A neural network driven battery acoustic pressure monitoring and early warning method and system

Abstract

The application discloses a neural network driven battery acoustic pressure monitoring and early warning method and system, aiming to realize all-round analysis and fault early warning of the battery pressure signal by constructing a multi-stage deep learning framework. The method adopts neural network coding technology, extracts the causal characteristics of the pressure data through reverse time evolution and chaotic attractor projection; uses a time convolution network to identify the pressure cycle rhythm, establishes a rhythm benchmark model and generates an abnormal index; introduces a mutual information resonance mechanism, determines the information correlation degree between data through phase slip analysis; uses a variational echo reconstruction to generate a structured feature map, and captures the evolution process of the features through a diffusion model; predicts the phase transition critical point based on the renormalization group theory, converts the early warning parameters into an oscillator network and analyzes the synchronization characteristics; and finally realizes hierarchical early warning through singular value decomposition and activation strength calculation, can accurately identify early abnormal signs of the battery, and provides reliable technical support for battery safety management.

Description

Technical Field

[0001] This invention relates to the field of battery safety monitoring technology, and in particular to a neural network-driven method and system for monitoring and warning of battery acoustic pressure. Background Technology

[0002] With the rapid development of the new energy industry, the safety of battery systems has become a key factor restricting their large-scale application. Batteries generate complex pressure changes during charging and discharging, and these pressure signals contain important information reflecting the battery's internal state. However, traditional pressure monitoring methods mainly rely on fixed threshold judgments and simple statistical analysis, making it difficult to capture subtle patterns of pressure changes and early signs of faults, resulting in insufficient accuracy and timeliness in early warning systems to meet practical needs.

[0003] Current battery monitoring technologies have significant limitations when processing high-dimensional, nonlinear pressure data. Existing methods typically employ single time-domain or frequency-domain analysis, lacking a comprehensive consideration of the multi-scale characteristics of pressure signals and failing to effectively identify anomalous evolution processes across different time scales. Furthermore, traditional techniques struggle to establish complex mappings between pressure changes and fault development, lacking predictive capabilities for system state transitions, resulting in fault warnings often lagging behind the actual occurrence of risks. In addition, existing monitoring systems often process data from independent sensors, neglecting the interrelationships between multiple monitoring points and failing to form a comprehensive understanding of the overall battery condition. Therefore, there is an urgent need to develop an intelligent battery pressure monitoring method to achieve early warning and accurate identification of battery faults. Summary of the Invention

[0004] This invention discloses a neural network-driven method and system for monitoring and warning of battery acoustic pressure, aiming to achieve intelligent analysis and fault warning of battery pressure signals through deep learning technology. The method extracts deep features from pressure data through neural network encoding, identifies abnormal patterns in the pressure cycle rhythm, maximizes the mining of intrinsic correlations between data at different times using mutual information, generates feature representations rich in structural information using variational echo reconstruction technology, predicts the critical state of the system based on phase transition theory, and finally constructs a multi-level early warning decision network to achieve graded early warning and intelligent decision-making for battery faults.

[0005] The first aspect of this invention proposes a neural network-driven method for monitoring and early warning of battery acoustic pressure, comprising the following steps:

[0006] Acquire pressure monitoring data during battery operation, and generate a training dataset by performing neural network encoding on the pressure monitoring data;

[0007] A temporal convolutional neural network is constructed based on the training dataset. The temporal convolutional neural network is trained to identify pressure periodic rhythms. Rhythm parameters are extracted from the pressure periodic rhythms to generate a rhythm benchmark model. Deviation analysis is performed on the rhythm benchmark model to generate rhythm abnormality indicators.

[0008] A resonance learning network is established by performing mutual information maximization processing on the training dataset. The information correlation of data at different times is determined through the resonance learning network. The information correlation is used to identify the resonance frequency pattern. The rhythm abnormality index is amplified based on the resonance frequency pattern to generate a mutual information resonance vector.

[0009] Variational echo reconstruction is performed on the mutual information resonance vector to generate variational coding features. Probabilistic modeling is performed on the variational coding features to determine the probability distribution of echo propagation. The propagation path is reconstructed by sampling from the probability distribution. Based on the propagation path, structural change features are extracted to obtain a variational echo feature map.

[0010] The rhythm anomaly index and the mutual information resonance vector are input into a deep classification network to generate a nonlinear transformation pattern. The phase transition critical point is predicted from the nonlinear transformation pattern. The phase transition early warning parameters are determined based on the phase transition critical point. The early warning decision network is constructed using the phase transition early warning parameters.

[0011] The early warning decision network integrates the variational echo feature map to output a graded early warning signal, thereby completing the neural network-driven monitoring and early warning of battery acoustic pressure.

[0012] A second aspect of this invention provides a neural network-driven battery acoustic pressure monitoring and early warning system, comprising:

[0013] The data encoding module is used to acquire pressure monitoring data during battery operation and to perform neural network encoding on the pressure monitoring data to generate a training dataset.

[0014] The rhythm analysis module is used to construct a temporal convolutional neural network based on the training dataset, train the temporal convolutional neural network to identify pressure periodic rhythms, extract rhythm parameters from the pressure periodic rhythms to generate a rhythm benchmark model, and perform deviation analysis through the rhythm benchmark model to generate rhythm abnormality indicators.

[0015] The resonance learning module is used to perform mutual information maximization processing on the training dataset to establish a resonance learning network, determine the information correlation of data at different times through the resonance learning network, identify the resonance frequency pattern using the information correlation, and amplify the rhythm abnormality index based on the resonance frequency pattern to generate a mutual information resonance vector.

[0016] The variational reconstruction module is used to perform variational echo reconstruction on the mutual information resonance vector to generate variational coding features, perform probability modeling on the variational coding features to determine the probability distribution of echo propagation, sample and reconstruct the propagation path from the probability distribution, and extract structural change features based on the propagation path to obtain a variational echo feature map.

[0017] The phase transition prediction module is used to input the rhythm anomaly index and the mutual information resonance vector into a deep classification network to generate a nonlinear transformation pattern, predict the phase transition critical point from the nonlinear transformation pattern, determine the phase transition early warning parameters based on the phase transition critical point, and construct an early warning decision network using the phase transition early warning parameters.

[0018] The early warning output module is used to output a graded early warning signal by integrating the variational echo feature map through the early warning decision network, thereby completing the neural network-driven monitoring and early warning of battery acoustic pressure.

[0019] The beneficial effects of this invention are reflected in the following points: 1. By combining neural network encoding with chaotic dynamics analysis, it is possible to capture weak disturbances and nonlinear evolution characteristics in pressure signals. The deviation analysis mechanism of the rhythm benchmark model can identify subtle changes in normal periodic rhythms, and abnormal signs can be detected in the early stage of fault formation. This multi-level feature extraction method realizes comprehensive monitoring of small pressure fluctuations, slow trend changes, and sudden anomalies, advancing the time window for anomaly detection from the time of fault occurrence to the budding stage of fault. 2. The data association network established through the mutual information resonance mechanism can track the propagation path of anomalies between different monitoring points and predict the development trend of faults. Variational echo reconstruction technology enhances the expressive power of features through multiple information echoes, and the probabilistic modeling of the diffusion model provides a quantitative assessment of uncertainty. The introduction of phase transition theory enables the system to accurately predict the arrival of critical states, realizing the transformation from passive response to active prevention. 3. The synchronous analysis of the oscillator network reveals the collective dynamic behavior of the system, giving the early warning decision clear physical meaning and interpretability. The five-level graded early warning system can provide differentiated handling suggestions according to the type and severity of anomalies, realizing precise policy implementation. The graph structure design of the early warning decision network retains the topological characteristics of the fault modes, enabling the system to adaptively handle new fault modes and improving the stability of long-term operation.

[0020] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0021] The accompanying drawings illustrate specific examples of the technical solutions described in this invention and, together with the detailed embodiments, form part of the specification, serving to explain the technical solutions, principles, and effects of this invention.

[0022] Unless otherwise specified or otherwise, the same reference numerals in different figures represent the same or similar technical features, and different reference numerals may be used to represent the same or similar technical features.

[0023] Figure 1 This is a flowchart illustrating a neural network-driven method for monitoring and warning of battery acoustic pressure according to the present invention.

[0024] Figure 2 This is a structural block diagram of a neural network-driven battery acoustic pressure monitoring and early warning system according to the present invention. Detailed Implementation

[0025] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0026] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0027] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0028] The technical solutions of the embodiments of this application will be described below.

[0029] like Figure 1 As shown, this embodiment of the invention provides a neural network-driven method for monitoring and warning of battery acoustic pressure, including the following steps S110-S160:

[0030] Step S110: Obtain pressure monitoring data during battery operation, and generate a training dataset by performing neural network encoding on the pressure monitoring data.

