Engine rul prediction method and device based on physical causal logic and linear complexity state space

Abstract

The application discloses an engine RUL prediction method and device based on physical causal logic and linear complexity state space, wherein first, vibration and sound pressure signals are synchronously collected, a maximum information transmission entropy (MITE) is used to construct a characteristic causal diagram, physical driving variables are accurately screened, and time window timing alignment is performed; secondly, a double-channel causal convolution is used to extract local features, and a dynamic weight mask is generated through an adaptive pruning module to realize online management of redundant features and lightweight calculation. The core layer uses a Mamba architecture with a selective scanning mechanism to capture long-range evolution rules, synchronously couples Fourier spectrum mixing and a bidirectional cross-attention mechanism, and realizes deep alignment of time-frequency semantics; in regression prediction, a physical dynamics constraint is embedded, and a prediction value with physical consistency is output through a joint optimization strategy. The method effectively solves problems such as large calculation overhead of a long sequence and unexplainable black box model, and significantly improves prediction accuracy and deployment efficiency.

Description

Technical Field

[0001] This invention belongs to the field of mechanical equipment condition monitoring, and specifically relates to an engine RUL prediction method and device based on physical causal logic and linear complexity state space. Background Technology

[0002] As industrial equipment rapidly evolves towards greater intelligence and complexity, higher demands are being placed on the stable and long-term operation of key components (such as engines and bearings). Accurately predicting the remaining useful life (RUL) of equipment has significant theoretical and practical value, effectively identifying potential failures and providing a scientific basis for equipment maintenance. Although deep learning methods have made significant progress in RUL prediction research due to their powerful feature extraction capabilities, existing technologies still have the following core limitations, restricting improvements in prediction accuracy and engineering applicability: I. Limitations of Multi-Source Feature Extraction and Temporal Dependency Modeling Limited data sources and insufficient feature representation: Existing studies mostly rely on single-type state information such as vibration signals for equipment health monitoring, which is insufficient to comprehensively represent the complex degradation states of equipment. Traditional feature extraction methods often suffer from difficulties in feature selection and insufficient representation of degradation states.

[0003] Temporal modeling limitations: Mainstream deep learning frameworks, such as traditional convolutional neural networks (CNNs), suffer from small receptive fields and difficulty in effectively learning long-term dependencies in signals. Furthermore, when dealing with time series problems, traditional convolutional operations may cause the output to depend on inputs at future times, leading to information leakage and affecting temporal consistency.

[0004] Lack of in-depth time-frequency fusion mining: Real-time sensor monitoring data has significant nonlinear characteristics. Existing methods struggle to efficiently integrate multi-source heterogeneous time-domain and frequency-domain features to construct accurate health indicators (HI) or degradation features, impacting the final prediction accuracy.

[0005] II. Subjectivity in the Division of Degradation Stages and Prediction of the Starting Time Traditional segmentation methods suffer from low robustness: the original data is subject to noise interference, causing local fluctuations in the constructed HI curve, which interferes with the judgment of degradation trends. Traditional threshold identification methods only detect anomalies when the data deviates significantly from the normal range, lacking sensitivity to the rate of data change and thus exhibiting low robustness.

[0006] III. Insufficient generalization capability across operating conditions Degradation distribution differences and limited generalization: Existing RUL prediction methods lack generalization ability under different operating conditions. There are significant differences in degradation distribution between training (source domain) and testing (target domain) devices, resulting in poor cross-domain adaptability and low robustness of the model in practical applications. At the same time, existing methods often rely on data from a single domain, ignoring cross-domain information integration, which increases model complexity and reduces training and prediction efficiency.

[0007] To address the aforementioned limitations, this invention proposes an engine RUL prediction method based on physical causal logic and linear complexity state space. Through deep network structure innovation, data preprocessing optimization, and cross-domain training strategies, it aims to comprehensively improve the accuracy, stability, and cross-condition adaptability of RUL prediction. Summary of the Invention

[0008] This invention proposes an engine RUL prediction method based on physical causal logic and linear complexity state space, comprising the following steps: Step 1: Simultaneously collect vibration and sound pressure signals during the operation of mechanical equipment; use a causal discovery algorithm based on maximum information transmission entropy to analyze the causal relationship between the sensors corresponding to the vibration and sound pressure signals as variables, and construct a feature causal graph reflecting the energy transfer and fault driving logic of engine components; remove irrelevant variables based on the causal graph, and perform time window timing alignment on key feature subsets; Step 2: The aligned temporal and frequency domain features are input into a dual-channel embedding layer. The embedding layer uses a causal convolution-based structure to extract local degradation features along the time or frequency axis and maintains the temporal causality of the prediction through a unidirectional information flow mechanism. The local degradation features are connected to an adaptive feature pruning module, which evaluates the contribution of different sensors to the degradation state representation in real time through an importance scoring layer based on nonlinear mapping and generates a dynamic weight mask. The dynamic weight mask is applied to the local degradation features to generate a treated feature sequence. Step 3: Input the treated feature sequence into a deep modeling architecture with linear complexity; use the state evolution mechanism to capture the transient dynamics of time-domain features under long periods, and simultaneously use the spectrum mixing mechanism to extract the nonlinear coupling information of frequency-domain features between channels; realize the deep interaction and alignment of time-domain semantic features and frequency-domain spectral features through the cross-domain association mechanism to generate enhanced degradation features with time-frequency coupling characteristics. Step 4: Use the feature fusion module to perform dimensional integration and weighted update on the enhanced degradation features; then, map the feature vector after dimensional integration and weighted update to the regression prediction space, and output the predicted value of the remaining service life of the engine by introducing a joint optimization strategy including physical dynamic constraints.

