Generator set vibration trend early warning method based on deep time sequence model
By constructing an enhanced Neural RDE model, combined with conditional coarse driving construction, frequency band gated vector field, and physical consistency constraints, the problem of insufficient prediction accuracy and robustness in generator vibration signal early warning is solved, achieving high-precision vibration trend early warning and safety assurance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI JINHAILONG INTELLIGENT TECHNOLOGY CO LTD
- Filing Date
- 2026-03-27
- Publication Date
- 2026-06-23
AI Technical Summary
Existing technologies for generator vibration signal early warning lack in-depth analysis of the coupling relationship between multi-dimensional operating data, resulting in limited prediction accuracy, insufficient convergence and robustness of the model training process, and low early warning timeliness.
An enhanced Neural RDE model is constructed, which introduces conditional coarse driving construction, frequency band gated vector field and physical consistency constraint mechanism. The loss is combined to optimize trend regression error, frequency band consistency error and dynamic residual constraint, and risk assessment is performed by combining dynamic threshold mechanism.
It achieves high-precision modeling of vibration trends, improves the accuracy and robustness of predictions, and ensures the operational safety and reliability of generator sets.
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Figure CN122263019A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power equipment condition monitoring and fault diagnosis, and in particular to a method for early warning of generator vibration trends based on a deep time series model. Background Technology
[0002] Currently, generator sets, as core equipment in the power system, are directly related to the continuity of power supply due to their operational safety and stability. Vibration signals, as an important monitoring quantity reflecting the health status of the unit, play a crucial role in early fault identification and trend prediction. Existing technologies typically rely on traditional frequency domain analysis and statistical modeling methods to process vibration data. While these methods can reflect the unit's operating status to a certain extent, they often fall short when facing complex operating conditions and long-term series predictions.
[0003] On the one hand, most existing modeling methods rely on fixed features or single frequency band indicators, lacking in-depth analysis of the coupling relationships between multidimensional operational data. This limits prediction accuracy, especially in scenarios with significant operating condition fluctuations or high noise levels, leading to frequent misjudgments and missed predictions. On the other hand, some studies have attempted to introduce deep learning models for time series prediction, but most models fail to effectively combine the frequency band characteristics of vibration signals with the dynamic constraints of the unit. The model outputs lack physical interpretability and stability, making it difficult to directly guide risk assessment and early warning decisions.
[0004] Furthermore, existing methods still have shortcomings in loss optimization and early warning threshold setting. Traditional loss functions often only consider a single error metric, failing to integrate trend deviation, frequency band consistency, and dynamic constraint errors, resulting in insufficient convergence and robustness during model training. Threshold setting typically relies on experience or static standards, making it difficult to adapt to the dynamic risk characteristics of long-term unit operation, thus leading to low early warning timeliness.
[0005] Therefore, how to provide an early warning method for generator vibration trends based on deep time series models is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0006] One objective of this invention is to propose a generator vibration trend early warning method based on a deep time-series model. This invention constructs an enhanced Neural RDE model and innovatively introduces conditional coarse driving construction, frequency band gated vector fields, and physical consistency constraint mechanisms to achieve joint modeling of multi-channel vibration signals, operating condition data, and dynamic characteristics. This enables accurate capture of vibration trend evolution and enhances physical interpretability. This invention improves the stability and robustness of model training by integrating trend regression error, frequency band consistency error, and dynamic residual constraints through joint loss optimization. Furthermore, it combines a dynamic threshold mechanism to achieve intelligent determination of risk advance, possessing advantages such as high prediction accuracy, strong early warning timeliness, and adaptability to complex operating conditions.
[0007] The generator set vibration trend early warning method based on a deep time series model according to an embodiment of the present invention includes the following steps: Collect generator set operating data, perform data preprocessing, and generate a coarse lifting input sequence; An enhanced Neural RDE model is constructed, including conditional coarsening driving construction units, frequency band gated vector field units, and physically consistent constraint units; The conditional coarse-driven construction unit is run, and a logarithmic signature feature set and a working condition vector sequence are generated based on the coarse-lifted input sequence. The operating frequency band gated vector field unit generates a set of gated coefficients based on the working condition vector sequence, drives the evolution of the hidden state sequence, and generates the hidden state sequence. Run the physical consistency constraint unit, calculate the dynamic residual set and topological consistency term based on the hidden state sequence, perform time alignment and normalization, and merge to generate a constraint signal sequence; Based on the hidden state sequence, the logarithmic signature feature set, and the constraint signal sequence, a set of trend indicators and a set of risk indicators are calculated and generated. Based on the set of trend indicators, the set of risk indicators, and the constraint signal sequence, the joint loss function is calculated, the parameters of the enhanced Neural RDE model are updated, and the set of parameters and thresholds after training are generated. Input real-time collected generator set operation data, logarithmic signature feature set and gating coefficient set, load trained parameter set and threshold set, and generate vibration trend early warning results and early warning lead time.
[0008] Optionally, the data acquisition and preprocessing to generate a parameter set includes: Collect generator set operating data, including multi-channel vibration signal data, speed data, load data, and temperature data; Perform data preprocessing, including normalization and scaling adjustment, generate a set of normalized sequences, perform envelope demodulation, generate a set of envelope spectrum energy, perform bandpass filtering, and calculate the energy characteristics of each order frequency band to generate a set of multi-order frequency band features. Lead-lag augmentation and timestamp interpolation are performed on generator set operating data to generate a coarsely boosted input sequence; During the data acquisition process of generator set operation, multiple vibration sensors are distributed at different installation positions of the unit. The connectivity between the measuring points is described in the form of an adjacency matrix, thereby forming a measuring point topology matrix. The initial set of dynamic parameters is obtained by performing frequency domain analysis, energy calculation, and physical parameter deduction on the generator set operation data.
