weak spectrum mask; after the index recovers, it rolls back and unfreezes the parameters according to importance, maintaining the stability of the learned weak fault representation and absorbing new operating condition characteristics; Furthermore, when any edge node detects an increase in anomaly confidence based on the updated model, an anomaly confidence heat map and cause link are automatically generated and pushed to the operation and maintenance interface.

[0008] Furthermore, a prediction-correction phase-locked algorithm is used at the edge node to achieve time baseline synchronization of multi-source signals, and Lyapunov energy normalization combined with complex wavelet coupling and pseudo-bilinear embedding is used to generate a unified feature tensor to ensure that the weak fault spectrum line still maintains three-dimensional consistency in phase, energy and frequency domain under cross-device sampling differences.

[0009] Furthermore, the unified feature tensor is compressed into a latent vector through a bidirectional mutual information constrained contrast encoder and multi-resolution self-gated projection, and the gradient is batch encrypted by calling the elliptic curve homomorphic encryption operator on the edge side, and then uploaded to the central node through RaptorQ slicing with divergence verification.

[0010] Furthermore, after the central node receives the encrypted gradient summary uploaded by the edge node, it maintains the encrypted state to complete the dense covariance reconstruction and uses the Riemann distance to evaluate the multi-domain distribution differences. The global central covariance is obtained using Karcher mean iteration, and the corresponding domain adaptation matrix is ​​generated based on the joint constraints of geometric regularization and physical regularization.

[0011] Furthermore, the mapping matrix is ​​subjected to orthogonal robust compression and link adaptive quantization, and is redundantly sliced ​​by RaptorQ and sent to the edge nodes. Edge feedback is synchronously collected to verify whether the divergence threshold is met, and the adaptation status is updated in the central database to perform feature drift suppression and global model distribution homogenization.

[0012] Furthermore, after the edge node receives the domain adaptation matrix, it uses high-order projection progressive stitching to inject the mapped feature tensor core statistics into the time-frequency fusion network. Then, through differentiated weight shrinkage combined with spectral gated gradient energy weighting, the convolution kernel is adjusted to make the network power spectrum consistent with the global central spectrum, and the low-amplitude frequency band output is kept stable under the protection of energy compensation residual.

[0013] Furthermore, after completing the weight calibration, the same node enables mutual information redistillation to undertake the comparative structural discrimination information, and then improves the resistance to link jitter and high-energy pseudo-peaks through noise-driven occlusion consistency and multi-scale spectral suppression, relying on disturbance-aware annealing to dynamically balance the loss weight.

[0014] Furthermore, the edge nodes perform high-order tensor entropy-driven compression to generate prototype vectors, and complete the prototype secure exchange through bidirectional homomorphic encryption exchange with random salt hash verification, and then synchronize the deep representation using weak spectral residual distillation; All nodes broadcast the prototype Bloom hash summary to the center. The center triggers the complementary exchange based on the coverage result and sends down random sampling retrieval for each node to perform Hadamard tensor consistency check.

[0015] Furthermore, after the consistency check, the center fuses the weak spectrum mask weights of each node to generate a weak spectrum common mode mask and broadcasts it again. The edge node updates the spectrum suppression module accordingly and uses Pareto pruning to maintain the size of the prototype library, performing cross-domain deep feature alignment and weak spectrum knowledge sharing.

[0016] Furthermore, the central node continuously aggregates the comprehensive loss, link divergence and consistency score to generate a spectral weighted index and calculates the incremental distance in real time, and updates the dynamic threshold through exponential sliding; When the spectral weighted index exceeds the threshold, the central node freezes the low-level and middle-level parameters according to the hierarchical importance, while increasing the high-level learning rate and authorizing the edge nodes to perform block-level fine-tuning based on the weak spectral mask.

[0017] Furthermore, during the freezing period, the central node continuously monitors the indicator curve. If the continuous window is lower than the rollback threshold, the frozen layers are unlocked in sequence and the learning rate is decayed to the original value, while confirming the updated weak spectrum mask.

[0018] Furthermore, the edge node concatenates the inference probability, frozen layer activation statistics, weak spectrum gradient direction and frozen layer gradient variance to generate a multi-source confidence tensor and forms a heat peak list through adaptive time-frequency kernel mapping, which is uploaded after information redundancy screening.

[0019] Furthermore, the central node assigns domain credibility to each domain and then uses self-attention weights to fuse heat peaks to construct a global heat map. It also connects the levels, bands, links, and working condition nodes in the mechanism attribution graph network to calculate the causal path. The attribution result triggers the policy rule engine to select the corresponding maintenance script or network self-test instruction, and pushes it to the monitoring screen, mobile terminal and email along with the global heat map and cause link in a unified message package format.

[0020] (3) Beneficial effects The present invention provides a method for enhancing vibration measurement information based on fused data, which has the following beneficial effects: The global central covariance and domain adaptation matrix are reconstructed and distributed under a homomorphic encryption environment, breaking through the bottleneck of plaintext alignment and achieving zero-leakage alignment of features across factories. Subsequently, the mapped feature tensor is rapidly integrated into the new energy shell through high-order projection progressive stitching and differentiated weight shrinkage, ensuring that weak fault spectra are fully significant without re-labeling. The combined loss and link divergence are then weighted by a weak spectral common mode mask to form a spectrum-aware threshold curve. This allows freeze-and-fine-tune decisions to address both model drift and network health, enabling stable weak fault representations with minimal parameter adjustments when incremental operating conditions arise. During the dual distillation phase, compressed prototypes are encrypted and exchanged using random salts, combined with residual distillation and Hadamard consistency tests to construct a high-order representation sharing network. This transforms the weak fault discrimination hyperplane from being specific to a single domain to a global consensus, significantly suppressing inter-domain recall fluctuations.

[0021] Dynamic threshold-driven progressive freezing locks only low- and mid-level parameters with a cumulative importance of 70%, while high-level learning rates adaptively absorb new operating condition information within a hundred-step gradient. The anomaly confidence tensor incorporates the frozen layer gradient variance and weak spectrum gradient direction, undergoes information redundancy screening, and is then compressed and uploaded. Heatmaps are inferred from the mechanism attribution graph network to determine the root cause, and the policy rule engine is then linked to generate a maintenance script containing the frozen layer set, weak spectrum update mask, and high-level learning rates, ultimately achieving a one-click closed loop for the "model-network-human" triad. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The figure is a flow chart of the vibration information enhancement method based on fusion data of the present invention. DETAILED DESCRIPTION

[0023] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0024] See also Figure 1 The present invention provides a method for enhancing vibration information based on fusion data, comprising: In the Industrial Internet, distributed vibration and acoustic emission monitoring systems, when faced with multiple factories, multiple machine types, and complex environmental background noise, often experience time base drift, energy scale imbalance, and heterogeneous operating conditions. These issues directly hinder the global diagnostic model from accurately capturing weak fault spectra. Relying solely on traditional synchronization or simple normalization methods often accumulates errors during cross-domain migration, amplifying the risk of false detections and missed detections.

[0025] Step 1: On the edge side, high-precision alignment and energy-to-scale mapping of multi-source signals are achieved with minimal communication overhead, and a gradient summary protected by homomorphic encryption is generated, providing a cross-domain feature base that can be directly spliced ​​for global fusion at the central node; The step 1 includes the following: Step 101: Unify time baseline and energy normalization The acquisition equipment at Factory AN has inconsistent manufacturers, sampling rates, and trigger clocks. Directly concatenating the multi-source signal matrices can easily cause phase misalignment in the short-time Fourier window overlap region, weakening weak fault spectrum peaks. Based on this, a dual-domain time baseline reconstruction and energy Lyapunov normalization chain is proposed. This ensures time alignment accuracy using a continuous minimum adjoint error, thereby improving the subsequent comparison encoder's ability to learn the significance of weak fault spectrum lines.

[0026] In most old production lines, the acquisition board is often asynchronous with the PLC clock, which causes the sampling points of different nodes for the same mechanical impact event to be staggered by tens to hundreds of sampling cycles. To this end, the original multi-source signal matrix is ​​first Execution sampling clock vector With the whole station reference clock The differential mapping is used to construct the synchronous shift function and obtain the optimal shift through saddle point iteration. ,in,

[0027] Where: is the instantaneous synchronization offset function, unit is s; is the window start time; is the sliding window length, unit s; is the time shift to be determined, with a value range of ; Euclidean norm, used to measure the difference between two trajectories.