[0009] Specifically, the causal discovery algorithm in step 1 is as follows: First, exponential smoothing is performed on the original vibration signal and sound pressure signal to suppress random industrial noise by adjusting the smoothing factor. Subsequently, the transfer entropy was used to measure the directional information flow between different sensor variables, and the directional driving relationship between sensor variables was established based on the asymmetry of information transfer. Simultaneously, the maximum information coefficient is introduced to identify nonlinear relationships between variables, and a feature causal graph is constructed in combination with the driving relationship to identify the core feature subset that has a direct physical driving effect on the device degradation path.

[0010] Specifically, the adaptive feature pruning module in step 2 includes: The importance scoring layer uses a non-linear activation function to evaluate the importance of each feature channel after causal convolution in real time and calculates its contribution score to the current degradation state. The contribution scores are sorted by numerical value, and the scores of the corresponding sorted positions are extracted as dynamic pruning thresholds; a dynamic weight mask composed of binary elements is generated by comparing the contribution scores with the dynamic pruning thresholds.

[0011] Specifically, the state evolution mechanism in step 3 is implemented using a state-space model with selective scanning characteristics. The state-space model introduces an input-dependent parameterized mapping function and performs dynamic weight updates based on the transient fluctuations of the input signal through the state transition matrix, thereby achieving synchronous capture of degradation trends and transient characteristics in the ultra-long sequence of the engine's entire lifespan under linear computational complexity.

[0012] Specifically, the spectral mixing mechanism in step 3 adopts a computational structure based on Einstein Fast Fourier Transform (EinFFT). The computational structure uses tensor multiplication in the frequency domain to achieve deep mixing of cross-channel features, and separates the high-frequency details and low-frequency semantic components of the signal through the principle of frequency energy compression, thereby extracting the implicit degradation features caused by mechanical nonlinear coupling.

[0013] Specifically, the cross-domain association mechanism in step 3 adopts a bidirectional cross-attention structure; the bidirectional cross-attention structure matches the query vector generated by the time channel with the key value vector generated by the frequency channel to adaptively identify the correspondence between the time-domain abrupt component and the frequency-domain harmonic features, thereby generating enhanced degradation features with strong noise resistance.

[0014] Specifically, the physical and dynamic constraints in step 4 include: During the training phase, automatic differentiation techniques are used to calculate the time derivative of the hidden state of the neural network. A physical residual loss term is constructed to force the evolution trajectory of the implicit state to conform to a preset first-order thermodynamic equation or mechanical wear differential equation, thereby ensuring that the remaining service life prediction trajectory maintains physical consistency and evolutionary logic coherence in the sparse data region.

[0015] Specifically, the joint optimization strategy in step 4 also introduces an uncertainty quantification mechanism; the uncertainty quantification uses conformal prediction technology to calibrate the regression prediction value and outputs a remaining useful life confidence interval with strict coverage guarantee, which is used to evaluate the reliability of the prediction results and guide predictive maintenance decisions.

[0016] Specifically, the prediction process further includes a cross-condition domain adaptation step: using the maximum mean difference metric to calculate the feature distribution difference between the training engine and the test engine in the regenerative kernel Hilbert space, and minimizing the distribution difference to achieve cross-domain alignment of degraded features, thereby enhancing the generalization accuracy of the model under variable speed and variable load environments.

[0018] This invention also discloses an engine RUL prediction device based on physical causal logic and linear complexity state space, comprising: A multi-source sensor array is used to acquire vibration and sound pressure signals in real time. Memory is used to store computer program instructions; The processor is configured to execute the computer program instructions to implement the RUL prediction method; the device achieves real-time health management based on a physical-data dual-drive mode through a cloud-edge collaborative architecture. Attached Figure Description

[0019] Figure 1 This is a flowchart of the engine RUL prediction method based on physical causal logic and linear complexity state space proposed in this invention. Detailed Implementation

[0020] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] This invention proposes an engine Remaining Useful Life (RUL) prediction method based on physical causal logic and a linear complexity state space. This embodiment details the complete process of data preprocessing and causal filtering in the engine RUL prediction framework. This process aims to transform highly redundant and noisy raw sensor data into a subset of key features with physical consistency and logical correlation through information theory.

[0022] The process of this method is as follows: Figure 1 As shown, it specifically includes: Step 1: Simultaneously collect vibration and sound pressure signals during the operation of mechanical equipment; use the causal discovery algorithm based on maximum information transfer entropy (MITE) to analyze the causal relationship between vibration and sound pressure sensor variables, and construct a feature causal graph reflecting the energy transfer and fault driving logic of engine components; eliminate irrelevant variables based on the causal graph, and perform time window timing alignment on key feature subsets.

