Vibration measurement information enhancement method based on fusion data

Abstract

The application discloses a vibration measurement information enhancement method based on fusion data, relates to the technical field of vibration measurement information enhancement, and generates a multi-source confidence tensor by splicing inference probability of an edge node, freezing layer activation statistics, weak spectrum gradient direction and freezing layer gradient variance, and forms a heat peak list through a self-adaptive time-frequency kernel mapping, and uploads after information redundancy screening; a center node allocates a domain trust weight to each domain, then fuses heat peaks by using a self-attention weight to construct a global heat map, and connects levels, frequency bands, links and working condition nodes in a mechanism attribution graph network to calculate a causal path; an attribution result triggers a strategy rule engine to select a corresponding maintenance script or a network self-check instruction, and pushes the global heat map and the reason link to a monitoring large screen, a mobile terminal and an email in a unified message package format, so that the display, explanation and operation and maintenance instruction closed loop of a weak fault anomaly are completed.

Description

Technical Field

[0001] This invention relates to the field of vibration information enhancement technology, specifically a vibration information enhancement method based on fused data. Background Technology

[0002] In the context of the Industrial Internet, equipment health management is rapidly shifting from "offline inspection" to a continuous sensing and intelligent decision-making model based on "edge-cloud collaboration." High-frequency vibration, acoustic emission, and current signals can be transmitted from field acquisition devices to edge nodes in 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, enterprises are increasingly inclined to aggregate multiple factory nodes into a global diagnostic model through federated or distributed learning frameworks to share fault knowledge, reduce training costs, and comply with data sovereignty regulations. Simultaneously, edge computing transforms fault diagnosis from a "single-point model" to a "heterogeneous multi-domain model"—each device possesses independent hardware, load, and environmental conditions, resulting in weak and dispersed spectral characteristics of similar faults under different operating conditions. To maintain diagnostic accuracy, the system must perform energy normalization and time baseline alignment on the device side, followed by 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 often focus on a single aspect: either emphasizing compression and encryption while neglecting the significance of weak fault spectra, or emphasizing high-level fine-tuning while lacking a fusion framework of hierarchical freezing and interpretation visualization. When deployed in multiple plants, they often encounter the dual dilemma of "model drift" and "surge in false alarms".

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

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

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

[0006] (a) Technical problems to be solved

[0007] To address the shortcomings of existing technologies, this invention provides a vibration information enhancement method based on fused data. This method can complete feature statistical alignment in the encrypted state, enhance weak spectral lines in a self-supervised manner at the edge, maintain model steady state at the center through dynamic freezing and high-level fine-tuning, and finally push the anomaly confidence level to the overall system of the operation and maintenance interface as a visual heatmap and cause chain. This ensures that cross-plant weak faults are reliably captured in their infancy and that remedial measures are clear and timely, avoiding false alarms, missed alarms and data leakage, thereby solving the technical problems described in the background art.

[0008] (II) Technical Solution

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] The vibration information enhancement method based on fused data includes: preprocessing the source signal at the edge node of each device, generating a unified feature tensor, compressing it by comparison encoder, and then forming a gradient summary by elliptic curve homomorphic encryption before uploading it to the central node;

[0011] The central node performs dense-state outer product and debiasing operations on each encrypted gradient digest, and uses Riemann distance and weighted Karcher mean to obtain the global central covariance, which is then compressed into a domain adaptation matrix and sent to the edge nodes.

[0012] After adapting the edge node receiver domain to the matrix, the time-frequency fusion network is recalibrated using high-order tensor progressive stitching, differential weight shrinking, and spectral gating gradient weighting, and spectral suppression is used to enhance the significance of weak spectral lines.

[0013] Each edge node compresses and generates a feature prototype, which is then bidirectionally exchanged and its security is verified by coupling with a salt value curve. After the cross-domain deep representation synchronization is completed, a global consistency verification is performed.

[0014] 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 mid-level parameters are frozen, the high-level learning rate is increased, and the weak spectral mask is fine-tuned. After the index recovers, it is rolled back and unfrozen according to the importance, maintaining the stability of the learned weak fault characterization and absorbing new operating condition characteristics.

[0015] Furthermore, when any edge node detects an abnormal increase in confidence based on the updated model, it automatically generates an abnormal confidence heatmap and the cause chain and pushes it to the operation and maintenance interface.

[0016] Furthermore, a prediction-correction phase-locked loop algorithm is used at the edge nodes to achieve time baseline synchronization of multi-source signals. Lyapunov energy normalization combined with complex wavelet coupling and pseudo-bilinear embedding is used to generate a unified feature tensor to ensure that weak fault spectral lines maintain three-dimensional consistency in phase, energy and frequency domain despite sampling differences across devices.

[0017] Furthermore, the unified feature tensor is compressed into a latent vector through a contrast encoder with bidirectional mutual information constraints and multi-resolution self-gated projection. The gradient is then batch encrypted by calling the elliptic curve homomorphic encryption operator at the edge side and uploaded to the central node via RaptorQ slice with divergence verification.

[0018] Furthermore, after receiving the encrypted gradient summary uploaded by the edge nodes, the central node maintains the encrypted state to complete the reconstruction of the dense state covariance and uses the Riemann distance to evaluate the multi-domain distribution difference. It uses the Karcher mean to iterate and obtain the global central covariance, and generates the corresponding domain adaptation matrix based on the joint constraints of geometric regularity and physical regularity.

[0019] Furthermore, the mapping matrix is ​​subjected to orthogonal robust compression and link adaptive quantization, and then redundantly sliced ​​by RaptorQ before being distributed to edge nodes. Edge feedback is collected synchronously to verify whether the divergence threshold is met, and the adaptation status is updated in the central database. Feature drift suppression and global model distribution homogenization are then performed.

[0020] Furthermore, after the edge node receives the domain adaptation matrix, it uses high-order projection progressive stitching to inject the core statistics of the mapping feature tensor into the time-frequency fusion network. Then, by combining differentiated weight shrinkage with spectral gating 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.

[0021] Furthermore, after completing the weight calibration, mutual information redistillation is enabled at the same node to receive the comparative structure discrimination information. Then, the resistance to link jitter and high-energy pseudo-peaks is improved by noise-driven occlusion consistency and multi-scale spectrum suppression. The loss weights are dynamically balanced by perturbation-aware annealing.

[0022] Furthermore, the edge nodes perform high-order tensor entropy-driven compression to generate prototype vectors, and complete the prototype secure exchange by carrying random salt hash verification through bidirectional homomorphic encryption exchange. Then, the deep representation is synchronized by weak spectral residual distillation.

[0023] All nodes broadcast the prototype Bloom hash digest to the center. The center triggers a replacement swap based on the coverage result and issues a random retrieval index to each node to conduct a Hadamard tensor consistency check.

[0024] Furthermore, after the consistency test passes, the center merges the weak spectral mask weights of each node to generate a weak spectral common mode mask, which is then broadcast again. The edge nodes update the spectral suppression module accordingly and use Pareto pruning to maintain the prototype library size, performing cross-domain deep feature alignment and weak spectral knowledge sharing.

[0025] 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, updating the dynamic threshold through exponential sliding.

[0026] When the spectral weighting index exceeds the threshold, the central node freezes the low-level and mid-level parameters according to the hierarchy importance, while increasing the learning rate of the high-level nodes and authorizing the edge nodes to perform block-level fine-tuning based on the weak spectral mask.

[0027] Furthermore, during the freeze period, the central node continuously monitors the indicator curve. If the continuous window is lower than the rollback threshold, the frozen layers are unlocked sequentially and the learning rate is decayed to the original value, while the updated weak spectral mask is confirmed.

[0028] Furthermore, edge node splicing inference probabilities, frozen layer activation statistics, weak spectral gradient directions, and frozen layer gradient variance generate a multi-source confidence tensor, which is then used to form a heat peak list through adaptive time-frequency kernel mapping. After information redundancy removal and filtering, the list is uploaded.

[0029] Furthermore, after the central node assigns domain trust weights to each domain, it uses self-attention weights to fuse heat peaks to construct a global heatmap, and connects hierarchy, frequency band, link and working condition nodes in the mechanism attribution graph network to calculate causal paths;

[0030] The attribution result triggers the policy rule engine to select the corresponding maintenance script or network self-test command, which is then pushed to the monitoring dashboard, mobile device and email in a unified message packet format along with the global heatmap and cause chain.

[0031] (III) Beneficial Effects

[0032] This invention provides a method for enhancing vibration measurement information based on fused data, which has the following beneficial effects:

[0033] The global central covariance and domain adaptation matrix are reconstructed and distributed in a homomorphic encryption environment, breaking through the plaintext alignment bottleneck and achieving zero-leakage alignment of cross-factory features. Subsequently, the mapping feature tensor is rapidly integrated into the new energy shell through high-order projection progressive stitching and differential weight shrinkage, ensuring that weak fault spectral lines can obtain sufficient significance without relabeling.