[0031] Specifically, pressure monitoring data is acquired during battery operation. Ultrasonic sensors are deployed on the battery casing surface to monitor internal pressure changes in real time using non-invasive ultrasonic technology. The ultrasonic testing system employs high-frequency ultrasonic probes, with one sensor positioned on the upper surface, lower surface, and center of each of the four sides of the battery cell, forming a three-dimensional acoustic monitoring network. The ultrasonic probes are made of piezoelectric ceramic material, with an operating frequency set in the 5-10MHz range to ensure that the ultrasonic waves can penetrate the battery casing and achieve sufficient detection accuracy. The ultrasonic testing principle is based on the acoustoelastic effect. When the internal pressure of the battery changes, it alters the density and elastic modulus of the battery material, thereby affecting the propagation speed, attenuation characteristics, and frequency characteristics of ultrasonic waves within the material. The testing system emits ultrasonic pulses and receives reflected echoes, measuring the propagation time, amplitude changes, and frequency shift of the ultrasonic waves. These acoustic parameters are converted into pressure values ​​using acoustoelastic calibration curves. The sensors maintain good acoustic contact with the battery casing through a coupling agent. The ultrasonic signals are processed by a preamplifier and bandpass filter, and then digitally acquired using a high-speed ADC. The acquisition system continuously records acoustic parameters at high frequencies in the kilohertz range to ensure the capture of transient pressure fluctuations and minute pressure changes. Pressure monitoring data includes information in four dimensions: timestamp, sensor location identifier, acoustic transit time, and amplitude ratio. A temperature compensation algorithm is implemented during data acquisition to eliminate the influence of temperature changes on the propagation speed of ultrasound. The acquired raw acoustic data undergoes preprocessing, including outlier removal, missing value imputation, and noise filtering, and is then converted into pressure values ​​using an acoustoelastic calibration curve to ensure data quality. It should be noted that the acoustoelastic calibration curve is a mapping relationship between acoustic parameters and pressure established through experiments or theoretical models, converting measured acoustic parameters (including acoustic transit time, amplitude attenuation, and frequency shift) into actual pressure values. Specifically, the experimental calibration steps for the acoustoelastic calibration curve include: applying a known gradient pressure to the battery in a controlled environment (such as a constant temperature chamber); measuring the acoustic parameters (including acoustic transit time, amplitude attenuation, and frequency shift) corresponding to each pressure point; and fitting the data to obtain the curve equation (polynomial), i.e., the acoustoelastic calibration curve.

[0032] In some embodiments, the step of generating a training dataset by performing neural network encoding on the pressure monitoring data includes: performing reverse time evolution on the pressure monitoring data to obtain causal precursor signals; applying chaotic attractor projection to the causal precursor signals to extract singular trajectories; using the singular trajectories as neuron dead zone activation modes to generate sparse codes; and constructing a training dataset based on the sparse codes.

[0033] The pressure monitoring data is subjected to reverse time evolution to obtain causal precursor signals. A time inversion operator is constructed to perform reverse integration on the pressure monitoring data P(t): P_pre(τ)=∫[t→t-Δt]P(t)·exp(-λ(t-τ))dt, where P_pre(τ) is the causal precursor signal, P(t) is the pressure data at time t, λ is the decay coefficient, τ is the reverse time variable, t is the current time, and Δt is the time window length. The reverse time evolution is calculated using a high-order numerical integration method, and adaptive step size control ensures numerical stability and computational accuracy. An exponential decay factor is introduced during the integration process, making the influence of recent historical data on the current state more significant, while the influence of long-term data gradually decreases. Through reverse time evolution, the pressure anomaly at the current moment is traced back to the time point of its cause, obtaining a precursor signal sequence containing causal relationships. The precursor signal not only preserves the historical dependence of pressure changes but also reveals the complete dynamic process of gas generation, accumulation, and release inside the battery. The calculation process employs a sliding window mechanism, with appropriate overlap between windows to ensure the capture of continuous causal evolutionary features and avoid information loss.

[0034] Singular trajectories are extracted by applying chaotic attractor projection to the causal precursor signal. The causal precursor signal is mapped into the Lorenz attractor phase space using a classical dynamical system containing three coupled differential equations. This system describes the interaction of three state variables: the first equation states that the rate of change of x is proportional to the difference between y and x; the second equation states that the rate of change of y consists of the nonlinear coupling term between x and z and the decay term of y; the third equation states that the rate of change of z is determined by the product term of x and y and the decay term of z. Standard Lorenz parameter values ​​are used for the system parameters. The normalized precursor signal and its first and second derivatives are used as initial conditions for the phase space, and the complete phase space trajectory is generated through iterative calculation. The trajectory S(t) is calculated using the fourth-order Runge-Kutta method to ensure the numerical accuracy of the dynamical system evolution. In the generated phase space trajectory, the deviation D = ||r(t) - r_center|| / ||r_center|| of each trajectory point is calculated, where r(t) is the current trajectory point position vector, and r_center is the attractor center position. When the deviation exceeds a dynamic threshold, the trajectory segment is marked as an anomalous trajectory. Anomalous trajectory identification employs a local density adaptive method, increasing the threshold in dense trajectory regions and decreasing it in sparse regions to ensure sensitivity in anomaly detection. The extracted anomalous trajectory sequences fully preserve the nonlinear dynamic characteristics of pressure anomaly evolution, reflecting early signs of potential faults such as imbalances in internal battery chemical reactions and abnormal gas generation.

[0035] Singular trajectories are used as the dead zone activation patterns of neurons to generate sparse codes. An activation function with a dynamic dead zone, f(x) = max(0, x - θ), is designed, where the dead zone threshold θ is dynamically determined by the statistical properties of the singular trajectories: θ = mean(S(t)) + 2 × std(S(t)), where S(t) is the sequence of singular trajectories. This activation function only responds to abnormal signals exceeding the normal fluctuation range, achieving automatic screening of pressure anomaly features. After processing the singular trajectories through the activation function, the resulting sparse activation vector is fed into a multilayer sparse autoencoder. The encoder adopts a progressively decreasing network structure, with the number of neurons in each layer decreasing according to a specific ratio, achieving gradual compression and refinement of features. L1 norm regularization is used during the encoding process to strictly control sparsity, ensuring that only a few key features are activated in the final encoded vector. Each activated non-zero element corresponds to a specific pressure anomaly pattern, such as instantaneous pressure spikes, slow pressure increases, or periodic pressure oscillations. Sparse coding not only significantly reduces feature dimensionality but also enhances the interpretability of anomalous features, with each coding dimension having a clear physical meaning.

[0036] A training dataset is constructed based on sparse coding. The generated sparse coded vectors are precisely paired with their corresponding battery state labels to form complete training samples. The battery state label system covers subcategories such as normal operation, mild overcharge, severe overcharge, mild over-discharge, deep over-discharge, initial stage of internal short circuit, development stage of internal short circuit, and precursor to thermal runaway. A multi-parameter joint determination method is used to determine state labels, comprehensively considering multi-dimensional monitoring information such as voltage, current, temperature, and internal resistance. An accurate labeling system is established through expert rules and historical fault cases. High-density sampling is performed for each complete charge-discharge cycle, focusing on data during state transitions to ensure the capture of key transitional features. An adaptive sampling strategy is used, reducing sampling density during periods of stable pressure change and increasing sampling density during periods of abnormality. Data augmentation techniques such as time-axis stretching, compression, and translation are used to simulate pressure change patterns under different operating conditions, expanding the original sample size several times. The augmented dataset is divided into training, validation, and test sets according to strict proportions to ensure the scientific rigor of model training and evaluation.

[0037] Step S120: Construct a temporal convolutional neural network based on the training dataset, train the temporal convolutional neural network to identify pressure periodic rhythms, extract rhythm parameters from the pressure periodic rhythms to generate a rhythm benchmark model, and perform deviation analysis through the rhythm benchmark model to generate rhythm abnormality indicators.

[0038] Specifically, a temporal convolutional neural network is constructed based on the training dataset. Using the training dataset as input, a specially designed one-dimensional temporal convolutional architecture processes pressure sequence data. The network input layer receives a 256-dimensional sparse encoded vector sequence with a sequence length of 128 consecutive time steps, covering the complete pressure change cycle. The first temporal convolutional layer is configured with 64 filters and a kernel size of 7. A causal convolution mechanism ensures temporal causality, avoiding the use of future information. Dilated convolutions are used to progressively expand the receptive field, with the dilation rate increasing exponentially in the order of 1, 2, 4, 8, and 16, enabling the network to capture pressure change patterns at different time scales. Each convolutional layer is followed by a batch normalization layer to stabilize the training process. The ReLU activation function is used to introduce nonlinearity, and residual connections are used to mitigate gradient problems in deep networks. The main body of the network contains six temporal convolutional blocks. Each block uses gated linear units to regulate information flow, selectively transmitting important temporal features. The gating mechanism uses a sigmoid function to control the opening and closing of information channels, achieving adaptive selection of different frequency components. Finally, the temporal features are aggregated using global average pooling and fed into a two-layer fully connected network to output a pressure period feature vector. The total number of network parameters is controlled at around two million, achieving a balance between model capacity and computational efficiency.

[0039] A temporal convolutional neural network was trained to identify pressure periodic rhythms. The network was trained end-to-end using a preprocessed training dataset, employing a composite loss function L = L_ce + α·L_period + β·L_reg, where L_ce is the multi-class cross-entropy loss, L_period is the periodic consistency constraint loss, L_reg is the weight regularization term, and α and β are balance coefficients set to 0.3 and 0.01, respectively. The periodic consistency loss constrains the network to learn stable periodic features by calculating the phase difference between the predicted and true rhythms. Training used the Adam optimizer with an initial learning rate of 0.001 and momentum parameters β1 = 0.9 and β2 = 0.999. A cosine annealing strategy was used to adjust the learning rate, with one annealing cycle completed every 50 epochs. The batch size was set to 256 samples, and the total number of training epochs was 200. During training, model performance was evaluated on the validation set every 5 epochs, monitoring changes in the loss curve and accuracy. An early stopping mechanism was triggered when the validation set loss stopped decreasing for 10 consecutive epochs to prevent overfitting. Through sufficient training, the network learns to automatically identify and extract various pressure cycle patterns from sparse coding sequences, including the main cycle synchronized with charging and discharging, the secondary cycle caused by the breathing effect of electrode materials, and the high-frequency micro-cycle caused by electrolyte convection, among other multi-scale rhythmic features.