[0023] Multi-source synchronous signal acquisition and hardware configuration, specifically in specific industrial application scenarios, this embodiment selects a high-precision data acquisition system to monitor the engine throughout its entire life cycle.

[0024] Sensor deployment: Two sets of heterogeneous sensor arrays are symmetrically arranged at horizontal positions on the surface of the engine housing.

[0025] Vibration monitoring unit: Employs two IEPE accelerometers, model CT1005LC (sensitivity...). Range It is used to capture high-frequency mechanical shock wave signals generated by tooth surface wear, pitting, or tooth breakage.

[0026] Acoustic monitoring unit: Two YSV5001 ICP-type sound pressure sensors are synchronously arranged (sensitivity) Range It is used to collect the air sound pressure change signal generated by the deterioration of lubrication condition and mechanical vibration radiation.

[0027] Data Acquisition Parameter Settings: The sampling frequency of the signal acquisition instrument (model DH5981) is set to... It adopts a timed trigger mode, automatically collecting 1 second of steady-state data every 3 minutes to ensure that the monitoring points cover the entire process from healthy operation to complete failure.

[0028] Industrial noise suppression based on exponential smoothing specifically includes addressing the issue that the original signal often contains random impulse noise and white noise from measuring instruments. Before performing causal inference, the system processes the original sequence... Perform simple exponential smoothing: Among them, smoothing factor The value is set to 0.3. This operation assigns a higher weight to recent observations, which, while filtering out random industrial fluctuations, enhances the significance of long-term degradation trends hidden in the signal, laying the foundation for the stability of subsequent Maximum Information Transfer Entropy (MITE) calculations.

[0029] Causal discovery algorithm based on Maximum Information Transmission Entropy (MITE) The system employs the MITE-CM (Most Information Transmission Entropy-Based Causal Modeling) algorithm to quantitatively analyze the directional information flow between vibration and sound pressure variables. The specific calculation logic is as follows: Transfer entropy (TE) calculation: for any two sensor variable sequences and The algorithm calculates Historical information on reducing The contribution of future state uncertainty is used to measure the directional impact: calculate and .

[0030] Determining the direction of cause and effect: If Then, it is established in terms of physical logic. For "driving source (cause)", The term "response term (effect)" is used to establish a directed causal edge between the two.

[0031] Nonlinear coupling capture: A maximum information coefficient (MIC) network is introduced to correct the bias of the transfer entropy when capturing extremely complex nonlinear interactions, ensuring that the non-steady-state correlations generated during the severe degradation phase of the engine are not missed.

[0032] Feature-based causal graph construction: Treating each sensor signal dimension as a node and the established directed causal relationships as edges, a topology graph reflecting the energy transfer and fault-driving logic of internal engine components is constructed. For example, the strongly directional edge between motor speed and vibration amplitude, and the coupling edge between main shaft vibration and air sound pressure.

[0033] Redundant variable removal and feature subset optimization specifically include: based on the generated feature causal graph, the implementation example performs dynamic governance on the input features. Removal principles include constant value filtering, removing features that appear as isolated nodes in the graph and whose mean drift is close to zero. For example, in testing, sensor signals such as S1 (inlet temperature), S5 (inlet pressure), and S10 (pressure ratio) were found to be almost constant throughout their lifespan, lacking explanatory power for equipment degradation; therefore, they were removed as redundant variables.

[0034] Non-causal node removal: Remove random perturbation variables that, although numerically weakly correlated with remaining lifetime, are outside the physical causal chain.

[0035] Key subset determination: Finally, 14 types of sensor variables (such as effective vibration bandwidth energy, sound pressure harmonic ratio, etc.) that have a direct physical driving effect on fault evolution were retained as the core feature subset.

[0036] To address the dimensional mismatch between heterogeneous multi-source data (time-domain normalized vibration and frequency-domain FFT sound pressure) during time window alignment and segmentation, the system employs a sliding time window alignment technique. Window parameters: Set the fixed time window length (i.e., containing 30 consecutive valid sampling points), with the sliding step size set to 1.

[0037] Alignment implementation: The time-domain feature sequence after Z-score normalization and the frequency-domain feature sequence after Fast Fourier Transform (FFT) are segmented and truncated under the same time base.

[0038] Feature concatenation: Using time window concatenation technology, the above-mentioned segmented features are strictly aligned and arranged according to the timeline order.

[0039] After the entire process of step 1 in this embodiment, the final output feature tensor not only eliminates environmental noise and redundant information through causal filtering, but also has a unified time dimension scale, providing high-quality logical input data for subsequent Mamba state evolution modeling or dual-channel CNN embedding layers with linear complexity.