[0028] After synchronization is completed, in order to avoid high energy channels drowning out weak signals, the Lyapunov energy function is introduced :

[0029] Reuse exponential decay Construct dimensionless, take value The convergent normalized coefficient of :

[0030] Where: is the signal after time base synchronization; : The mean vector of the window signal; Positive definite weight matrix, ensuring Zhengding; is the Lyapunov attenuation coefficient, ; Among them, the vibration levels of industrial pump stations and precision electric spindles can differ by two orders of magnitude; if simply normalized by maximum-minimum value, low-energy signals will be lost due to quantization error, so the Lyapunov energy function is introduced. The reason is that it can measure the stability of the instantaneous energy deviation from the mean, and through the Lyapunov attenuation coefficient The adjustable exponential attenuation allows the weak energy channel to obtain higher dynamic gain while maintaining the stable output of the strong energy channel.

[0031] After unifying the energy scale, the complex Morlet-Bérenger wavelet packet is introduced To perform bidirectional coupling:

[0032] Where: is the energy normalized signal; is the center frequency ,scale The complex wavelet basis of is the frequency domain coupling coefficient; is an imaginary unit; Among them, the frequency domain coupling coefficient Weighted priors for specific equipment categories are introduced during the construction phase; for example, a spectral weight of 0.6 is assigned to the high-speed spindle channel and 0.3 to the low-speed hydraulic pump channel, thereby strengthening the voice of high-speed fault components in the overall characteristics.

[0033] By frequency domain coupling coefficient Perform bilinear embedding mapping to obtain a time-frequency embedding tensor that is consistent with the input dimension of the subsequent comparison encoder :

[0034] Where: 、 : Trainable mapping matrix, size is and ; is the bias vector; is the hyperbolic tangent nonlinear function.

[0035] Establishing a unified time-energy-frequency embedding tensor through continuous mapping , laying a high consistency feature foundation for low-occupancy broadband gradient generation; Output time-frequency embedding tensor and convergent normalization coefficients This will be used as a benchmark for comparing coding loss and gradients in step 102, enabling horizontal threading parameter reuse. Unlike traditional CNN-LSTM splicing, bilinear embedding preserves phase-amplitude coupling information, enabling subsequent mutual information loss to directly detect slight drifts in phase space for weak faults.

[0036] When used, sub-step 101 achieves precise alignment of time baselines across factories and equipment and dynamic equipotentialization of energy scales. After the phase reference is unified, the time domain subtle changes of weak faults are no longer masked by sampling offsets; Lyapunov gain allows very low-amplitude early defect spectra to be significantly amplified in the energy domain, while high-energy impacts are suppressed to prevent quantization degradation caused by excessive dynamic range. Wavelet-weight coupling further allows signals with different speeds and different excitation modes to be comparable in the multi-resolution frequency domain, providing the generated time-frequency embedding tensor. Provide a cross-domain homogeneous foundation.

[0037] In the past, energy normalization mostly used RMS or piecewise normalization, which made it difficult to dynamically resist energy drift. By binding the stability criterion of the Lyapunov function to the exponential decay gain, the gain is made adaptive to the energy distribution of each window, rather than a global fixed ratio. In addition, the weighted complex wavelet energy is aligned and embedded in a learnable prior, so that the frequency weights no longer rely on manual adjustment, but are self-consistently updated through subsequent gradients, ensuring that the most diagnostically valuable spectral lines can still be highlighted under different working conditions. Finally, time-frequency pseudo-bilinear embedding achieves dimensionality reduction while maintaining phase-amplitude correlation, providing a low-latency, highly consistent input facade for subsequent contrast coding, breaking the limitation of traditional CNNs that require a large number of convolutional layers to capture phase information.

[0038] Step 102: Compare encoder compression and encrypted gradient summary reports Embed high-dimensional time-frequency into tensors while maintaining weak fault discrimination Compression into Encrypted Gradient Summaries via Self-Supervised Contrastive Learning , and securely upload to the central node. Even after unified normalization, edge nodes still face dual constraints of bandwidth and privacy. Traditional dimensionality reduction sacrifices fine-grained spectral patterns. A contrast encoder based on maximizing bidirectional mutual information, supplemented by elliptic curve homomorphic encryption, achieves a "high-fidelity, high-security, and low-overhead" gradient transmission chain.

[0039] First embed the time-frequency tensor Generate positive sample tensor and pseudo-negative tensors , define the mutual information enhancement loss:

[0040] in 、 They are query-key mapping functions; is the vector dot product; To compare the distribution temperature, ; is the negative sample set; is the information constraint loss.

[0041] Among them, classic MoCo or SimCLR often only focus on the one-way query-positive sample cohesion, which is extended here to a two-way mutual information constraint, which not only penalizes positive samples that are too far away, but also penalizes negative samples that are too close together; Through noise adaptive regulation, when the edge node detects an increase in on-site electromagnetic interference, the temperature coefficient is automatically reduced to prevent gradient explosion.

[0042] The output of the encoder is gated and projected to obtain the gated latent vector. :

[0043] in, For the stage Generalized mean pooling of Sigmoid activation; is the Hadamard product; 、 is a trainable gating parameter; is the generalized mean order, ; is the gated latent vector; Among them, the gating matrix During the projection process, it automatically switches on and off according to the signal energy density, leaving enough representation space for high-frequency sparse signals.

[0044] Based on gated latent vector Calculate the detection loss gradient , and then perform elliptic curve homomorphic encryption to ensure that the central node can directly perform gradient aggregation without being able to reverse the original features:

[0045] Where: is the elliptic curve homomorphic encryption operator; is the node public key; is the encrypted gradient summary.

[0046] Among them, the elliptic curve homomorphic encryption operator Encrypted gradient summary guaranteed The central node can directly perform weighted averaging in the encrypted domain and output the aggregated gradient without decryption.

[0047] Encrypting the gradient summary Perform RaptorQ-FEC slicing and use Hamiltonian cross-divergence to monitor packet-level consistency. If the threshold is exceeded, re-encoding is triggered:

[0048] Where: is the mask distribution of adjacent slices; is the Hamiltonian cross divergence; the divergence threshold Set to: .

[0049] Through the triple chain of information temperature-gating-homomorphic encryption, the fault judgment gradient is retained and the data leakage surface is minimized; Hamiltonian divergence verification further ensures transmission integrity in weak network environments.

[0050] RaptorQ-FEC Pair Encryption Gradient Summary After performing slice redundant coding, the Hamiltonian cross divergence is introduced As a real-time packet similarity indicator: if the distribution difference between two consecutive pieces increases suddenly, it means that one piece has a bit flip due to noise damage, and a retransmission will be requested immediately instead of waiting for the central node to time out and reply.

[0051] Final output encrypted gradient summary , information constraint loss Hamiltonian cross divergence ; where encrypted gradient summary In step 2, it is used to count the covariance differences between domains, and the information constraint loss Hamiltonian cross divergence It serves as the loss fluctuation benchmark for subsequent progressive weight freezing, thereby achieving horizontal concatenation of parameters throughout the entire process.

[0052] When used, sub-step 102 compresses highly redundant features with more than 100 dimensions into encrypted gradient summaries And encrypted reporting, significantly reducing network bandwidth and storage overhead; at the same time, the bidirectional mutual information constraint ensures that the latent vector still contains the discriminant dimension that is most sensitive to weak faults. Gated projection combined with generalized mean pooling effectively avoids the amplification of high-order sparse noise during the dimensionality reduction process. Elliptic curve homomorphic encryption ensures that the central node can directly perform gradient fusion without any decryption steps, eliminating the high-latency link of "first decomposition and then aggregation" in the traditional federation mechanism. RaptorQ-FEC combined with Hamiltonian cross divergence Checksum further ensures data integrity on links with high bit errors or high packet loss.

[0053] Through steps 101 and 102 , the edge node achieves lossless and low-load conversion from original multi-source signals to encrypted gradient summaries.

[0054] The central node receives the encrypted gradient summary Afterwards, the covariance difference calculation and domain adaptation matrix generation can be directly performed in step 2, completely avoiding repeated synchronization and normalization overhead, and achieving a closed-loop edge-cloud collaboration. Furthermore, because elliptic curve homomorphic encryption ensures gradient additivity, global fusion of central nodes does not destroy the encrypted state, making it perfectly compatible with privacy collaboration strategies such as dual distillation.