[0040] Rhythm parameters were extracted from the pressure periodic rhythm to generate a rhythm baseline model. Short-time Fourier transform was used to perform time-frequency analysis on the pressure periodic rhythm, with a window length of 32 time steps and an overlap rate of 50%, to obtain the time-varying spectrum of the pressure signal. Frequency components with concentrated energy were identified from the spectrum to determine the dominant rhythm frequency f_i and its harmonic components. The main rhythm types identified included: basic charge-discharge rhythm f_base (cycle 2-4 hours), electrode breathing rhythm f_breath (cycle 10-30 minutes), electrolyte convection rhythm f_conv (cycle 1-5 minutes), and interface reaction rhythm f_interface (cycle 10-60 seconds). A complete set of feature parameters was extracted for each rhythm: frequency f, amplitude A, initial phase φ, duty cycle D, modulation depth m, and frequency stability σ_f. The rhythm parameter extraction employed a combination of adaptive bandpass filtering and Hilbert transform to ensure the accuracy of parameter estimation. All rhythm parameters were organized into a structured parameter matrix P∈R^(n×6), where n is the number of identified rhythms. Through statistical analysis of tens of thousands of samples under normal operating conditions, a probability distribution model for each rhythm parameter was established using the kernel density estimation method. The distribution model adopts a Gaussian mixture form, and the mixture components are automatically determined using the Bayesian information criterion. By integrating the parameter distribution model, normal range thresholds, and anomaly detection rules, a complete rhythm benchmark model is constructed.

[0041] In some embodiments, the step of generating rhythm abnormality indicators through deviation analysis using the rhythm benchmark model includes: activating the self-diagnosis mode of the rhythm benchmark model and obtaining an internal parameter distribution map; identifying weight imbalance regions in the parameter distribution map and establishing an imbalance pattern classification, wherein the imbalance pattern classification includes gradient explosion, gradient vanishing, and oscillating divergence; and performing severity assessment processing on the imbalance pattern classification to generate rhythm abnormality indicators.

[0042] Activate the self-diagnostic mode of the rhythm baseline model to obtain an internal parameter distribution map. Switch the rhythm baseline model from the regular inference mode to the self-diagnostic mode. In this mode, the model not only outputs rhythm analysis results but also monitors and records detailed information about the internal calculation process in real time. By registering forward hook functions at each layer of the network, intermediate results such as the input tensor, weight matrix, and activation output of each layer are captured. Perform comprehensive statistical analysis on the captured tensor data to calculate statistics such as mean μ, standard deviation σ, maximum value, minimum value, 25th percentile, 75th percentile, kurtosis coefficient, and skewness coefficient. Organize the statistical indicators of each layer into a multidimensional array and use heatmap visualization technology to generate a panoramic view of parameter distribution. The distribution map uses a logarithmic color scale mapping to enhance the visual sensitivity to abnormal parameter changes. The horizontal axis arranges each layer according to the network depth, and the vertical axis displays different statistical indicators, with color intensity indicating numerical magnitude. At the same time, an activation value histogram is plotted to statistically analyze the activation rate distribution of neurons in each layer and identify the proportion of dead neurons (activation value is always 0) and saturated neurons (activation value is always at its maximum). The high-dimensional weight space is projected onto a two-dimensional plane using the t-SNE dimensionality reduction algorithm, allowing observation of the evolution trajectory and clustering patterns of parameters during the training process.

[0043] The algorithm identifies weight imbalance regions in the parameter distribution map and establishes an imbalance pattern classification. Computer vision algorithms are applied to automatically detect abnormal regions on the generated parameter distribution map. A 5×5 sliding window is used to traverse the entire distribution map, and the statistical anomaly score within each window is calculated. An imbalance metric B = σ² / μ² is defined, where σ is the standard deviation of the parameters within the window, and μ is the mean of the parameters. Based on the imbalance metric, the detected abnormal regions are classified into three patterns: Gradient explosion imbalance (B > 10), where parameter values ​​grow exponentially, the distribution exhibits extreme long-tail characteristics, and the histogram shows a large number of extremely large values; Gradient vanishing imbalance (B < 0.01), where parameter values ​​rapidly decay towards zero, the distribution is highly concentrated near the zero point, and information transmission between network layers is severely hindered; and Oscillating divergence imbalance (multiple separate peaks in the parameter distribution, with the distance between peaks exceeding twice the standard deviation, and parameter values ​​repeatedly jumping between different orders of magnitude). Feature vectors are extracted for each imbalance pattern, including attributes such as the area of ​​the imbalance region, its center location, diffusion speed, and depth of influence. Establish an imbalance pattern library to store feature templates for typical imbalance cases. Automatically determine the imbalance type by matching the current detection result with the template library using cosine similarity.

[0044] Imbalance patterns are classified and severity assessments are performed to generate rhythm anomaly indicators. A quantitative severity assessment system is designed for each identified imbalance pattern. The severity calculation formula for gradient explosion is: S_exp=log(max(|W|) / threshold_exp), where |W| is the maximum absolute value of the weights, and threshold_exp=100 is the preset explosion threshold. When the maximum weight exceeds the threshold, the severity increases logarithmically. The severity calculation formula for gradient vanishing is: S_van=-log(mean(|W|) / threshold_van), where mean(|W|) is the mean absolute value of the weights, and threshold_van=0.001 is the vanishing threshold. The smaller the mean weight, the higher the severity. The severity calculation formula for oscillatory divergence is: S_osc=N_peaks×D_peaks / D_ref, where N_peaks is the number of detected peaks, D_peaks is the average distance between peaks, and D_ref is the reference distance. Considering the varying impacts of different imbalance patterns on rhythm recognition accuracy, weighting coefficients w1=0.5, w2=0.3, and w3=0.2 were set. The comprehensive severity score was calculated as: S_total=w1×S_exp+w2×S_van+w3×S_osc. The severity score was mapped to the [0,1] standard interval using the sigmoid function: RAI=1 / (1+exp(-k×(S_total-S_mid))), where k=2 is the steepness parameter and S_mid=5 is the midpoint parameter. The generated rhythm anomaly index RAI not only quantifies the health status of the model's internal parameters but also reflects the reliability of pressure rhythm recognition.

[0045] Step S130: Perform mutual information maximization processing on the training dataset to establish a resonance learning network. Use the resonance learning network to determine the information correlation of data at different times, use the information correlation to identify resonance frequency patterns, and amplify rhythm abnormality indicators based on the resonance frequency patterns to generate mutual information resonance vectors.

[0046] Specifically, a resonant learning network is established by maximizing mutual information in the training dataset. A variational mutual information estimation method is used to process the temporal sample pairs in the training dataset, constructing a dual-tower resonant learning network. The left tower receives data x(t) at time t, and the right tower receives data x(t+τ) at time t+τ, where τ is the time delay parameter. Each tower contains three encoding layers with 128, 64, and 32 neurons respectively, using the LeakyReLU activation function to maintain gradient flow. The feature vectors output by the two towers are processed through a bilinear layer to calculate the mutual information estimate: I(x,y)=E[log(f(x,y) / f(x)f(y))], where f is the ratio function of the joint distribution and the marginal distribution. The training objective is to maximize the mutual information under different time delays, and the loss function adopts a noise-contrast estimation form. By comparing the score differences between positive sample pairs (true temporal pairs) and negative sample pairs (randomly shuffled temporal pairs), the network learns to capture the inherent correlation patterns between temporal data. In the resonant learning process, an adaptive temperature parameter is introduced to adjust the difficulty of the contrastive learning. The initial temperature value is set to 0.07 and dynamically adjusted as the training progresses. The network training uses the SGD optimizer with a learning rate of 0.01, momentum of 0.9, and a batch size of 512. After sufficient training, the resonant learning network can accurately quantify the degree of information dependence between data at any two time points.

[0047] In some embodiments, determining the information correlation degree of data at different times through the resonant learning network includes: mapping the training dataset to the complex domain to construct an analytic signal; performing a Hilbert-Huang transform on the analytic signal to obtain the instantaneous phase; calculating the phase slip rate based on the instantaneous phase; and using the stability index of the phase slip rate as the information correlation degree.

[0048] The training dataset is mapped to the complex domain to construct an analytic signal. A Hilbert transform is applied to the real-valued pressure signal x(t) in the training dataset to generate the corresponding imaginary part: y(t) = H[x(t)] = (1 / π)·PV∫[-∞,+∞]x(τ) / (t-τ)dτ, where PV represents the Cauchy principal value integral. The real and imaginary parts are combined to form the complex analytic signal z(t) = x(t) + j·y(t), where j is the imaginary unit. The analytic signal is constructed using the Fast Hilbert Transform algorithm, with FFT accelerating the computation process. The signal is preprocessed, including detrending and endpoint extension, to reduce boundary effects. Mirror-symmetric extension is used, with an extension length of 10% of the signal length. The constructed analytic signal retains all the information of the original signal and provides direct access to the instantaneous amplitude A(t) = |z(t)| and the instantaneous phase φ(t) = arg(z(t)). Analytical signal representation makes subsequent phase analysis and frequency estimation more accurate and stable.

[0049] The instantaneous phase is obtained by performing a Hilbert-Huang transform on the analytic signal. The complex analytic signal z(t) is input into the Hilbert-Huang transform algorithm, and the signal is decomposed into multiple intrinsic mode functions (IMFs) through empirical mode decomposition. The decomposition process uses an ensemble empirical mode decomposition method, adding white noise and performing multiple decompositions, averaging the results. The noise standard deviation is set to 0.2 times the original signal, and the ensemble size is 100 times. The analytical form of each IMF component is calculated, and the instantaneous phase is extracted. Phase unwrapping employs the Itoh algorithm to ensure phase continuity: φ_unwrap(t) = φ(t) + 2πk, where k is an integer chosen to minimize phase jumps. The instantaneous frequency is calculated using the time derivative of the phase: f(t) = (1 / 2π)·dφ / dt. The instantaneous frequency is smoothed using a 5-point moving average filter to remove high-frequency noise. The obtained instantaneous phase sequence fully describes the phase evolution of the signal, laying the foundation for subsequent phase dynamics analysis.