[0034] The loss and link divergence are weighted by a weak spectral common-mode mask to form a spectral awareness threshold curve. This allows the freeze-fine-tuning decision to consider both model drift and network health, enabling the use of minimal parameters to stabilize weak fault representations during incremental scenarios. In the dual distillation stage, the compressed prototype uses random salt encryption and exchange, combined with residual distillation and Hadamard consistency testing, to construct a high-order representation sharing network. This elevates the weak fault discrimination hyperplane from a single-domain specific feature to a global consensus, significantly suppressing inter-domain recall fluctuations.

[0035] Dynamic threshold-driven progressive freezing locks only the low and mid-level parameters with a cumulative importance of 70%, while the adaptive learning rate of higher layers absorbs new working condition information within a hundred-step gradient. Anomaly confidence tensors are added to the gradient variance and weak spectral gradient direction of the frozen layers, and after information redundancy removal and filtering, they are compressed and uploaded. The heatmap is used to infer the root cause through the mechanism attribution graph network, and then linked with the policy rule engine to generate a maintenance script containing the frozen layer set, weak spectral update mask, and high-level learning rate, ultimately achieving a one-click closed loop for the "model-network-human" three parties. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the vibration information enhancement method based on fused data according to the present invention. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] Please see Figure 1 This invention provides a method for enhancing vibration information based on fused data, including:

[0039] In industrial internet scenarios, distributed vibration-acoustic emission monitoring systems often encounter problems such as time base drift, energy scale imbalance, and heterogeneous operating conditions when facing multiple factories, multiple machine models, and complex environmental background noise. This directly leads to the difficulty of the global diagnostic model in accurately capturing weak fault spectrum lines. If only traditional synchronization or simple normalization methods are relied upon, errors often accumulate during cross-domain migration, thereby amplifying the risk of false positives and false negatives.

[0040] Step 1: Achieve high-precision alignment and energy-scale mapping of multi-source signals with minimal communication overhead at the edge side, and generate gradient summaries protected by homomorphic encryption, providing a cross-domain feature base that can be directly spliced ​​for global fusion of the central node.

[0041] Step one includes the following:

[0042] Step 101: Unify time baseline and energy normalization

[0043] The manufacturers of the data acquisition equipment, sampling rates, and trigger clocks in the factory's AN system are not consistent. If a multi-source signal matrix is ​​directly spliced, phase misalignment is easily generated in the short-time Fourier window superposition region, weakening the weak fault spectrum peaks. Based on this, a dual-domain time baseline reconstruction-energy Lyapunov normalization chain is proposed to ensure time alignment accuracy in the form of continuous minimum adjoint error, thereby improving the subsequent contrast encoder's ability to learn the saliency of weak fault spectrum lines.

[0044] In most older production lines, the data acquisition board is often asynchronous with the PLC clock, causing the sampling points of different nodes for the same mechanical impact event to be misaligned by tens to hundreds of sampling cycles. Therefore, the original multi-source signal matrix is ​​first... Execute sampling clock vector With the station's reference clock The differential mapping is used to construct the synchronous offset function, and the optimal shift is obtained through saddle point iteration. ,in,

[0045]

[0046] In the formula: This is the instantaneous synchronization offset function, in seconds (s). The window starts at time; The length of the sliding window is in seconds (s). Let be the time shift to be determined, and let be the range of values. ; The Euclidean norm is used to measure the difference between two trajectories.

[0047] After synchronization is complete, to prevent the high-energy channel from overwhelming the weak signal, a Lyapunov energy function is introduced. :

[0048]

[0049] Reusing exponential decay Construct a dimensionless value and take values Convergent normalization coefficients :

[0050]

[0051] In the formula: The signal is synchronized with the time base; : The mean vector of the signal in this window; Positive definite weight matrix, ensuring Zhengding; Lyapunov attenuation coefficient, ;

[0052] The vibration levels of industrial pump stations and precision electric spindles can differ by two orders of magnitude. If normalization is simply performed by subtracting the maximum and minimum values, low-energy signals will be lost due to quantization errors. Therefore, the Lyapunov energy function is introduced. The reason is that it can measure the stability of instantaneous energy deviation from the mean, and through the Lyapunov decay coefficient The adjustable exponential decay allows the weak energy channel to achieve higher dynamic gain while maintaining stable output from the strong energy channel.

[0053] After unifying the energy scale, the complex Morlet-Bérenger wavelet packet is introduced. Perform bidirectional coupling:

[0054]

[0055] In the formula: This is an energy normalization signal; Center frequency ,scale Complex wavelet basis; These are the frequency domain coupling coefficients; The imaginary unit;

[0056] Among them, frequency domain coupling coefficient Weighted priors for specific equipment categories were introduced during the construction phase; for example, a spectral weight of 0.6 was assigned to the high-speed spindle channel and 0.3 to the low-speed hydraulic pump channel, thereby strengthening the influence of high-speed fault components on the overall characteristics.

[0057] By analyzing the frequency domain coupling coefficients Perform a bilinear embedding mapping to obtain a time-frequency embedding tensor with the same input dimension as the subsequent comparison encoder. :

[0058]

[0059] In the formula: , : Trainable mapping matrix, size is and ;

[0060] It is the bias vector; It is a hyperbolic tangent nonlinear function.

[0061] Establish a time-frequency embedding tensor with a unified time-energy-frequency domain through continuous mapping. This lays a highly consistent feature base for gradient generation with low bandwidth usage;

[0062] Output time-frequency embedding tensor and convergent normalization coefficients This will serve as the benchmark for calculating the comparative encoding loss and gradient in step 102, enabling lateral parameter reuse. Unlike traditional CNN-LSTM concatenation, bilinear embedding preserves the phase-amplitude coupling information, allowing the subsequent mutual information loss to directly perceive the slight drift of weak faults in the phase space.

[0063] In practice, sub-step 101 achieves precise alignment of time baselines across plants and equipment, as well as dynamic equipotentialization of the energy scale. After unifying the phase reference, the time-domain variations of weak faults are no longer masked by sampling offsets; Lyapunov gain allows for considerable amplification of early defect spectral lines with extremely low amplitudes in the energy domain, while high-energy impacts are suppressed, preventing quantization degradation caused by excessive dynamic range. Wavelet-weighted coupling further establishes comparability of signals with different rotational speeds and excitation modes in the multi-resolution frequency domain, providing a basis for the generated time-frequency embedding tensor. Provides a homogeneous foundation across domains.

[0064] Traditional energy normalization methods often employ RMS or piecewise normalization, which struggle to dynamically mitigate energy drift. By binding the stability criterion of the Lyapunov function to exponentially decaying gain, the gain adapts to the energy distribution of each window, rather than being a globally fixed proportion. Furthermore, weighted complex wavelet energy alignment and the incorporation of learnable priors eliminate the need for manual adjustment of frequency weights. Instead, subsequent gradient self-consistent updates ensure that the most diagnostically valuable spectral lines are highlighted under various conditions. Finally, time-frequency pseudo-bilinear embedding achieves dimensionality reduction while preserving phase-amplitude correlation, providing a low-latency, high-consistency input gateway for subsequent contrastive coding. This overcomes the limitation of traditional CNNs requiring numerous convolutional layers to capture phase information.

[0065] Step 102: Compare the encoder compression and encryption gradient summary reports

[0066] While maintaining weak fault detection capability, high-dimensional time-frequency embedding tensor Compressed into an encrypted gradient summary through self-supervised contrastive learning. The data is then securely uploaded 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. Based on a contrastive encoder that maximizes bidirectional mutual information, supplemented by elliptic curve homomorphic encryption, a gradient transmission chain of "high fidelity-high security-low overhead" is achieved.

[0067] First, the time-frequency embedding tensor Generate positive sample tensor With pseudo-negative tensors Define mutual information enhancement loss:

[0068]

[0069] in , These are query-key mapping functions; It is the dot product of vectors; To compare the temperature distribution, ; The set of negative samples; This is due to information constraint loss.

[0070] Among them, classic MoCo or SimCLR often only focus on one-way query-positive sample cohesion. Here, it is extended to two-way mutual information constraints, which penalize both positive samples that are too far apart and negative samples that are too tightly clustered; compare the distribution temperature. Through noise adaptive adjustment, the temperature coefficient is automatically reduced when the edge node detects an increase in on-site electromagnetic interference to prevent gradient cracking.

[0071] The encoder output is compared and projected through a gate to obtain the gate latent vector. :

[0072]

[0073] in, For the order Generalized mean pooling, Activated for Sigmoid; The product of Hadamard; , These are trainable gating parameters; The order of the generalized mean. ; For gating latent vectors;

[0074] Among them, the gate matrix The system automatically switches on and off based on the signal energy density during projection, leaving sufficient space for the representation of high-frequency sparse signals.