[0055] In the cross-factory industrial Internet scenario, the edge node has uploaded the encrypted gradient summary to the central node through step 1. The central node must complete cross-domain distribution statistics in a confidential state and generate a domain adaptation matrix in real time to offset feature drift caused by different equipment operating conditions. If only gradients are simply averaged or a fixed mapping is used, the high-energy channel will suppress the covariance of the low-energy channel, and weak fault spectra will be diluted after the global model is merged.

[0056] Step 2: Under the condition of maintaining the dense state, the high-order covariance difference of the encrypted gradient summary of each domain is estimated, and the global Riemann center covariance is iteratively solved to generate the domain adaptation matrix, which is sent to the edge node to suppress feature drift in real time; The second step includes the following: Step 201: Estimation of the dense state covariance difference and solution of the global central covariance Encrypted gradient summary uploaded by each edge node It has homomorphic additivity, but its distribution state is hidden by the curve mapping; if the central node rashly decrypts it, it will violate privacy compliance requirements, so statistics must be completed directly in the secret state. The current mainstream federated method only calculates the mean and ignores the covariance, making it impossible to correct cross-domain energy shell differences. To this end, the covariance tensor is reconstructed through secret state operations, the Riemann metric is introduced to quantify the differences, and the weighted Karcher mean iteration is used to obtain the global covariance. .

[0057] The central node first uses the homomorphic multiplication property to perform a dense outer product operation on the gradient summaries of the same batch:

[0058] Among them, the high-level fine-tuning learning rate is the original gradient matrix of the i-th domain; is the encrypted gradient summary of the i-th domain; It is the homomorphic outer product, and the corresponding curve is mapped to the new point set after multiplication; is the unencrypted gradient outer product, which is kept encrypted here.

[0059] Among them, the central node, without knowing the plaintext gradients of each domain, still uses the "product mapping closure" property of the homomorphic operator to convert each encrypted gradient summary into After grouping by batch, a point-to-point curve product is performed and written to the secret tensor pool. This process does not generate additional decryption keys and does not introduce information leakage, because the outer product result remains in the curve domain element set. Any observer without the key can only see a random point cloud.

[0060] Among them, the outer product result contains the gradient mean shift term. To avoid the covariance estimation bias, the central node uses dense linear combination to debias:

[0061] in 、 are respectively under-curve addition and scalar multiplication, is the homomorphic outer product; The mean of the gradient summary of the i-th domain can be obtained homomorphically; is the dense debiased covariance matrix of the ith domain.

[0062] Because the gradients uploaded from each domain have been gated and compressed, the density of the vector dimensions is uneven. Directly using the outer product as the covariance would cause mean shift to multiply noise in weak domains. In the dense state, a curve addition operator is used to "dimension-by-dimension" offset the mean term, while a dynamic threshold selection option is used to suppress Gaussian noise mapping points in sparse dimensions, thereby constructing a zero-mean covariance without exposing any statistics.

[0063] The covariance matrix is ​​naturally on a symmetric positive definite manifold, and the Frobenius distance underestimates the spectral difference, so the Riemann logarithmic mapping is used:

[0064] in: is the matrix logarithm operator, approximated by Taylor series in the dense state; is the Frobenius norm, which is used to quantify the distance within the manifold; is the Riemann distance, used as the difference weight; is the debiased covariance matrix of the j-th domain, Among them, in order to avoid the underestimation caused by the “straight line approximation” of the Euclidean metric on high-dimensional positive definite manifolds, each debiased covariance matrix Projecting to the tangent space and then approximating the Riemann distance with a logarithmic mapping sequence not only preserves the spectral structure information but also gives the distance quantity the weighted property of weak peak tilt.

[0065] Considering that the number of domains can reach thousands in large factory clusters, a single global iteration requires traversing all covariances if traditional averaging is used, which results in unacceptable latency. Therefore, the covariances of each domain are projected into the manifold tangent space, and the weighted Karcher mean iteration is used to solve the global central covariance until ,in:

[0066] in: is the number of domains, Depend on The normalized weighting coefficient is is the matrix index, used to return the manifold from the tangent space, is the convergence threshold, which is always set ; is the global central covariance; By completing covariance reconstruction, difference quantization and center solution in the dense state, an accurate benchmark is provided for the next step of generating the domain adaptation matrix.

[0067] When used, sub-step 201 allows the central node to obtain the geometric center of the covariance of each domain without touching any plaintext, significantly improving the accuracy of subsequent feature alignment. Because the Riemann distance can better reveal spectral structure differences than the Euclidean distance, the response delay to sudden changes in equipment load is compressed to seconds; and the batched Karcher mean ensures that the convergence speed remains stable when the domain is expanded on a large scale, avoiding the disadvantage of traditional global averaging that slows down the entire federated training rhythm when the number of domains increases sharply. With the help of curve operators, the outer product and additive closure are maintained, cleverly avoiding the decryption operation. At the same time, the batched Karcher mean is recursively applied in the manifold space, breaking through the bottleneck of the traditional requirement of simultaneous iteration of the entire domain, solving the problem of "domain massive + high-level fine-tuning of learning rate in real time" that cannot be achieved at the same time, and realizing a highly privacy-compliant, scalable, and explainable distribution alignment foundation in industrial weak fault diagnosis scenarios.

[0068] Step 202: Generate and send synchronous feedback of domain adaptation matrix Get the global central covariance After that, the central node needs to construct a linear mapping for each domain so that the corresponding time-frequency embedding tensor After mapping, the covariance space and the global center covariance Alignment, while ensuring the matrix is ​​invertible and numerically stable. Relying solely on Cholesky decomposition will amplify noise on weak domains, so the following process is used to generate the domain adaptation matrix And send it synchronously.

[0069] Define a mapping for each domain so that the covariance after mapping satisfies ,in:

[0070] in: is the identity matrix, and the debiased covariance matrix Same level; is Tikhonov regularization, take To suppress singular values; is the domain adaptation matrix; In order to reduce the bandwidth of the delivery, the domain adaptation matrix Perform orthogonal singular value truncation: retain the singular value energy high-level fine-tuning learning rate> 99.5% corresponding column vector and re-orthogonalize to generate the compressed adaptation matrix , will be sent to the edge; this operation reduces the communication load and avoids numerical amplification, where the singular value energy threshold is fixed to the high-level fine-tuning learning rate 0.995.

[0071] Global Central Covariance After the calculation is completed, the central node constructs the domain adaptation matrix for each domain When calculating the covariance, not only does it mathematically ensure covariance alignment, but it also injects dual-label information of model and state: by consulting the "device-load" comparison table, the regularization term is adjusted according to the device category and real-time speed. , increase the penalty on high-speed models to prevent singular values ​​from amplifying high-frequency noise; reduce the penalty on low-speed hydraulic systems to ensure that weak vibration channels are not over-compressed.

[0072] According to the link strength mark reported by each domain handshake, the compression adaptation matrix The bit width b selected by SNR is divided into four levels according to SNR. . Then use the Hamiltonian cross divergence upper bound for downlink verification They are encapsulated together into RaptorQ slices to achieve synchronous delivery and verification.

[0073] The quantization bit width b is not fixed but is derived from the real-time SNR measured during the handshake phase. If the edge-to-center link SNR drops below 12dB, the quantization bit width b is reduced to 8 high-level fine-tuning learning rate bits and two-fold redundant slices are automatically inserted. When the SNR recovers above 22dB, the quantization bit width b is increased to 12 high-level fine-tuning learning rate bits and the additional redundancy is removed.

[0074] The central node receives the edge confirmation packet and verifies the downlink divergence indicator of the edge return After that, the domain status is marked as "adaptation completed"; if it exceeds the limit, the corresponding slice is automatically resent and the link risk is highlighted on the monitoring dashboard.

[0075] Output compression adaptation matrix In step 3, we will directly apply the edge time-frequency embedding tensor to the And the corresponding weights, Tikhonov regularization Downward Divergence Then the process flows horizontally to the progressive weight freezing threshold calculation path in step five.

[0076] In order to shorten the round-trip delay of confirmation, the central node sends the checksum of the first row of the mapping matrix before compression when sending. The edge node directly calculates the local checksum after unpacking and returns the downlink divergence index. and two status flags. If the two are inconsistent or the divergence exceeds the threshold, the central node immediately resends the missing slice instead of the entire packet; By using the generalized inverse mapping of "geometric-physical dual regularization" and the robust compression of "orthogonal-random filling" in parallel, the statistical distribution is aligned and the device mechanism constraints are embedded; link adaptive quantization enables real-time linkage between model updates and network conditions.