[0009] Optionally, the generation of the logarithmic signature feature set and the working condition vector sequence includes: In the conditional coarse drive construction unit, the speed sequence, load sequence and temperature sequence in the standardized sequence set are timestamp aligned and scale normalized to form a unified working condition input stream. A multi-level iterative integral path representation is constructed based on the coarse lifting input sequence. The unified working condition input stream is embedded into the path representation, high-order interaction features are extracted, and a coarse path stabilization term is introduced during the path integration process to generate a logarithmic signature feature set. The multi-level iterative integral path representation is a temporal feature expansion method based on rough path theory. On the basis of rough lifting the input sequence, the time series is segmented according to time windows, and iterative integration is performed layer by layer within each time window. The first-order integral captures the overall trend of the signal, the second-order integral describes the synergistic effect between different variables, and the third-order and above integrals further reflect the complex nonlinear interaction relationship. The integration results of each level are spliced and normalized in time order to form a multi-level iterative integral path representation. The coarse path stabilization term consists of a growth constraint factor and an amplitude modulation factor. By combining the higher-order interaction features with the coarse path stabilization term, the features of each order are subjected to constraint weighting and normalization. The input stream under the unified operating condition is mapped to different channels. The speed sequence, load sequence and temperature sequence are transformed into corresponding operating condition factor vectors through sliding window feature extraction and Z-score normalization. They are then combined under the same time index to generate a sequence of operating condition vectors.
[0010] Optionally, the generation of the hidden state sequence includes: In the frequency band gated vector field unit, the envelope spectrum energy set and the multi-order frequency band feature set are mapped in a frequency band layer. The frequency band features are weighted and adjusted by combining the working condition vector sequence to form a frequency band adjustment feature set. A gating function is constructed based on the set of frequency band adjustment features, and a set of gating coefficients is generated. The construction of the gate function includes indexing the frequency band adjustment feature set by time. With frequency band index The organization is a two-dimensional sequence. At each time index, the fused feature vector is calculated. Based on the fused feature vector, a gating function is defined and three constraints are introduced: monotonicity, sparsity competition, and total amount. The gating coefficient is then calculated. The gate function is defined as follows: ; in, Indicates time index The Bandgap control coefficient, Indicates the number of frequency bands. Indicates the temperature coefficient. Represents the fused feature vector. Indicates the first Small feedforward mapping parameters of the frequency band, Indicates the stabilization factor. Indicates time index The weighted mean of the fusion features, Represents the Euclidean norm; Meanwhile, in order to obtain a time-stable set of gating coefficients, an exponential moving average and hysteresis update are applied to the gating coefficients on the time axis to obtain smoothed gating coefficients. Finally, the smoothed gating coefficients, arranged by time index and frequency band index, form a set of gating coefficients. The set of gating coefficients is fused with the set of logarithmic signature features, and the hidden state sequence is updated through a vector field evolution mechanism, forming a hidden state sequence by iterating layer by layer at a time step.
[0011] Optionally, the generation of the constraint signal sequence includes: In the physical consistency constraint unit, displacement estimation is obtained based on the hidden state sequence through mapping relationship, and velocity and acceleration estimation are further calculated and output; Based on the initial set of dynamic parameters, the mass matrix, damping matrix, and stiffness matrix are constructed. At the same time, the load sequence is converted into the corresponding load vector. The dynamic residual set is calculated by combining displacement estimation, velocity estimation, acceleration estimation, and load vector. Based on the topological relationship matrix of measurement points, establish topological constraints and calculate topological consistency terms; The dynamic residual set and the topological consistency term are aligned according to the time index, and a normalization method is used to eliminate the influence of different dimensions on subsequent calculations. The normalized set of dynamic residuals and the topological consistency term are merged according to preset weights to generate a constraint signal sequence.
[0012] Optionally, the generation of the trend indicator set and the risk indicator set includes: Based on the hidden state sequence, logarithmic signature feature set and constraint signal sequence, the future time window length and time step are set, the RMS slope and key order envelope energy growth rate are calculated at each time index, and a set of trend indicators is generated and arranged by time index. Based on hidden state sequences, logarithmic signature feature sets, and constraint signal sequences, a risk intensity function is constructed by combining future time windows and the early warning lead time is calculated to generate a risk indicator set. The trend indicator set and the risk indicator set are organized to correspond under the same future time window.
[0013] Optionally, the generation of the trained parameter set and threshold set includes: Based on the set of trend indicators, the set of risk indicators, and the constraint signal sequence, the trend regression error, frequency band consistency error, dynamic residual error, topological consistency term error, and risk intensity partial likelihood are calculated within the training batch. Time index alignment and normalization are performed on each error component to form an error component vector. Within each training batch, a joint loss function is constructed based on the error component vector. An adaptive weighting factor is introduced to dynamically adjust the weight of each error component in the joint loss function. The weight adjustment is based on the gradient sensitivity and variance characteristics of the error components to generate the joint loss function. The parameter gradient is calculated based on the joint loss function. A regularization term is introduced in combination with the consistency condition of the constrained signal sequence. The parameters of the enhanced Neural RDE model are iteratively updated. When the loss converges and the constraint consistency is satisfied, the set of parameters after training is output. Based on the joint distribution of the trend indicator set and the risk indicator set during the training process, the threshold set is determined by using the dynamic quantile statistical method combined with the stability range of the constraint signal sequence.
[0014] Optionally, the generation of the vibration trend early warning result and the early warning lead time includes: During the online inference phase, continuous data streams are acquired in real time. Data preprocessing and time alignment are performed on the continuous data streams to obtain a standardized sequence set, an envelope spectrum energy set, a multi-order frequency band feature set, and a coarse boosted input sequence. The logarithmic signature feature set and the gating coefficient set are aligned with the above sequences according to the time index. Load the trained parameter set and threshold set, drive the enhanced Neural RDE model for online inference based on the log signature feature set and gating coefficient set, update the hidden state sequence, calculate the RMS slope and key order envelope energy growth rate within the sliding window to generate a trend indicator set, and calculate the risk indicator set based on the risk intensity function and future time window. By comparing and judging the set of trend indicators, risk indicators, and thresholds, we can obtain the vibration trend early warning result and the early warning lead time.
[0015] The beneficial effects of this invention are: First, by introducing a conditional coarse-driven construction mechanism, this invention effectively integrates multi-channel vibration signals and operating conditions, extracts a stable set of logarithmic signature features, overcomes the problem of unstable features under operating condition fluctuations and noise interference in traditional methods, and achieves high-precision modeling of the evolution law of vibration trends.