[0075] Based on gated latent vectors Calculate the detection loss gradient Then, elliptic curve homomorphic encryption is performed to ensure that gradient aggregation can be directly performed on the central node without reversing the original features:

[0076]

[0077] In the formula: For elliptic curve homomorphic encryption operators; For the node's public key; This is for encrypted gradient digest.

[0078] Among them, elliptic curve homomorphic encryption operators Ensuring encrypted gradient digest The additivity of the central node is such that it can directly perform weighted averaging in the encrypted domain and output aggregate gradients without decryption.

[0079] Encrypt gradient digest RaptorQ-FEC slicing is performed, and Hamiltonian cross-divergence is used to monitor packet-level consistency. If the threshold is exceeded, recoding is triggered.

[0080]

[0081] In the formula: The mask distribution for adjacent slices; Hamiltonian cross divergence; divergence threshold Set as: .

[0082] By employing a triple chain of information temperature, gating, and homomorphic encryption, the fault identification gradient is preserved while minimizing data leakage. Hamiltonian divergence verification further ensures transmission integrity in weak network environments.

[0083] RaptorQ-FEC for Encryption Gradient Digestion After performing slice redundancy coding, Hamiltonian cross divergence is introduced. As a real-time packet similarity indicator: if the distribution difference between two consecutive packets suddenly increases, it indicates that one packet has undergone bit flipping due to noise damage, and a retransmission will be requested immediately instead of waiting for the central node to time out and send a reply packet.

[0084] The final output is a cryptographic gradient digest. Information constraint loss cross divergence with Hamilton ; including encrypted gradient digest Step two is used to statistically analyze the inter-domain covariance differences and information constraint loss. cross divergence with Hamilton This serves as a benchmark for loss fluctuations during subsequent gradual weight freezing, thereby enabling horizontal linkage of parameters throughout the entire process.

[0085] When used, sub-step 102 compresses highly redundant features of more than 100 dimensions into an encrypted gradient digest. Encrypted reporting significantly reduces network bandwidth and storage overhead; simultaneously, bidirectional mutual information constraints ensure that the latent vector still contains the discriminant dimension most sensitive to weak faults. Gated projection combined with generalized mean pooling effectively avoids the amplification of high-order sparse noise during dimensionality reduction. Elliptic curve homomorphic encryption ensures that the central node can directly perform gradient fusion without any decryption steps, eliminating the high-latency "decrypt-then-converge" step in traditional federated mechanisms. RaptorQ-FEC combined with Hamiltonian cross divergence... Verification further ensures data integrity on links with high bit error rates or high packet loss.

[0086] Through steps 101 and 102, the edge node achieves a lossless and low-load transformation from the original multi-source signal to the cryptographic gradient digest.

[0087] The central node receives the encrypted gradient digest Afterwards, we can directly proceed to step two, which involves calculating the covariance difference and generating the domain adaptation matrix, completely avoiding the overhead of repeated synchronization and normalization, thus achieving a closed loop for edge-cloud collaboration. Meanwhile, because elliptic curve homomorphic encryption guarantees gradient additivity, the global fusion of the central node does not destroy the encrypted state, perfectly compatible with privacy-preserving collaborative strategies such as dual distillation.

[0088] In a cross-factory industrial internet scenario, edge nodes have already uploaded encrypted gradient digests to the central node via step one. The central node needs to complete cross-domain distribution statistics and generate a domain adaptation matrix in real time in a confidential state to offset feature drift caused by different equipment operating conditions. If only simple gradient averaging or fixed mapping is used, it will lead to covariance suppression of low-energy channels by high-energy channels, and weak fault spectral lines will be diluted after global model merging.

[0089] Step 2: Under the condition of maintaining the dense state, perform high-order covariance difference estimation on the encrypted gradient summary of each domain, and iteratively solve the global Riemann center covariance to generate the domain adaptation matrix, which is then distributed to the edge nodes to suppress feature drift in real time.

[0090] Step two includes the following:

[0091] Step 201: Estimation of the covariance difference in the dense state and solution of the global central covariance

[0092] Encrypted gradient digests uploaded by each edge node While exhibiting homomorphic additivity, its distribution is hidden by a curve mapping; premature decryption by the central node would violate privacy compliance requirements, therefore statistics must be performed directly in the dense state. Current mainstream federated methods only calculate the mean while ignoring the covariance, thus failing to correct for cross-domain energy shell differences. To address this, we reconstruct the covariance tensor through dense-state operations, introduce a Riemannian metric to quantify the differences, and use weighted Karcher mean iteration to obtain the global covariance. .

[0093] The central node first utilizes the homomorphic multiplication property to perform a dense outer product operation on the gradient summaries of the same batch:

[0094]

[0095] Among them, high-level fine-tuning of the learning rate Let be the original gradient matrix of the i-th domain; Let be the cryptographic gradient digest of the i-th domain; The outer product of the homomorphism corresponds to the curve dot product, which is then mapped to a new point set. This is the unencrypted gradient outer product, where the dense state is preserved.

[0096] In this process, the central node, without knowing the plaintext gradients of each domain, still utilizes the "product mapping closure" property of homomorphic operators to digest each encrypted gradient. After grouping by batch, a point-to-point curve product is performed and written to the dense tensor pool. This process does not generate additional decryption keys or introduce information leakage, because the outer product result is still in the set of elements in the curve domain, and any observer without the key can only see a random point cloud.

[0097] The outer product result includes a gradient mean offset term. To avoid bias in the covariance estimation, the center node is debiased using a dense linear combination.

[0098]

[0099] in , These are addition under the curve and scalar multiplication, respectively. It is a homomorphic outer product; The mean gradient summary of the i-th domain can be obtained homomorphically. Let be the dense-state departitioned covariance matrix of the i-th domain.

[0100] Since the gradients uploaded from each domain have been gated and compressed, the vector density is uneven across dimensions. If the outer product is directly used as the covariance, the mean drift will generate amplified noise in the weak domain. In the dense state, the mean term is "cancelled dimension by dimension" by the curve addition operator, and the Gaussian noise mapping points in the sparse dimension are suppressed by the dynamic threshold selection term, thereby constructing a zero mean covariance without exposing any statistics.

[0101] The covariance matrix naturally lies in a symmetric positive definite manifold, and the Frobenius distance underestimates the spectral shape difference; therefore, the Riemann logarithmic mapping is used.

[0102]

[0103] in: It is a matrix logarithm operator, which is approximated by a Taylor series in the dense state; is the Frobenius norm, used to quantify the distance within a manifold; The Riemann distance is used as the difference weight; Let be the partial covariance matrix of the j-th domain.

[0104] To avoid underestimation of Euclidean metrics on high-dimensional positive definite manifolds due to the "straight-line approximation," each partial covariance matrix is... Projecting onto the tangent space and then approximating the Riemann distance with a logarithmic mapping sequence preserves spectral structure information while giving the distance a weighted property that tilts towards weak peaks.

[0105] Considering that the number of domains can reach thousands in large factory clusters, a single global iteration using traditional averaging would require traversing all covariances, resulting in unacceptable latency. Therefore, the covariances of each domain are projected onto the tangent space of the manifold, and the global central covariance is solved iteratively using weighted Karcher's mean until... ,in:

[0106]

[0107] in: For the number of fields, Depend on The weighted coefficients obtained by normalization The matrix index is used to revert the manifold from the tangent space. The convergence threshold is set to a constant value. ; The central covariance of the entire domain;

[0108] By completing covariance reconstruction, difference quantification, and center solution in the dense state, an accurate benchmark is provided for the next step of generating the domain adaptation matrix.

[0109] In practice, substep 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. Since Riemann distance reveals spectral structure differences better than Euclidean distance, the response latency to sudden changes in device load is compressed to the second level. Furthermore, batch Karcher averaging ensures stable convergence speed during large-scale domain expansion, avoiding the drawback of traditional global averaging slowing down the entire federated training process when the number of domains surges. Curve operators are used to maintain the closure of outer products and addition, cleverly avoiding decryption operations. Simultaneously, batch Karcher averaging is recursively applied in the manifold space, breaking through the bottleneck of requiring simultaneous iteration across the entire domain, and solving the dilemma of the incompatibility between "domain-massive" and "real-time high-level fine-tuning of the learning rate." This provides a highly privacy-compliant, scalable, and interpretable distribution alignment foundation in industrial weak fault diagnosis scenarios.

[0110] Step 202: Synchronous Feedback on Domain Adaptation Matrix Generation and Distribution

[0111] Obtain the global central covariance Then, the central node needs to construct a linear mapping for each domain, so that the corresponding time-frequency embedding tensor After mapping, the central covariance in the covariance space is compared with the global central covariance. Alignment is achieved while ensuring matrix invertibility and numerical stability. Relying solely on Cholesky decomposition amplifies noise in weak domains; therefore, the following procedure is used to generate the domain-fit matrix. And it will be distributed simultaneously.