[0077] Step 2: The multi-domain feature statistical differences are accurately captured through the “dense covariance reconstruction-Riemannian metric difference estimation-Karcher mean iteration” in step 201, and the domain adaptation matrix is ​​generated in step 202 through “generalized covariance inverse mapping-orthogonal robust compression-link adaptive quantization”. Send to edge nodes.

[0078] The entire chain remains in homomorphic encryption without decryption, which not only meets the privacy requirements of GDPR and corporate internal control, but also ensures the accuracy and real-time performance of matrix calculations; edge nodes can use the lightweight domain adaptation matrix in step 3. The time-frequency fusion network weights are recalibrated, and the consistency loss is combined to enhance the significance of weak fault spectra, thereby continuously improving the diagnostic sensitivity in global collaboration while ensuring the robust evolution of the model during equipment operating condition drift.

[0079] In step 2, the domain adaptation matrix is ​​completed. After the release of Mapping to global covariance Homogeneous linear tools. However, linear alignment alone is not enough to completely suppress the attenuation of weak fault spectra in deep networks, because the time-frequency fusion network (TF-Net) of the edge model has formed "inertia weights" for the local energy distribution during the early training phase. Without targeted recalibration, the new input distribution will mismatch the old weights, causing diagnostic performance fluctuations. At the same time, the central node does not have timely access to all incremental labels for each production line; therefore, the edge side must rely on a self-supervised consistency mechanism to continuously emphasize weak fault spectra in unlabeled or weakly labeled conditions to ensure agile and stable convergence of the global model. To solve this problem, the following approach is adopted: Step 3: Recalibrate the edge TF-Net weights based on the domain adaptation matrix and inject a self-supervised consistency loss chain to ensure that weak fault spectra maintain high significance and continuously enhance diagnostic sensitivity after cross-domain feature alignment.

[0080] The step three includes the following: Step 301: Recalibrate the time-frequency fusion network weights Although there is a compression adaptation matrix As a linear alignment tool, the convolution kernels and channel attention within TF-Net are locally distributed. Directly applying a new mapping will cause rotational misalignment in the high-level feature space, resulting in a sharp drop in recall during the first round of inference. To address this issue, the following approach is adopted: The edge node first performs a fourth-order tensor projection on the mapped feature tensor and converts the high-order statistical kernel into The Tucker kernel is written as a high-order statistical prior into the first layer of TF-Net BatchNormalization center vector coal, where:

[0081] Where: is a fourth-order flatten-fold operator used to generate a fourth-order tensor; Tucker kernel: a core tensor extracted by high-order SVD, used to capture high-order correlations; By injecting high-order correlations at once, the lower layers of the network can quickly align to the new distribution without the need for large-scale gradient backpropagation; the network recovers a stable activation distribution in just a few hundred steps.

[0082] Subsequently, a weight contraction term is introduced into the TF-Net backbone. This term drives the weights to be compressed in the consistent direction after mapping to avoid overfitting local noise, where:

[0083] in, is the historical weight before mapping, is the shrinkage coefficient, and its value is , regulate the regression speed; For the current layer convolution kernel; and, in order to make the contraction direction more consistent with the physical characteristics of the domain, It is no longer globally fixed, but is dynamically adjusted by the proportion of power spectrum energy occupied by the convolution kernel channel; Then, a spectral gating unit is inserted after each convolution layer, and the power spectral density vector of the output tensor is calculated by fast Fourier transform. , and with the global center spectrum (Depend on Diagonal element conversion) Calculate Jensen-Renyi distance ,dynamically adjust the gating tensor to allow channels with large spectrum gaps to obtain higher learning rates; Get the layer learning rate gain as follows :

[0084] Where: is the spectrum gating smoothing coefficient, with a value of 5-10; For the Layer learning rate gain.

[0085] In addition to the aforementioned learning rate modulation, the spectral gating unit also performs energy weighting on the gradient in the back propagation phase: the gradient of the row vector corresponding to the frequency is calculated according to Scaling allows the network to see a clear signal of "shifting energy to the weak spectrum" in one forward-backward cycle, without having to wait for multiple rounds of training to accumulate.

[0086] Finally, in order to prevent the weak domain energy from being diluted by high-order projection, the final feature tensor is introduced :

[0087] in, is the mean-zero noise base, energy compensation coefficient and energy normalized gain Homologous but compressed by Sigmoid to .

[0088] This compensates for low-amplitude spectral lines without excessively raising the noise floor; thus, TF-Net fully realigns parameters and spectral density in a short period of time, ensuring that the subsequent self-supervision mechanism can strengthen weak fault spectral lines on a stable baseline rather than repairing distribution dislocations, generating a new set of network weights. With dynamic learning rate gain , both will serve as important inputs for calculating consistency loss and mutual information distillation in step 302; high-order statistical kernel and global central spectrum Continue to flow horizontally to the dual distillation in step 4, which is used for high-order statistical verification when exchanging feature prototypes. Specifically, the network weight set The edge node receives the domain adaptation matrix and then maps the final feature tensor to the unified map. Perform progressive stitching of high-order tensors and backpropagate updates in real time according to a differentiated weight contraction rule.

[0089] When in use, progressive stitching of high-order statistics ensures a stable transition of network activation, differentiated contraction fully releases the degrees of freedom of the weak spectrum convolution kernel, spectral density gating directly amplifies the global central spectrum information in the reverse path through gradient reweighting, and the energy compensation satellite head monitors and corrects high-frequency noise in real time, providing timely and stable weight accommodation space for weak fault spectrum lines; combining progressive stitching of high-order tensors with differentiated contraction makes the high-dimensional statistical prior injection process have a "breathable" rhythm, fundamentally avoiding the activation oscillation formed by one-time injection.

[0090] Step 302: Self-supervised consistency loss and weak line saliency enhancement Even if the weights are linearly and spectrally aligned, weak fault features may still be masked by other high-energy patterns in unlabeled scenarios. Traditional contrastive learning and occlusion prediction each focus on local or global consistency, and cannot simultaneously amplify weak spectral lines while maintaining temporal stability. To address this, the following approach is adopted: The edge node first uses the query-key mapping generated in step 1 For the teacher network, the final feature tensor Generate teacher output; the student network is the calibrated TF-Net branch , lost through distillation Let the student network inherit the mutual information structure while keeping the new distribution adaptation, as follows:

[0091] Where: is the distillation weight, which is 0.5; KL is the Kullback-Leibler divergence; is the distillation temperature, and the comparison distribution temperature is continued The mean of is a function that maps a vector to a probability distribution; Mapping for students; The distillation strategy adds a new "local mutual information probe": mapping query-key The output is intercepted at the middle convolution layer, and the mutual information density is measured in a sliding window manner, allowing the student network to not only learn the global structure but also reproduce local sensitive patterns.

[0092] Apply random time shifts in the time dimension With random occlusion of 10% multi-scale wavelet blocks, consistency loss is applied to the two perturbation samples :

[0093] in is the consistency loss weight, with a value of 0.3. This loss ensures that the network output maintains a similar response to slight asynchrony and bandwidth loss, avoiding distortion of weak signals in actual acquisition noise; is the disturbance output, is random occlusion; Introducing frequency domain mask in frequency domain , applied to the high energy non-fault frequency band Weight, so that the gradient is mainly concentrated in the neighborhood of weak spectrum peak; mask frequency domain mask , from the aforementioned global central spectrum The difference between the current output power spectrum is thresholded and updated at the same frequency as the training step to ensure alignment with dynamic changes.

[0094] Frequency domain mask The activation threshold is no longer static, but reads the student-teacher KL divergence curve in real time. If the divergence drops too quickly, it means that the student has overfitted certain frequency bands. The mask threshold is automatically raised to suppress the gradient of the frequency band to prevent false confidence. This ensures that the inhibition logic avoids information loss caused by long-term suppression and prevents weak spectral lines from being re-submerged by other strong peaks after instantaneous overfitting.

[0095] Constructing comprehensive losses :

[0096] The annealing weight Adaptive annealing with distillation temperature:

[0097] 、 ,The annealing mechanism prevents the mutual information gradient from over-dominance in the late stage of training, and ensures that the final confidence distribution of the model is balanced.

