Isolator remaining service life prediction method based on deep learning

Abstract

The invention relates to the technical field of isolator service life prediction, and discloses an isolator remaining service life prediction method based on deep learning. The method comprises the following steps: acquiring a vibration signal and a temperature signal when the isolator operates, and constructing a multi-dimensional sensor sequence; dividing a plurality of sub-sequence units containing a fixed time window; extracting time domain and frequency domain features of each sub-sequence unit, and generating a fusion feature vector; calculating statistical distribution characteristics and variation trend characteristics of key indexes in the vector, and outputting a health state index; through a bidirectional recurrent neural network model containing an attention mechanism, taking the health state index and the historical degradation data as input, processing a time sequence dependency relationship through multi-layer residual error connection, and generating a residual service life prediction value; and updating the multi-dimensional sensor sequence according to the real-time sensor signal, and dynamically correcting the predicted value. According to the method, multi-dimensional data are integrated, degradation characteristics are deeply mined, and the accuracy and adaptability of prediction of the remaining service life of the isolator can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of isolator life prediction, and specifically to a method for predicting the remaining useful life of an isolator based on deep learning. Background Art

[0002] Isolators, as key components in mechanical and electronic equipment, are widely used in aerospace, rail transit, industrial manufacturing, and other fields. Their operational status is directly related to the safety and stability of the entire system. Over the long term, isolators will gradually degrade due to factors such as material aging, mechanical wear, and environmental corrosion. Failure to promptly assess their remaining service life can lead to sudden equipment failure, resulting in serious consequences such as production interruptions and safety accidents.

[0003] Currently, methods for predicting the remaining useful life of isolators primarily include physics-based models and data-driven approaches. Physics-based methods establish mathematical equations for isolator degradation and combine them with physical information such as material properties and structural parameters to predict lifetime. However, the isolator degradation process is influenced by the coupling of multiple complex factors, and its physical mechanisms are often difficult to accurately model, resulting in significant errors in the prediction results.

[0004] Data-driven approaches rely on operational data collected by sensors, using statistical analysis or machine learning algorithms to uncover the degradation patterns implicit in the data. Traditional data-driven approaches often employ shallow machine learning models, such as support vector machines and random forests. These models struggle to effectively extract deep features when processing high-dimensional, nonlinear time series data, resulting in limited accuracy in predicting the remaining useful life of the isolator. Furthermore, existing methods often rely solely on a single type of sensor signal, ignoring the correlation between different signals and failing to fully reflect the health status of the isolator. Furthermore, traditional models lack the ability to adaptively adjust to dynamically changing operating environments, making it difficult to ensure the stability of long-term predictions. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the remaining useful life of an isolator based on deep learning to solve the problems raised in the above background technology.

[0006] To achieve the above objectives, the present invention provides a method for predicting the remaining useful life of an isolator based on deep learning, the method comprising:

[0007] Acquire vibration and temperature signals during the operation of the isolator to construct a multidimensional sensor sequence; perform time-frequency analysis on the multidimensional sensor sequence to divide it into multiple subsequence units containing fixed time windows; extract time-domain and frequency-domain features of each subsequence unit through a deep convolutional network to generate a fused feature vector;

[0008] Calculating the statistical distribution characteristics and change trend characteristics of key indicators in the fused feature vector, and outputting the isolator health status index;

[0009] A bidirectional recurrent neural network model including an attention mechanism is constructed, which takes the isolator health status index and historical degradation data as input, processes the temporal dependency through multi-layer residual connections, and generates a remaining useful life prediction value;

[0010] updating the multi-dimensional sensor sequence according to the sensor signals collected in real time, and dynamically correcting the remaining useful life prediction value;

[0011] The method for calculating the isolator health status index includes: calculating the skewness and kurtosis of the data in each dimension of the fused feature vector to generate a statistical distribution index; calculating the dynamic time warping distance between the fused feature vectors of adjacent subsequence units to generate a trend change index; weighted aggregation of the statistical distribution index and the trend change index, and outputting the isolator health status index after normalization.

[0012] Preferably, the method for dividing the subsequence units includes: performing wavelet packet decomposition on the vibration signal to obtain energy distribution in different frequency bands; detecting the position of the extreme points of the energy distribution of each frequency band, and dividing the vibration subsequence with adjacent extreme points as boundaries; taking the mean and variance of the temperature signal in the corresponding time window as the temperature subsequence; and combining the vibration subsequence and its associated temperature subsequence to form the subsequence unit.

[0013] Preferably, the method for generating the fused feature vector includes: inputting the vibration subsequence into a one-dimensional convolution layer to extract time domain waveform features; performing Fourier transform on the frequency band energy distribution and then inputting the resultant into a two-dimensional convolution layer to extract frequency domain texture features; inputting the temperature subsequence into a fully connected layer to extract thermodynamic features; splicing the time domain waveform features, frequency domain texture features and thermodynamic features, and outputting the fused feature vector after dimensionality reduction through a feature compression layer.

[0014] Preferably, the method for constructing the bidirectional recurrent neural network model includes: setting a gated recurrent unit as a basic unit to receive a sequence of isolator health status indexes arranged in chronological order; embedding an attention weight module in the input layer to calculate the contribution weight of the features of each time step; capturing forward and reverse temporal dependencies through a bidirectional hidden layer; adding residual connection paths between hidden layers to fuse shallow and deep features; connecting a fully connected network in the output layer to map it to a remaining service life prediction value.

[0015] Preferably, the dynamic correction method includes: appending the newly collected sensor signal to the end of the multidimensional sensor sequence to generate a new subsequence unit; extracting the fusion feature vector of the new subsequence unit and calculating its isolator health status index; inputting the isolator health status index into a trained bidirectional recurrent neural network model to replace the input feature of the earliest time step; re-executing the timing calculation process to update the remaining service life prediction value.

[0016] Preferably, the model training steps of the bidirectional recurrent neural network model include: collecting historical isolator full life cycle sensor data and marking the true label of the remaining service life; dividing the sensor data into a training set and a validation set; initializing the bidirectional recurrent neural network model parameters; using the stochastic gradient descent method to minimize the mean square error between the predicted value and the true label; and stopping training when the validation set loss function converges.