[0050] For example, the step of calculating the phase slip rate based on the instantaneous phase includes: performing time differentiation based on the instantaneous phase to generate a phase change rate and a phase acceleration; using the phase acceleration to perform abrupt detection on the phase change rate to form a slip event; performing time interval statistics on the slip event to generate a slip period; and performing a reciprocal operation on the slip period to obtain the phase slip rate.

[0051] Phase change rate and phase acceleration are generated by time differentiation based on instantaneous phase. An improved numerical differentiation method is used to process the instantaneous phase sequence φ(t), and a Savitzky-Golay filter is employed to simultaneously achieve smoothing and differentiation. The filter window length is set to 11 points, and the polynomial order is 3, to suppress noise amplification while preserving signal details. The first derivative yields the phase change rate ω(t) = dφ / dt, representing the instantaneous angular frequency. The second derivative yields the phase acceleration α(t) = d²φ / dt², reflecting the rate of frequency change. Outlier detection is performed on the calculation results, using the median absolute deviation method to identify outliers. Data points exceeding 5 times the MAD are marked as outliers and corrected using linear interpolation. The differentiation results are post-processed using a zero-phase filter, with the cutoff frequency set to 0.8 times the Nyquist frequency. The generated sequence of phase dynamic parameters accurately reflects the instantaneous frequency characteristics and frequency modulation mode of the signal.

[0052] A mutation detection algorithm is used to identify abrupt changes in the phase change rate, forming slip events. A mutation detection algorithm is constructed to identify anomalous changes in phase dynamics. A mutation index J(t) = |α(t)|·|Δω(t)| is defined, where Δω(t) = ω(t) - ω(t-1) is the difference in the phase change rate. When J(t) exceeds an adaptive threshold J_th(t), it is identified as a mutation point. The adaptive threshold is determined using a local statistical method: J_th(t) = μ_local(t) + k·σ_local(t), where μ_local and σ_local are the local mean and standard deviation within a 100-point window, and k = 3 is the threshold coefficient. The DBSCAN algorithm is used for mutation point clustering, grouping mutation points with a time distance of less than 5 sampling points into the same slip event. Each slip event is characterized by its start time, duration, peak intensity, and cumulative phase change. A slip event database is established to record all detected events and their characteristic parameters. Event pattern analysis identifies different types of slip, such as periodic slip, random slip, and trend slip.

[0053] The slip events are statistically analyzed by time interval to generate a slip period. The detected slip event sequence {E} is then analyzed. i Perform time interval analysis to calculate the interval between adjacent events. Statistical analysis of the interval sequences employed robust estimation methods, using the HuberM estimator to calculate location and scale parameters. Interval histograms were constructed, with interval widths automatically determined using the Freedman-Diaconis rule. Kernel density estimation was performed on the histograms using a Gaussian kernel function, with bandwidth selected through cross-validation. The dominant peak position, corresponding to the most probable slip period T_mode, was identified from the density distribution. Several statistics of the slip period were calculated: the arithmetic mean T_mean, the geometric mean T_geo, and the harmonic mean T_harm. The stability of the period was assessed using the coefficient of variation (CV) and the interquartile range (IQR). A slip process was considered to have good periodicity when CV < 0.3 and IQR / T_median < 0.2. For multimodal distributions, the periodic component corresponding to each peak was identified, and possible physical mechanisms were analyzed.

[0054] The phase slip rate is obtained by taking the reciprocal of the slip period. The statistically obtained slip period T is converted into a slip rate v = 1 / T, representing the number of slips per unit time. The rate calculation considers the uncertainty of the period, using the error propagation formula: σ_v = σ_T / T², where σ_T is the standard deviation of the period. A time-varying model v(t) of the slip rate is established using local polynomial regression with adaptive window length adjustment. The model order is selected based on the Akaike information criterion, balancing goodness of fit and model complexity. The spectral characteristics of the slip rate are calculated to identify the main frequency components of the rate variation. Wavelet transform is used to analyze the multi-scale characteristics of the rate, with Morlet wavelet selected as the mother wavelet. Features such as energy distribution, ridges, and modulus maxima are extracted from the wavelet coefficients. The stability of the slip rate is evaluated using the Lyapunov exponent; a positive exponent indicates chaotic behavior, while a negative exponent indicates stable convergence. The final generated phase slip rate sequence and its statistical characteristics serve as core indicators of information correlation.

[0055] The stability index of the phase slip rate is used as the information correlation degree. The stability index S is defined as S = exp(-CV_v) / (1+σ_v / μ_v), where CV_v is the coefficient of variation of the slip rate, and σ_v and μ_v are the standard deviation and mean, respectively. The stability index is in the interval [0,1], and a larger value indicates more stable phase evolution and more reliable information transmission between time points. The stability index S(τ) under different time delays τ is calculated to construct the information correlation degree curve. The decay characteristics of the curve reflect the time scale of information transmission, and the characteristic time constant is extracted through exponential fitting. Fourier analysis is performed on the correlation degree curve to identify periodic correlation patterns. The stability index is extended to two dimensions to calculate the correlation degree S(t1,t2) between any two time points t1 and t2. The constructed correlation degree matrix is ​​symmetric and normalized to ensure the rationality of the mathematical properties. The main correlation patterns are extracted through eigenvalue decomposition, and the first few eigenvectors correspond to the dominant information transmission channels. The spatial distribution map of the information correlation degree intuitively displays the temporal correlation structure and causal relationship network of the pressure data.

[0056] Resonant frequency patterns are identified using information correlation. A two-dimensional Fourier transform is performed on the information correlation matrix to convert the time-domain correlation patterns to the frequency domain for analysis. The transformed spectrum shows the resonance intensity between different frequency components, and the spectral amplitude |F(u,v)| represents the resonance degree between frequencies u and v. A resonance detection threshold is set to three times the average spectral amplitude; frequency pairs exceeding the threshold are marked as resonance patterns. Typical identified resonance patterns include: fundamental frequency and second harmonic resonance (f0-2f0), crossover frequency resonance (f1-f2), sum-frequency resonance (f1+f2), and difference-frequency resonance (|f1-f2|). For each resonance pattern, the quality factor Q = f_center / Δf is calculated, where f_center is the center frequency and Δf is the 3dB bandwidth. The quality factor reflects the selectivity and energy concentration of the resonance; a higher Q value indicates a sharper resonance. The phase relationship of the resonance patterns is determined through phase spectrum analysis; in-phase resonance enhances the signal, while out-of-phase resonance attenuates it. A resonance frequency spectrum was constructed, with the horizontal and vertical axes representing the two frequency components involved in the resonance, and the color depth representing the resonance intensity. Bright spots and lines in the spectrum reveal the energy transfer paths and frequency coupling mechanisms within the pressure signal.

[0057] Mutual information resonance vectors are generated by amplifying rhythm anomaly indicators based on resonant frequency modes. A resonance amplification operator A(f) is designed to selectively amplify rhythm anomaly indicators of specific frequency components according to the identified resonance modes. The amplification factor is calculated as: A(f) = 1 + β·R(f)·Q(f), where R(f) is the resonance intensity at frequency f, Q(f) is the quality factor, and β = 0.5 is the amplification gain parameter. The original rhythm anomaly indicator RAI is decomposed into N frequency band components RAI_i through a frequency domain filter bank, with each frequency band corresponding to a resonance mode. The corresponding amplification factor is applied to each frequency band component: RAI_i' = A(f_i)·RAI_i, achieving resonance-driven selective amplification. The amplified components are reconstructed through inverse transform to generate an enhanced anomaly indicator sequence. The enhanced indicator sequence is concatenated with the resonance mode features to form a mutual information resonance vector V_mir∈R^D, where D = 256 is the vector dimension. The first 128 dimensions of the vector encode the temporal features of the amplified anomaly indicators, and the last 128 dimensions encode the frequency domain features of the resonance modes. Each vector element undergoes batch normalization to ensure numerical stability. The mutual information resonance vector integrates time-domain anomaly information and frequency-domain resonance features.

[0058] Step S140: Perform variational echo reconstruction on the mutual information resonance vector to generate variational coding features, perform probability modeling on the variational coding features to determine the probability distribution of echo propagation, sample and reconstruct the propagation path from the probability distribution, and extract structural change features based on the propagation path to obtain the variational echo feature map.

[0059] Specifically, variational echo reconstruction is performed on the mutual information resonance vector to generate variational encoded features. The mutual information resonance vector V_mir is input into a variational autoencoder architecture. The encoder part adopts a multilayer perceptron structure with three hidden layers, and the number of neurons decreases layer by layer. The encoder outputs a mean vector μ and a log-variance vector log(σ²), both with a dimension of 32. A reparameterization technique is used to sample latent variables from a Gaussian distribution: z = μ + σ·ε, where z is the sampled latent variable, μ is the mean vector output by the encoder, σ is the standard deviation vector, and ε is the noise vector sampled from a standard normal distribution. An echo mechanism is introduced, generating multiple echo versions of the latent variable through a time-delay network. Each echo is achieved through exponential decay and cosine modulation. The echo sequence is generated according to different delay times and attenuation intensities, simulating multiple reflections of the signal in a complex medium. The original latent variable is concatenated with multiple echo versions to form extended variational encoded features. The variational loss function is: L_VAE = ||x - x'||² + β·KL(q(z|x)||p(z)), where x is the original input vector, x' is the output reconstructed by the decoder, ||·||² represents the square of the Euclidean distance, β is a balancing coefficient controlling the weights of the KL terms, KL(·||·) is the KL divergence, q(z|x) is the posterior distribution generated by the encoder, and p(z) is the standard normal prior distribution. During training, the encoder learns to extract the essential features of the data, and the decoder learns to reconstruct the original data from the latent representation.