[0016] Secondly, by designing a frequency band gated vector field unit, this invention hierarchically adjusts the envelope spectrum energy features and multi-order frequency band features, and introduces a set of gated coefficients in the time dimension, thereby realizing the dynamic selection and weighting of different frequency band features. This avoids the limitations of traditional methods that have fixed frequency band feature processing methods and lack adaptive capabilities, and significantly improves the accuracy and robustness of trend prediction.
[0017] Furthermore, this invention introduces a physical consistency constraint mechanism into the deep time series model, using the initial set of dynamic parameters and the topological relationship matrix of measurement points to constrain the hidden state sequence. This effectively ensures the rationality and interpretability of the prediction results at the physical level, overcoming the deficiency of existing models that lack physical constraints. By simultaneously considering trend regression error, frequency band consistency error, dynamic residual error, and risk intensity likelihood through joint loss optimization, the model exhibits stronger convergence and generalization capabilities during training. This achieves high-precision and robust generator vibration trend early warning, contributing to ensuring the safety and reliability of generator operation. Attached Figure Description
[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is an overall flowchart of a generator set vibration trend early warning method based on a deep time series model proposed in this invention; Figure 2 This is a schematic diagram illustrating the data processing and logarithmic signature feature generation of conditional coarsening-driven constructs in the enhanced Neural RDE model proposed in this invention. Figure 3 This is a schematic diagram of the structure of the frequency band gated vector field unit in the enhanced Neural RDE model proposed in this invention. Detailed Implementation
[0019] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.
[0020] refer to Figure 1-3 A generator set vibration trend early warning method based on a deep time series model includes the following steps: The system collects generator set operation data, including multi-channel vibration signal data, speed data, load data, and temperature data. It performs data preprocessing, including bandpass filtering, envelope demodulation, order energy calculation, normalization, and scaling, generating a standardized sequence set, an envelope spectrum energy set, and a multi-order frequency band feature set. It then performs lead-lag augmentation and timestamp interpolation on the generator set operation data to generate a coarse lifting input sequence. Simultaneously, it constructs a measurement point topology matrix and a set of initial dynamic parameter values. The system outputs a standardized sequence set, an envelope spectrum energy set, a multi-order frequency band feature set, a coarse lifting input sequence, a measurement point topology matrix, and a set of initial dynamic parameter values. An enhanced NeuralRDE model is constructed, including conditional coarse driving construction units, frequency band gated vector field units, and physical consistency constraint units. A data flow structure is established, consisting of a logarithmic signature feature set, a working condition vector sequence, a gating coefficient set, a hidden state sequence, a dynamic residual set, and a topological consistency term. The conditional coarsening drive construction unit generates a logarithmic signature feature set and a working condition vector sequence based on the speed sequence, load sequence and temperature sequence in the coarsening input sequence and the normalized sequence set, and outputs the logarithmic signature feature set and the working condition vector sequence. The operating frequency band gated vector field unit generates a set of gated coefficients based on the envelope spectrum energy set, the multi-order frequency band feature set, and the operating condition vector sequence. It then drives the evolution of the hidden state sequence by combining the logarithmic signature feature set to generate the hidden state sequence. Run the physical consistency constraint unit, calculate the dynamic residual set and topology consistency term based on the hidden state sequence, the initial value set of dynamic parameters and the topology relation matrix of the measurement points, perform time alignment and normalization on the dynamic residual set and topology consistency term, merge to generate constraint signal sequence, and output constraint signal sequence; Perform trend regression and risk assessment. Based on the hidden state sequence, logarithmic signature feature set and constraint signal sequence, calculate the RMS slope of the future time window and the growth rate of the key order envelope energy to generate a set of trend indicators. At the same time, construct the risk intensity function and calculate the early warning lead time to generate a set of risk indicators. Output the set of trend indicators and the set of risk indicators. Perform joint loss optimization. Based on the trend indicator set, risk indicator set, and constraint signal sequence, calculate the joint loss function, including trend regression error, frequency band consistency error, dynamic residual error, topological consistency term error, and risk intensity partial likelihood. Update the parameters of the enhanced NeuralRDE model and generate the trained parameter set and threshold set. Perform online inference and early warning judgment, input continuous data stream, logarithmic signature feature set and gating coefficient set, load trained parameter set and threshold set, and generate vibration trend early warning result and early warning lead time.
[0021] In this embodiment, the data acquisition, preprocessing, and parameter set generation include: Collect generator set operating data, including multi-channel vibration signal data, speed data, load data, and temperature data; Data preprocessing is performed, including normalizing and scaling the acquired multi-channel vibration signal data, rotational speed data, load data, and temperature data to form a unified input format, generating a standardized sequence set, performing envelope demodulation on the vibration signal, extracting the spectral components of the envelope signal, calculating energy characteristics, generating an envelope spectrum energy set, performing bandpass filtering on the vibration signal, separating the target order frequency band, calculating the energy characteristics of each order frequency band, and generating a multi-order frequency band feature set. The standardized sequence set includes multi-channel vibration signal sequences, rotational speed sequences, load sequences, and temperature sequences; Lead-lag augmentation and timestamp interpolation are performed on generator set operating data to generate a coarsely boosted input sequence; The lead-lag augmentation specifically involves: expanding the time series of generator set operation data by copying the original time series into two parallel channels, one being the lead channel at the current moment and the other a lag channel delayed by one time step. These channels are then concatenated under the same time index to form a two-dimensional extended path representation, thereby enhancing the sequential dependency and temporal feature expression capability of the input sequence. Simultaneously, to address the uneven or missing sampling intervals in the collected data, a linear interpolation method is used to fill in the missing points and correct the sampling intervals along the time index dimension. This aligns the multi-channel vibration signal data, speed data, load data, and temperature data on a unified time axis, thereby generating a continuous and consistent coarse boost input sequence, providing a stable temporal input foundation for the conditional coarse drive construction unit. During the data acquisition process of generator set operation, multiple vibration sensors are distributed at different installation locations within the unit. To characterize the spatial connection relationships and structural transmission paths between each measuring point, a measuring point topology matrix needs to be constructed. Specifically, the connectivity between measuring points can be described using an adjacency matrix: if two measuring points have a physical connection or vibration transmission path within the unit structure, a value of 1 is assigned to the corresponding position in the adjacency matrix; otherwise, a value of 0 is assigned. Furthermore, the adjacency matrix is normalized to eliminate the influence of differences in the number of measuring points and signal amplitude, thereby forming a measuring point topology matrix. This matrix can accurately characterize the topological structure between the generator set measuring points, providing a basic input for the subsequent physical consistency constraint unit. By performing frequency domain analysis, energy calculation, and physical parameter deduction on generator set operating data, an initial set of dynamic parameters is obtained, which is used to provide initial dynamic conditions for subsequent physical consistency constraint units. Specifically, after acquiring speed, load, and temperature data, the multi-channel vibration signal data is analyzed in the frequency domain using Fast Fourier Transform or Welch power spectral density estimation to extract the dominant frequency component and natural frequency of the vibration signal. Near the main peak of the spectrum, the bandwidth range is determined using the half-power bandwidth method, from which the damping ratio is obtained. The initial value of the damping coefficient is then calculated using the Rayleigh damping model. Combining speed and load data, the initial value of the moment of inertia is estimated by analyzing the relationship between power and speed changes. Then, based on the obtained natural frequencies and equivalent mass, the initial value of the stiffness coefficient is calculated. Simultaneously, the energy distribution of key orders is extracted using the order energy calculation method of the vibration signal to assist in correcting the initial values of stiffness and damping. Finally, the above dynamic parameters are corrected by combining the unit's design parameters and operating calibration values, and then normalized and structured to form a set of initial values for the dynamic parameters.