[0040] Step 2: Input the aligned time-domain features and frequency-domain features into the dual-channel embedding layer respectively; The embedding layer uses a causal convolution-based structure to extract local degradation features along the time or frequency axis, and strictly maintains the temporal causality of the prediction through a unidirectional information flow mechanism; The local degradation features are connected to the adaptive feature pruning module, which evaluates the contribution of different sensors to the degradation state representation in real time through an importance scoring layer based on nonlinear mapping, and generates a dynamic weight mask.

[0041] This stage achieves efficient dimensionality reduction and redundancy management of multi-source heterogeneous signals (such as vibration and sound pressure) by constructing a parallel embedding architecture with temporal causality protection and coupling a nonlinear scoring-driven pruning mechanism, laying a logical data foundation for subsequent linear complexity state space modeling.

[0042] Step 2.1: Dual-channel causal feature extraction The aligned multi-source signals enter the parallel embedding channel.

[0043] Time channel processing: for vibration signals Through two sets of causal convolution modules, using the convolution kernel size Step length Fill the left side of the sequence. Zero elements. Physically, this ensures that the engine... The time prediction is based solely on The study of its prior mechanical wear history eliminates the "prophetic bias" in industrial diagnostics.

[0044] Frequency channel processing: for FFT sound pressure signals Using a smaller max-pooling kernel ( Feature compression is performed. By using a smaller pooling receptive field, higher harmonic components in the acoustic pressure spectrum can be preserved more completely, which is crucial for capturing transient vibrations caused by bearing pitting.

[0045] Step 2.2: Calculation of nonlinear importance score The system calls formula (E2-1) to score the primary degradation features extracted from the dual channels.

[0046] The importance scoring layer quantifies the contribution of channel features using formula (E2-1): : Input feature tensor. Where For batch size, The time window length (e.g., 30 sampling points). The total number of sensor channels (e.g., 14 key variables after MITE filtering). : Dimensionality reduction weight matrix. Its algorithm aims to compress the input feature dimension to half and learn cross-modal correlations between channels through parameter sharing (cooperative feature extraction). Physically, it represents the common mapping of vibration and sound pressure signals in terms of degradation trends. : The bias term of the first-layer mapping. Used to correct the feature distribution offset caused by differences in sensor range. Activation function. Its core function is to introduce nonlinear features, eliminate interference components with negative contributions, and ensure that only degraded signal features with positive gain are retained. Feature aggregation weights. The latent variables, after dimensionality reduction, are weighted and aggregated into a single-dimensional raw score. (Sigmoid function): A probability mapping operator. It compresses the score to... The range is defined as follows: the closer the score is to 1, the stronger the sensor channel's ability to characterize the current engine wear state; the closer it is to 0, the more redundant noise the channel represents at that moment.

[0047] The scoring layer learns automatically during training using the backpropagation algorithm. and The parameters. If at a certain moment the sensor The (inlet temperature) signal is almost constant, then It will be automatically adjusted to an extremely low level.

[0048] Step 2.3: Dynamic Pruning and Mask Generation Based on the current layer depth, calculate the number of features that should be retained using formula (E2-2). .

[0049] The pruning scale is dynamically adjusted with network depth using formula (E2-2): The number of valid feature channels retained in the current network layer. Initial input feature size (in this example, set to 14 or 21 types of sensor input). (Attenuation rate): Preset coefficient (set to 0.9 in this embodiment). It reflects the natural compression ratio as features evolve from "low-level perception" to "high-level abstraction" with increasing network depth. Network layer index (incrementing from 0). Ensures that deeper networks process more refined high-level semantic features. Lower bound for feature retention. This serves as a fallback for the algorithm, preventing overfitting and the complete loss of crucial information in deep networks.

[0050] Sort and filter: sort the rating vectors Sort by numerical value in descending order.

[0051] Threshold extraction: Take the first threshold value from the sorted results. The score for each position is a dynamic threshold. .

[0052] Mask construction: Generate a binary weighted mask according to formula (E2-3). Any score lower than The mask bit of the channel is set to 0; otherwise, it is set to 1.

[0053] in, Indicates the first The mask value for each feature channel. A value of 1 indicates that the channel is a "valid feature" and is allowed to proceed to the subsequent deep modeling stage. A value of 0 indicates that the channel is "redundant noise" and the data in that channel will be physically removed.

[0054] : Represents the first The non-linear importance score of each channel. This score is calculated by formula (E2-1) through a scoring layer, and the value typically ranges from [value range missing]. Between 1 and 0. The closer the score is to 1, the stronger the sensor signal's ability to characterize the engine's degradation state; the closer it is to 0, the higher the redundancy.

[0055] : Represents the dynamic pruning threshold. Extraction logic: The system calculates the scores of all channels. Sort in descending order, take the first... The score at each position serves as the dividing line. Dynamism: It will change dynamically as the network depth increases because the number of features is preserved. It evolves with the number of network layers.

[0056] This mask is applied to the original feature tensor via a Hadamard product (element-wise multiplication): This allows sensor signals such as S1 (temperature) and S5 (pressure), whose values ​​remain essentially unchanged throughout their lifespan and therefore fail to reflect degradation trends, to be eliminated in real time.