[0017] Preferably, the method also includes abnormal operating condition processing: if the isolator health status index continuously decreases by more than a degradation threshold, a high-priority sampling instruction is triggered; the acquisition frequency of the multi-dimensional sensor sequence is increased; and the high-frequency sampling data is input into a bidirectional recurrent neural network model to perform real-time life prediction compensation calculations.

[0018] Preferably, the real-time life prediction compensation calculation includes: using a sliding time window to intercept high-frequency sampling data; extracting the fusion feature vector of the multidimensional sensor sequence in the window; calculating the decay rate of the health status index of the current window and the previous window; adjusting the forget gate parameters of the bidirectional recurrent neural network model according to the decay rate; and performing prediction value recalculation.

[0019] Preferably, the operation of the feature compression layer includes: calculating the variance contribution rate of the spliced ​​features; screening feature dimensions whose variance contribution rate is greater than a set threshold; mapping the screened features to a low-dimensional space through a linear projection matrix; and outputting a fused feature vector after dimensionality reduction.

[0020] The residual connection path is implemented by adding the output features of the previous hidden layer to the input features of the next hidden layer; adjusting the scale of the added features through a learnable weight matrix; inputting the adjusted features into a gated recurrent unit; and transmitting the final residual output to the next time series calculation node.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] By collecting vibration and temperature signals during isolator operation, a multidimensional sensor sequence is constructed, overcoming the limitations of traditional methods that rely on a single signal. Vibration signals can reflect changes in the isolator's mechanical structure, such as wear and looseness, while temperature signals can reveal its heat dissipation performance and the aging of internal components. The combination of these two provides a more comprehensive picture of the isolator's health, providing a richer basis for subsequent lifespan prediction.

[0023] By performing time-frequency analysis on multidimensional sensor sequences and dividing them into multiple subsequence units containing fixed time windows, the originally continuous time series data is converted into a collection of units with local characteristics. This processing method not only preserves the temporal characteristics of the data, but also facilitates targeted analysis of state characteristics at different time periods, avoiding feature dilution caused by excessively long data, and helping to more accurately extract degradation characteristics of isolators at different operating stages.

[0024] A deep convolutional network extracts the time-domain and frequency-domain features of each subsequence unit and generates a fused feature vector, leveraging its strengths in processing grid-like data and extracting local features. Time-domain features reflect the temporal trends of a signal, while frequency-domain features reveal the underlying changes in frequency components. The fusion of these two enables a multi-dimensional characterization of the isolator's state characteristics, enhancing their richness and discernibility.

[0025] The statistical distribution characteristics and trend characteristics of key indicators in the fused feature vector are calculated and output as the isolator health index, transforming the high-dimensional feature vector into a quantitative indicator that can intuitively reflect the health status. The statistical distribution characteristics reflect the overall distribution of key indicators, while the trend characteristics show their evolution over time. The combination of the two makes the isolator health status quantifiable and traceable, and can more clearly demonstrate its degradation process.

[0026] A bidirectional recurrent neural network model with an attention mechanism was constructed, taking the health status index and historical degradation data as input. Multi-layer residual connections were used to handle temporal dependencies, effectively resolving the vanishing or exploding gradient problems that traditional recurrent neural networks face when processing long time series data. The attention mechanism automatically focuses on the historical data segments that are most critical for lifespan prediction, enhancing the model's ability to capture important information. The bidirectional recurrent neural network can simultaneously utilize past and future time series information, improving its ability to model temporal dependencies. Multi-layer residual connections, through skip connections, alleviate the difficulty of training deep networks and ensure the model's ability to accurately fit complex degradation patterns.

[0027] By updating the multidimensional sensor sequence and dynamically revising the remaining useful life prediction based on real-time sensor signals, the model adapts to the dynamic changes in the isolator's operation. As new data is continuously input, the model continuously learns the latest degradation characteristics and promptly adjusts the prediction results, avoiding prediction bias caused by fixed model parameters and ensuring that the prediction results remain consistent with the actual state of the isolator during long-term operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a working principle diagram of the deep learning-based isolator remaining service life prediction method of the present invention;

[0029] Figure 2 Flowchart for fusion feature vector generation;

[0030] Figure 3 Flowchart built for the bidirectional recurrent neural network model;

[0031] Figure 4 This is a flow chart for dynamic correction;

[0032] Figure 5 Flowchart of compensation calculation for real-time lifetime prediction. DETAILED DESCRIPTION

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0034] See also Figure 1 The present invention provides a method for predicting the remaining useful life of an isolator based on deep learning, the method comprising:

[0035] During isolator operation, the vibration accelerometer and temperature sensor synchronously acquire signals, forming a multidimensional sensor sequence with timestamps. After preprocessing, the original signal is divided into fixed-length subsequence units using a sliding time window. Each unit contains a vibration signal segment and the temperature statistics of its corresponding time window. A deep convolutional network performs parallel feature extraction on the subsequences: a one-dimensional convolutional layer processes the vibration waveform, a two-dimensional convolutional layer analyzes the frequency domain energy distribution, and a fully connected layer processes the temperature characteristics. The extracted features are fused through a compression layer, and the statistical distribution characteristics and trend change characteristics are calculated to output a health status index ranging from 0 to 1. A bidirectional recurrent neural network model is constructed, with an embedded attention mechanism in the input layer, residual-connected GRU units in the hidden layer, and the output layer mapped to the remaining service life value. During operation, the model continuously receives new sensor data, dynamically updates the prediction results, and triggers the abnormal condition handling mechanism.

[0036] Example 1: See Figure 2 Vibration signals are collected using a triaxial accelerometer with a sampling frequency of 10kHz. After anti-aliasing filtering, the signal enters the preprocessing stage. Preprocessing includes DC component removal and amplitude normalization, with the normalization range limited to the ±5V sensor range. Wavelet packet decomposition uses the Daubechies4 wavelet basis function with three decomposition layers, generating an energy distribution in eight frequency bands. The signal envelope of each frequency band is extracted using the Hilbert transform. Local extreme points of the envelope signal are detected using a sliding window comparison method with a window width of 50 sampling points. When the amplitude of a sampling point is simultaneously greater than the amplitudes of the previous 25 points and the next 25 points within the window range, it is determined to be a local extreme point. Signal segments between adjacent extreme points are truncated into vibration subsequences with a minimum length constraint of 100 sampling points. Segments that are shorter than the previous valid subsequence are merged with the previous valid subsequence.