[0022] In this embodiment, constructing the enhanced NeuralRDE model includes establishing a data flow structure consisting of a logarithmic signature feature set, a sequence of operating condition vectors, a set of gating coefficients, a sequence of hidden states, a set of dynamic residuals, and a topological consistency term.
[0023] In this embodiment, the generation of the logarithmic signature feature set and the working condition vector sequence includes: In the conditional roughness drive construction unit, the input roughness lifting input sequence and the set of normalized sequences are input. The speed sequence, load sequence and temperature sequence in the set of normalized sequences are time-stamp aligned and scale normalized to form a unified working condition input stream. A multi-level iterative integral path representation is constructed based on the coarse lifting input sequence. The unified operating condition input stream is embedded into the path representation to extract high-order interaction features. A coarse path stabilization term is introduced during the path integration process to suppress the amplification effect of sudden changes in operating conditions or sampling noise on logarithmic signature features, thereby generating a set of logarithmic signature features. The multi-level iterative integral path representation is a temporal feature expansion method based on coarse path theory. It roughly improves the input sequence by segmenting the time series according to time windows and performing layer-by-layer iterative integration within each time window. First-order integration captures the overall trend of signal change, second-order integration characterizes the synergistic effect between different variables, and third-order and higher integrations further reflect complex nonlinear interactions. The integration results at each level are concatenated and normalized in chronological order to form the multi-level iterative integral path representation. This representation can simultaneously retain information in both the time and frequency domains, enabling subsequent feature extraction to have higher expressive power. In the generated multi-level iterative integral path representation, each level corresponds to a different feature dimension. First-order features are used to characterize the temporal evolution of a single variable, second-order features reflect the bidirectional coupling relationship between variables, and third-order and above features are used to capture the complex coupling patterns between nonlinear and multivariable variables. Tensor expansion is performed on higher-order terms, and principal component analysis is combined for decomposition and dimensionality reduction to extract higher-order interaction features. These features are then orthogonalized and dimensionality reduced to eliminate redundant information and enhance stability. Finally, the extracted higher-order interaction features are combined into a logarithmic signature feature set to drive the hidden state evolution process in the enhanced NeuralRDE model. To avoid excessive amplification of sudden changes in operating conditions or sampling noise during high-order feature extraction, a coarse path stabilization term is introduced during feature combination. This term consists of a growth constraint factor and an amplitude modulation factor. The growth constraint factor, based on a time window smoothing function, limits the cumulative contribution of high-order terms in a short period of time. The amplitude modulation factor, based on regularized weights, suppresses feature weights in outliers and abrupt change intervals. By combining high-order interactive features with the coarse path stabilization term, constrained weighting and normalization are applied to features of each order, thereby generating a stable logarithmic signature feature set. This feature set retains the complex interactive relationships between variables and is robust to sudden changes in operating conditions and noise, providing reliable input for the hidden state evolution of the enhanced NeuralRDE model. The input stream under the unified operating condition is mapped to different channels. The speed sequence, load sequence and temperature sequence are transformed into corresponding operating condition factor vectors through sliding window feature extraction and Z-score normalization. They are then combined under the same time index to generate a sequence of operating condition vectors. The output logarithmic signature feature set and operating condition vector sequence are used as inputs to the subsequent frequency band gated vector field unit and physical consistency constraint unit.