[0098] When consistency is lost If it is continuously higher than the baseline by 20%, it means that the occlusion disturbance has not been eliminated; slow down The decay rate allows the mutual information gradient to maintain its guiding role for a longer time. This dual regulation ensures that annealing neither cools down prematurely nor dominates the total loss weight for a long time. The final output is the updated student network parameters , comprehensive loss curve With the mask in the frequency domain , where the comprehensive loss curve In step 5, the frequency domain mask is used as the global loss fluctuation monitoring benchmark. In step 4, they are exchanged together with the feature prototypes to constrain the frequency band consistency during dual distillation.

[0099] Dynamic probe distillation enables the student network to remain sensitive to local textures, noise-driven occlusion ensures close coupling of consistency targets with real-world perturbations, adaptive thresholding for multi-scale spectral suppression maintains the focus of weak spectral lines, and perturbation-aware annealing balances the relative strengths of mutual information and consistency at different stages. These synergistically improve the recall rate of weak faults in unlabeled scenarios and significantly suppress false positive spikes caused by link packet loss and electromagnetic noise.

[0100] Step 3 focuses on the local re-learning challenge after the application of the domain adaptation matrix. Through step 301, the TF-Net parameters, spectral domain distribution and global covariance center are quickly adjusted. Synchronization; then step 302 further maintains the weak line significance and output confidence stability in the unlabeled scenario.

[0101] The new weight set, comprehensive loss curve and spectral mask output by the two steps all maintain parameter uniqueness and are connected with the variables of the first two steps, providing a high-order statistical kernel for the dual distillation in step 4. and frequency domain mask Verification provides real-time loss baseline and divergence indicators for the progressive weight freezing in step five, which can ensure that cross-domain weak fault features are amplified while keeping the model stable, and ultimately improve the sensitivity of multi-source signal diagnosis in the industrial Internet environment.

[0102] Steps 1 to 3 have completed the significant amplification of weak fault spectrum from the data side to the model side, but the TF-Net of each plant area is at the center of the global covariance. Invisible high-order representation differences may still occur. Once these differences accumulate with environmental drift, they will form "grayscale distortion" in the central fusion model, causing the confidence level of cross-domain inference to fluctuate, weakening the stability of early fault warnings. To quickly smooth out high-order differences without exposing the original data or increasing the communication burden, the following measures are taken: Step 4: Through dual distillation and consistent verification of encrypted high-dimensional feature prototypes, edge nodes can complete cross-domain high-order representation alignment under the premise of privacy compliance, further improving the consistent learning ability of weak fault modes.

[0103] The step 4 includes the following contents: Step 401: High-dimensional feature prototype encryption exchange and dual distillation TF-Net has been calibrated to the covariance center in step 3, but the deep feature space may be dispersed due to differences in high-order phase-amplitude coupling. The central node cannot directly aggregate the plaintext feature prototypes; and one-way distillation makes the convergence speed limited by the performance of the teacher node. To address this, the following approach is adopted: Edge nodes for the latest student network parameters The output tensor performs high-order tensor partitioning, first compressing each local block to 64 dimensions using manifold-preserving projection, and then using reversible Hadamard embedding mapping Generate compressed feature prototypes :

[0104] in, is the k-th block high-order tensor of the i-th domain, which is composed of high-order statistical kernel Obtained after dividing by frequency-time-channel; is a second-order folding operation, flattening the high-order blocks into matrices, Hadamard embedding mapping to preserve the manifold topology; is the kth compressed feature prototype of the i-th domain, with a dimension of 64; When high-order statistical kernel Enter the Hadamard embedding map after folding-flattening When the entropy distribution diagram is first established according to the three axes of frequency band, time and channel, the blocks with the highest information entropy concentration of 70% are selected and placed in the priority compression queue. Each block retains the tensor main direction angle of no more than , thus maintaining curvature continuity in low-dimensional space.

[0105] Generate prototype sets per domain After that, call with encrypted gradient summary Elliptic curve homomorphic encryption operators with the same family parameters:

[0106] Unicast to a randomly selected dual domain j over a secure channel; domain j simultaneously performs a symmetric operation, encrypts its own prototype, and transmits it back to domain i. The encryption uses a temporary session key and is bound to a one-time random salt to prevent replay attacks. in: is the dual domain public key; is the encryption prototype vector; random salt: 32-bit encryption session identifier, generated together with the key derivation; A one-time random salt; After receiving the encrypted prototype, domain i and domain j cross-check the random salt hash in a secret state:

[0107] Then verify it with homomorphic addition: If there is any inconsistency, the distillation is terminated immediately. This can avoid the replacement of the middleman. The random salt hash adopts two-way authentication: after each domain decrypts the received vector, it writes the other party's salt value into a dedicated register and waits for the next round. The curve point multiplication factor is introduced during the operation; if the salt value is misplaced, the curve multiplication output point set will fall into an invalid subgroup, causing the verification hash to mismatch.

[0108] After completing the two-way decryption, the two domains input the mutually obtained prototype into the local auxiliary branch , calculate the residual :

[0109] And the residual distillation loss Converges to a minimum, where:

[0110] in: is the local auxiliary branch of domain i, is the residual distillation weight, which is 0.2; is the decrypted plaintext of domain j prototype; is the decrypted plaintext of domain i prototype; Local auxiliary branches during distillation Only the weights of the first three layers of the TF-Net convolution kernel are reused, and the remaining layers share the main branch and lock the gradient and residual After L2 regularization, it is multiplied by the updated weak spectrum mask , so that the distillation gradient only focuses on the global weak spectrum area, preventing high-energy strong peaks from generating erroneous traction when learning from each other.

[0111] In summary, the high-dimensional feature prototypes are exchanged securely in a secret state and serve as teachers to each other, which can significantly shorten the high-order representation alignment time without leaking node-specific data, and finally output a shared prototype set. and residual distillation loss , both need to continue to participate in global consistency verification and dynamic iteration in step 402.

[0112] When in use, the Hadamard embedding manifold projection is integrated with the one-time pad elliptic curve encryption API; the random salt is used as a curve subgroup selector and verification factor, integrating the authentication logic into the encrypted state calculation, greatly reducing the protocol complexity and communication load; the coupled residual distillation directly multiplies the global weak spectrum mask at the gradient end, so that knowledge transfer and weak spectrum significance are enhanced in parallel, breaking through the limitation of traditional distillation that only focuses on prediction probability and ignores frequency band attention.

[0113] Step 402: High-order consistency check and global weak fault common benchmark update After pairwise distillation is completed, cross-population drift may still occur due to multiple pairwise exchanges. A round of global verification and iterative update is required to avoid local optimal traps. Therefore, the following approach is adopted: All edge nodes make a bloom hash summary of their own prototype set and broadcast it to the central node:

[0114] The central summary Bloom filter determines whether the coverage rate exceeds 92%. If it is less than 92%, it randomly restarts several dual exchanges to fill the blind spots. The number of hash functions is set to 4; is the prototype bloom summary of domain i; if the heat is lower than the formula threshold Trigger the replacement exchange immediately to avoid missing out on unpopular and weak scores.

[0115] The central node randomly extracts the prototype index of the hash matching uploaded by the two domains , sent to all nodes, each domain will construct the tensor of the corresponding prototype through Hadamard product :

[0116] Then use the high-order statistical kernel saved in step 3 Calculating consistency scores ,If the lowest score falls below 0.85, it indicates that the high-order alignment fails, ,which triggers re-distillation.

[0117]

[0118] in: 、 are the prototype vectors after random selection and exchange of the first and second domains respectively; To extract the search results, is the Hadamard element-wise multiplication; represents the Frobenius norm; To prevent feature drift from being masked by average, the consistency test not only takes extreme values , and also monitor the quantile difference When the quantile difference is higher than 0.06, the central node considers that there is still hidden inconsistency and automatically increases the pruning threshold, allowing subsequent distillation to focus on the subspace with the largest difference.

[0119] When all consistency scores When the value exceeds the corresponding threshold, the central node recycles the online spectrum mask of each domain in a Bloom-summary manner. The weak spectral coordinate set of , the global weak spectrum common mode is recalculated by taking the union-mutual information weighted average, and broadcasted to each node to update the local mask, so that the subsequent distillation can further concentrate the firepower, where:

[0120] in, is the domain set; Information Constraint Loss The mutual information contribution weight obtained by normalizing the hierarchical contribution; is the global weak spectrum common mode mask; is the discrete frequency index, is the edge domain index; further, the new mask is broadcast and written into the TF-Net spectrum suppression module, so that all edge nodes can instantly focus on the same weak spectrum area.