[0112] Define a mapping for each domain such that the covariance after the mapping satisfies ,in:

[0113]

[0114] in: The identity matrix and the partial covariance matrix are given. Same order;

[0115] For Tikhonov regularization, take To suppress singular values; For the domain adaptation matrix;

[0116] To reduce the bandwidth required for data delivery, the domain adaptation matrix will be used. Perform orthogonal singular value truncation: retain the column vectors corresponding to singular value energies when the high-level fine-tuning learning rate is >99.5% and re-orthogonalize them to generate a compressed fitting matrix. This will be sent to the edge; this operation reduces communication load and avoids numerical amplification, where the singular value energy threshold is fixed at a high-level fine-tuning learning rate of 0.995.

[0117] Global central covariance After the calculation is completed, the central node constructs a domain adaptation matrix for each domain. At the same time, not only is covariance alignment guaranteed mathematically, but also dual-label information of machine type and status is injected: consult the "equipment-load" lookup table, and adjust the regularization term according to the equipment category and real-time speed. In high-speed models, the penalty is increased to prevent outliers from amplifying high-frequency noise; in low-speed hydraulic systems, the penalty is reduced to ensure that weak vibration channels are not over-compressed.

[0118] Based on the link strength flags reported by each domain handshake, the compression adaptation matrix will be... Compared to a specific point format, the quantization bit width b selected with SNR is divided into four levels according to SNR. This is then compared with the upper bound of the Hamiltonian cross divergence used for downlink verification. They are encapsulated together into a RaptorQ slice to achieve synchronous delivery and verification.

[0119] The quantization bit width b is not fixed, but is derived from the SNR measured in real time during the handshake phase. Once the edge-to-center link drops below 12dB in SNR, the quantization bit width b is reduced to 8 higher-layer fine-tuning learning rate bits and double the redundant slices are automatically inserted; when the SNR recovers to above 22dB, the quantization width is increased to 12 higher-layer fine-tuning learning rate bits and the additional redundancy is removed.

[0120] The central node receives the edge acknowledgment packet and verifies the downlink divergence metric transmitted back from the edge. Then, mark the domain status as "adaptation complete"; if the limit is exceeded, automatically resend the corresponding slice and highlight the link risk on the monitoring dashboard.

[0121] Output compression adaptation matrix The edge time-frequency embedding tensor will be directly applied in step three. And the corresponding weights, Tikhonov regularization Downward divergence index Then the flow will proceed horizontally to the progressive weight freeze threshold calculation path in step five.

[0122] To shorten the round-trip confirmation latency, the central node sends the first row checksum of the uncompressed mapping matrix along with the data transmission. The edge nodes then directly calculate their local checksums after unpacking and return the downlink divergence index. And two status markers. If the two are inconsistent or the divergence exceeds the threshold, the central node immediately retransmits the missing slice instead of the entire packet;

[0123] By using the generalized inverse mapping of "geometric-physical double regularization" and robust compression of "orthogonal-random filling" in parallel, the statistical distribution is aligned and the device mechanism constraints are embedded; the link adaptive quantization enables the model update to be linked with the network conditions in real time.

[0124] Step 2 accurately captures the statistical differences of multi-domain features through the "dense covariance reconstruction - Riemannian metric difference estimation - Karcher mean iteration" in step 201, and generates the domain adaptation matrix in step 202 through "generalized covariance inverse mapping - orthogonal robust compression - link adaptive quantization". Deploy to edge nodes.

[0125] The entire chain maintains a homomorphic encrypted state without decryption, satisfying both GDPR and corporate internal control privacy requirements while ensuring the accuracy and real-time performance of matrix calculations; edge nodes can utilize the lightweight domain adaptation matrix in step three. The weights of the time-frequency fusion network are recalibrated, and the significance of weak fault spectral lines is enhanced by combining consistency loss, thereby continuously improving diagnostic sensitivity in global collaboration, while ensuring the robust evolution of the model in equipment operating condition drift.

[0126] Complete the domain adaptation matrix in step two. After the distribution, edge nodes now have the ability to embed time and frequency into tensors. Mapping to global covariance Homogeneous linear tools are used. However, linear alignment alone is insufficient 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 "inertial weights" for the local energy distribution during the early training phase. Without targeted recalibration, the new input distribution will mismatch with the old weights, causing oscillations in diagnostic performance. At the same time, the central node does not keep up with all the incremental labels of 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 that the global model converges quickly and stably. To solve this problem, the following approach is adopted:

[0127] 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 spectrum lines maintain high significance after cross-domain feature alignment and continuously enhance diagnostic sensitivity.

[0128] Step three includes the following:

[0129] Step 301: Recalibrate the weights of the time-frequency fusion network

[0130] Although a compression adaptation matrix already exists As a linear alignment tool, TF-Net's internal convolutional kernels and channel attention have long followed local distributions. Directly applying new mappings 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:

[0131] Edge nodes first perform a fourth-order tensor projection on the mapped feature tensor, and then apply a higher-order statistical kernel. The Tucker kernel is written as a higher-order statistical prior into the first layer of TF-Net's BatchNormalization center vector, where:

[0132]

[0133] In the formula: The fourth-order flattening-folding operator is used to generate fourth-order tensors; the Tucker kernel is the core tensor extracted by higher-order SVD and used to capture higher-order correlations.

[0134] By injecting high-order correlations in one go, the lower layers of the network can quickly align with the new distribution without large-scale gradient backpropagation; the network only needs a few hundred steps to restore a stable activation distribution.

[0135] Subsequently, a weight shrinkage term is introduced into the TF-Net backbone. This term drives the weights to compress in the mapped direction, avoiding overfitting to local noise.

[0136]

[0137] in, The historical weights before mapping, The shrinkage coefficient is denoted by , and its value is . Adjusting the regression speed; For the current number Layer convolution kernel; and, in order to make the contraction direction more closely match the physical properties within the domain. Instead of being globally fixed, it is dynamically adjusted by the proportion of power spectrum energy occupied by the convolution kernel channels;

[0138] Next, a spectral gating unit is inserted after each convolutional layer, and the power spectral density vector of the output tensor is calculated using a fast Fourier transform. and with the global central spectrum (Depend on (Diagonal element conversion) Calculate Jensen-Renyi distance Dynamically adjust the gating tensor to allow channels with a large difference from the central spectrum to obtain a higher learning rate;

[0139] Obtain the layer learning rate gain as follows: :

[0140]

[0141] In the formula: is the spectral gating smoothing coefficient, with a value of 5–10; For the first Layer learning rate gain.

[0142] In addition to the aforementioned learning rate modulation, the spectral gating unit also performs energy weighting on the gradient during the backpropagation phase: it weights the gradient of the row vector corresponding to the frequency according to... Scaling allows the network to see a clear signal to "shift energy to the weak spectrum" within a single forward-backward loop, without having to wait for multiple training iterations to accumulate.

[0143] Finally, to prevent the energy of the weak region from being diluted by higher-order projections, a final feature tensor is introduced. :

[0144]

[0145] in, For a zero-mean noise basis, the energy compensation coefficient is... With energy normalization gain Homogeneous but compressed to Sigmoid .

[0146] This approach compensates for low-amplitude spectral lines without excessively raising the noise floor; thus enabling TF-Net to fully realign from parameters to spectral density in a short time. This ensures that the subsequent self-supervised mechanism can reinforce weak faulty spectral lines on a stable baseline rather than repairing distribution misalignments, generating a new set of network weights. With dynamic learning rate gain Both will serve as important inputs for calculating the consistency loss and mutual information distillation in step 302; higher-order statistical kernels With global center spectrum Continuing the lateral flow to the dual distillation in step four, used for higher-order statistical verification during feature prototype exchange, specifically, the network weight set. After the edge nodes adapt the receptive domain to the matrix, the final feature tensor of the unified mapping is obtained. Perform progressive stitching of higher-order tensors and update the results in real time through backpropagation according to the differentiated weight shrinkage rule.

[0147] In use, progressive stitching of higher-order statistics ensures a stable transition of network activation, differential shrinkage fully releases the degrees of freedom of weak spectral convolution kernels, spectral density gating directly amplifies global central spectral information in the reverse path through gradient reweighting, and energy compensation satellite head monitors and corrects high-frequency noise in real time, providing timely and stable weighting space for weak fault spectral lines. Combining progressive stitching of higher-order tensors with differential shrinkage gives the high-dimensional statistical prior injection process a "breathable" rhythm, fundamentally avoiding activation oscillations caused by one-time injection.