[0060] In some embodiments, determining the probability distribution of echo propagation by probabilistically modeling the variational coding features includes: inputting the variational coding features into a diffusion model to obtain a forward trajectory; performing time inversion on the forward trajectory to generate a reverse path; sampling on the reverse path to obtain an intermediate state distribution; and aggregating the intermediate state distribution into a probability distribution of echo propagation.

[0061] Variational coding features are input into a diffusion model to obtain the forward trajectory. A denoising diffusion probability model is constructed to process the variational coding features. The forward process converts the data into pure noise by progressively adding Gaussian noise. The conditional distribution for noise addition is: q(z_t|z_{t-1})=N(z_t|√(1-β_t)z_{t-1},β_tI), where z_t is the state vector at time step t, z_{t-1} is the state at the previous time step, β_t is the noise intensity parameter at time t controlling the amount of noise added, √(1-β_t) is the signal preservation coefficient, I is the identity matrix, and N(·|μ,Σ) represents a Gaussian distribution with mean μ and covariance Σ. The noise intensity varies according to a cosine scheduling strategy to ensure the smoothness of the diffusion process. The total number of diffusion steps is set to 1000 steps, which is sufficient to completely randomize the structured data. The state distribution at any time step can be directly calculated through cumulative multiplication, avoiding the computational overhead of progressive simulation. The forward process records the state at each time step, forming a complete diffusion trajectory. The trajectory illustrates the dynamic process of data structures gradually disappearing and information being lost step by step.

[0062] A reverse path is generated by temporal inversion of the forward trajectory. The state evolution information recorded in the forward trajectory is used as training data to train a neural network to learn the inverse denoising process. The network input includes the noise state at each time step in the forward trajectory and the corresponding time step information. The network architecture adopts a U-Net design, maintaining the flow of multi-scale information through skip connections. Temporal information is embedded in the network through sinusoidal coding, enabling the model to adapt to different noise levels. The training objective is to minimize the noise prediction error by learning the data distribution pattern by learning the noise added at each step in the forward process. After training, the learned inverse sampling formula is used: , Where μ_θ is the predicted denoised mean, and α_t=1-β_t is the signal retention rate. Let ε_θ(z_t,t) be the cumulative retention rate from the initial state to time t, and let ε_θ(z_t,t) be the noise predicted by the neural network. Backsampling is performed starting from pure Gaussian noise to gradually denoise and generate clear data.

[0063] Intermediate state distributions are obtained by sampling along the reverse path. Dense sampling is performed at key time points in the reverse denoising process, specifically selecting three time points t∈{250,500,750}, corresponding to positions 0.25, 0.5, and 0.75 of the total 1000 steps, respectively. These sampling points cover the early, middle, and late stages of the reconstruction process, capturing the complete evolution of structure formation. Each sampling point is independently run 100 times in the denoising process to generate the state set for that time point, ensuring statistical reliability. The probability density at each time point is fitted using a kernel density estimation method, with a Gaussian kernel chosen as the kernel function and the bandwidth adaptively determined using the Silverman rule. The 2-Wasserstein distance between distributions at different time points is calculated, a distance metric that considers differences in the geometric structure of the distributions. Analysis of the distance matrix reveals the non-uniformity of the reconstruction process: slow changes in the early stage (0-250 steps), mainly removing high-frequency noise; rapid formation of the main structure in the middle stage (250-500 steps); and fine-tuning of local details in the late stage (500-750 steps). The intermediate states are visualized in a reduced-dimensional space, and the t-SNE algorithm is used to project the high-dimensional distribution onto a two-dimensional plane. The visualization clearly shows how data points gradually aggregate from a random distribution into meaningful structural clusters.

[0064] The intermediate state distributions are aggregated into a probability distribution for echo propagation. An intelligent weighting strategy is designed to integrate the intermediate state distributions at three key moments, avoiding the ambiguity caused by simple averaging. Weights are calculated based on the information gain at each moment relative to the initial pure noise state, with the information gain measured by relative entropy. A soft maximization function is used for the specific weight calculation to ensure smooth weight distribution and numerical stability. The temperature parameter is set to 0.1 to maintain diversity while avoiding extreme weight allocation. The aggregation formula is: p_echo(z) = Σ_tw_t·p_t(z), where p_echo(z) is the final echo propagation probability distribution, w_t is the normalized weight at time t satisfying Σw_t = 1, and p_t(z) is the intermediate state distribution at time t. The summation iterates through the three sampling moments. The Student's t-distribution family is used as the parameterized form of the aggregated distribution, as its thick-tailed characteristic better captures rare events and anomalous patterns compared to the Gaussian distribution. The three core parameters of the t-distribution are estimated iteratively using the expectation-maximization algorithm: the position vector μ, the scale matrix Σ, and the degrees of freedom ν. The adaptive estimation of the degree-of-freedom parameter ν is particularly crucial, as it controls the thickness of the distribution tail and reflects the degree of data heterogeneity. After the algorithm converges, confirmatory sampling is performed on the aggregated distribution to ensure that the generated samples cover the typical patterns of each intermediate state. The moments and information entropy of the aggregated distribution are calculated to evaluate its statistical properties and expressive power. The final echo propagation probability distribution p_echo fully integrates the characteristics of different stages of the diffusion-reconstruction process, providing a rich probabilistic representation for anomaly detection.

[0065] Propagation paths are reconstructed by sampling from probability distributions. Representative samples are generated from the learned probability distribution using the Markov chain Monte Carlo method. Hamiltonian Monte Carlo is chosen as the sampling algorithm, which utilizes gradient information to guide the sampling process, improving efficiency in high-dimensional spaces. The potential energy function is defined as U(z) = -logp(z), where U(z) is the potential energy function and p(z) is the target probability density. The negative logarithmic transformation converts the probability maximization problem into an energy minimization problem. A Hamiltonian system incorporating potential and kinetic energy is constructed, and efficient sampling is achieved by simulating the dynamic evolution of the physical system. The Hamiltonian equation is numerically solved using a leapfrog integrator, preserving the symplectic structure and energy conservation of the system. The integration step size is adjusted using an adaptive algorithm to monitor numerical errors and maintain a suitable acceptance rate. Each sampling trajectory records a complete state evolution sequence, and the trajectory length is set sufficiently long to explore various distribution patterns. Statistical analysis is performed on the generated trajectory set to calculate the similarity and differences between trajectories. Trajectories are grouped using cluster analysis, with each group representing a typical propagation path. Smooth interpolation is performed on discrete trajectory points to generate continuously differentiable path functions.

[0066] Variational echo feature maps are obtained by extracting structural change features from the propagation path. Differential geometric features are calculated for each propagation path, with a focus on extracting curvature information. The curvature calculation formula is: κ(s) = ||dz / ds × d²z / ds²|| / ||dz / ds||³, where κ(s) is the curvature value at the arc length parameter s, z(s) is the parameterized path vector function, dz / ds is the first derivative of the path (i.e., the tangent vector), d²z / ds² is the second derivative, × represents the cross product operation, and ||·|| represents the Euclidean norm of the vector. Curvature reflects the local bending degree of the path, with high curvature regions corresponding to abrupt changes in the propagation process. Simultaneously, other geometric quantities such as torsion are calculated to describe the three-dimensional torsional characteristics of the path. Feature points on the path are identified, including curvature extrema, zero curvature points, and high torsion regions. A graph structure is constructed to represent the topological relationships between feature points, with node attributes containing local geometric information. The edge weights of the graph are determined using a Gaussian kernel function to ensure stronger connections between spatially neighboring nodes. A graph convolutional network is applied to extract multi-scale structural features; the network learns higher-order representations by aggregating neighborhood information. The extracted features are organized into a spatial feature map with a resolution of 64×64 and containing 16 feature channels.

[0067] Step S150: Input the rhythm anomaly index and mutual information resonance vector into the deep classification network to generate a nonlinear transformation pattern, predict the phase transition critical point from the nonlinear transformation pattern, determine the phase transition early warning parameters based on the phase transition critical point, and construct an early warning decision network using the phase transition early warning parameters.

[0068] Specifically, rhythm anomaly indicators (RAIs) and mutual information resonance vectors (MIRVs) are input into a deep classification network to generate nonlinear transformation patterns. A deep neural network architecture specifically designed to handle multimodal inputs is constructed. The first input branch receives the scalar form of the RAI, and the second input branch receives the 256-dimensional MIRV vector V_mir. The two branches employ different feature extraction strategies: the scalar branch is expanded to a high-dimensional representation through embedding layers, while the vector branch extracts local correlations through convolutional layers. The first branch contains embedding layers and three fully connected layers with 64, 128, and 128 neurons, respectively, using batch normalization and a dropout of 0.3 to prevent overfitting. The second branch employs a one-dimensional convolutional structure with three convolutional layers containing 32, 64, and 128 filters, a kernel size of 5, and uses the ReLU activation function. The features from the two branches are weighted and combined in the fusion layer using a learnable attention mechanism: F_fused = α·F_RAI + (1-α)·F_mir, where α is the attention weight of the gating unit output, and F_RAI and F_mir are the 128-dimensional feature representations extracted from the two branches, respectively. The fused features are input to the backbone network consisting of six residual blocks, each containing two convolutional layers, batch normalization, ReLU activation, and skip connections. The network output layer generates a 64-dimensional nonlinear transformation pattern vector through fully connected mapping, with each dimension encoding a specific system state transition path. Training employs a combination of triplet loss and cross-entropy loss, enabling the network to learn to distinguish different nonlinear evolution patterns while maintaining the discriminative nature of the features.