[0121] To prevent the prototype library from expanding infinitely and occupying memory, each domain performs information entropy-KL cross-index pruning on the prototype set again after completing the common mode update, retaining the prototypes with the top 70% of information content, and then starts lightweight dual distillation to refine the residual. This self-loop is performed for a maximum of three rounds, and in practice, one round can reduce the information constraint loss. Converges to 0.03; ultimately, the bidirectional distillation results can be fully verified and the weak spectrum focus can be unified. At the same time, the storage and computing costs are controlled through the pruning mechanism to ensure that the iteration continues to cycle within the acceptable resource range of the edge.

[0122] This step outputs the global weak spectrum common mode mask and eventual consistency scoring , both will be used as the global loss fluctuation threshold and freezing level judgment criteria in step 5; and will be embedded in the cause link when generating the anomaly confidence heat map in step 6.

[0123] Step 4 extends the alignment effect to the entire domain and verifies it efficiently through steps 401 and 402. The entire chain uses homomorphic encryption and random salt from the same source as the steps to ensure privacy, and uses the high-order statistical kernel of step 3 to with online spectrum mask Verification and common mode generation are performed, ensuring parameter uniqueness throughout all stages. Dual distillation and high-order consistency verification work together to not only stabilize the significance of weak fault spectra but also provide the central node with precise freezing thresholds and hierarchical information in step 5, "Progressive Weight Freezing," and provide a causal link benchmark in step 6, "Anomaly Confidence Heat Map."

[0124] When used, Bloom hash broadcasting and coverage heat maps allow central nodes to observe the distribution of weak spectrum prototypes in real time, ensuring that no factory is overlooked. Hadamard consistency testing, under the dual constraints of a 0.85 threshold and quantile difference, significantly reduces alignment blind spots. Common mode mask dynamic weighting amplifies the contribution of weak network domains, allowing microcrack peaks previously buried by link noise to regain global model attention. The low-overhead probabilistic nature of Bloom filters enables full-domain prototype coverage detection, and a coverage-hotspot heat map is introduced to create an intuitive monitoring interface, making the weak spectrum knowledge distribution "visible at a glance" for the first time on an industrial cloud management platform. Hadamard consistency testing combines random sampling with manifold cosine similarity to avoid the time-consuming centralized calculation of all-to-all similarities.

[0125] The central node has obtained the global covariance center through steps one to four , domain adaptation matrix , global weak spectrum common mode mask and the latest comprehensive losses in each domain . As production batches, raw material batches, and ambient temperature and humidity continue to evolve, the statistical distribution of incremental samples will deviate from the current global model. Without timely intervention, the weights of weak fault spectrum lines will be eroded by new noise patterns, resulting in false positives and missed positives. In order to lock the learned high-order representations of weak faults while ensuring adaptability, when loss fluctuations exceeding the threshold are detected, only low-level and mid-level parameters are frozen, and high-level fine-tuning and mask fine-tuning are enabled, allowing the model to quickly absorb new working condition characteristics while stabilizing the learned features.

[0126] Step 5: Through global loss monitoring and progressive weight freezing strategy, the weak fault representation is kept stable while the model continues to adapt to new working conditions.

[0127] The step five includes the following: Step 501: Dynamic monitoring of global loss and adaptive threshold generation The central node requires a composite indicator that takes into account weak spectral significance, link health, and high-order consistency to assess the impact of new samples on model reliability. A single loss cannot easily reflect multi-dimensional drift, so the following approach is adopted: Central nodes are stacked continuously The comprehensive loss vector of the time window is normalized by the matrix Mapping to a unified dimension is as follows:

[0128] in, is the global indicator vector at time t; is the comprehensive loss from step 3; is the Hamiltonian cross divergence; The lowest consistency score; is a dimensionally normalized matrix with a fixed diagonal form; When integrating comprehensive loss, Hamiltonian cross divergence, and consistency score in real time, the central node assigns an independent timestamp and sampling sequence number to each indicator and maintains a ring buffer in the memory layer.

[0129] Multiply each dimension index by the spectral weight vector , whose elements are masked by the weak spectral common mode Points earned:

[0130] in, is the spectrum sensitivity weight, the element value ; is the spectral weighted global index scalar; To avoid false freezing triggered by noise spikes, the spectrum weighted index is calculated in Riemann incremental distance of the step time window ;

[0131] in, is the scalar logarithm; For the window span, set it to 5; is the incremental distance, used for threshold determination; When evaluating the incremental distance, the central node records each incremental distance The corresponding sampling window number is used for subsequent freeze and rollback analysis of link causality. If the incremental distance increases twice in a row, it generally indicates a gradual drift in the true distribution rather than instantaneous noise. The next evaluation period is automatically shortened to improve detection sensitivity. When the incremental distance falls back into the stable range, the evaluation period is gradually lengthened to ensure sufficient computing resources without wasting them.

[0132] In order to ensure that the threshold is sensitive to weak spectral anomalies but does not over-respond to transient noise and improve the reliability of freezing decisions, the results of the first three steps are input into the exponential sliding filter to obtain the real-time threshold:

[0133] First value Take the empirical constant as 0.02; is the sliding coefficient, which is 0.3; is the current threshold; Finally, the output spectral weighted index , incremental distance With dynamic threshold The three will directly drive the freeze-fine-tune process in step 502 and be used in the abnormal confidence explanation link in step 6; dynamic threshold It is not only used for single-point triggering, but also drawn as a "trough-peak" strip chart on the visualization panel to show the "model stability margin".

[0134] By introducing weak spectral common mode weighting and Riemann incremental distance, sub-step 501 upgrades traditional single-path loss monitoring to a multi-metric, three-dimensional assessment. This not only captures overall gradient drift caused by new operating conditions, but also maintains high sensitivity to hidden risks caused by link jitter or decreased mutual information consistency. The dynamic threshold curve exhibits a "breathing" state under all-weather scheduling, preventing redundant alarms from disturbing on-duty personnel at night while ensuring rapid identification of potential hazards during the daytime production cycle.

[0135] The Riemannian metric is used in the incremental distance instead of the Euclidean distance, emphasizing the geometric structure of the indicator space, making the threshold more sensitive to exponential changes; furthermore, the dynamic threshold curve switches the sliding coefficient according to the production shift , organically combining manual management rhythm with algorithm sensitivity.

[0136] Step 502: Progressive Weight Freeze and High-Level Fine-tuning-Rollback Mechanism once , the central node needs to quickly freeze the bottom layer of the network and authorize the edge nodes to only fine-tune at the high level, while maintaining knowledge distillation and weak spectrum significance; if the subsequent indicators recover, it needs to be unfrozen and rolled back to avoid model rigidity. The specific operation is as follows: The central node uses the layer learning rate gain saved in step 3 Construct the importance distribution and divide the convolution layer into Ascending sort as frozen priority sequence:

[0137] in, For the Layer importance; For the Layer learning rate gain, is the learning rate gain of the jth layer; the value is between 0 and 1; Calculating importance distribution Finally, the central node compares historical importance curves to identify two types of layers: "persistently high importance" and "one-time bursts." The persistently high importance layer is designated as a permanent key protection zone and will not be frozen regardless of future fine-tuning. The burst-like layer, on the other hand, enters the monitoring queue. If it surges again in the future, it will be immediately marked as "prone to drift" and prioritized for freezing.

[0138] Freeze the layers with the lowest cumulative importance of 70% in priority order and relax the learning rate in the remaining layers :

[0139] in, is the original learning rate; is the learning rate gain factor, the value ; Fine-tune learning rates for high layers; When freezing layers with a cumulative importance of 70% or less, we first bypass these layers for idle inference and measure the impact of the freeze on inference latency. If the latency savings meet the hard real-time requirements of the edge, the freeze takes effect. Otherwise, we roll back some layers and re-evaluate.