[0037] The temperature signal is collected using a PT100 platinum resistance temperature sensor. The sampling frequency is synchronized with the vibration signal and set to 1kHz. Within the time window corresponding to the vibration subsequence, the temperature signal is first median filtered to remove pulse interference. Then, a 60-second moving average and standard deviation are calculated. Temperature statistics are calculated using an overlapping window method with a sliding step of 1 second to ensure time alignment with the vibration subsequence. The temperature feature vector consists of four components: the mean temperature within the window, the standard deviation of the temperature, the rate of temperature change, and the temperature difference from the previous window.

[0038] The time-domain feature extraction network uses a three-layer one-dimensional convolutional architecture. The input layer receives the raw waveform data of the vibration subsequence. The first convolutional layer contains 16 convolution kernels of length 5 with a stride of 1, and symmetric padding is used to maintain the feature map size. The activation function uses LeakyReLU with a negative slope coefficient set to 0.01. The number of convolution kernels increases to 32 in the second layer and 64 in the third layer. Each layer is followed by batch normalization. A max pooling layer is placed between each convolution layer, with a pooling window size of 2 and a stride of 2. In the frequency-domain feature extraction path, the energy distribution of each frequency band is first subjected to a 256-point fast Fourier transform, then combined into a time-frequency matrix and input into the two-dimensional convolutional network. The first two-dimensional convolution layer uses 32 convolution kernels of 3×3 size, which increases to 64 in the second layer, with a stride of 2×2. The frequency-domain network adds a spatial pyramid pooling layer after each convolutional layer, outputting a fixed-dimensional feature vector.

[0039] The temperature feature processing path uses a fully connected network structure. The first layer contains 128 neurons with the Reluctant Unit (ReLU) activation function, and the second layer is compressed to 64 dimensions. The network input includes the temperature statistics of the current window and the temperature trend of the previous three historical windows. A 20% dropout layer is added after each fully connected layer to prevent overfitting. During the feature fusion stage, the time domain features, frequency domain features, and temperature features are each L2 normalized before concatenation. The fused high-dimensional features are then reduced in dimension using principal component analysis, retaining 95% of the cumulative variance contribution. The PCA calculation uses an incremental learning method to adapt to the needs of online updates.

[0040] The feature compression layer is implemented using a two-stage processing strategy. The first stage calculates the covariance matrix between feature dimensions to determine the variance contribution of each dimension. The second stage constructs an orthogonal projection matrix to linearly map the high-dimensional features into a 256-dimensional latent space. The projection matrix is ​​updated using a sliding window approach, recalculating the PCA parameters after processing every 1,000 subsequences. The fused feature vectors after dimensionality reduction are appended with timestamp information and stored in a circular buffer for subsequent processing. The buffer is managed using a least recently used strategy, with a maximum capacity of 10,000 feature vectors.

[0041] During vibration subsequence segmentation, when the interval between three consecutive extreme points exceeds 200ms, a virtual segmentation point is automatically inserted to avoid generating overly long subsequences. The segmentation algorithm maintains a priority queue and dynamically adjusts the sensitivity threshold for extreme point detection. In temperature signal processing, when a sample value jump exceeding 5°C is detected, an outlier removal procedure is initiated, replacing the outlier with the median of the 10 preceding and following samples. All convolutional layers of the feature extraction network use the He normal initialization method, with the bias initialized to zero. The learnable parameters of the batch normalization layer are initialized to unit scale and zero offset.

[0042] The time-frequency analysis phase incorporates a quality monitoring mechanism. If the energy percentage of a frequency band falls below 0.1% of the total energy for five consecutive subsequences, the feature extraction path for that band is automatically blocked. The frequency domain convolutional network utilizes a separable convolution structure, with a depthwise to pointwise ratio of 3:1. The temperature feature network employs a residual connection structure, adding the output of the first layer to the output of the second layer before activation. Normalization prior to feature fusion includes a learnable scaling factor, initially set to the inverse of the standard deviation of the outputs of each feature path.

[0043] During online processing, the system maintains a feature extraction pipeline consisting of three parallel threads: vibration signal processing, temperature signal processing, and feature fusion. Each thread utilizes a double buffering mechanism to ensure continuous real-time data processing. The vibration feature extraction path utilizes a dynamic computational graph that automatically adjusts the padding parameters of the convolutional layer based on the length of the input subsequence. The frequency domain analysis path utilizes a polyphase filter bank, combining wavelet packet decomposition and Fourier transform into a single computational process. The temperature feature network is implemented as a lightweight structure, utilizing 8-bit integer quantization for computational acceleration.

[0044] Feature storage uses a columnar compression format, with each feature vector accompanied by a timestamp, device ID, and signal quality flag. Signal quality is assessed based on three metrics: the vibration signal's signal-to-noise ratio, the temperature signal's stability, and the feature vector's reconstruction error. When any metric exceeds a preset threshold, the corresponding feature vector is marked as a low-quality sample. The feature buffer implements automatic cleanup, removing historical data older than seven days every 24 hours. Intermediate results generated during feature extraction are stored in memory-mapped files, supporting breakpoint-resume processing.

[0045] The entire processing flow utilizes an event-driven architecture, triggering the feature extraction pipeline when new sensor data arrives. Events generated by the vibration signal processing thread include: subsequence segmentation completed, time domain feature extraction completed, and frequency domain analysis completed. Events generated by the temperature signal processing thread include: temperature statistics calculation completed, temperature feature extraction completed, and so on. The feature fusion thread monitors these events and performs feature concatenation and dimensionality reduction operations when all preconditions are met. The system status monitoring module tracks latency and resource usage at each processing stage in real time, dynamically adjusting thread priorities and computing resource allocation.