[0069] In some embodiments, predicting the phase transition critical point from the nonlinear conversion mode includes: constructing a renormalized stream for the nonlinear conversion mode; tracing the fixed point trajectory in the renormalized stream; identifying the bifurcation value from which the fixed point trajectory changes from stable to unstable; and marking the parameter point corresponding to the bifurcation value as the phase transition critical point.

[0070] A renormalized stream is constructed for the nonlinear transformation mode. The 64-dimensional nonlinear transformation mode is considered as the field variable φ(x) in statistical field theory, and a momentum shell renormalization transformation is defined to gradually eliminate high-frequency fluctuations. The renormalization transformation consists of two steps: first, mode elimination in momentum space is performed, integrating the degrees of freedom within the momentum shell Λ / b<|k|<Λ, where Λ is the ultraviolet cutoff and b>1 is the scale factor; then, the remaining field variables and spatial coordinates are rescaled. The specific transformation form is: φ'(k)=b^(d / 2-[φ])φ(k / b), where d is the spatial dimension, and [φ] is the scaling dimension of the field, determined through dimensional analysis. The renormalization of the coupling constant follows: g'_i=b^(y_i)g_i+Σ_jkB_ijkg_jg_k, where y_i is the scaling dimension of the coupling constant g_i, and B_ijk is the coefficient of the beta function. A continuous RG stream is constructed by iteratively applying the renormalization transformation T. Where l = ln(b) is the flow parameter and β_i is the beta function. Numerical implementation employs the Monte Carlo renormalization group, with real-space renormalization achieved through block variable techniques. The evolution of the effective action is calculated in momentum space using truncated Dyson-Schwinger equations. Maintaining the Helmholtz free energy under renormalization, the scaling relationship between critical exponents is determined. The constructed RG flow fully describes the system's effective theory at different energy scales, revealing the scale invariance of the phase transition.

[0071] Tracing fixed-point trajectories within a renormalized group flow. Fixed points g* in the renormalized group are determined by solving for the zeros β(g*) = 0 of the beta function; these points correspond to scale-invariant critical points. The nonlinear equations are solved using the multidimensional Newton method, with the Jacobian matrix approximated by finite differences. Stability analysis is performed on each found fixed point, and the linearized RG transformation matrix is ​​calculated. The eigenvalue spectrum. The sign of the eigenvalue λ_α determines the correlation of the corresponding eigendirection: λ_α>0 indicates a correlated direction (growth), λ_α<0 indicates an uncorrelated direction (decay), and λ_α=0 indicates a marginal direction. The correlation index is calculated using y_α=ln|λ_α| / ln(b) and is directly related to the critical index of the physical quantity. Tracing the RG trajectory starting from different initial conditions, the fourth-order Runge-Kutta method is used to integrate the flow equation. The attraction domain of a stable fixed point corresponds to all systems of the same universal class, with the boundary being the critical surface. Unstable fixed points act as saddle points on the critical surface, separating different phase regions. The trajectory of the fixed point moving with external parameters (such as temperature and pressure) is traced through parametric extension. When two fixed points collide and annihilate, a topological phase transition occurs in the system. A complete RG flow graph is drawn, with arrows indicating the direction of flow and colors encoding the velocity of the flow.

[0072] Identify bifurcation values ​​at which the trajectory of a fixed point transitions from stable to unstable. Systematically analyze the stability of the fixed point as a function of control parameters, focusing on cases where the eigenvalues ​​of the stability matrix cross zeros. When the maximum eigenvalue λ_max(p) changes from negative to positive with the parameter p, the fixed point loses stability. A bifurcation occurs at λ_max(p_c) = 0, where p_c is the bifurcation parameter value. Classify bifurcation types based on the way the eigenvalues ​​cross zeros: a single real eigenvalue crossing zero corresponds to a saddle-node bifurcation, and a pair of conjugate complex eigenvalues ​​crossing zeros corresponds to a Hopf bifurcation. Calculate the normal form of the bifurcation to determine the expansion coefficients and the influence of nonlinear terms. For a saddle-node bifurcation: dx / dt = r + x², where r = p - p_c is the deviation parameter; for a Hopf bifurcation, the complex amplitude equation needs to be considered. Use the central manifold theorem to reduce the high-dimensional system to the bifurcation subspace, simplifying the analysis. Construct bifurcation equations using the Lyapunov-Schmidt method to systematically handle high-codimensional bifurcations. Numerically, pseudo-arc length extension is used to trace the bifurcation curve, handling inflection points and branch points. For each identified bifurcation point, its homology and heteroclimate orbits are calculated; these special orbits determine the dynamic path of the phase transition.

[0073] The parameter points corresponding to the bifurcation values ​​are marked as phase transition critical points. A quantitative mapping relationship between mathematical bifurcation parameters and physical control parameters is established, and the conversion coefficients are determined through dimensional analysis and experimental calibration. For each bifurcation value p_c, the corresponding physical quantities are calculated: temperature T_c, pressure P_c, concentration C_c, etc., considering measurement units and scaling factors. The thermodynamic characteristics of the phase transition are verified, and the behavior of free energy and its derivatives at the critical point is calculated. The scaling behavior of the order parameter η near the critical point is: η ~ |T-T_c|^β, where β is the critical exponent. Response functions such as specific heat, compressibility, and magnetic susceptibility exhibit power-law divergence or finite jumps at the critical point. The effects of finite systems are handled using finite-scale scaling theory, and the critical behavior of the thermodynamic limit is extracted. Data collapse analysis verifies the scaling hypothesis: F(L^{1 / ν}t)=L^{-β / ν}η(t,L), where L is the system scale, and t=(T-T_c) / T_c. Examine various scaling relationships and verify the internal consistency of the critical exponent. For first-order phase transitions, determine the coexistence curve, metastable region, and hysteresis effect. Construct a complete phase diagram, labeling all phase transition lines, triple points, and critical endpoints. The phase transition critical point database contains precise parameter values, error ranges, applicable conditions, and relevant physical quantities.

[0074] Phase transition warning parameters are determined based on phase transition critical points. For each phase transition critical point, its precursor characteristics are calculated, including the decay time of the autocorrelation function, the abnormal increase in variance, and the enhancement of low-frequency components of the power spectrum. A comprehensive warning parameter is defined as: P_w = (σ² / μ²)·exp(τ / τ_0)·(1+λ·S), where σ² is the variance of the state variable within the sliding window, μ is the mean, τ is the autocorrelation time obtained by integrating the autocorrelation function, τ_0 is the characteristic time scale of the system, S is the asymmetry of the skewness quantitative distribution, and λ is the skewness influence coefficient. An adaptive sliding window algorithm is designed, with the window length W = W_0·(1+κ·|dP / dt|) dynamically adjusted, where W_0 is the baseline window length, κ is the adjustment coefficient, and |dP / dt| is the parameter change rate. A multi-scale warning parameter set is constructed, including instantaneous parameters (fast response but high noise), short-term parameters (balancing timeliness and stability), and long-term parameters (stable but with large delays). By fusing multi-scale information through Bayesian inference, the posterior probability P(phase transition|parameter) ∝ P(parameter|phase transition)·P(phase transition). Four warning thresholds are set: Normal (P_w < 0.3), Attention (0.3 ≤ P_w < 0.5), Warning (0.5 ≤ P_w < 0.7), and Danger (P_w ≥ 0.7). Corresponding response strategies and intervention measures are developed for each warning level.

[0075] In some embodiments, constructing an early warning decision network using the phase transition early warning parameters includes: converting the phase transition early warning parameters into oscillator coupling strength; constructing an oscillator network based on the oscillator coupling strength; performing synchronization analysis on the oscillator network to obtain a critical topology; and solidifying the critical topology into an early warning decision network.

[0076] The phase transition warning parameters are converted into oscillator coupling strength. A nonlinear mapping function is designed to convert the multidimensional warning parameters P_w into the coupling matrix of the oscillator network. The coupling strength is calculated using a Gaussian kernel function: K_ij=K_0·exp(-||P_i-P_j||² / (2σ²))·H(r_c-||P_i-P_j||), where K_ij is the coupling strength between nodes i and j, K_0 is the baseline strength, ||P_i-P_j|| is the Euclidean distance between the warning parameter vectors, σ is the interaction range parameter, H is the step function to achieve distance truncation, and r_c is the truncation radius. A directional factor is introduced to reflect the causal relationship: K_ij^{dir}=K_ij·(1+α·TE_ij), where TE_ij is the transfer entropy from node j to i, and α is the directional strength parameter. Time-varying coupling is updated exponentially: K_ij(t) = γ·K_ij(t-Δt) + (1-γ)·K_ij^{new}, where γ is the forgetting factor, Δt is the update time interval, and K_ij^{new} is the newly calculated coupling strength. The coupling matrix is ​​spectrally normalized to ensure that the largest eigenvalue is within a reasonable range, avoiding numerical instability. A multi-layer coupling network is constructed, with different layers corresponding to different time scales such as seconds, minutes, and hours. Inter-layer coupling is determined by a scale-matching function to maintain the consistency of multi-scale dynamics.