[0140] At the same time, it allows edge nodes to make fine-grained adjustments to the weak spectrum mask:

[0141] in is the mask learning step size, The updated mask; mask fine-tuning does not modify directly Instead of full-scale, a convolution band block-level incremental method is used; If continuous Window satisfies , the central node unfreezes the next 15% importance interval and decays the learning rate back to the original value:

[0142] Among them, the rollback attenuation rate , is the number of consecutive recovery windows, is the dynamic threshold; Number of consecutive recovery windows It not only affects the learning rate rollback, but also determines the order of unlocking frozen layers: first unlocking layers with high gradient accumulation in the latest drift samples to ensure that resources are invested in the most urgent representation space. At the same time, the system records the corresponding The value of is used as the baseline for the next round of trigger threshold; it effectively avoids frequent “threshold touch-threshold” jitter; if If there is still no fluctuation after reaching 10 windows, all freezes will be automatically released and the threshold curve will be reset to prevent rigidity.

[0143] Finally, the low-middle layers that are accumulated and covered constitute the frozen layer set , fine-tune the learning rate of high-level , update mask and rollback status , they will enter step 6 to annotate the cause path and visualize the frozen level of the anomaly confidence heatmap.

[0144] Construct multi-source spectrum weighted index through step 501 And generate dynamic thresholds using Riemann incremental distance and exponential filtering , enabling the central node to accurately determine the stability of the model on incremental samples; then step 502 triggers hierarchical importance sorting, segmented freezing, and high-level fine-tuning based on the threshold, while allowing fine-tuning of the weak spectrum mask and rolling unfreezing based on the recovery criterion, which can maintain rapid adaptation to new working conditions without forgetting weak fault characteristics.

[0145] When used, the progressive weight freezing strategy selects frozen layers by importance while preserving weak spectral representations, avoiding the loss of representational power caused by a "one-size-fits-all" approach. The learning rate of high-level fine-tuning adapts to the incremental distance, improving convergence speed for new working conditions. Mask fine-tuning adheres to the dual insurance of "blocking-observation" to ensure that weak spectral enhancement behavior does not generate secondary noise due to over-amplification. Dynamic rollback eliminates the risk of model rigidity caused by over-freezing, allowing the system to smoothly switch between the "steady state-adaptive" bipolarity. A delayed evaluation of "idle inference" is performed before segment freezing, aligning resource scheduling with business real-time performance. Mask fine-tuning uses gradient-KL dual gating to achieve precise weighting at the frequency band block level.

[0146] In the collaborative flow of steps one to five, high-saliency learning and dynamic steady-state maintenance of cross-domain weak fault representation have been completed from raw signal unification, dense state statistical alignment, self-supervised reinforcement, dual distillation to progressive weight freezing. However, the real value of the industrial site lies in the "diagnosis-treatment closed loop". Although the center-edge model continues to evolve, if the abnormal confidence cannot be quickly transmitted to the operation and maintenance personnel in an interpretable form at the incipient stage of the fault, it will be difficult to realize the benefits of preventive maintenance. On the other hand, alarms based on a single-point confidence threshold are extremely susceptible to interference from new working condition drift and link noise, resulting in false alarms, missed alarms, or information overload. To this end, the following countermeasures have been adopted: Step 6: Use multi-dimensional confidence tensors to drive the generation of heat maps and cause links, allowing operations personnel to understand and locate potential faults in seconds.

[0147] The step six includes the following contents: Step 601: Edge anomaly confidence tensor construction and local heat encoding After step 5, the edge node already has a frozen layer set , update mask and spectral weighted index If only a single prediction probability is reported, the information dimension is insufficient; if all intermediate features are uploaded, privacy and bandwidth requirements are violated. Therefore, the following approach is adopted: The edge node outputs the latest inference vector with frozen layer activation statistics and spectral mask gradient Concatenate along a new dimension:

[0148] Where, : inference output vector; Activate the mean vector for the frozen layer; is the frequency-sensitive gradient of the mask; is the vector concatenation operator; is the discrete frequency index; Among them, the "frozen layer gradient variance" vector is added on the basis of the original splicing, which records the mean square value of the residual gradient of each frozen convolution kernel in the latest batch to form a new four-element confidence block; in this way, if high residual gradients still appear in the frozen layer, the system can expose the risk signal of "insufficient freezing" in the heat map.

[0149] Using weighted voiceprint Multi-source confidence tensor Mapping to time-frequency plane heat :

[0150] in 、 is the Gaussian kernel density, is the frequency domain kernel function, is the time domain kernel function, is time-frequency heat; Time-frequency heat Perform density peak clustering and extract Peak heat , the number of peaks changes dynamically with the multi-source spectrum weighted index Relaxation, when the indicator is above the dynamic threshold More peaks are allowed when sampling, ensuring that abnormal details are not missed. Density peak clustering uses a local neighborhood slope threshold to prevent small noise from being mistakenly identified as peaks at high sampling rates. The system sets a minimum peak width equal to the inverse of half the rotational speed to ensure that each peak represents a complete mechanical cycle.

[0151] According to the peak energy and the corresponding frozen layer weight Calculation priority:

[0152] Before upload only indivual The highest peak, compressed bandwidth to 4kB, Score peak priority; Finally, the output heat peak set Multi-source spectrum weighted index Both will be used for cross-domain aggregation and cause link inference in step 602.

[0153] When used, the multi-source confidence tensor complements the model's internal tension dimension by incorporating frozen layer gradient variance. The spectral-temporal adaptive kernel allows the heat map to address the resolution requirements of both high-speed and low-speed machines. Cluster-coded directional markers provide direct positive and negative feedback for center attribution, and the information de-redundancy mechanism ensures peak diversity even under stringent bandwidth conditions. The adaptive kernel width algorithm links device dynamic parameters with heat rendering, achieving unified visualization across models. Information de-redundancy combines the time-frequency-gradient distances into a single spatial dimension, establishing a multi-scale sparsity criterion for edge uploads, breaking through the traditional "fixed peak number" bandwidth allocation strategy.

[0154] Step 602: Central abnormality heat map aggregation, cause link inference and operation and maintenance strategy push The central node needs to synthesize the heat peaks from multiple domains into a global anomaly view, and combine the model freeze-thaw history, weak spectrum mask changes, and link health to infer the root cause, and then output an actionable maintenance plan. To this end, the following plan is selected for execution: The central node aggregates the heat peaks of each domain Map to a unified time axis and generate a global heat map by self-attention weight fusion ,in:

[0155] Where, is the attention weight of the qth heat peak in domain i, which is amplified by the priority index; Prioritize heat peaks, peak energy and the corresponding frozen layer importance The multiplied score is Similar meanings; Construct node sets {level, frequency band, link, working condition} and edge sets {activation causality, spectrum coupling, link amplification}, and apply graph convolutional networks to calculate node importance If the edge node is above the 95th percentile in both the frozen layer activation and the weak spectral gradient, the center is inferred to be an "internal feature drift amplification" path; if the Hamiltonian cross divergence increases simultaneously, it is inferred to be a "link-model composite" path. The graph network not only calculates the node importance, but also outputs an edge attention matrix, which is superimposed on the edge of the heat map with pseudo-color to show the "potential causal arrows." For example, the "link amplification" edge highlight means that the noise is amplified by the network layer and misleads the model, thus guiding operations and maintenance to first check the network.

[0156] The maintenance strategy library is called based on the attribution results: internal drift triggers "model high-level fine-tuning extension" and "device status check"; link-model compound triggers "network self-check" and "local resampling" dual instructions. Instruction carries parameters: frozen layer set , fine-tune the learning rate of high-level , update mask For edge and network teams to execute. A new "frozen layer review" entry has been added to the policy library: when the attribution result points to "insufficient freezing", a "layer-by-layer unfreeze-observation" process script is automatically generated and pushed to the central operation and maintenance platform; the script has embedded high-level fine-tuning of learning rates The attenuation curve and observation window length can be sent by the operation and maintenance personnel by simply clicking confirm.

[0157] The global heat map, cause links and strategic points are packaged in JSON-LD format and pushed to the desktop monitoring screen, mobile app and email; the heat map is rendered in pseudo-color, and the color mapping is adjusted according to the self-attention weight. Automatic adjustment. After the central node integrates the heat peak into the global abnormal heat map, it constructs an attribution graph containing four types of nodes (level, frequency band, link, and working condition) and multiple causal edges; then it uses the graph convolutional network to forward propagate the graph and output the weight score of each node. This weight score is the node importance. Its value reflects the criticality of the corresponding node in the fault mechanism link, and will be pushed to the operation and maintenance interface together with the cause link.