[0046] Example 2: See Figure 3, calculate the health status index and construct a recurrent neural network, and achieve quantitative assessment of degradation status and life prediction through multi-dimensional feature analysis and time series modeling. After integrating the feature vector input analysis module, the system first selects the top 20 feature dimensions with the highest variance contribution as the core analysis objects. The skewness calculation uses the standard definition method to calculate the ratio of the third-order central moment of the data distribution of each dimension to the cube of the standard deviation. The kurtosis calculation analyzes the relationship between the fourth-order central moment and the square of the variance to quantitatively characterize the long-tail distribution. The outlier processing mechanism uses the Huber loss function principle, setting the transition point to 3 times the standard deviation. Data exceeding this point is rescaled. The calculation results form a 20-dimensional statistical distribution indicator matrix.

[0047] The trend change detection module activates the dynamic time warping algorithm, configuring a curved path window constraint of 15% of the current sequence length. The feature vector of the current subsequence is compared one by one with the five most recent subsequences in the historical buffer, which uses a circular queue structure. Distance calculations use the Euclidean distance metric, with the deformed distance after path constraints serving as the similarity criterion. The algorithm outputs five distance values, and the minimum is recorded as the trend change indicator. The historical buffer management strategy is set to a fixed capacity of 200 data sets, with new calculation results updated and stored on a first-in, first-out basis.

[0048] During the health status index synthesis phase, pre-set weighting coefficients are applied, with statistical distribution indicators accounting for 60% of the overall weight and trend change indicators accounting for 40%. Weighting is performed using element-by-element multiplication followed by linear addition, resulting in an intermediate variable with a value range of [-1, 1]. The normalization module uses a modified form of the hyperbolic tangent function to map the intermediate variable to the range [0, 1]. The system appends a timestamp and device identification information, encapsulates the data into a health status record, and writes it to the time series database.

[0049] The bidirectional recurrent neural network has a two-layer structure, with 128 gated recurrent units in each layer. The attention module deployed in the input layer involves three computational steps: the feature vector is passed through a fully connected layer to generate a 128-dimensional latent state representation; the dot product score between the latent state and the trainable query vector is calculated; and the softmax function with a temperature parameter of 0.5 is applied to obtain normalized weights. The weighted input sequence is processed in two directions: the original time series data is fed into the forward recurrent layer, and the reversed time series data is fed into the backward recurrent layer. The output state of each recurrent layer is a 128-dimensional vector. The two output directions at the same time step are concatenated in the channel dimension to form a 256-dimensional representation.

[0050] Residual connections operate between hidden layers of the network. The output of the first-layer recurrent network is convolved with a 1×1 convolution kernel to adjust the number of channels. The convolution kernel is initialized to the identity matrix. The adjusted features are element-wise added to the original features of the second-layer input, and the sum vector is directly input to the second-layer recurrent unit. The internal computation of the gated recurrent unit is divided into three branches: the update gate uses a sigmoid activation to determine the proportion of historical states to be retained; the reset gate controls the extent to which historical states are involved in the calculation of the current candidate state; and the candidate state is generated using the hyperbolic tangent function. The three gated outputs are combined to form the new hidden state.

[0051] The output layer structure consists of two fully connected modules. The first module linearly transforms the concatenated features into a 64-dimensional space, using a rectified linear unit as the activation function. The second module maps the 64-dimensional features into a scalar output, using a smoothed variant of the Reluctant Linear Unit (ReLU) as the activation function. The network's predicted output is the estimated remaining useful life, expressed in the same units as the training data. The model is trained using a historical dataset containing health status sequences and remaining useful life labels for various devices, from initial operation to failure.

[0052] The hidden state transfer mechanism is maintained throughout the system's operation cycle. After each time step, the current hidden state is retained for initialization in the next iteration. The sequence processing length is set to 200 time steps, and very long input sequences are processed using a sliding window split. Gaussian noise is added to the input features, with the noise standard deviation set to 5% of the feature standard deviation. Gradient calculations use a truncation method, with a norm threshold of 1.0 to prevent numerical instability.

[0053] The network parameter initialization strategy uses the orthogonal initialization method, and inter-unit connection weights are initialized using a Gaussian distribution. Bias terms are configured in three parts: the update gate bias is initialized to an all-one vector, the reset gate bias is set to -1, and the state transition bias is initialized to zero. The network runtime environment is configured for double-precision floating-point operations, and activation function derivatives are calculated using analytical expressions. Layer normalization is applied to each layer output before the inner loop calculation to reduce the impact of covariate shift.

[0054] The time series data processing pipeline incorporates a feature caching mechanism. The health status calculation module stores output results in a circular buffer with a capacity of 1,000 records. A recurrent neural network reads data from the buffer in chronological batches, with the batch size dynamically adjusted to 80% of the device's processing capacity. Long-term dependency modeling utilizes a segmented recurrence strategy, storing the hidden state in long-term memory after every 50 time steps. This memory uses key-value pairs, where the key is the device state hash and the value is the corresponding hidden state tensor.

[0055] Regularization constraints are applied to the parameters of the residual connections, and an L2 penalty term with a coefficient of 0.001 is added to the loss function. A straight-through estimator design is used for gradient propagation within the multi-layer structure, skipping the complex calculation of gated unit derivatives during backpropagation. State diagnostics are implemented within the network, monitoring the distribution of unit activation values ​​in real time and automatically inserting reset instructions when saturation occurs. The model serving layer maintains multiple computational graph instances, dynamically loading pre-trained parameters based on device type, supporting parallel prediction tasks across heterogeneous device groups.

[0056] The health index calculation module incorporates output validation. Statistical and trend indicators each have valid range thresholds. Exceeding these thresholds triggers a data re-collection command. The recurrent neural network verifies timestamp continuity when receiving input data, automatically performing linear interpolation to fill in data gaps. Model version management utilizes a blue-green deployment approach, with the old and new models running in parallel. Correlation testing of prediction results determines the final switchover timing. The entire prediction system monitors device resource usage throughout its operation, initiating an intermediate data rollover mechanism when memory usage reaches 80%.