[0148] Step 302: Self-supervised consistency loss and enhancement of weak spectral line significance

[0149] Even with linear weights and spectral alignment, weak fault features may still be masked by other high-energy modes in unlabeled scenarios. Traditional contrastive learning and occlusion prediction each focus on local or global consistency, failing to simultaneously ensure that weak spectral lines are both amplified and temporally stable. Therefore, the following approach was adopted:

[0150] Edge nodes are first mapped using the query-key mapping generated in step one. For the teacher network, the existing final feature tensor The teacher output is generated; the student network is a calibrated TF-Net branch. Loss through distillation The student network inherits the mutual information structure while adapting to the new distribution, as follows:

[0151]

[0152] In the formula: The distillation weight is set to 0.5; KL represents the Kullback-Leibler divergence. The distillation temperature is used as the reference temperature for the comparative distribution temperature. The mean, This is a function that maps a vector to a probability distribution; Mapping for students;

[0153] The distillation strategy now includes a "local mutual information probe": mapping query-key. The output is truncated in the middle layer of the convolution and the mutual information density is measured in a sliding window manner, so that the student network can not only learn the global structure but also reproduce local sensitive patterns.

[0154] Applying random time shifts in the time dimension Apply consistency loss to two perturbed samples with random occlusion of 10% multi-scale wavelet blocks. :

[0155]

[0156] in The consistency loss weight is set to 0.3. This loss ensures that the network output maintains a similar response to slight asynchrony and bandwidth loss, thus avoiding the distortion of weak signals in actual acquisition noise. For perturbation output, For random occlusion;

[0157] Introducing a frequency domain mask in the frequency domain Applying to high-energy non-faulty frequency bands Weights are applied to concentrate the gradient primarily in the neighborhood of weak spectral peaks; frequency domain masking. From the aforementioned global center spectrum The difference between the current output power spectrum and the thresholded value is used to obtain the update frequency, which is the same as the training step, to ensure alignment with dynamic changes.

[0158] 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 to certain frequency bands. The mask threshold is automatically raised to suppress the gradient of that frequency band to prevent false confidence. This ensures that the suppression logic avoids information loss due to long-term suppression, and also prevents weak spectral lines from being submerged by other strong peaks after instantaneous overfitting.

[0159] Construct comprehensive loss :

[0160]

[0161] Annealing weight Adaptive annealing with distillation temperature:

[0162]

[0163] , The annealing mechanism prevents the mutual information gradient from being over-dominated in the later stages of training, ensuring that the final confidence distribution of the model is balanced.

[0164] When consistency loss When the value remains 20% above the baseline, it indicates that the occlusion disturbance has not yet been eliminated; mitigation The decay rate allows the mutual information gradient to maintain its guiding effect for a longer period. This dual regulation ensures that annealing neither cools down prematurely nor dominates the total loss weights for too long. The final output is the updated student network parameters. Comprehensive loss curve With frequency domain mask The comprehensive loss curve In step five, the frequency domain mask is used as a benchmark for global loss fluctuation monitoring. In step four, it is exchanged along with the feature prototype for frequency band consistency constraints during dual distillation.

[0165] In practice, dynamic probe distillation keeps the student network sensitive to local textures, noise-driven occlusion ensures that the consistency target is tightly coupled with real-world acquisition perturbations, adaptive thresholding of multi-scale spectral suppression maintains the focus of weak spectral lines, and perturbation-aware annealing balances the relative strength of mutual information and consistency at different stages. This synergistic approach improves the recall rate of weak faults in unlabeled scenarios and significantly suppresses false alarm spikes caused by link packet loss and electromagnetic noise.

[0166] Step 3 addresses the challenge of local relearning after the application of the domain adaptation matrix, and uses the rapid adjustment of TF-Net parameters, spectral domain distribution, and global covariance center in step 301. Synchronization; then step 302 further maintains the significance of weak spectral lines and the stability of output confidence in the unlabeled scenario.

[0167] The new weight set, comprehensive loss curve, and spectral mask output from the two steps all maintain parameter uniqueness and are consistent with the variables from the first two steps, providing a higher-order statistical kernel for the dual distillation in step four. and frequency domain mask The verification process provides a real-time loss baseline and divergence index for the progressive weight freezing in step five, ensuring that cross-domain weak fault characteristics are amplified while maintaining model stability, ultimately improving the sensitivity of multi-source signal diagnosis in the industrial internet environment.

[0168] Steps one through three have completed the significant amplification of weak fault spectrum lines from the data side to the model side, but the TF-Net of each plant area is still at the global covariance center. Even so, invisible higher-order representation differences may still arise. These differences, once accumulated with environmental drift, will create "grayscale distortion" in the central fusion model, causing fluctuations in cross-domain inference confidence and weakening the stability of early fault alarms. To quickly smooth out higher-order differences without exposing raw data or increasing communication burden, the following measures are taken:

[0169] Step 4: By using encrypted high-dimensional feature prototype dual distillation and consistency verification, edge nodes can complete cross-domain high-order representation alignment under the premise of privacy compliance, further improving the consistency learning capability of weak fault modes.

[0170] Step four includes the following:

[0171] Step 401: High-dimensional feature prototype encryption exchange and dual distillation

[0172] TF-Net has been calibrated to the covariance center after step three, but the deep feature space may be dispersed due to differences in high-order phase-amplitude coupling. The center node cannot directly aggregate plaintext feature prototypes; and one-way distillation limits the convergence speed to the performance of the teacher node. Therefore, the following approach is adopted:

[0173] Edge nodes for the latest student network parameters The output tensor undergoes high-order tensor block decomposition, first compressing each local block to 64 dimensions using manifold-preserving projection, and then mapping it using reversible Hadamard embedding. Generate compressed feature prototypes :

[0174]

[0175] in, For the higher-order tensor of the i-th domain and the k-th block, the higher-order statistical kernel is used. Obtained after being divided by frequency, time, and channel;

[0176] This is a second-order folding operation, which flattens the higher-order blocks into a matrix. To preserve the Hadamard embedding map of the manifold topology;

[0177] Let be the prototype of the k-th compressed feature in the i-th domain, with a dimension of 64;

[0178] When higher-order statistical kernels Entering the Hadama embedding map after folding-flattening First, an entropy distribution map is established according to the three axes of frequency band, time, and channel. The blocks with the highest information entropy concentration are selected and placed in a priority compression queue. During the manifold-preserving projection process, the tensor principal direction angle of each block is retained to be no more than [a certain value]. Thus, curvature continuity is maintained even in low-dimensional space.

[0179] Each domain generates a prototype set. Then, call and encrypt gradient digest. Elliptic curve homomorphic encryption operators with the same family of parameters:

[0180]

[0181] The secure channel unicasts to the randomly selected dual domain j; at the same time, domain j performs a symmetric operation, encrypts its own prototype and sends 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.

[0182] in: For the public key of the dual domain; For encrypted prototype vectors; Random salt: 32-bit encrypted session identifier, generated along with key derivation; A single-use random salt;

[0183] After receiving the encrypted prototype, domain i and domain j perform a cross-validation of the random salt hash in the encrypted state:

[0184]

[0185] Let's verify this using homomorphic addition: If a discrepancy is found, distillation is immediately stopped to prevent man-in-the-middle substitution. Random salt hashing employs two-way authentication: after each field decrypts the received vector, it writes the other party's salt value into a dedicated register for the next round. When performing the operation, the curve multiplication factor is included; if the salt value is misaligned, the output point set of the curve multiplication will fall into the invalid subgroup, which will cause the check hash to mismatch.

[0186] After completing bidirectional decryption, both domains will obtain the prototype input local auxiliary branch from each other. Calculate the residual :

[0187]

[0188] and residual distillation loss It converges to a minimum, where:

[0189]

[0190] in: For the local auxiliary branch of domain i, The residual distillation weight is set to 0.2; The plaintext of the prototype of field j after decryption; The plaintext of the domain i prototype after decryption;

[0191] Local auxiliary branches during distillation Only the weights of the first three layers of the TF-Net convolutional kernel are reused; the remaining layers share the main branch and lock the gradients, with residuals... After L2 regularization, multiply by the updated weak spectral mask This allows the distillation gradient to focus only on the global weak spectral region, preventing erroneous pull from high-energy strong peaks during mutual learning.

[0192] In summary, by securely exchanging high-dimensional feature prototypes in dense mode and having them serve as teachers for each other, the alignment time of high-order representations can be significantly shortened without leaking node-specific data, ultimately outputting a shared prototype set. and residual distillation loss Both need to continuously participate in global consistency verification and dynamic iteration in step 402.