[0158] The "estimated impact threshold" field is added to the message package. The calculation method refers to the average of the last three values ​​of the spectrum weighted index, which can help on-duty engineers determine the emergency level of the fault; the mobile app supports one-click transfer of work orders, automatically assigning node importance to the work order. As a work order priority, shorten the on-site dispatch time.

[0159] Final output global heat map , node importance and strategy instruction package; and record the alarm ID and multi-source spectrum weighted index For subsequent audit and model evolution analysis.

[0160] Step 6 relies on the multi-source confidence tensor concentration in step 601 to map the inference probability, frozen activation, weak spectral gradient, and link indicators into time-frequency heat peaks and filter and upload them, achieving a dual balance of bandwidth and privacy on the edge side. Then, step 602 uses self-attention aggregation and graph network attribution to generate a global heat map and cause links, and pushes maintenance instructions through the policy rule engine, allowing operation and maintenance personnel to obtain intuitive fault areas and actionable suggestions within seconds, achieving the ultimate goal of early warning of weak faults and precise operation and maintenance in industrial Internet scenarios.

[0161] When used, the domain trust weight suppresses the pollution of the global view by the noise domain, ensuring the accuracy of the abnormal heat map in locating the real fault; Self-attention fusion superimposes domain trustworthiness, introducing link health and consistency scores into visual weight decisions, breaking the convention that "heat map brightness only depends on peak values"; the graph network simultaneously outputs node importance and edge attention, realizing real-time coupling of fault mechanism and visualization; the policy rule engine scripts the freeze-thaw logic, and for the first time uses model adaptive parameters as part of the operation and maintenance execution script; the message package-work order direct connection seamlessly connects the AI ​​alarm chain with the operation and maintenance process pipeline, allowing diagnosis and maintenance to truly form a data closed loop.

[0162] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0163] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0164] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is only for some logical functions. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0165] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0166] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A vibration information enhancement method based on fused data, characterized by: include, The source signal is pre-processed at each device edge node to generate a unified feature tensor, which is then compressed by a contrast encoder and encrypted using elliptic curve homomorphic encryption to form a gradient summary that is uploaded to the central node. The central node performs dense outer product and debiasing operations on each encrypted gradient summary, uses Riemann distance and weighted Karcher mean to obtain the global central covariance, compresses it into a domain adaptation matrix and sends it to the edge node; After the edge node receives the adaptation matrix, the time-frequency fusion network is recalibrated by progressive stitching of high-order tensors, differential weight shrinkage, and spectral gated gradient weighting, and spectral suppression is used to enhance the significance of weak spectral lines. Each edge node compresses and generates feature prototypes, exchanges them bidirectionally, and verifies security through salt value curve coupling. After verifying the cross-domain deep representation synchronization, a global consistency check is performed. The central node continuously monitors the spectral weighted comprehensive index and calculates the Riemann incremental distance to generate a dynamic threshold; When the spectral weighted comprehensive index exceeds the threshold, the low and middle layer parameters are frozen, the high layer learning rate is increased, and the weak spectrum mask is allowed to be fine-tuned; after the index is restored, it is rolled back and unfrozen according to the importance, maintaining the stability of the learned weak fault representation and absorbing the new working condition characteristics.

2. The method for enhancing vibration information based on fused data according to claim 1, characterized in that: When any edge node detects an increase in anomaly confidence based on the updated model, an anomaly confidence heat map and cause link are automatically generated and pushed to the operation and maintenance interface.

3. The method for enhancing vibration information based on fused data according to claim 2, characterized in that: At the edge node, a prediction-correction phase-locked algorithm is used to synchronize the time baseline of multi-source signals. Lyapunov energy normalization is combined with complex wavelet coupling and pseudo-bilinear embedding to generate a unified feature tensor to ensure that the weak fault spectrum line maintains three-dimensional consistency in phase, energy and frequency domain despite cross-device sampling differences.

4. The method for enhancing vibration information based on fused data according to claim 3, characterized in that: The unified feature tensor is compressed into a latent vector through a bidirectional mutual information constrained contrast encoder and multi-resolution self-gated projection. The elliptic curve homomorphic encryption operator is called on the edge side to batch encrypt the gradients and upload them to the central node after being sliced ​​with divergence verification through RaptorQ.

5. The method for enhancing vibration information based on fused data according to claim 4, characterized in that: After the central node receives the encrypted gradient summary uploaded by the edge node, it maintains the encrypted state to complete the dense state covariance reconstruction and uses the Riemann distance to evaluate the multi-domain distribution difference. The global central covariance is obtained using Karcher mean iteration, and the corresponding domain adaptation matrix is ​​generated based on the joint constraints of geometric regularization and physical regularization.

6. The method for enhancing vibration information based on fused data according to claim 5, characterized in that: Orthogonal robust compression and link adaptive quantization are implemented on the mapping matrix and sent to the edge node via RaptorQ redundant slicing. Edge feedback is simultaneously collected to verify whether the divergence threshold is met, and the adaptation status is updated in the central database to perform feature drift suppression and global model distribution homogenization.

7. The method for enhancing vibration information based on fused data according to claim 6, characterized in that: After the edge node receives the domain adaptation matrix, it uses high-order projection progressive stitching to inject the mapping feature tensor core statistics into the time-frequency fusion network; through differentiated weight shrinkage combined with spectral gated gradient energy weighting, the convolution kernel is adjusted to make the network power spectrum consistent with the global central spectrum, and the low-amplitude frequency band output is kept stable under the protection of energy compensation residual.

8. The method for enhancing vibration information based on fused data according to claim 7, characterized in that: After completing the weight calibration, the same node enables mutual information redistillation to undertake the comparative structural discrimination information, and then uses noise-driven occlusion consistency and multi-scale spectrum suppression to improve the resistance to link jitter and high-energy pseudo-peaks, relying on disturbance-aware annealing to dynamically balance the loss weight.

9. The method for enhancing vibration information based on fused data according to claim 8, characterized in that: Edge nodes perform high-order tensor entropy-driven compression to generate prototype vectors, and complete prototype secure exchange through bidirectional homomorphic encryption exchange with random salt hash verification. Then, weak spectral residual distillation is used to synchronize deep representations. All nodes broadcast the prototype Bloom hash summary to the center. The center triggers the complementary exchange based on the coverage result and sends down random sampling retrieval for each node to perform Hadamard tensor consistency check.

10. The method for enhancing vibration information based on fused data according to claim 9, characterized in that: After the consistency check passes, the center fuses the weak spectrum mask weights of each node to generate a weak spectrum common mode mask and broadcasts it again. The edge node updates the spectrum suppression module accordingly and uses Pareto pruning to maintain the size of the prototype library, performing cross-domain deep feature alignment and weak spectrum knowledge sharing.

11. The method for enhancing vibration information based on fused data according to claim 10, characterized in that: The central node continuously aggregates the comprehensive loss, link divergence and consistency score to generate a spectral weighted index and calculates the incremental distance in real time, updating the dynamic threshold through exponential sliding; When the spectral weighted index exceeds the threshold, the central node freezes the low-level and middle-level parameters according to the hierarchical importance, while increasing the high-level learning rate and authorizing the edge nodes to perform block-level fine-tuning based on the weak spectral mask.

12. The method for enhancing vibration measurement information based on fused data according to claim 11, characterized in that: During the freezing period, the central node continuously monitors the indicator curve. If the continuous window is lower than the rollback threshold, the frozen layers are unlocked in sequence and the learning rate is decayed to the original value, while confirming the updated weak spectrum mask.

13. The method for enhancing vibration measurement information based on fused data according to claim 12, characterized in that: The edge node splicing inference probability, frozen layer activation statistics, weak spectrum gradient direction and frozen layer gradient variance are used to generate a multi-source confidence tensor, and a heat peak list is formed through adaptive time-frequency kernel mapping, which is then uploaded after information redundancy screening.

14. The method for enhancing vibration information based on fused data according to claim 13, characterized in that: After assigning domain credibility to each domain, the central node uses self-attention weights to fuse heat peaks to construct a global heat map, and connects the levels, frequency bands, links, and working condition nodes in the mechanism attribution graph network to calculate the causal path; The attribution results trigger the policy rule engine, select the corresponding maintenance script or network self-test instruction, and push it to the monitoring screen, mobile terminal and email in a unified message package format along with the global heat map and cause link.

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