[0057] Example 3: See Figure 4 , dynamic correction mechanism and model training process, through real-time data update and optimization algorithm to achieve continuous improvement of the prediction system. During the operation of the system, the newly collected sensor data triggers the multi-dimensional sequence update process, which uses a sliding window mechanism to maintain fixed-length time series data. The window size is set to 200 subsequence units. When new data arrives, the system implements a first-in-first-out strategy, removes the data of the earliest time step and appends the latest collected information. The feature extraction path of the newly added subsequence unit maintains structural consistency with the offline training stage. All convolution kernel weights and fully connected parameters are frozen to the trained values ​​to ensure consistent expression of the feature space. The health status index calculation module loads a predefined statistical weight vector, which determines the contribution of each feature dimension through principal component analysis during the training phase.

[0058] The core of dynamic correction lies in the incremental inference mechanism of the time series model. The bidirectional recurrent neural network model maintains hidden state memory, whose dimensions match the network structure. When a new health status index input is added, the model performs a local forward calculation, processing only the newly added time series node. This calculation process involves the dynamic adjustment of attention weights, and the importance score of the current time step is calculated using the following formula:

[0059]

[0060] in, Indicates the The attention weight of time steps, is a trainable parameter vector, and The transformation matrices corresponding to the hidden state and input features respectively, is the hidden state at the previous moment, is the current input feature, represents the total length of the sequence, It is the index variable of the time step, which is used to traverse all moments of the entire time series (from step 1 to step Step, where is the total length of the sequence), :It is the index variable in the summation process, used to traverse from 1 to At each time step, :It is The hidden state of the moment, :For the The input features of time steps, : Exponential function, used to map the calculation results to the positive range to facilitate subsequent normalization processing, : Hyperbolic tangent function, as the activation function, is used to perform nonlinear processing on the transformed hidden state and input features. :Summation symbol, used to sum from 1 to The exponential calculation results of each time step are accumulated to achieve normalization of the attention weight. The parameter symbols in this formula are unique in this embodiment and do not repeat the mathematical expressions of other embodiments.

[0061] During the model training phase, samples are constructed from a full lifecycle dataset. Each sample contains a complete sequence of health states from the time the device is activated to its retirement. Data preprocessing performs time alignment to unify sensor data with different sampling frequencies to a common time base. The training and validation sets are divided based on the hash value of the device serial number to ensure that data from the same device does not appear in both sets. Network parameters are initialized using an orthogonal matrix method, and the weight matrix of the recurrent connections is obtained through QR decomposition to obtain an orthogonal basis. A variant of Adam is used as the optimization algorithm, with the momentum parameter β1 set to 0.9 and β2 adjusted to 0.999. The learning rate is initialized to 0.001 and adjusted using a cosine annealing strategy.

[0062] The loss function is designed as a weighted sum of a smoothed L1 loss and a prediction deviation penalty. The former measures the difference between the predicted value and the true remaining lifetime, while the latter constrains the magnitude of the sudden change between consecutive predictions. An early stopping strategy monitors the trend of the validation loss and terminates training when it fails to decrease for 15 consecutive training epochs. The data augmentation module injects two types of perturbations during training: Gaussian process noise in the time dimension, with an intensity of 10% of the feature standard deviation; and a random mask in the feature dimension, with a dropout probability of 5%. The model is saved using a checkpoint mechanism, with a snapshot of the optimal parameters recorded every five training epochs.

[0063] During the online update process, the system maintains two independent memory areas: a real-time inference buffer and a historical reference database. The real-time inference buffer stores feature vectors and model states for the last 200 time steps, utilizing a shared memory design to support multi-process access. The historical reference database maintains the complete device operation history, compressed and archived using a columnar storage format. When new data triggers a forecast update, the system first verifies timestamp continuity and supplements missing data using linear interpolation of adjacent values. Model inference results are filtered using a moving average with a window width of five time steps. The smoothing coefficient is dynamically adjusted to accommodate forecast fluctuations.

[0064] The abnormality recovery mechanism incorporates three layers of protection. Primary protection checks the reasonable range of input features. Data outside the physical range is discarded and retransmission is requested. Intermediate protection analyzes the self-consistency of feature vectors, calculates the reconstruction error using a pre-trained autoencoder, and triggers feature recalculation for samples exceeding a threshold. Advanced protection monitors the temporal consistency of prediction results. If the predicted lifetime decay rate exceeds the maximum degradation rate for three consecutive times, a model state rollback is initiated, reloading the parameters of the previous stable version to resume service.

[0065] Model version management utilizes a differential update strategy. Each parameter adjustment transmits only the differences from the previous version, and the update package uses cyclic redundancy checking to ensure integrity. Deployment utilizes a blue-green release model, where the new model runs in shadow mode. Its predictions are correlated with the output of the actual service model, and traffic is only switched after quality is confirmed to meet standards. A fallback mechanism maintains two stable versions, allowing for rapid recovery to the previous version if anomalies occur in the new version.

[0066] The resource management subsystem dynamically allocates computing resources. CPU-intensive tasks such as feature extraction are deployed on dedicated compute nodes optimized for the AVX instruction set. Memory-intensive operations such as recurrent network inference run in large memory containers with a NUMA core binding strategy. GPU resources are shared through a round-robin time-slicing system, with each task receiving a fixed-duration computing quota. A 20% margin is reserved for network bandwidth to accommodate sudden data transfers. All computing tasks are prioritized, and a quality of service (QoS) degradation mechanism is activated when system load exceeds 70%, suspending non-critical background tasks.

[0067] The status monitoring component collects three types of operational metrics: time series feature extraction latency, model inference throughput, and prediction confidence. These metrics are smoothed using an exponentially weighted moving average algorithm and then fed into the resource scheduling decision maker. If any metric falls outside a preset range, the system automatically adjusts the parallelism or computational precision of the relevant modules. For example, if feature extraction latency increases, floating-point operations might be temporarily downgraded from double precision to single precision. All adjustments are recorded in the audit log for subsequent performance analysis.

[0068] The data persistence solution utilizes a tiered storage architecture. The latest 200 records are stored in an in-memory database to ensure real-time access. Interim historical data is written to solid-state drives with a compression ratio set to 30% of its original size. Long-term archived data is transferred to a distributed file system, using erasure coding for fault tolerance. The data migration process is completely transparent, with applications accessing data at different tiers through a unified interface, and the system automatically handles location resolution and format conversion. The backup strategy implements daily incremental backups and weekly full backups, with a three-month rolling window for retention.