[0057] By masking unimportant feature bits to zero, the processed feature tensor becomes sparse, which significantly reduces the computational density of matrix operations in subsequent backbone networks (such as the Mamba state-space model or Transformer), and the number of model parameters can be reduced by more than 98%.

[0058] This mechanism forces the model to ignore subtle disturbances caused by random environmental noise, ensuring that RUL (Remaining Useful Life) predictions always focus on the physical causal variables that truly drive mechanical failure.

[0059] Step 2.4: Element-level governance and output Perform the Hadamard product operation: .

[0060] Algorithm Results: Redundant channel data values ​​are directly zeroed out, eliminating invalid information flow at the tensor level. The processed tensor retains its original dimensions but increases sparsity, significantly reducing the computational density of the state transition matrix in subsequent Mamba blocks. In a full-lifecycle experiment for a certain type of industrial engine, this step achieved the following technological breakthroughs: Optimized computational efficiency: Through dynamic pruning, the number of effective parameters entering the deep backbone network is reduced by approximately 98.1%, enabling the RUL model to have real-time inference capabilities on resource-constrained industrial edge gateways. Improved diagnostic accuracy: Compared to traditional full-channel input, the pruning mechanism, through "refining," filters out random environmental noise interference (such as motor electromagnetic noise), improving the RMSE index of RUL prediction by approximately 6% on complex subsets such as FD004. Enhanced feature interpretability: Through visualization masks... By observing the changing patterns, maintenance personnel can clearly understand which sensors play a leading role in early warning under what load conditions, thereby improving the transparency of the industrial PHM system.

[0061] Step 3: Input the treated feature sequence into a deep modeling architecture with linear complexity; use the state evolution mechanism to capture the transient dynamics of time-domain features under long periods, and simultaneously use the spectrum mixing mechanism to extract the nonlinear coupling information of frequency-domain features between channels; realize the deep interaction and alignment of time-domain semantic features and frequency-domain spectral features through the cross-domain association mechanism to generate enhanced degradation features with time-frequency coupling characteristics.

[0062] The input data is the enhanced feature sequence output from "Step 2", specifically including the time-domain input: denoted as ,in For dynamic masking The processed, effective sensor channels. These signals retain the original impact components caused by engine mechanical fatigue. For batch size, The time window length (e.g., 30 sampling points).

[0063] Frequency domain input: denoted as The signal originates from the FFT transform in step 1 and the frequency embedding in step 2, and includes the fault characteristic frequency and its harmonic clusters.

[0064] State evolution mechanism: Based on long-range temporal modeling using the selective scan model (Mamba), the system first performs state evolution... Initiate state-space modeling with selective scan characteristics. Compared to traditional Transformers... Complexity, this embodiment achieves The core logic of linear evolution is as follows: When the input depends on parameterized mapping, the model no longer uses a static state transition matrix, but instead uses three linear mapping layers. Current input Mapping to dynamic parameters of dependent content ; This represents the current input vector extracted from the processed time-domain sequence at time step t.

[0065] , representing the dynamic input projection matrix. It determines the extent to which degenerate information of the current input (such as instantaneous vibration amplitude) is absorbed into the latent state space; This represents the dynamic output mapping matrix. It is responsible for extracting the features most relevant to the RUL prediction from the hidden layers, enabling targeted feature selection. To represent the step size parameter, introduce... Activation function; This represents a linear mapping that is dependent on the input; it is a learnable linear layer. Its function is to map the original feature space to a control space, making the step size parameter no longer statically fixed but content-dependent. This gives the model the ability to adaptively adjust its "attention" at different degradation stages. This represents a learnable baseline parameter, typically used as a bias term or base step size for the linear transformation. It learns the average rate of device degradation during training, providing a global physical baseline for Δt.

[0066] In a physical sense, when an engine experiences a momentary impact or a "capacity regeneration" phenomenon, The step size parameter dynamically adjusts the absorption weights for the current state, ensuring that the model can accurately capture non-stationary degradation fluctuations.

[0067] The linear complexity evolution equation is discretized using the zero-order preservation (ZOH) technique, and the state variables... Follow the trajectory below: Through this mechanism, the model can perform real-time inference on data spanning thousands of sampling points throughout its entire lifecycle without losing long-range dependencies.

[0068] Spectral Mixing Mechanism: Frequency Domain Feature Extraction Based on Einstein Fast Fourier Transform (EinFFT) Simultaneously, for the frequency domain branch In this embodiment, the EinFFT structure is used to extract cross-channel nonlinear coupling information: Spectral transformation: Performing a 2D-FFT on the input projects the features into the complex space. Separate high-frequency details (wear spikes) from low-frequency semantics (steady-state loads).

[0069] Tensor Multiplication Spectral Mixing: Channel interaction in the frequency domain is achieved using Einstein matrix multiplication (EMM). This involves adjusting the channel dimensions... Split into subgroups Perform tensor shrinkage operation: in It is a learnable complex weight tensor.

[0070] Energy compression and inverse transformation: Based on the principle of energy compression, low-energy noise components in the frequency domain are removed, and then... Mapping the signal back to the real domain outputs high-level frequency domain features with cross-channel coupling characteristics. .