[0193] When used, the Hadamard embedding manifold projection is fused with the one-time pad elliptic curve cryptography API; the random salt is used as both a curve subgroup selector and a verification factor, integrating the authentication logic into the cryptographic computation, which greatly reduces the protocol complexity and communication load; coupled residual distillation directly multiplies the global weak spectrum mask at the gradient end, enabling knowledge transfer and weak spectrum saliency to be enhanced in parallel, breaking through the limitation of traditional distillation that only focuses on prediction probability and ignores frequency band attention.

[0194] Step 402: High-order consistency check and global weak fault common benchmark update

[0195] Even after dual distillation, cross-population drift may still occur due to multiple swaps, requiring a round of global-level verification and iterative updates to avoid local optimum traps. Therefore, the following approach is adopted:

[0196] All edge nodes perform a Bloom hash digest of their own prototype set and broadcast it to the central node:

[0197]

[0198] The central Bloom filter determines whether the coverage exceeds 92%. If it is insufficient, it randomly restarts several pairs of filters to fill the blind spots. The number of hash functions is set to 4; For domain i, the prototype Bloom summary is provided; where the popularity is below the formula threshold. Instantly trigger replacement swaps to avoid missing less common or weak spectrum elements.

[0199] The central node randomly selects two domains to upload the prototype index for hash matching. The data is distributed to all nodes, and each domain constructs a tensor based on the corresponding prototype using the Hadamard product. :

[0200]

[0201] Then use the higher-order statistical kernel saved in step three. Calculate the consistency score If the lowest score falls below 0.85, it indicates that the higher-order alignment has failed, triggering a second distillation.

[0202]

[0203] in: , These are the prototype vectors after random selection and swapping of the first and second domains, respectively; For extraction retrieval index, For Hadamard element-wise multiplication; Denotes the Frobenius norm;

[0204] To prevent feature drift from being masked by averaging, the consistency test not only takes extreme values. Also monitors percentile differences When the quantile difference is higher than 0.06, the central node considers that there is still a latent inconsistency and automatically raises the pruning threshold, so that subsequent distillation focuses on the subspace with the greatest difference.

[0205] When all consistency scores Once the values ​​exceed the corresponding threshold, the central node retrieves the online spectral masks for each domain using a Bloom-summary method. weak spectral coordinate set The global weak spectral common mode is recalculated by taking the union-mutual information weighted average and broadcast to each node to update the local mask, so that subsequent distillation can further concentrate firepower, wherein:

[0206]

[0207] in, For a set of fields; Loss due to information constraints Mutual information contribution weights obtained by hierarchical contribution normalization;

[0208] For global weak spectrum common-mode mask; For discrete frequency indexing, The edge domain is indexed; furthermore, the new mask is broadcast and written to the TF-Net spectral suppression module, so that all edge nodes instantly focus on the same weak spectral region.

[0209] To prevent the prototype library from expanding indefinitely and consuming excessive memory, after each domain completes the common mode update, it performs information entropy-KL cross-index pruning again on the prototype set, retaining the top 70% of prototypes in terms of information content, and then initiates lightweight dual distillation to refine the residuals. This self-loop executes a maximum of three rounds; in practice, one round is sufficient to minimize information constraint loss. The convergence to 0.03 ultimately enabled the bidirectional distillation results to be validated across the entire domain and the weak spectral focus to be unified. At the same time, the storage and computation costs were controlled through a pruning mechanism to ensure that the iteration continued to cycle within the acceptable range of marginal resources.

[0210] This step outputs the global weak spectral common-mode mask. With final consistency score Both will be used as the global loss fluctuation threshold and freeze level criterion in step five; and the cause link will be embedded when generating the anomaly confidence heatmap in step six.

[0211] Step four extends the alignment effect to the entire domain and performs efficient verification, following steps 401 and 402. The entire chain uses homomorphic encryption and random salt, consistent with the methods used in steps three, to ensure privacy, leveraging the higher-order statistical kernel from step three. With online spectral masks Verification and common mode generation are performed, with parameter uniqueness maintained throughout all stages. Dual distillation and high-order consistency verification work together to not only solidify the significance of weak fault spectral lines, but also provide the central node with precise freezing thresholds and hierarchical information in step five, "progressive weight freezing," and provide a causal link benchmark in step six, "anomaly confidence heatmap."

[0212] In practice, Bloom hash broadcasting and coverage heatmaps allow central nodes to observe the distribution of weak spectral prototypes in real time, ensuring no factory is overlooked. The Hadamard consistency test, constrained by a 0.85 threshold and quantile difference, significantly reduces alignment blind spots. The common-mode mask's dynamic weighting amplifies the contribution of weak network domains, allowing previously buried micro-crack spectral peaks to regain global model attention. The low-overhead probabilistic characteristics of Bloom filters enable full-domain prototype coverage detection, and a coverage-hotspot heatmap is introduced as an intuitive monitoring interface, achieving "at-a-glance" weak spectral knowledge distribution for the first time on an industrial cloud management platform. The Hadamard consistency test combines random sampling with manifold cosine similarity, avoiding the time-consuming centralized calculation of full-match full similarity.

[0213] The central node has obtained the global covariance center through steps one through four. Domain adaptation matrix Global weak spectrum common mode mask and the latest comprehensive losses in each region As production batches, raw material batch numbers, and environmental temperature and humidity continuously evolve, the statistical distribution of incremental samples will deviate from the current global model. Without timely intervention, this will cause the weights of weak fault spectral lines to be eroded by new noise patterns, leading to false alarms and missed alarms. To ensure adaptability while locking in the learned high-order representations of weak faults, when loss fluctuations exceed a threshold, only low-level and mid-level parameters are frozen, while high-level fine-tuning and mask fine-tuning are enabled. This allows the model to quickly absorb new operating condition features while stabilizing the learned features.

[0214] Step 5: By using global loss monitoring and a progressive weight freezing strategy, the model maintains stable weak fault representation while continuously adapting to new operating conditions.

[0215] Step five includes the following:

[0216] Step 501: Dynamic Monitoring of Global Loss and Adaptive Threshold Generation

[0217] The central node needs a composite metric that considers weak spectral significance, link health, and high-order consistency to assess the impact of new samples on model reliability; a single loss is insufficient to reflect multidimensional drift, therefore the following approach is adopted:

[0218] Central nodes stacked continuously The combined loss vector for each time window is then normalized by a matrix. Mapping to a unified dimension, specifically as follows:

[0219]

[0220] in, Let be the global index vector at time t; This represents the combined loss from step three; The Hamiltonian cross divergence; This represents the lowest possible consistency score. For dimensionally normalized matrices, fixed diagonal form;

[0221] When fusing 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 circular buffer in the memory layer.

[0222] For each dimension index, multiply by the spectral weight vector Its elements are composed of weak spectral common-mode masks. Points earned:

[0223]

[0224] in, For spectral sensitivity weights, the element values ​​are... ; A scalar of global index weighted by spectrum;

[0225] To avoid noise spikes triggering false freezing, the calculated spectral weighting index is... Riemann increment distance within a time window ;

[0226]

[0227] in, It is the scalar logarithm; Set the window span to 5; This is the incremental distance, used for threshold determination;

[0228] When evaluating incremental distance, the central node records each incremental distance. The corresponding sampling window number is used for subsequent freeze-rollback analysis of causal links. If the incremental distance jumps twice consecutively, it generally means that the true distribution has gradually drifted rather than being instantaneous noise; the next evaluation cycle is automatically shortened to improve detection sensitivity. When the incremental distance falls back to the stable range, the evaluation cycle is gradually lengthened to ensure that computing resources are fully utilized without being wasted.

[0229] To ensure the threshold is sensitive to weak spectral anomalies without over-responding to transient noise and to improve the reliability of the freeze decision, the results of the first three steps are input into an exponential sliding filter to obtain the real-time threshold:

[0230]

[0231] First value Take the empirical constant 0.02; The sliding coefficient is set to 0.3. This is the current threshold.

[0232] Finally, the output spectral weighting index Incremental distance With dynamic threshold These three factors will directly drive the freeze-fine-tuning process in step 502 and are used in step six for the anomaly confidence interpretation link; dynamic threshold. It is not only used for single-point triggering, but also drawn as a "trough-peak" band chart in the visualization panel to show the "model stability margin".

[0233] In practice, by introducing weak spectral common-mode weighting and Riemann incremental distance, sub-step 501 upgrades traditional single-path loss monitoring to a multi-indicator three-dimensional evaluation. This not only captures the 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 "breathes" under all-weather scheduling, avoiding redundant alarms at night from disturbing on-duty personnel while ensuring rapid identification of potential hazards during daytime production.

[0234] The incremental distance uses a Riemannian metric instead of Euclidean distance, emphasizing the geometric structure of the indicator space, making the threshold more sensitive to exponential changes; furthermore, the dynamic threshold curve is adjusted according to the production shift switching sliding coefficient. This organically combines manual management of the beat with algorithmic sensitivity.