[0069] Example 4: See Figure 5 The system implements a mechanism for handling abnormal operating conditions and providing real-time compensation. Through multi-level monitoring and dynamic adjustment, it ensures stable operation of the prediction system during periods of accelerated equipment degradation. For example, in monitoring the isolators of a centrifuge unit at a chemical plant, the system triggered an abnormality handling process after 8,760 hours of continuous operation. The health status index monitoring module recorded a decrease in values ​​for three consecutive sampling periods. The specific data changes are shown in Table 1.

[0070] Table 1: The specific data changes for three consecutive sampling periods are as follows.

[0071] Timestamp Health Status Index Single change Cumulative change Sampling frequency flag 2024-03-0514:00 0.82 -0.03 -0.03 Standard (1Hz) 2024-03-0515:00 0.78 -0.04 -0.07 Standard (1Hz) 2024-03-0516:00 0.71 -0.07 -0.14 Standard (1Hz) 2024-03-0516:05 0.69 -0.02 -0.16 Enhanced (4Hz) 2024-03-0516:10 0.67 -0.02 -0.18 Enhanced (4Hz)

[0072] When the cumulative change exceeds a preset threshold of 0.15, the system automatically activates high-priority sampling mode. The vibration sensor sampling rate is increased from 1Hz to 4Hz, and the temperature sensor sampling rate is increased from 0.2Hz to 1Hz. The data acquisition card switches to direct memory access mode, bypassing the system buffer and writing the measured values ​​directly to a designated memory area. High-frequency sampled data is temporarily stored in a circular buffer divided into 16 data blocks, each containing 5 minutes of raw waveform data. The real-time processing thread extracts the latest data block from the buffer and performs fast feature extraction calculations.

[0073] The decay rate analysis module uses a sliding window comparison method. The current window selects high-frequency data from the last 10 minutes, and the baseline window selects normal sampling data from the hour before the anomaly is triggered. After the feature vectors of the two windows are aligned through dynamic time warping, the relative change rate of the features in each dimension is calculated. Among the vibration features, the energy change in the 2-4kHz frequency band is the most significant, reaching 2.3 times the baseline value. In the temperature feature, the gradient change rate increases to 1.8 times that of normal operating conditions. These indicators are input into the decision tree model, and the output forget gate adjustment coefficient is 0.65, indicating that the model needs to strengthen the memory weight of recent data.

[0074] After the real-time compensation calculation is initiated, the system creates a dedicated prediction instance. This instance loads the same network parameters as the main model, but with three key configuration changes: the time step is compressed to 1 / 4 to accommodate high-frequency data, the forget gate parameters are multiplied by an adjustment coefficient, and a sliding average filter is added to the output layer. This instance runs on a separate computing unit to avoid interfering with the main prediction process. Each calculation consumes four consecutive high-frequency sampling points, outputs an intermediate prediction result, and marks it as the compensation value. The main prediction system continues to receive standard frequency data but uses the compensation value to correct the final output.

[0075] Sampling frequency management utilizes a gradual adjustment strategy. During the initial ramp-up phase, sampling is maintained at 4Hz for 30 minutes. If the decay rate remains above the threshold, the frequency is increased to 8Hz. Recovery conditions require a health index fluctuation range of less than 0.01 for six consecutive sampling cycles. During frequency switching, the system performs a sensor recalibration process, including zero-point correction and sensitivity verification. The data acquisition unit automatically records the switching timestamp and parameter snapshot during mode transitions for subsequent analysis.

[0076] Abnormal event reports generate structured logs consisting of five sections: trigger condition record, data quality assessment, treatment action details, resource consumption statistics, and forecast variance comparison. Log entries are sent to the central monitoring platform via a message queue, while a rolling cache is maintained locally. The platform's analytics service automatically extracts key fields and generates device health trend charts and treatment effectiveness heatmaps. Operations and maintenance personnel can view an overlay of the original waveform and characteristic changes to assist in determining the nature of the anomaly.

[0077] Resource guarantee mechanisms are dynamically adjusted during exception handling. The computing task scheduler prioritizes compensation calculations to real-time levels, and CPU core binding avoids context switching. Memory allocation uses a pre-reservation strategy to ensure that high-frequency sampling buffers are not reclaimed due to system pressure. A dedicated channel is enabled for network transmission, reducing the transmission interval of sampling data packets from the conventional 10 seconds to 1 second. When the overall system load exceeds 85%, non-essential background services such as data archiving and periodic diagnostics are automatically suspended.

[0078] The quality control module implements a triple verification mechanism. Raw data verification checks the physical plausibility of sampled values, flagging segments with vibration amplitudes exceeding 80% of the measured range. Feature verification compares homologous features extracted at different frequencies, triggering feature recalculation when differences exceed 10%. Predictive verification monitors the output discrepancy between the primary and compensation models, initiating a model consistency check when three consecutive deviations exceed 15%. A verification report is generated for all abnormal events, detailing environmental variables and system status.

[0079] The fault recovery process is designed as a step-by-step rollback. The first stage attempts to recalculate the last five minutes of data, using backed-up feature extraction parameters. If the problem persists, the second stage rolls back to the last stable model version, maintaining high-frequency sampling and continuing observation. Finally, after two consecutive recovery attempts fail, the system switches to safe mode, providing only raw sensor data without prediction. Each recovery operation generates an audit trail, including the timestamp, operation type, scope of impact, and execution results.

[0080] Version compatibility management maintains three interface adaptation layers. The data format adapter handles data structure conversion at different sampling frequencies, ensuring that new and old modules can correctly parse input. The feature space mapper aligns feature dimension differences between different model versions, maintaining compatibility through linear projection. The prediction result converter unifies output scales and units, eliminating display differences caused by version iterations. Adaptation layer configuration information is stored in a separate metadata repository, supporting dynamic loading and hot updates.