[0071] Cross-domain association mechanism: Time-frequency semantic alignment based on bidirectional cross-attention To address the semantic mismatch between time-domain abrupt changes and frequency-domain spectral features, the system introduces a bidirectional cross-attention module for deep interaction. 1. Querying and cross-domain generation of key-value pairs Generate query vectors from time-domain state evolution results Generate key-value pairs from the frequency domain spectral mixing results. .

[0072] 2. Dynamic alignment mapping Identify the association weights between two domains using scaled dot product attention: The process aims to identify which segment of abnormal vibration peaks in the time domain is caused by a specific inter-tooth meshing frequency or its harmonic failure in the frequency domain.

[0073] Through two-way interaction, that is: simultaneous execution and Through careful computation, the model can mutually suppress independent random noise in each domain, ultimately outputting an enhanced degradation feature with "time-frequency coupling characteristics". .

[0074] In the engine RUL test of this embodiment, the specific technical gain of step 3 is as follows: Leap in computational efficiency: Leveraging Mamba's linear complexity, inference speed is improved by approximately 66.4% compared to the traditional Transformer when processing long sequences with more than 60 time windows.

[0075] Coupling feature accuracy: The nonlinear high-frequency coupling features caused by pitting on the tooth surface were captured by EinFFT, which made the prediction accuracy (RMSE) of the subsequent step 4 on the complex subset of FD004 significantly better than that of the single branch model.

[0076] Physical consistency alignment: The cross-domain association mechanism ensures that the model output is no longer an isolated value, but an enhanced degenerate representation verified by time-frequency logic, providing a higher quality feature benchmark for subsequent embedding of physical dynamic constraints.

[0077] Step 4: The enhanced degradation features are integrated and weighted using the feature fusion module. Then, the fused feature vector is mapped to the regression prediction space. By introducing a joint optimization strategy including physical and dynamic constraints, the remaining service life prediction value of the engine is output.

[0078] The input data for this step is the enhanced degradation feature vector output from "Step 3". .

[0079] Feature fusion module: Dimensional integration and weighted update The system first performs further spatial dimension compression and weight refinement on the input coupled features: Step 4.1. Feature Connectivity and Multi-Head Self-Attention Fusion The features of the time path and frequency path are concatenated along the channel dimension, and then a feature with... The layer's feature fusion encoder (using a Transformer block structure) utilizes four internally configured attention heads to dynamically evaluate the relative contributions of temporal semantics and frequency domain details at the current degradation stage. This process enables real-time updates of feature weights, ensuring that the model focuses more on steady-state load features during the engine's "stable period" and automatically shifts its focus to high-frequency impact features during the "severe degradation period".

[0080] Step 4.2. Global Pooling and Dimension Degradation To transform the temporal tensor into a decision vector, Performing global average pooling eliminates time axis redundancy, resulting in a compact vector representing the current health state of the device. .

[0081] Regression Prediction Module: Mapping to RUL Space The pooled feature vectors are mapped to the scalar prediction space through a multilayer perceptron (MLP) architecture: Structure configuration: The MLP contains three fully connected layers, with the following number of neurons: .

[0082] Activation function: The first two layers use To maintain nonlinear characteristics, the final output layer adopts... The function normalizes the RUL predictions to The interval, in which Represents the initial state of health. This indicates that the equipment has failed.

[0083] Joint optimization strategy: embedding physical and dynamic constraints The core innovation of this embodiment lies in not relying entirely on data fitting, but rather using the principle of Physical Information Neural Network (PINN) to forcibly embed the physical evolution law of engine degradation into the loss function.

[0084] When constructing the physical dynamic residuals, the differentiability of the neural network is utilized to calculate the degradation state predicted by the model through automatic differentiation techniques. (i.e., hidden layer states) relative to time The derivative of . Assume engine degradation follows a first-order wear kinetic model: in, Represents Physical Dynamics Residual Loss, a core component of the Physical Information Neural Network (PINN) framework, used to transform prior physical laws into constraints during neural network training. The current load collected by the sensor, For real-time temperature, and These are learnable or pre-defined mechanical and physical constants. This loss term forces the model's characteristic evolution to conform to the physical laws of energy dissipation and wear accumulation. These are the external environmental state variables collected in real time by sensors during equipment operation, used to describe the thermal field background outside the equipment.

[0085] The process of co-updating the total loss function and hyperparameters includes: constructing the total loss function. Jointly optimize regression error, physical residuals, and cross-condition distribution differences (MMD): In this embodiment, the weight coefficients are determined by grid search: (Ensure basic accuracy). (Enhancing physical consistency) (Improving generalization). The system uses the Adam optimizer and iteratively updates with an initial learning rate of 0.00005.

[0086] Through the deep integration and physical constraints of this step, the present invention achieves the following technical effects: Predicted stability: Even when industrial sensors are subjected to strong electromagnetic interference that generates severe noise (such as random jumps that were not completely filtered out in steps 1 and 2), the physical constraint term... It can also "correct" the predicted trajectory back to a smooth degradation path that aligns with physical intuition.