[0024] In this embodiment, the generation of the hidden state sequence includes: In the frequency band gated vector field unit, the envelope spectrum energy set, the multi-order frequency band feature set and the operating condition vector sequence are input. Frequency band layer mapping is performed on the envelope spectrum energy set and the multi-order frequency band feature set. The frequency band features are weighted and adjusted in combination with the operating condition vector sequence to form a frequency band adjustment feature set. The frequency band hierarchical mapping is specifically performed as follows: the input envelope spectrum energy set is divided into frequency intervals, and the signal is segmented into low-frequency band, mid-frequency band and high-frequency band. Then, the multi-order frequency band feature set is aligned with the divided frequency intervals, and features of different orders are assigned to the corresponding frequency bands. Then, within each frequency band interval, the envelope energy and order features are combined into frequency band hierarchical units to fully characterize the energy distribution and order characteristics under that frequency band. Finally, each frequency band hierarchical unit is combined in frequency order to form a frequency band hierarchical mapping result with a hierarchical structure, providing structured input for subsequent feature adjustment. After obtaining the frequency band layer mapping results, the operating condition vector sequence is aligned with each frequency band layer unit to ensure that the fusion of operating conditions and frequency band features is completed under the same time index. Then, based on the speed, load and temperature factors contained in the operating condition vector sequence, the frequency band features are weighted and adjusted to dynamically adjust the contribution ratio of each frequency band feature. The weighted results are further normalized to ensure the consistency and comparability of different frequency band features on the numerical scale. Finally, the adjusted features of each frequency band are combined to generate a frequency band adjustment feature set, which provides input for the construction of the gating function and the generation of the gating coefficient set. A gating function is constructed based on the set of frequency band adjustment features, and a set of gating coefficients is generated to allocate dynamic weights among different frequency band features, so as to ensure the adaptability of feature weights under the conditions of speed, load and temperature changes. The construction of the gate function includes indexing the frequency band adjustment feature set by time. With frequency band index Organized as a two-dimensional sequence, the fused feature vector is calculated at each time index. , ,in For frequency band energy, The energy slope, For ravine, For the order energy percentage, To determine the working condition sensitivity ratio, a gating function is defined based on the fused feature vector, and three constraints—monotonicity, sparsity competition, and total quantity—are introduced to calculate the gating coefficient. The gate function is defined as follows: ; in, Indicates time index The Bandgap control coefficient, Indicates the number of frequency bands. This represents the temperature coefficient, used to control the intensity of sparsity competition. Represents the fused feature vector. Indicates the first The small feedforward mapping parameters of the frequency band are non-negative to satisfy the monotonicity constraint (the score is not reduced as the fusion feature increases). Indicates the stabilization factor. Indicates time index The weighted mean of the fused features, with weights derived from the sequence of operating condition vectors to reflect operating condition adaptation. Representing the Euclidean norm, the denominator implements the total constraint. ; Meanwhile, to obtain a time-stable set of gating coefficients, an exponential moving average and hysteresis update are applied to the gating coefficients on the time axis to obtain smoothed gating coefficients: ; in, Indicates time index Below, frequency band The smoothed gating coefficients are obtained by weighting historical smoothed values and the current original gating values, and are used as the final smoothing gating weights for model-driven processing to reduce noise and jitter. This represents the smoothing coefficient (exponential smoothing factor), which controls the weighting ratio between historical and current information. The closer the value is to 1, the greater the historical influence and the stronger the smoothing effect; the closer it is to 0, the greater the weight of the current value and the faster the response. Indicates the index at the previous time. Below, frequency band The smoothed gating coefficients provide historical information to maintain the temporal continuity of the gating coefficients. This represents the weighting factor of the current value, ensuring and The sum is 1, maintaining the weighted balance. Indicates time index Below, frequency band The original gating coefficients are directly calculated from the gating function and reflect the real-time frequency band adjustment results at the current moment. They may contain large jitter or noise before smoothing is added. Finally, the smoothed gating coefficients arranged by time index and frequency band index form a gating coefficient set, which is used to fuse with the logarithmic signature feature set to drive the evolution of the hidden state sequence; The set of gating coefficients is fused with the set of logarithmic signature features, and the hidden state sequence is updated through a vector field evolution mechanism, forming a hidden state sequence by iterating layer by layer under the time step. Output the hidden state sequence as input to the subsequent physical consistency constraint unit.
[0025] In this embodiment, the generation of the constraint signal sequence includes: In the physical consistency constraint unit, displacement estimation is obtained based on the hidden state sequence through mapping relationship, and velocity and acceleration estimation are further calculated using the time difference method, and the displacement, velocity and acceleration estimates are output. Based on the initial set of dynamic parameters, the mass matrix, damping matrix, and stiffness matrix are constructed. At the same time, the load sequence is converted into the corresponding load vector. The dynamic residual set is calculated by combining displacement estimation, velocity estimation, acceleration estimation, and load vector. The specific formula for calculating the dynamic residual set is as follows: ; in: Indicates a time index; This indicates that the displacement estimate originates from the mapping of the hidden state sequence; The velocity estimate is obtained from the time difference of the displacement estimate. This indicates that the acceleration estimate is obtained from the second-order time difference of the displacement estimate; , , These represent the mass matrix, damping matrix, and stiffness matrix, respectively, constructed from the initial set of dynamic parameters; This represents the load vector, obtained from the load sequence through mapping. The kernel representing the classical dynamic residual; Let represent the modal basis matrix, and let the column vectors be the modal vectors determined by the initial set of dynamic parameters. This represents the graph Laplacian matrix generated from the topological relationship matrix of the measurement points, used to characterize the coupling between measurement points; This represents the topology adjustment factor, which controls the strength of the weighting of residuals by topology consistency. Indicates and Identity matrices of the same dimension This represents the weighted dynamic residual vector, which serves as the time index for the dynamic residual set. The elements are used for subsequent time alignment, normalization, and merging with topology consistency items; Based on the topological relationship matrix of the measurement points, topological constraints are established, and the topological consistency term is calculated using the graph Laplace matrix to reflect the structural relationship and spatial coupling characteristics between the measurement points. The dynamic residual set and the topological consistency term are aligned according to the time index, and a normalization method is used to eliminate the influence of different dimensions on subsequent calculations. The normalized dynamic residual set and the topological consistency term are merged according to preset weights to generate a constraint signal sequence, which is then output.