[0235] Step 502: Gradual weight freezing and high-level fine-tuning - rollback mechanism

[0236] once The central node needs to quickly freeze the lower layers of the network and authorize edge nodes to fine-tune only at the higher layers, while maintaining knowledge distillation and weak spectral saliency. If the subsequent indicators recover, the network needs to be unfrozen and rolled back to avoid model rigidity. The specific operation method is as follows:

[0237] The central node utilizes the hierarchical learning rate gain saved in step three. Construct importance distribution and sort convolutional layers according to Increasing sort as the freeze priority sequence:

[0238]

[0239] in, For the first Layer importance; For the first Layer learning rate gain, This represents the learning rate gain for the j-th layer; its value is between 0 and 1.

[0240] In calculating importance distribution Subsequently, the central node compares historical importance curves to identify two categories: "persistently high importance" and "one-off surge". The persistently high importance layer is designated as a permanent key protection zone and will not participate in the freezing process regardless of future minor adjustments; while the surge layer is placed in the monitoring queue and will be immediately marked as "easily drifting" if it surges again in the future, and will be frozen first.

[0241] Freeze the layers with the lowest cumulative importance (70%) according to priority, and relax the learning rate for the remaining layers. :

[0242]

[0243] in, The original learning rate; This is the learning rate gain factor, with values ​​ranging from [value missing]. ; For fine-tuning of the learning rate by higher management;

[0244] When freezing layers with less than 70% cumulative importance, first bypass these layers once for "idle inference" and measure the impact of freezing on inference latency; if the latency savings have met the edge hard real-time requirements, the freeze takes effect; otherwise, roll back a portion of the layers and re-evaluate.

[0245] It also allows edge nodes to fine-grained adjust the weak spectral mask:

[0246]

[0247] in It is the mask learning step size. This is the updated mask; minor mask adjustments do not involve direct modification. Instead of using the full-width method, it adopts a convolutional frequency band block-level incremental approach;

[0248] If continuous Each window satisfies The central node unfreezes the next 15% importance interval and decays the learning rate back to its original value:

[0249]

[0250] Among them, rollback decay rate , To continuously restore the number of windows, For dynamic thresholds;

[0251] Number of consecutive recovery windows This not only affects the learning rate rollback but also determines the order in which frozen layers are unlocked: layers with high gradient accumulation in the latest drifted samples are unlocked first to ensure resources are allocated to the most critical representation space. Simultaneously, the system records the corresponding data during rollback. The value is used as the baseline for the next trigger threshold; effectively avoiding frequent "threshold triggering-threshold de-thresholding" jitter; if If there is still no fluctuation when the window reaches 10, automatically unfreeze all windows and reset the threshold curve to prevent stagnation.

[0252] Ultimately, the accumulated low- and mid-layers form the frozen layer set. High-level fine-tuning of the learning rate Update mask and rollback status They will then proceed to step six for labeling the cause path and visualization freeze level of the anomaly confidence heatmap.

[0253] Construct multi-source spectral weighting index through step 501. Dynamic thresholds are generated using Riemann incremental distance and exponential filtering. This enables 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 thresholds, while allowing fine-tuning of weak spectral masks and rolling unfreezing according to recovery criteria, which can keep the model adapting quickly to new operating conditions without forgetting weak fault representations.

[0254] In practice, the progressive weight freezing strategy selects freezing layers by importance ranking 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 incremental distance, improving the convergence speed under new conditions. Mask fine-tuning follows a "block-observation" double insurance to ensure that weak spectral enhancement does not generate secondary noise due to over-amplification. Dynamic rollback mitigates the risk of model rigidity caused by over-freezing, allowing the system to smoothly switch between "steady-state" and "adaptive" bipolar states. Latency assessment of "idle inference" is performed before segmented freezing, binding resource scheduling to business real-time requirements. Mask fine-tuning uses gradient-KL dual gating to achieve precise weighting at the frequency band block level.

[0255] In the collaborative flow of steps one through five, high-saliency learning and dynamic steady-state maintenance of cross-domain weak fault representation have been achieved, progressing from original signal unification, dense-state statistical alignment, self-supervised reinforcement, dual distillation to progressive weight freezing. However, the true value of industrial sites lies in the "diagnosis-treatment closed loop." Although the center-periphery model continues to evolve, if it cannot quickly transmit abnormal confidence levels in an interpretable form to maintenance personnel during the fault nascent stage, it will be difficult to realize the benefits of preventative maintenance. On the other hand, alarms based solely on a single confidence threshold are highly susceptible to drift from new operating conditions and interference from link noise, leading to false alarms, missed alarms, or information overload. Therefore, the following countermeasures have been adopted:

[0256] Step 6: Use multidimensional confidence tensors to drive the generation of heatmaps and cause chains, enabling operations and maintenance personnel to understand and locate potential faults within seconds.

[0257] Step six includes the following:

[0258] Step 601: Construction of Marginal Anomaly Confidence Tensor and Local Heat Encoding

[0259] After step five, the edge nodes now have a set of frozen layers. Update mask and spectral weighting index If only a single predicted probability is reported, the information dimension is insufficient; if all intermediate features are uploaded, it violates privacy and bandwidth requirements. Therefore, the following approach was adopted:

[0260] Edge nodes will display the latest inference output vector. Activation statistics of frozen layer and spectral mask gradient Connect along a new dimension:

[0261]

[0262] In the formula, : Inference output vector; Activate the mean vector for the frozen layer; For the frequency-sensitive gradient of the mask; For vector concatenation operators; For discrete frequency indexing;

[0263] In addition to the original stitching, a "frozen layer gradient variance" vector was added to record the mean square value of the residual gradient of each frozen convolution kernel in the latest batch, forming a new quaternary confidence block; in this way, if the frozen layer still has a high residual gradient, the system can expose the risk signal of "insufficient freezing" in the heat map.

[0264] Using weighted voiceprint Multi-source confidence tensor Mapping to time-frequency plane heat :

[0265]

[0266] in , For Gaussian kernel density, For frequency domain kernel function, For time-domain kernel functions, Time-frequency heat;

[0267] Time-frequency heat Perform density peak clustering and extract Peak popularity The number of peaks dynamically varies with the multi-source spectral weighting index. Relaxed when the indicator is higher than the dynamic threshold More peak values ​​are allowed to ensure that abnormal details are not missed. Density peak clustering is changed to use a local neighborhood slope threshold to avoid small noise being misjudged as peaks at high sampling rates; the system sets the minimum peak width to be equal to half the reciprocal of the rotational speed to ensure that each peak represents a complete mechanical cycle.

[0268] Based on peak energy and corresponding frozen layer weight Calculation priority:

[0269]

[0270] Before uploading indivual The highest peak value was achieved by compressing the bandwidth to 4kB. Score the peak priority.

[0271] Finally, the set of heat peaks is output. Weighted index of multi-source spectrum Both will be used in step 602 for cross-domain aggregation and cause link inference.

[0272] In practice, the multi-source confidence tensor compensates for the internal tension dimension of the model by adding the gradient variance of the frozen layer. The spectral-temporal adaptive kernel allows the heatmap to meet the resolution requirements of both high-speed and low-speed machinery. The directional labeling of the clustered encoding provides direct positive and negative feedback for center attribution. The information redundancy removal mechanism still ensures peak diversity under stringent bandwidth conditions. The adaptive kernel width algorithm links device dynamic parameters with heatmap rendering to achieve unified visualization across different models. The information redundancy removal unifies the time-frequency-gradient spatial distances, establishing a multi-scale sparsity criterion for edge uploading, breaking through the traditional "fixed peak number" bandwidth allocation strategy.

[0273] Step 602: Central anomaly heatmap aggregation, cause chain inference, and operation and maintenance strategy push.

[0274] The central node needs to synthesize heat peaks from multiple domains into a global anomaly view, and combine this with model freeze-thaw history, weak spectral mask changes, and link health to infer the root cause, thereby outputting an operable maintenance plan. Therefore, the following plan is selected for execution:

[0275] The central node aggregates the heat peaks of each domain. Mapped to a unified timeline, a global heatmap is generated by fusion with self-attention weights. ,in:

[0276]

[0277] In the formula, The attention weight for the q-th heat peak in domain i is increased exponentially with priority. Scoring based on peak popularity priority, peak energy Importance of the corresponding frozen layer The score obtained by multiplication Similar in meaning;

[0278] Construct a node set {hierarchy, frequency band, link, operating condition} and an edge set {activation causality, spectral coupling, link amplification}, and apply a graph convolutional network to calculate node importance. If an edge node's activation and weak spectral gradient in the frozen layer are both above the 95th percentile, the center is inferred to be on an "internal feature drift amplification" path; if the Hamiltonian cross divergence increases synchronously, it is inferred to be on a "link-model composite" path. The graph network not only calculates node importance but also outputs an edge attention matrix, which is overlaid with pseudo-color onto the edges of the heatmap to display "potential causal arrows." For example, highlighting "link amplification" edges means that noise is amplified through network layers, misleading the model, thus guiding operations and maintenance to first check the network.