[0087] Zero-shot adaptability: When target working condition data is extremely scarce (small sample size), the generalization accuracy of the model is improved by about 15.6% compared with the pure data-driven model by relying on the transfer learning strategy guided by physical laws.

[0088] Decision credibility: With the help of conformal prediction technology, step 4 not only outputs point estimates, but also provides a 95% confidence interval, which effectively supports predictive maintenance decisions in high-safety-demand scenarios such as nuclear power and aviation.

[0089] Furthermore, in order to address the problem of decreased generalization accuracy caused by the mismatch between the data distribution of the training domain (source domain) and the measured domain (target domain) in industrial engines under variable speed and variable load environments, this embodiment introduces a domain adaptation mechanism based on Maximum Mean Discrepancy (MMD) in the regression prediction process of step 4.

[0090] The system will use the enhanced degradation features generated in step 3 Divided into source domains (Training engine from known lifecycle data) and target domain (From the engine under test in the field). To measure the difference between the two in a nonlinear space, this embodiment utilizes a nonlinear mapping function. The features are projected into a high-dimensional regenerative kernel Hilbert space (RKHS).

[0091] In this high-dimensional space, the difference in distribution between two domains is quantified as the distance between their feature means. According to Mercer's Theorem, this mapping can be achieved using the kernel trick, thus avoiding explicit computation. The resulting dimensional catastrophe.

[0092] This embodiment uses a mathematical model metric based on the maximum mean difference (MMD), and its loss function... As a penalty for cross-domain inconsistency, its specific calculation formula is as follows: in: and These represent the sample sizes of the source and target domains, respectively. and The output of step 3 is a feature vector that incorporates high-level time-frequency semantics; This represents the squared norm in RKHS.

[0093] By minimizing The model mandates that the degradation characterization extracted from the dual-channel, especially the Mamba and EinFFT coupling layer, be “condition-independent,” meaning that the model focuses more on the intrinsic degradation trend caused by wear, rather than the signal amplitude jump caused by load variations.

[0094] During the training phase, the processor executes instructions from memory to construct the total loss function. This achieves a synergistic balance between regression accuracy and domain generalization performance. This embodiment optimizes the combination of trade-off parameters using a grid search algorithm. and .

[0095] : Represents the mean squared error (MSE) between the predicted RUL of the source domain sample and the true label, ensuring the basic accuracy of the prediction.

[0096] : Represents cross-domain distribution differences. As a regularization term, it guides the network to optimize the weights of the feature extraction layer during backpropagation, thereby forcing the degenerate features of the source and target domains to align spatially.

[0097] In experimental verification based on a certain type of 2-stage reduction engine, this embodiment demonstrates significant technical advantages: Cross-condition adaptability: When the engine switches from rated load (0.8A) to overload condition (1.2A), the prediction error of the basic model without integrated MMD module will increase sharply; however, the method in this embodiment stabilizes the cross-domain prediction accuracy (MAE) at around 0.061 by aligning the distribution in RKHS, and the generalization performance is improved by more than 15% compared with the traditional data-driven method.

[0098] Enhanced temporal consistency: By combining the causal convolution in step 2 with the MMD alignment in step 4, the model can accurately identify the "effective degradation signal" during speed fluctuations, avoiding the pseudo "capacity regeneration" phenomenon caused by operating condition switching, and ensuring the smoothness and physical rationality of the RUL prediction trajectory.

[0099] This invention also discloses an engine RUL prediction device based on physical causal logic and linear complexity state space, comprising: A multi-source sensor array is used to acquire the vibration signal and sound pressure signal in real time; Memory is used to store computer program instructions; The processor is configured to execute the computer program instructions to implement the RUL prediction method; the device achieves real-time health management based on a physical-data dual-drive mode through a cloud-edge collaborative architecture.

[0100] Through the above architecture design, this embodiment achieves significant improvements in the following dimensions: due to the embedding of physical dynamics "hard constraints", the prediction results avoid physical logic paradoxes that may occur in traditional black box models, such as the sudden rebound of RUL in the severe wear stage.

[0101] The cloud-edge collaboration mechanism reduces edge-side inference latency by 66.4%, and maintains control accuracy above 97.3% even in data-sparse (small sample) scenarios. It should be understood that the processor in this embodiment may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method embodiment can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software module can reside in a mature storage medium in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0102] It is understood that the memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). It should be noted that the memory used in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