[0026] In this embodiment, the generation of the trend indicator set and the risk indicator set includes: Based on the hidden state sequence, logarithmic signature feature set and constraint signal sequence, the future time window length and time step are set, the RMS slope and key order envelope energy growth rate are calculated at each time index, and a set of trend indicators is generated and arranged by time index. The generation of the trend indicator set is specifically as follows: For each time index, the corresponding window data is extracted; within this window, the root mean square sequence of the multi-channel vibration signal is calculated, and the slope of the time-root mean square curve is fitted using the linear least squares method, which is then used as the RMS slope under this window; simultaneously, envelope demodulation is performed within the frequency band corresponding to the key order, the envelope energy difference between the start and end points of the window is calculated and normalized according to the time length to obtain the envelope energy growth rate of the key order; the RMS slope and the envelope energy growth rate of the key order are combined to form an indicator vector, which is then arranged according to the time index order to finally generate the trend indicator set. Based on hidden state sequences, logarithmic signature feature sets, and constraint signal sequences, a risk intensity function is constructed by combining future time windows and the early warning lead time is calculated to generate a risk indicator set. The risk intensity function is defined as follows: ; in, Indicates the current time index; This represents the risk intensity function value at time index t and future time offset u. It is used to measure the intensity of the system entering a risk state within a future time period and is a core component of the risk indicator set. It represents an exponential function, ensuring that the risk intensity function is always positive, and can produce a nonlinear amplification effect on the linear combination of inputs; This represents a parameter vector used to adjust the weights of the hidden state's influence on the risk intensity. A vector representing the hidden state sequence at time index t. It reflects the contribution of the hidden state sequence to the risk intensity; This represents a parameter vector used to adjust the weights of the logarithmic signature feature set on the risk intensity. This represents the aggregate vector of the logarithmic signature feature set at time index t. It reflects the contribution of the logarithmic signature feature set to the risk intensity; This represents a parameter vector used to adjust the weights of the constraint signal sequence on the risk intensity. A vector representing the constrained signal sequence at time index t. It reflects the contribution of the constraint signal sequence to the risk intensity; The time sensitivity coefficient is a scalar. Represents the future time offset, defined in the interval Inside, Used to control the increasing trend of risk intensity over future time; Simultaneously calculate the cumulative risk intensity: ; in, The value represents the upper limit of the integral, and the value represents the length of time from the current point in time to the future, with a range of values. The lower limit of 0 indicates that the integral starts from a future offset of zero at the "current moment"; The risk intensity function at a future offset u under time index t is non-negative and has been obtained by weighting the hidden state sequence, the logarithmic signature feature set, and the constraint signal sequence. Represents a infinitesimal element with respect to future offsets. Indicates the cumulative risk intensity, representing the period from now to the future. The integral of the risk intensity between them, a total measure, is monotonically non-decreasing; And define the early warning lead time using a risk threshold parameter: ; in, This indicates the lead time for early warning, from now until the earliest time the risk threshold is first reached; Describe the infimum operator, and take the smallest one that satisfies the condition. ; This indicates that the candidate time is within a future time window, and the window length is [value missing]. ; Indicates the cumulative risk intensity; Represents the risk threshold parameter, a positive scalar, which gives the cumulative intensity threshold for triggering a warning; Summarize on time index , and Generate a set of risk indicators; in, Indicates the future offset under time index t. The risk intensity function value at a given time represents the instantaneous risk intensity at that moment, reflecting the system's risk level at that point in time. As part of a set of risk indicators, it is used to determine whether there are any abnormal trends at present. This indicates that, under time index t, the risk intensity function is related to the future time window length. The integral value within a given time window represents the cumulative risk intensity over that window. It is used to measure the overall risk trend and, as part of a set of risk indicators, is used to comprehensively assess the degree of risk that may occur in the future. This represents the future time offset corresponding to the first time the cumulative value of the risk intensity function exceeds the preset threshold under time index t. It reflects how long in the future the system will enter a risk state from the current moment and is used to give the length of time for early warning. It is a key quantity in the risk indicator set. The trend indicator set and the risk indicator set are reorganized under the same future time window, and the trend indicator set and the risk indicator set are output.
[0027] In this embodiment, the generation of the trained parameter set and threshold set includes: Based on the set of trend indicators, the set of risk indicators, and the constraint signal sequence, the trend regression error, frequency band consistency error, dynamic residual error, topological consistency term error, and risk intensity partial likelihood are calculated within the training batch. Time index alignment and normalization are performed on each error component to form an error component vector. Specifically, based on the set of trend indicators and the set of standardized sequences, the mean square error method is used to generate trend regression error; based on the set of constrained signal sequences and the set of envelope spectrum energy, the normalized Euclidean distance method is used to generate frequency band consistency error; based on the set of dynamic residuals and the observed dynamic response, the weighted norm method is used to generate dynamic residual error; based on the topological consistency term and the topological relationship matrix of the measurement points, the graph structure regularization method is used to generate topological consistency term error; and based on the set of risk indicators and the risk intensity function, the partial likelihood of risk intensity is generated using the partial likelihood calculation method. Within each training batch, a joint loss function is constructed based on the error component vector. An adaptive weighting factor is introduced to dynamically adjust the weight of each error component in the joint loss function. The weight adjustment is based on the gradient sensitivity and variance characteristics of the error components to generate the joint loss function. The joint loss function is specifically as follows: ; ; in, Let represent the joint loss function, and represent the overall optimization objective. This represents the set of five error component indices, including trend regression error, band consistency error, dynamic residual error, topological consistency term error, and risk intensity partial likelihood. Indicates the first The normalized scalar loss of each error component in the current training batch; obtained by aligning the corresponding sets / items by time index, normalizing the units, and aggregating them within the batch, and used for joint optimization; Indicates the first The adaptive weights of each error component are obtained through soft maximum normalization, satisfying... , ; Indicates the first The exponential moving average (gradient sensitivity) of the gradient norm of each component loss with respect to the parameters of the enhanced Neural RDE model is used to measure the strength of the influence of that component on the current parameter update; the larger the gradient, the more likely that the component is not yet fully optimized and its weight tends to increase. Indicates the relationship with the first The exponential moving average of the variance of the in-batch index corresponding to each component (a measure of noise / uncertainty). The larger the variance, the more unstable or noisy the component is, and the weight tends to decrease. This represents a sensitivity index, used to suppress instability caused by extreme gradients. Gentle compression is applied to abnormally large gradients. This represents the temperature coefficient and controls the sharpness of the weighting distribution. Larger ones are even sparser. Smaller sizes result in a more balanced outcome; This represents a numerical stability constant, avoiding zero denominators and improving computational stability. The parameter gradient is calculated based on the joint loss function. A regularization term is introduced in combination with the consistency condition of the constrained signal sequence. The parameters of the enhanced Neural RDE model are iteratively updated. When the loss converges and the constraint consistency is satisfied, the set of parameters after training is output. Based on the joint distribution of the trend indicator set and the risk indicator set during the training process, the threshold set is determined by using the dynamic quantile statistical method combined with the stability range of the constraint signal sequence, and the parameter set and threshold set after training are output.
[0028] In this embodiment, the generation of the vibration trend early warning result and the early warning lead time includes: During the online inference phase, continuous data streams are acquired in real time. Data preprocessing and time alignment are performed on the continuous data streams to obtain a standardized sequence set, an envelope spectrum energy set, a multi-order frequency band feature set, and a coarse boosted input sequence. The logarithmic signature feature set and the gating coefficient set are aligned with the above sequences according to the time index. Load the trained parameter set and threshold set, drive the enhanced Neural RDE model for online inference based on the log signature feature set and gating coefficient set, update the hidden state sequence, calculate the RMS slope and key order envelope energy growth rate within the sliding window to generate a trend indicator set, and calculate the risk indicator set based on the risk intensity function and future time window. The set of trend indicators, risk indicators, and thresholds are compared and judged to obtain the vibration trend warning result and warning lead time, and the vibration trend warning result and warning lead time are output.