[0279] Based on the attribution results, the maintenance strategy library is invoked: internal drift triggers "model high-level fine-tuning extension" and "device status check"; link-model composite triggers "network self-check" and "local resampling" dual commands. Commands carry the parameter: frozen layer set. High-level fine-tuning of the learning rate Update mask For edge and network teams to execute. A new "Freeze Layer Review" entry has been added to the policy library: when the attribution result points to "insufficient freeze," a "layer-by-layer unfreeze-observation" process script is automatically generated and pushed to the central operations platform; the script already includes embedded high-level fine-tuning of the learning rate. The attenuation curve and observation window length can be distributed by the maintenance personnel simply by clicking "confirm".

[0280] The global heatmap, cause-and-effect relationships, and key strategy points are packaged in JSON-LD format and pushed to desktop monitoring dashboards, mobile apps, and emails. The heatmap uses pseudo-color rendering, with color mapping adjusted according to attention weights. Automatic adjustment. After the central node integrates the heat peak into the global anomaly heatmap, it constructs an attribution graph containing four types of nodes ("hierarchy, frequency band, link, and operating condition") and various causal edges. Then, a graph convolutional network is used to perform forward propagation on this graph, outputting the weight score of each node; this weight score represents the node's importance. The value reflects the criticality of the corresponding node in the fault mechanism chain, and will be pushed to the operation and maintenance interface along with the cause chain.

[0281] Adding an "Expected Impact Threshold" field to the message package, calculated using the average of the three most recent spectral weighted indices, can help on-duty engineers determine the urgency level of a fault; the mobile app supports one-click conversion to a work order, automatically assigning node importance. Prioritize work orders to shorten on-site dispatch time.

[0282] The final output is a global heatmap. Node importance Includes strategy instruction packages; and records alarm IDs and multi-source spectral weighted indicators. For subsequent auditing and model evolution analysis.

[0283] Step 6, relying on the multi-source confidence tensor condensation in step 601, maps inference probability, frozen activation, weak spectral gradient, and link indicators to time-frequency heat peaks and filters and uploads them, achieving a dual balance between bandwidth and privacy on the edge side. Subsequently, step 602 generates a global heat map and causal links through self-attention aggregation and graph network attribution, and pushes maintenance instructions through the policy rule engine, enabling operation and maintenance personnel to obtain intuitive fault areas and actionable suggestions within seconds, achieving the ultimate goal of early warning and precise operation and maintenance of weak faults in industrial Internet scenarios.

[0284] 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.

[0285] The self-attention fusion and overlay domain trust weight introduces link health and consistency scores into visual weight decision-making, breaking the convention that "heatmap brightness only depends on peak value"; 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 incorporates model adaptive parameters as part of the operation and maintenance execution script; the message packet-work order direct connection seamlessly connects the AI ​​alarm chain with the operation and maintenance process pipeline, enabling diagnosis and maintenance to truly form a data closed loop.

[0286] Those skilled in the art will recognize that the units and algorithm steps of the various examples 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 implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art 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.

[0287] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0288] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0289] The units described as separate components may or may not be physically separate. 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 the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0290] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for enhancing vibration measurement information based on fused data, characterized in that: include, The source signal is preprocessed at each device edge node to generate a unified feature tensor. After being compressed by the comparison encoder, the gradient summary is generated by elliptic curve homomorphic encryption and uploaded to the central node. The central node performs dense-state outer product and debiasing operations on each encrypted gradient digest, and uses Riemann distance and weighted Karcher mean to obtain the global central covariance, which is then compressed into a domain adaptation matrix and sent to the edge nodes. After adapting the edge node receiver domain to the matrix, the time-frequency fusion network is recalibrated using high-order tensor progressive stitching, differential weight shrinking, and spectral gating gradient weighting, and spectral suppression is used to enhance the significance of weak spectral lines. Each edge node compresses and generates a feature prototype, which is then bidirectionally exchanged and its security is verified by coupling with a salt value curve. After the cross-domain deep representation synchronization is completed, a global consistency verification is performed. The central node continuously monitors the spectrum weighted comprehensive index and calculates the dynamic threshold for generating the Riemann incremental distance; When the spectral weighted composite index exceeds the threshold, the low and mid-level parameters are frozen, the high-level learning rate is increased, and the weak spectral mask is fine-tuned. After the index recovers, it is rolled back and unfrozen according to importance to maintain the stability of the learned weak fault characterization and absorb new operating condition features.

2. The vibration information enhancement method based on fused data according to claim 1, characterized in that: When any edge node detects an abnormal increase in confidence based on the updated model, it automatically generates an abnormal confidence heatmap and the cause chain and pushes it to the operation and maintenance interface.

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

4. The vibration information enhancement method based on fused data according to claim 3, characterized in that: The unified feature tensor is compressed into a latent vector by a contrast encoder with bidirectional mutual information constraints and multi-resolution self-gated projection. The elliptic curve homomorphic encryption operator is called at the edge side to encrypt the gradients in batches. The gradients are then uploaded to the central node via RaptorQ slices with divergence verification.

5. The vibration information enhancement method based on fused data according to claim 4, characterized in that: After receiving the encrypted gradient summary uploaded by the edge nodes, the central node maintains the encrypted state, completes the reconstruction of the dense state covariance, and uses the Riemann distance to evaluate the multi-domain distribution difference. It uses the Karcher mean iteration to obtain the global central covariance and generates the corresponding domain adaptation matrix based on the joint constraints of geometric regularity and physical regularity.

6. The vibration information enhancement method based on fused data according to claim 5, characterized in that: The mapping matrix is ​​subjected to orthogonal robust compression and link adaptive quantization, and then distributed to the edge nodes via RaptorQ redundant slicing. Edge feedback is collected synchronously to verify whether the divergence threshold is met, and the adaptation status is updated in the central database. Feature drift suppression and global model distribution homogenization are performed.

7. The vibration information enhancement method based on fused data according to claim 6, characterized in that: After the edge node receives the domain adaptation matrix, the mapping feature tensor core statistics are injected into the time-frequency fusion network by using high-order projection progressive stitching. The convolution kernel is adjusted by combining differential weight shrinkage with spectral gating gradient energy weighting 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 vibration information enhancement method based on fused data according to claim 7, characterized in that: After weight calibration is completed, mutual information redistillation is enabled at the same node to receive the comparative structure discrimination information. Then, noise-driven occlusion consistency and multi-scale spectrum suppression are used to improve the resistance to link jitter and high-energy pseudo-peaks. The loss weights are dynamically balanced by perturbation-aware annealing.

9. The vibration information enhancement method 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 by carrying random salt hash verification through bidirectional homomorphic encryption exchange. Then, deep representation is synchronized using weak spectral residual distillation. All nodes broadcast the prototype Bloom hash digest to the center. The center triggers a replacement swap based on the coverage result and issues a random retrieval index to each node to conduct a Hadamard tensor consistency check.

10. The vibration information enhancement method based on fused data according to claim 9, characterized in that: After the consistency test is passed, the center merges the weak spectral mask weights of each node to generate a weak spectral common mode mask and broadcasts it again. The edge nodes update the spectral suppression module accordingly and use Pareto pruning to maintain the prototype library size, and perform cross-domain deep feature alignment and weak spectral knowledge sharing.

11. The vibration information enhancement method based on fused data according to claim 10, characterized in that: The central node continuously aggregates the comprehensive loss, link divergence and consistency scores 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 weighting index exceeds the threshold, the central node freezes the low-level and mid-level parameters according to the hierarchy importance, while increasing the learning rate of the high-level nodes and authorizing the edge nodes to perform block-level fine-tuning based on the weak spectral mask.

12. The vibration information enhancement method based on fused data according to claim 11, characterized in that: During the freeze 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. At the same time, the updated weak spectral mask is confirmed.

13. The vibration information enhancement method based on fused data according to claim 12, characterized in that: Edge node splicing inference probability, frozen layer activation statistics, weak spectral gradient direction and frozen layer gradient variance generate a multi-source confidence tensor and form a heat peak list through adaptive time-frequency kernel mapping, which is then uploaded after information redundancy removal and filtering.

14. The vibration information enhancement method based on fused data according to claim 13, characterized in that: After the central node assigns domain trust weights to each domain, it uses self-attention weights to fuse heat peaks to construct a global heatmap, and connects hierarchical, frequency band, link and working condition nodes in the mechanism attribution graph network to calculate causal paths. The attribution results trigger the policy rule engine, select the corresponding maintenance script or network self-test command, and push it to the monitoring dashboard, mobile device and email in a unified message packet format along with the global heat map and cause chain.

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