[0077] An oscillator network is constructed based on oscillator coupling strength. A generalized Kulamoto model is used to describe the collective dynamics of N coupled oscillators, with each oscillator representing a monitoring node. The dynamic equation is: dθ_i / dt=ω_i+Σ_jK_ij·f(θ_j-θ_i)+ξ_i(t), where θ_i is the phase of the i-th oscillator, ranging from [0,2π], ω_i is the natural frequency, f(Δθ)=sin(Δθ)+(ε / 2)sin(2Δθ) is the coupling function including the second harmonic, ε controls the nonlinear strength, and ξ_i(t) is the Gaussian white noise term. The natural frequency is sampled from the Lorentz distribution, and the center frequency and half-width are set according to the system characteristics. The network topology is obtained by thresholding the coupling matrix, retaining connections with strength exceeding the threshold. A community structure is introduced to reflect functional modules, with strong coupling within the same community and weak coupling between communities. Numerical integration is performed using an adaptive step-size stochastic differential equation solver. Monitoring macroscopic order parameters: r(t)e^{iψ(t)}=(1 / N)Σ_je^{iθ_j(t)}, where r is the degree of synchronization, ranging from 0 to 1, ψ is the average phase, and i is the imaginary unit. Recording local order parameters characterizes the synchronization within the community and identifies partial synchronization states. Power spectrum analysis identifies collective oscillation modes and frequency locking phenomena.

[0078] Synchronization analysis is performed on oscillator networks to obtain critical topologies. Linear stability analysis is used to determine the stability conditions of the oscillator network's synchronization state, and the master stability function method is employed to handle complex coupled oscillator networks. The transverse Lyapunov exponent of the oscillator network is calculated; the network is stable in its synchronization state when the maximum value is less than zero. The critical value K_c for synchronization transition is determined by scanning the coupling strength between oscillators, at which point the oscillator network undergoes desynchronization bifurcation. Finite-time Lyapunov exponents are used to identify Lagrange pseudo-order structures in the oscillator phase space. A modularity optimization algorithm is used to detect synchronization clusters in the oscillator network, maximizing the network's modularity function. The phase difference distribution between different clusters in the oscillator network is calculated, identifying phase locking and phase slip phenomena. The spectral properties of the oscillator network are analyzed; the eigenvalue spectrum of the Laplace matrix determines the time scale of energy diffusion in the network, and the spectral radius of the adjacency matrix affects the oscillator's synchronization capability. The eigenmode that contributes most to the oscillator network's synchronization is identified, and the eigenvector corresponding to the smallest non-zero eigenvalue is the Fiedler vector. A targeted attack strategy is used to identify key nodes and key edges in the oscillator network; their removal significantly degrades the network's synchronization performance. The synchronization modes of the oscillator network in different parameter regions are recorded, including complete synchronization, cluster synchronization, traveling wave, spiral wave, and singular state. These synchronization modes and key structures together constitute the critical topology of the oscillator network.

[0079] The critical topology is solidified into an early warning decision network. The critical topology features obtained from oscillator network analysis are transformed into a graph neural network architecture. Key nodes in the critical topology are mapped to the core processing units of the network, and key connections are transformed into information transmission paths. The network adopts a hierarchical structure: the input layer receives real-time early warning parameter streams, the hidden layer simulates the coupling dynamics of the oscillator according to the critical topology, and the output layer generates decision results. Node design employs gated recurrent units, controlling information retention and updating through a gating mechanism. Edge information transmission uses a message passing framework, where nodes update their own state by aggregating neighbor messages. A multi-head graph attention mechanism is introduced, with different attention heads focusing on different types of coupling patterns. The network contains four layers of graph convolutions, each followed by normalization and residual connections to maintain gradient flow and training stability. Global information is aggregated through virtual nodes or readout functions, and attention weights are adaptively learned. The output layer employs a hybrid expert system, with different experts responsible for different types of fault modes. Decision outputs include fault type probability distribution, occurrence time estimation and uncertainty, severity score (0 to 10), and recommended action ranking. Knowledge distillation encodes the dynamic behavior of the oscillator network into static network parameters. The decision-making strategy is fine-tuned using reinforcement learning, with the reward function: R = α·TPR - β·FPR - γ·delay, where TPR is the true positive rate, FPR is the false positive rate, delay is the detection latency, and α, β, and γ are weight coefficients. During deployment, the network structure is fixed, and only the hidden states of nodes are updated, with inference time controlled within 10 milliseconds.

[0080] Step S160: The early warning decision network outputs a graded early warning signal by integrating the variational echo feature map, thus completing the neural network-driven monitoring and early warning of battery acoustic pressure.

[0081] In some embodiments, the step of outputting a graded early warning signal by integrating the variational echo feature map through the early warning decision network includes: performing multi-resolution decomposition on the variational echo feature map to extract singular value spectra; inputting the singular value spectra into the early warning decision network to calculate activation intensity; and determining a graded early warning signal based on the distribution range of the activation intensity.

[0082] The variational echo feature map is decomposed into singular value spectra at multiple resolutions. Singular value decomposition is performed channel-by-channel on the input variational echo feature map, with each channel treated as a 64×64 matrix. Singular value decomposition is performed on the c-th channel: F_c = U_c·Σ_c·V_c^T, where F_c is the feature matrix of the c-th channel, U_c is the left singular vector matrix containing the spatial basis functions, Σ_c is a diagonal matrix whose diagonal elements are singular values ​​representing the importance of each basis function, V_c is the right singular vector matrix encoding the combination pattern of features, and the superscript T indicates matrix transpose. The singular value sequence of each channel is extracted and arranged in descending order to form a feature representation with decreasing energy. A multi-resolution pyramid is constructed, and features are reconstructed using different numbers of principal singular values, selecting 4, 8, 16, and 32 principal components corresponding to coarse to fine resolution levels. The energy retention rate at each resolution is calculated, i.e., the proportion of the sum of squares of the first k singular values ​​to the sum of squares of all singular values. This metric quantifies the information integrity at different resolutions. Logarithmic transformation and normalization are applied to the singular value sequences to enhance the discriminative power of small singular values ​​and make the features more numerically stable. The singular value spectra of the 16 channels are combined in channel order to form a singular value spectrum matrix S∈R^(16×64), with each row corresponding to a complete singular value sequence of one channel. Higher-order statistical features of the singular value spectrum are calculated, including spectral entropy to measure complexity, effective rank to assess information dimensionality, condition number to reflect numerical stability, and spectral gaps to identify the boundaries between principal and secondary components. Multi-scale analysis of the singular value sequences is performed using discrete wavelet transform; wavelet coefficients reveal the energy distribution of different frequency components, and abrupt changes correspond to the occurrence of anomalous patterns.

[0083] The singular value spectrum is input into the early warning decision network to calculate the activation intensity. The singular value spectrum matrix S and the extracted statistical feature vector are concatenated and fed into a specially designed spectral analysis module of the early warning decision network. This module first processes the singular value sequence of each channel through parallel one-dimensional convolutional groups, with different sized convolutional kernels (3, 5, 7) capturing spectral patterns at different scales. After batch normalization and activation functions, the convolutional outputs are adaptively adjusted for the importance of each channel using a channel attention mechanism. Multi-scale features are fused and input into a self-attention layer to calculate the long-range dependencies within the singular value sequence. The attention mechanism learns which singular value locations are most critical for anomaly detection through query-key-value transformation. The attention-weighted features are mapped to the anomaly pattern space through a two-layer fully connected network, which includes a dropout layer to prevent overfitting. The activation intensity of M predefined anomaly patterns is calculated, each corresponding to a specific fault mechanism, such as thermal runaway precursors, internal short circuit development, and electrolyte leakage. The activation intensity is calculated using a normalized exponential function to ensure numerical stability and interpretability. A temperature parameter T is introduced to adjust the sharpness of the activation; the value of T is optimized through a grid search on the validation set. The activation intensity sequence is time-domain filtered, and an exponential moving average is used to eliminate transient perturbations while preserving persistent anomalous patterns.

[0084] The graded early warning signals are determined based on the distribution range of activation intensity. The distribution characteristics of the M-dimensional activation intensity vector A=[A_1,A_2,...,A_M] are analyzed, and a multi-level decision logic is designed to map continuous activation values ​​to discrete early warning levels. Five early warning levels are defined: normal state, minor anomaly, moderate risk, high risk, and emergency state. The boundaries of the activation intensity intervals corresponding to each level are determined by the quantiles of historical data to ensure that the probability of occurrence of each level conforms to the actual distribution. The comprehensive early warning index is calculated as: W=Σ_mw_m·A_m, where W is the weighted early warning index, w_m is the hazard weight of the m-th abnormal mode reflecting the probability of this mode causing a serious failure, and A_m is the normalized activation intensity. The summation iterates through all M abnormal modes. The hazard weight is determined through fault tree analysis and expert knowledge, considering the severity, development speed, and controllability of the failure. Fuzzy logic is used to handle cases where the activation intensity is close to the level boundary, and a trapezoidal membership function μ_L(W) is defined to calculate the membership degree of the early warning index W to each level L. When the membership degrees of multiple levels are similar, evidence theory is used to integrate judgments from different information sources, including historical trends, environmental factors, and system status. A dynamic threshold mechanism is introduced to adjust the judgment criteria for the warning level based on the battery's usage stage, environmental conditions, and historical performance. A time consistency constraint is implemented, requiring that changes in the warning level must be confirmed over multiple sampling periods to prevent false alarms caused by momentary interference. The warning change rate index is calculated as: R = |W(t) - W(t - Δt)| / Δt, where R is the change rate and Δt is the time interval. This index is used to assess the swiftness of abnormal development. A structured warning output is generated, including the primary warning level, secondary risk factors, development trend prediction, suggested response time window, and tiered handling plan, ultimately completing the neural network-driven battery acoustic pressure monitoring and warning system.