[0029] Example 1: To verify the feasibility of this invention in practice, it was applied to the vibration trend monitoring and early warning process of a large operating generator unit. This unit is characterized by significant load fluctuations, strong environmental noise interference, and long operating times. Traditional methods based on frequency domain analysis and empirical thresholds are insufficient in terms of prediction accuracy and early warning timeliness. By introducing the enhanced Neural RDE model of this invention, combined with multi-channel vibration signals, speed data, load data, and temperature data, the operating status of the unit under different operating conditions was monitored and trend analyzed over a long period. The aim was to verify the vibration trend prediction accuracy and early warning timeliness of this invention under complex operating conditions.
[0030] In this scenario, vibration signals from multiple measuring points of the generator set are first collected using sensors, while speed, load, and temperature parameters are recorded simultaneously. The collected data undergoes bandpass filtering, envelope demodulation, and order energy calculation, while normalization and scaling are performed to generate a standardized sequence set. Subsequently, lead-lag augmentation and timestamp interpolation are used to construct a coarse lifting input sequence, establishing a topological relation matrix of measuring points and an initial set of dynamic parameters, serving as the basic input conditions for model operation. During model operation, conditional coarsening-driven construction units extract logarithmic signature feature sets to ensure feature stability under varying operating conditions and noise interference. Frequency band-gated vector field units perform hierarchical adjustment of the envelope spectrum energy set and multi-order frequency band feature sets, dynamically generating a set of gating coefficients that, together with the logarithmic signature feature set, drive the evolution of the hidden state sequence. Physical consistency constraint units introduce dynamic residuals and topological consistency terms, effectively enhancing the physical rationality of the prediction results.
[0031] In the risk assessment process, the model calculates the RMS slope and key-order envelope energy growth rate of the future time window based on the hidden state sequence and constraint signal sequence, generating a set of trend indicators, and further constructs a risk intensity function to obtain a set of risk indicators. Experimental data shows that this invention can issue an early warning on average 6.5 hours before the potential failure trend of the unit appears, while the average lead time of traditional methods is only 2.3 hours. This invention not only extends the early warning time, but also maintains the stability of prediction under different load fluctuation conditions and reduces the false alarm rate.
[0032] To verify the performance improvement, a comparative experiment was conducted between this invention and traditional frequency domain analysis methods and LSTM-based time series prediction methods. Evaluation metrics included prediction accuracy, average warning lead time, false alarm rate, and missed alarm rate. The experimental results are shown in the table below.
[0033] Table 1. Performance Comparison of the Invention Method and Traditional Methods
[0034] As shown in the table, this invention improves trend prediction accuracy by approximately 15.3 percentage points compared to traditional frequency domain analysis methods and by approximately 8.5 percentage points compared to LSTM prediction methods. Regarding the average warning lead time, this invention extends it by 4.2 hours compared to traditional frequency domain analysis methods and by 2.7 hours compared to LSTM methods. Furthermore, this invention significantly reduces both false alarm and false negative rates, with the false alarm rate reduced to less than 5% and the false negative rate controlled at around 5%. This indicates that this invention can not only detect potential risks at an earlier stage but also reduce false alarms and false negatives in complex operating environments, thereby improving the reliability of early warnings.
[0035] The performance improvement is mainly due to three factors: First, the conditional coarse-driven construction unit can capture high-order interaction features, enhancing the model's ability to represent nonlinear trends. Second, the frequency band-gated vector field unit enables dynamic adjustment of key frequency band features, allowing the model to adaptively adjust its focus under complex operating conditions. Third, the physical consistency constraint unit introduces dynamic constraints and topological relationships, ensuring the physical rationality and stability of the prediction results. These innovations work together to significantly improve the accuracy of vibration trend prediction and the timeliness of early warning.
[0036] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.
Claims
1. A method for early warning of generator vibration trends based on a deep time series model, characterized in that, Includes the following steps: Collect generator set operating data, perform data preprocessing, and generate a coarse lifting input sequence; An enhanced Neural RDE model is constructed, including conditional coarsening driving construction units, frequency band gated vector field units, and physically consistent constraint units; The conditional coarse-driven construction unit is run, and a logarithmic signature feature set and a working condition vector sequence are generated based on the coarse-lifted input sequence. The operating frequency band gated vector field unit generates a set of gated coefficients based on the working condition vector sequence, drives the evolution of the hidden state sequence, and generates the hidden state sequence. Run the physical consistency constraint unit, calculate the dynamic residual set and topological consistency term based on the hidden state sequence, perform time alignment and normalization, and merge to generate a constraint signal sequence; Based on the hidden state sequence, the logarithmic signature feature set, and the constraint signal sequence, a set of trend indicators and a set of risk indicators are calculated and generated. Based on the set of trend indicators, the set of risk indicators, and the constraint signal sequence, the joint loss function is calculated, the parameters of the enhanced Neural RDE model are updated, and the set of parameters and thresholds after training are generated. Input real-time collected generator set operation data, logarithmic signature feature set and gating coefficient set, load trained parameter set and threshold set, and generate vibration trend early warning results and early warning lead time.
2. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The data acquisition, preprocessing, and parameter set generation process includes: Collect generator set operating data, including multi-channel vibration signal data, speed data, load data, and temperature data; Perform data preprocessing, including normalization and scaling adjustment, generate a set of normalized sequences, perform envelope demodulation, generate a set of envelope spectrum energy, perform bandpass filtering, and calculate the energy characteristics of each order frequency band to generate a set of multi-order frequency band features. Lead-lag augmentation and timestamp interpolation are performed on generator set operating data to generate a coarsely boosted input sequence; During the data acquisition process of generator set operation, multiple vibration sensors are distributed at different installation positions of the unit. The connectivity between the measuring points is described in the form of an adjacency matrix, thereby forming a measuring point topology matrix. The initial set of dynamic parameters is obtained by performing frequency domain analysis, energy calculation, and physical parameter deduction on the generator set operation data.
3. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the logarithmic signature feature set and the working condition vector sequence includes: In the conditional coarse drive construction unit, the speed sequence, load sequence and temperature sequence in the standardized sequence set are timestamp aligned and scale normalized to form a unified working condition input stream. A multi-level iterative integral path representation is constructed based on the coarse lifting input sequence. The unified working condition input stream is embedded into the path representation, high-order interaction features are extracted, and a coarse path stabilization term is introduced during the path integration process to generate a logarithmic signature feature set. The multi-level iterative integral path representation is a temporal feature expansion method based on rough path theory. On the basis of rough lifting the input sequence, the time series is segmented according to time windows, and iterative integration is performed layer by layer within each time window. The first-order integral captures the overall trend of the signal, the second-order integral describes the synergistic effect between different variables, and the third-order and above integrals further reflect the complex nonlinear interaction relationship. The integration results of each level are spliced and normalized in time order to form a multi-level iterative integral path representation. The coarse path stabilization term consists of a growth constraint factor and an amplitude modulation factor. By combining the higher-order interaction features with the coarse path stabilization term, the features of each order are subjected to constraint weighting and normalization. The input stream under the unified operating condition is mapped to different channels. The speed sequence, load sequence and temperature sequence are transformed into corresponding operating condition factor vectors through sliding window feature extraction and Z-score normalization. They are then combined under the same time index to generate a sequence of operating condition vectors.
4. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the hidden state sequence includes: In the frequency band gated vector field unit, the envelope spectrum energy set and the multi-order frequency band feature set are mapped in a frequency band layer. The frequency band features are weighted and adjusted by combining the working condition vector sequence to form a frequency band adjustment feature set. A gating function is constructed based on the set of frequency band adjustment features, and a set of gating coefficients is generated. The construction of the gate function includes indexing the frequency band adjustment feature set by time. With frequency band index The organization is a two-dimensional sequence. At each time index, the fused feature vector is calculated. Based on the fused feature vector, a gating function is defined and three constraints are introduced: monotonicity, sparsity competition, and total amount. The gating coefficient is then calculated. The gate function is defined as follows: ; in, Indicates time index The Bandgap control coefficient, Indicates the number of frequency bands. Indicates the temperature coefficient. Represents the fused feature vector. Indicates the first Small feedforward mapping parameters of the frequency band, Indicates the stabilization factor. Indicates time index The weighted mean of the fusion features, Represents the Euclidean norm; Meanwhile, in order to obtain a time-stable set of gating coefficients, an exponential moving average and hysteresis update are applied to the gating coefficients on the time axis to obtain smoothed gating coefficients. Finally, the smoothed gating coefficients, arranged by time index and frequency band index, form a set of gating coefficients. The set of gating coefficients is fused with the set of logarithmic signature features, and the hidden state sequence is updated through a vector field evolution mechanism, forming a hidden state sequence by iterating layer by layer at a time step.
5. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the constraint signal sequence includes: In the physical consistency constraint unit, displacement estimation is obtained based on the hidden state sequence through mapping relationship, and velocity and acceleration estimation are further calculated and output; Based on the initial set of dynamic parameters, the mass matrix, damping matrix, and stiffness matrix are constructed. At the same time, the load sequence is converted into the corresponding load vector. The dynamic residual set is calculated by combining displacement estimation, velocity estimation, acceleration estimation, and load vector. Based on the topological relationship matrix of measurement points, establish topological constraints and calculate topological consistency terms; The dynamic residual set and the topological consistency term are aligned according to the time index, and a normalization method is used to eliminate the influence of different dimensions on subsequent calculations. The normalized set of dynamic residuals and the topological consistency term are merged according to preset weights to generate a constraint signal sequence.
6. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the trend indicator set and risk indicator set includes: Based on the hidden state sequence, logarithmic signature feature set and constraint signal sequence, the future time window length and time step are set, the RMS slope and key order envelope energy growth rate are calculated at each time index, and a set of trend indicators is generated and arranged by time index. Based on hidden state sequences, logarithmic signature feature sets, and constraint signal sequences, a risk intensity function is constructed by combining future time windows and the early warning lead time is calculated to generate a risk indicator set. The trend indicator set and the risk indicator set are organized to correspond under the same future time window.
7. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the parameter set and threshold set after training is completed includes: Based on the set of trend indicators, the set of risk indicators, and the constraint signal sequence, the trend regression error, frequency band consistency error, dynamic residual error, topological consistency term error, and risk intensity partial likelihood are calculated within the training batch. Time index alignment and normalization are performed on each error component to form an error component vector. Within each training batch, a joint loss function is constructed based on the error component vector. An adaptive weighting factor is introduced to dynamically adjust the weight of each error component in the joint loss function. The weight adjustment is based on the gradient sensitivity and variance characteristics of the error components to generate the joint loss function. The parameter gradient is calculated based on the joint loss function. A regularization term is introduced in combination with the consistency condition of the constrained signal sequence. The parameters of the enhanced Neural RDE model are iteratively updated. When the loss converges and the constraint consistency is satisfied, the set of parameters after training is output. Based on the joint distribution of the trend indicator set and the risk indicator set during the training process, the threshold set is determined by using the dynamic quantile statistical method combined with the stability range of the constraint signal sequence.
8. The generator set vibration trend early warning method based on a deep time series model according to claim 1, characterized in that, The generation of the vibration trend early warning result and early warning lead time includes: During the online inference phase, continuous data streams are acquired in real time. Data preprocessing and time alignment are performed on the continuous data streams to obtain a standardized sequence set, an envelope spectrum energy set, a multi-order frequency band feature set, and a coarse boosted input sequence. The logarithmic signature feature set and the gating coefficient set are aligned with the above sequences according to the time index. Load the trained parameter set and threshold set, drive the enhanced Neural RDE model for online inference based on the log signature feature set and gating coefficient set, update the hidden state sequence, calculate the RMS slope and key order envelope energy growth rate within the sliding window to generate a trend indicator set, and calculate the risk indicator set based on the risk intensity function and future time window. By comparing and judging the set of trend indicators, risk indicators, and thresholds, we can obtain the vibration trend early warning result and the early warning lead time.