[0081] During an actual event, the system detected an abnormal decrease in the health index at 2:15 PM and confirmed the system had entered the accelerated degradation phase at 4:20 PM. High-frequency sampling continued until 2:00 AM the following day, during which time 47 real-time compensation calculations were performed. The main model's predicted remaining life gradually decreased from 650 hours to 320 hours, while the compensation model output was 290 hours. The weighted average result of 305 hours was ultimately used as the official prediction, remaining within a reasonable error range from the actual failure time of 312 hours. The entire event processing consumed 2.3 times the computing resources of normal operating conditions and did not impact data collection at other monitoring points. The root cause analysis automatically generated in the event report identified insufficient bearing lubrication, leading to a sudden change in vibration characteristics, as the primary causative factor, consistent with the findings of subsequent disassembly inspections. Bearing lubrication specifically refers to the lubrication status of the isolator's core rotating components, such as bearings. As a critical component in a mechanical system, the isolator's bearings use lubricants (such as oil and grease) to reduce friction losses and maintain stable operation. When lubrication is insufficient, the friction coefficient of the bearing contact surface increases, which will lead to an increase in vibration amplitude (especially in the high-frequency band of 2-4kHz, where the energy increases significantly). At the same time, the temperature signal gradient increases due to frictional heat. These changes will be captured by the vibration sensor and temperature sensor and reflected in the multi-dimensional sensor sequence.

[0082] Example 5: Specific implementation details of feature compression and residual connections, enhancing the expressive power of deep neural networks through dimensionality reduction optimization and information preservation strategies. The feature compression layer begins with the calculation of the covariance matrix of the concatenated features, using a randomized singular value decomposition algorithm to process the high-dimensional matrix. This method first projects the original features through a Gaussian random matrix to generate a low-dimensional approximate matrix, which is then subjected to precise singular value decomposition. During the decomposition process, a convergence threshold of 1e-6 (in scientific notation, corresponding to 0.000001, or one part per million) is set, and the maximum number of iterations is limited to 100. Variance contribution analysis selects the right singular vectors corresponding to the first k singular values, with the value of k dynamically determined based on a preset cumulative energy percentage. During the feature screening phase, a dimension importance score is established, comprehensively considering each dimension's variance contribution, its correlation with other dimensions, and its business interpretability.

[0083] The projection matrix is ​​constructed using truncated singular vectors as basis vectors, with orthogonality ensured through the Gram-Schmidt orthogonalization process. Matrix elements are stored as single-precision floating-point numbers with compressed sign and exponent bits. The dimensionality reduction mapping operation is a two-step process: first, the original features are centered by subtracting the mean vector, and then right-multiplied by the projection matrix to obtain a low-dimensional representation. Two metadata fields are appended to the compressed feature vectors: the original variance ratio for each dimension and the upper bound of the reconstruction error, which are referenced by subsequent modules. The feature buffer is stored as a memory-mapped file, supporting multi-process shared access and fast serialization.

[0084] The implementation of the residual connection path includes the initialization and optimization of a learnable weight matrix. The matrix dimensions are automatically calculated based on the feature dimensions of the previous and next layers. When the dimensions match, they are initialized to the identity matrix; otherwise, Xavier initialization is used. During forward propagation, the residual branch performs identity mapping or linear projection and is element-wise added to the output of the main path. The added features are scaled using a trainable scaling factor, which is initialized to 0.5 and constrained to the interval [0.1, 2.0]. During backward propagation, gradients flow separately to the main and residual paths, with the gradient ratio of the two paths controlled by adaptive weights.

[0085] The introduction of residual connections in the internal state update of the gated recurrent unit changes the process for generating candidate states. The previous hidden state is filtered by the reset gate and then concatenated with the current input features. The dimensionality reduction is then performed using a projection matrix. The reduced features are then added to the skipped features of the residual connection and then input into a hyperbolic tangent activation function. The update gate controls the mixing ratio of the new and old states by additionally considering the confidence score of the residual path. This score is calculated based on the reconstruction error of the residual features; smaller errors give higher weight to the residual contribution.

[0086] During network training, a special regularization strategy is implemented for residual connections. A path difference penalty is added to the loss function to encourage the main and residual paths to learn complementary representations. Gradient clipping is used to limit the maximum norm of gradients flowing through the residual connections to prevent excessive amplitudes from interfering with the learning of the main path. During parameter updates, the learning rate of the residual path is set to 1.2 times that of the main path to accelerate feature reuse. After each training batch, the activation sparsity of each residual connection is calculated, and dropout enhancement is applied to underused connection paths.

[0087] The online update mechanism for the feature compression layer uses incremental learning. Newly arriving sample features are first normalized, followed by an update of the running mean and variance estimates. Covariance matrix maintenance is achieved through rank-1 updates, triggering a singular value decomposition recalculation every 100 new samples. Projection matrices are versioned using generational tagging, retaining the three most recent valid versions for rollback. When feature distribution drift is detected, matrix retraining is automatically initiated, and updates are completed in a background thread without impacting real-time predictions.

[0088] The dynamic adjustment module for residual connections monitors the effectiveness of feature fusion. Evaluation metrics include path correlation coefficient, contribution balance factor, and information entropy ratio. When the output correlation between the main and residual paths exceeds 0.7, feature decorrelation is automatically inserted. When the contribution imbalance reaches a ratio of 3:1, the learning rate of the scaling factor is adjusted to correct it. The information entropy ratio reflects the diversity of the two paths, and maintaining it in the range of 1.5-2.0 is considered ideal. All monitoring data is visualized to help understand the information flow within the network.

[0089] Computational graph optimizations provide specific acceleration for residual structures. Adjacent linear projection and addition operations are fused into a single operator, reducing memory accesses. Operations on multiple residual branches are parallelized, enabling asynchronous execution using CUDA streams. Static memory allocation reserves fixed space for residual features, avoiding the overhead of dynamic allocation. Operator-level optimizations include loop unrolling, use of vectorized instructions, and shared memory caching, particularly for matrix-vector multiply-add operations.

[0090] During deployment, quantization is configured separately for the residual connection path. The main path uses 8-bit integer quantization, while the residual path retains 16-bit floating-point precision. This mixed-precision strategy balances computational efficiency and numerical stability. Quantization parameter calibration uses a moving average method to track the minimum and maximum value range of each connection. Dynamic range adjustment provides a safety margin to prevent feature distortion caused by overflow. During edge device deployment, the scaling coefficients of the residual connections are converted to fixed-point representation, and the bit width is configured based on the device capabilities.