Claims

1. A method for predicting the RUL (Restricted Limiting Rank) of an engine based on physical causal logic and a linear complexity state space, characterized in that, Includes the following steps: Step 1: Simultaneously collect vibration and sound pressure signals during the operation of mechanical equipment; use a causal discovery algorithm based on maximum information transmission entropy to analyze the causal relationship between the sensors corresponding to the vibration and sound pressure signals as variables, and construct a feature causal graph reflecting the energy transfer and fault driving logic of engine components; remove irrelevant variables based on the causal graph, and perform time window timing alignment on key feature subsets; Step 2: The aligned temporal and frequency domain features are input into a dual-channel embedding layer. The embedding layer uses a causal convolution-based structure to extract local degradation features along the time or frequency axis and maintains the temporal causality of the prediction through a unidirectional information flow mechanism. The local degradation features are connected to an adaptive feature pruning module, which evaluates the contribution of different sensors to the degradation state representation in real time through an importance scoring layer based on nonlinear mapping and generates a dynamic weight mask. The dynamic weight mask is applied to the local degradation features to generate a treated feature sequence. Step 3: Input the treated feature sequence into a deep modeling architecture with linear complexity; The transient dynamics of time-domain features under long periods are captured by the state evolution mechanism, and the nonlinear coupling information of frequency-domain features between channels is extracted by the spectrum mixing mechanism. The deep interaction and alignment of time-domain semantic features and frequency-domain spectral features are realized through the cross-domain correlation mechanism to generate enhanced degradation features with time-frequency coupling characteristics. Step 4: Use the feature fusion module to perform dimensional integration and weighted update on the enhanced degradation features; then, map the feature vector after dimensional integration and weighted update to the regression prediction space, and output the predicted value of the remaining service life of the engine by introducing a joint optimization strategy including physical dynamic constraints.

2. The method according to claim 1, characterized in that, The causal discovery algorithm in step 1 is specifically as follows: First, exponential smoothing is performed on the original vibration signal and sound pressure signal to suppress random industrial noise by adjusting the smoothing factor. Subsequently, the transfer entropy was used to measure the directional information flow between different sensor variables, and the directional driving relationship between sensors as variables was established based on the asymmetry of information transfer. Simultaneously, the maximum information coefficient is introduced to identify nonlinear relationships between variables, and a feature causal graph is constructed in combination with the driving relationship to identify the core feature subset that has a direct physical driving effect on the device degradation path.

3. The method according to claim 1 or 2, characterized in that, The adaptive feature pruning module in step 2 specifically includes: The importance scoring layer uses a non-linear activation function to evaluate the importance of each feature channel after causal convolution in real time and calculates its contribution score to the current degradation state. The contribution scores are sorted by numerical value, and the scores of the corresponding sorted positions are extracted as dynamic pruning thresholds; a dynamic weight mask composed of binary elements is generated by comparing the contribution scores with the dynamic pruning thresholds.

4. The method according to claim 1, characterized in that, The state evolution mechanism in step 3 is implemented using a state-space model with selective scanning characteristics. The state-space model introduces an input-dependent parameterized mapping function and performs dynamic weight updates based on the transient fluctuations of the input signal through the state transition matrix, thereby achieving synchronous capture of degradation trends and transient characteristics in the ultra-long sequence of the engine's entire lifespan under linear computational complexity.

5. The method according to claim 4, characterized in that, The spectral mixing mechanism in step 3 adopts a computational structure based on Einstein Fast Fourier Transform (EinFFT). The computational structure uses tensor multiplication in the frequency domain to achieve deep mixing of cross-channel features, and separates the high-frequency details and low-frequency semantic components of the signal through the principle of frequency energy compression, thereby extracting the implicit degradation features caused by mechanical nonlinear coupling.

6. The method according to claim 1, characterized in that, The cross-domain association mechanism in step 3 adopts a bidirectional cross-attention structure. The bidirectional cross-attention structure matches the query vector generated by the time channel with the key value vector generated by the frequency channel to adaptively identify the correspondence between the time-domain abrupt component and the frequency-domain harmonic features, thereby generating an enhanced degradation feature with strong noise resistance.

7. The method according to claim 1, characterized in that, The physical and dynamic constraints in step 4 specifically include: During the training phase, automatic differentiation techniques are used to calculate the time derivative of the hidden state of the neural network. A physical residual loss term is constructed to force the evolution trajectory of the implicit state to conform to a preset first-order thermodynamic equation or mechanical wear differential equation, thereby ensuring that the remaining service life prediction trajectory maintains physical consistency and evolutionary logic coherence in the sparse data region.

8. The method according to claim 1, characterized in that, The joint optimization strategy in step 4 also introduces an uncertainty quantification mechanism; the uncertainty quantification uses conformal prediction technology to calibrate the regression prediction value and outputs a remaining useful life confidence interval with strict coverage guarantee, which is used to evaluate the reliability of the prediction results and guide predictive maintenance decisions.

9. The method according to claim 8, characterized in that, The prediction process further includes a cross-condition domain adaptation step: using the maximum mean difference metric to calculate the feature distribution difference between the training engine and the test engine in the regenerative kernel Hilbert space, and minimizing the distribution difference to achieve cross-domain alignment of the degraded features, thereby enhancing the generalization accuracy of the model under variable speed and variable load environments.

10. An engine RUL prediction device based on physical causal logic and linear complexity state space, characterized in that, include: A multi-source sensor array for real-time acquisition of the vibration signal and sound pressure signal as described in claim 1; Memory is used to store computer program instructions; The processor is configured to execute the computer program instructions to implement the RUL prediction method according to any one of claims 1 to 9; the device realizes real-time health management based on a physical-data dual-drive mode through a cloud-edge collaborative architecture.

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