[0085] To implement the above-described method embodiments, a neural network-driven battery acoustic pressure monitoring and early warning method is proposed to achieve the corresponding functions and technical effects. See also... Figure 2 , Figure 2 This diagram illustrates a structural block diagram of a neural network-driven battery acoustic pressure monitoring and early warning system 200 according to an embodiment of this application. For ease of explanation, only the parts relevant to this embodiment are shown. The neural network-driven battery acoustic pressure monitoring and early warning system 200 provided in this embodiment includes:

[0086] The data encoding module 201 is used to acquire pressure monitoring data during battery operation and to perform neural network encoding on the pressure monitoring data to generate a training dataset.

[0087] Rhythm analysis module 202 is used to construct a temporal convolutional neural network based on the training dataset, train the temporal convolutional neural network to identify pressure periodic rhythms, extract rhythm parameters from the pressure periodic rhythms to generate a rhythm benchmark model, and perform deviation analysis through the rhythm benchmark model to generate rhythm abnormality indicators.

[0088] The resonance learning module 203 is used to perform mutual information maximization processing on the training dataset to establish a resonance learning network, determine the information correlation degree of data at different times through the resonance learning network, identify the resonance frequency pattern using the information correlation degree, and amplify the rhythm abnormality index based on the resonance frequency pattern to generate a mutual information resonance vector.

[0089] The variational reconstruction module 204 is used to perform variational echo reconstruction on the mutual information resonance vector to generate variational coding features, perform probability modeling on the variational coding features to determine the probability distribution of echo propagation, sample and reconstruct the propagation path from the probability distribution, and extract structural change features based on the propagation path to obtain a variational echo feature map.

[0090] The phase transition prediction module 205 is used to input the rhythm abnormality index and the mutual information resonance vector into a deep classification network to generate a nonlinear transformation pattern, predict the phase transition critical point from the nonlinear transformation pattern, determine the phase transition early warning parameters based on the phase transition critical point, and construct an early warning decision network using the phase transition early warning parameters.

[0091] The early warning output module 206 is used to output a graded early warning signal by integrating the variational echo feature map through the early warning decision network, thereby completing the neural network-driven battery acoustic pressure monitoring and early warning.

[0092] The aforementioned neural network-driven battery acoustic pressure monitoring and early warning system 200 can implement the neural network-driven battery acoustic pressure monitoring and early warning method of the above-described method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining content of this application embodiment can be referred to the content of the above method embodiments, and will not be repeated in this embodiment.

[0093] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

[0094] The above embodiments are not an exhaustive list based on the present invention, and there may be many other embodiments not listed. Any substitutions and improvements made without departing from the concept of the present invention are within the protection scope of the present invention.

Claims

1. A neural network-driven method for monitoring and early warning of battery acoustic pressure, characterized in that, include: Acquiring pressure monitoring data during battery operation and generating a training dataset by performing neural network encoding on the pressure monitoring data includes: performing reverse time evolution on the pressure monitoring data to obtain causal precursor signals; applying chaotic attractor projection to the causal precursor signals to extract singular trajectories; using the singular trajectories as neuron dead zone activation modes to generate sparse codes; and constructing a training dataset based on the sparse codes. A temporal convolutional neural network is constructed based on the training dataset. This network is then trained to identify pressure cycle rhythms. Rhythm parameters are extracted from these rhythms to generate a rhythm baseline model. Deviation analysis is performed on this baseline model to generate rhythm anomaly indicators. The process includes: activating the self-diagnostic mode of the baseline model to obtain an internal parameter distribution map; identifying weight imbalance regions on the parameter distribution map and establishing imbalance pattern classifications, including gradient explosion, gradient vanishing, and oscillatory divergence; and performing severity assessment on the imbalance pattern classifications to generate rhythm anomaly indicators. A resonance learning network is established by maximizing mutual information on the training dataset. This network determines the information correlation of data at different times, identifies resonance frequency patterns using these correlations, and amplifies the rhythm anomaly index based on these patterns to generate a mutual information resonance vector. The determination of information correlation of data at different times using the resonance learning network includes: mapping the training dataset to the complex domain to construct an analytic signal; performing a Hilbert-Huang transform on the analytic signal to obtain the instantaneous phase; calculating the phase slip rate based on the instantaneous phase; and using the stability index of the phase slip rate as the information correlation. Variational echo reconstruction is performed on the mutual information resonance vector to generate variational coding features. Probabilistic modeling is performed on the variational coding features to determine the probability distribution of echo propagation. The propagation path is reconstructed by sampling from the probability distribution. Based on the propagation path, structural change features are extracted to obtain a variational echo feature map. The rhythm anomaly index and the mutual information resonance vector are input into a deep classification network to generate a nonlinear transformation pattern. The phase transition critical point is predicted from the nonlinear transformation pattern. The phase transition early warning parameters are determined based on the phase transition critical point. The early warning decision network is constructed using the phase transition early warning parameters. The early warning decision network integrates the variational echo feature map to output a graded early warning signal, thereby completing the neural network-driven monitoring and early warning of battery acoustic pressure.

2. The method according to claim 1, characterized in that, The step of probabilistically modeling the variational coding features to determine the probability distribution of echo propagation includes: The variational coding features are input into the diffusion model to obtain the forward trajectory; The forward trajectory is time-reversed to generate a reverse path; The intermediate state distribution is obtained by sampling along the reverse path; The intermediate state distribution is aggregated into a probability distribution for echo propagation.

3. The method according to claim 1, characterized in that, Predicting the phase transition critical point from the nonlinear conversion mode includes: A renormalized group flow is constructed for the aforementioned nonlinear transformation mode; Tracing the fixed point trajectory in the renormalized group flow; Identify the bifurcation value at which the fixed point trajectory changes from stable to unstable; The parameter points corresponding to the bifurcation values ​​are marked as phase transition critical points.

4. The method according to claim 1, characterized in that, The construction of the early warning decision network using the phase transition early warning parameters includes: The phase transition early warning parameters are converted into oscillator coupling strength; An oscillator network is constructed based on the oscillator coupling strength; Synchronization analysis is performed on the oscillator network to obtain the critical topology; The critical topology is solidified into an early warning decision network.

5. The method according to claim 1, characterized in that, The step of outputting a graded early warning signal by integrating the variational echo feature map through the early warning decision network includes: The variational echo feature map is decomposed into singular value spectra using multi-resolution decomposition. The singular value spectrum is input into the early warning decision network to calculate the activation intensity; The graded early warning signal is determined based on the distribution range of the activation intensity.

6. The method according to claim 1, characterized in that, The calculation of the phase slip rate based on the instantaneous phase includes: The phase change rate and phase acceleration are generated by time differentiation based on the instantaneous phase; The phase acceleration is used to detect abrupt changes in the phase change rate to form a slip event; The slip events are statistically analyzed at time intervals to generate a slip cycle; The phase slip rate is obtained by performing a reciprocal operation on the slip period.

7. A neural network-driven battery acoustic pressure monitoring and early warning system, characterized in that, include: The data encoding module is used to acquire pressure monitoring data during battery operation and to perform neural network encoding on the pressure monitoring data to generate a training dataset, including: performing reverse time evolution on the pressure monitoring data to obtain causal precursor signals; applying chaotic attractor projection to the causal precursor signals to extract singular trajectories; using the singular trajectories as neuron dead zone activation modes to generate sparse codes; and constructing a training dataset based on the sparse codes. The rhythm analysis module is used to construct a temporal convolutional neural network based on the training dataset, train the temporal convolutional neural network to identify pressure cycle rhythms, extract rhythm parameters from the pressure cycle rhythms to generate a rhythm benchmark model, and perform deviation analysis on the rhythm benchmark model to generate rhythm abnormality indicators. This includes: activating the self-diagnosis mode of the rhythm benchmark model and obtaining an internal parameter distribution map; identifying weight imbalance regions on the parameter distribution map and establishing imbalance pattern classifications, including gradient explosion, gradient vanishing, and oscillating divergence; and performing severity assessment on the imbalance pattern classifications to generate rhythm abnormality indicators. The resonance learning module is used to establish a resonance learning network by maximizing mutual information on the training dataset. The network determines the information correlation of data at different times, identifies resonance frequency patterns using these correlations, and amplifies the rhythm anomaly index based on the resonance frequency patterns to generate a mutual information resonance vector. The step of determining the information correlation of data at different times using the resonance learning network includes: mapping the training dataset to the complex domain to construct an analytic signal; performing a Hilbert-Huang transform on the analytic signal to obtain the instantaneous phase; calculating the phase slip rate based on the instantaneous phase; and using the stability index of the phase slip rate as the information correlation. The variational reconstruction module is used to perform variational echo reconstruction on the mutual information resonance vector to generate variational coding features, perform probability modeling on the variational coding features to determine the probability distribution of echo propagation, sample and reconstruct the propagation path from the probability distribution, and extract structural change features based on the propagation path to obtain a variational echo feature map. The phase transition prediction module is used to input the rhythm anomaly index and the mutual information resonance vector into a deep classification network to generate a nonlinear transformation pattern, predict the phase transition critical point from the nonlinear transformation pattern, determine the phase transition early warning parameters based on the phase transition critical point, and construct an early warning decision network using the phase transition early warning parameters. The early warning output module is used to output a graded early warning signal by integrating the variational echo feature map through the early warning decision network, thereby completing the neural network-driven monitoring and early warning of battery acoustic pressure.

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