[0091] Error recovery mechanisms are designed for specific checkpoints in feature compression and residual operations. The feature compression layer records the input-output norm ratio, and unusual fluctuations trigger data renormalization. Residual connections check for signs of exploding gradients and automatically switch to safe mode when an anomaly is detected, temporarily disabling the residual path. Memory error handling includes buffer overflow protection and wild pointer detection, and all array accesses are bounds-checked. Computational consistency verification compares results from different precision modes, and falls back to high-precision calculations when a threshold is exceeded.

[0092] Performance analysis tools are integrated into each key link. The feature compression layer records the information loss rate before and after dimensionality reduction and plots the energy distribution spectrum. The residual connection analyzer counts path activation frequency, gradient propagation strength, and parameter update amplitude. The real-time monitoring interface displays feature evolution along the depth of the network and uses heatmaps to illustrate the effect of residual compensation. Performance counters measure the latency and throughput of each module to identify computational bottlenecks. All analysis data is timestamped to support cross-module correlation analysis.

[0093] Version compatibility is ensured through an interface abstraction layer. Feature compression algorithms are encapsulated in a unified interface, and internal implementations can be interchanged with different dimensionality reduction methods. Residual connections standardize the input and output tensor formats, hiding specific implementation details. A module registry manages available implementation versions, dynamically loading them based on configuration at runtime. A data format converter transparently converts between different precision levels, ensuring seamless integration between modules. A compatibility test suite covers edge cases and exception scenarios to ensure that upgrades do not affect existing functionality.

[0094] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0095] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the remaining useful life of an isolator based on deep learning, characterized in that: include: Collect vibration and temperature signals during the operation of the isolator and construct a multi-dimensional sensor sequence; Performing time-frequency analysis on the multidimensional sensor sequence to divide it into multiple subsequence units containing fixed time windows; extracting time domain features and frequency domain features of each subsequence unit through a deep convolutional network to generate a fusion feature vector; Calculating the statistical distribution characteristics and change trend characteristics of key indicators in the fused feature vector, and outputting the isolator health status index; A bidirectional recurrent neural network model including an attention mechanism is constructed, which takes the isolator health status index and historical degradation data as input, processes the temporal dependency through multi-layer residual connections, and generates a remaining useful life prediction value; updating the multi-dimensional sensor sequence according to the sensor signals collected in real time, and dynamically correcting the remaining useful life prediction value; The method for calculating the isolator health status index includes: calculating the skewness and kurtosis of each dimension of the fused feature vector to generate a statistical distribution index; The dynamic time warping distance between the fused feature vectors of adjacent subsequence units is calculated to generate a trend change index; the statistical distribution index and the trend change index are weighted and aggregated, and the isolator health status index is output after normalization.

2. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 1, wherein: The subsequence unit division method includes: performing wavelet packet decomposition on the vibration signal to obtain energy distribution in different frequency bands; detecting the position of the extreme points of the energy distribution of each frequency band, and dividing the vibration subsequence with adjacent extreme points as boundaries; using the mean and variance of the temperature signal in the corresponding time window as the temperature subsequence; and combining the vibration subsequence and its associated temperature subsequence to form the subsequence unit.

3. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 2, wherein: The method for generating the fused feature vector includes: inputting the vibration subsequence into a one-dimensional convolution layer to extract time domain waveform features; performing Fourier transform on the frequency band energy distribution and then inputting the resulting input into a two-dimensional convolution layer to extract frequency domain texture features; inputting the temperature subsequence into a fully connected layer to extract thermodynamic features; splicing the time domain waveform features, frequency domain texture features and thermodynamic features, and outputting the fused feature vector after dimensionality reduction through a feature compression layer.

4. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 3, wherein: The method for constructing the bidirectional recurrent neural network model includes: setting a gated recurrent unit as a basic unit to receive a chronological sequence of isolator health status indexes; embedding an attention weight module in the input layer to calculate the contribution weight of each time step feature; capturing forward and reverse temporal dependencies through a bidirectional hidden layer; adding residual connection paths between hidden layers to fuse shallow and deep features; and connecting a fully connected network in the output layer to map the remaining service life prediction value.

5. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 4, wherein: The dynamic correction method includes: appending the newly collected sensor signal to the end of the multidimensional sensor sequence to generate a new subsequence unit; extracting the fusion feature vector of the new subsequence unit and calculating its isolator health status index; inputting the isolator health status index into a trained bidirectional recurrent neural network model to replace the input feature of the earliest time step; and re-executing the time series calculation process to update the remaining service life prediction value.

6. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 5, wherein: The model training steps of the bidirectional recurrent neural network model include: collecting historical sensor data of the entire life cycle of the isolator and marking the true label of the remaining service life; dividing the sensor data into a training set and a validation set; initializing the parameters of the bidirectional recurrent neural network model; using the stochastic gradient descent method to minimize the mean square error between the predicted value and the true label; and stopping training when the validation set loss function converges.

7. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 1, wherein: It also includes abnormal working condition processing: if the isolator health status index continuously decreases by more than the degradation threshold, a high-priority sampling instruction is triggered; the acquisition frequency of the multi-dimensional sensor sequence is increased; and the high-frequency sampling data is input into a bidirectional recurrent neural network model to perform real-time life prediction compensation calculations.

8. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 7, wherein: The real-time life prediction compensation calculation includes: using a sliding time window to intercept high-frequency sampling data; extracting the fusion feature vector of the multidimensional sensor sequence in the window; calculating the decay rate of the health status index of the current window and the previous window; adjusting the forget gate parameter of the bidirectional recurrent neural network model according to the decay rate; and performing prediction value recalculation.

9. The method for predicting the remaining useful life of an isolator based on deep learning according to claim 4, wherein: The operation of the feature compression layer includes: calculating the variance contribution rate of the spliced ​​features; screening the feature dimensions whose variance contribution rate is greater than a set threshold; mapping the screened features to a low-dimensional space through a linear projection matrix; and outputting a fusion feature vector after dimensionality reduction. The residual connection path is implemented by adding the output features of the previous hidden layer to the input features of the next hidden layer; adjusting the scale of the added features through a learnable weight matrix; inputting the adjusted features into a gated recurrent unit; and transmitting the final residual output to the next time series calculation node.

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