Fault prediction system and method based on chaos theory and hidden Markov model

Abstract

The invention discloses a fault prediction system and method based on a chaos theory and a hidden Markov model. According to the method, the features extracted through the chaos theory are extremely sensitive to tiny changes of the initial state of equipment, early nonlinear dynamic anomalies can be accurately recognized, maintenance personnel can find potential problems when faults are not obviously shown, and serious shutdown caused by missing report of the early faults is avoided. The chaotic features deeply excavate system nonlinear dynamic behaviors hidden in monitoring signals, even weak fault symptoms can be captured, a reliable basis is provided for extremely early fault early warning, the chaotic features serve as input of the hidden Markov model, the strong time sequence modeling capability of the hidden Markov model is utilized, and the fault early warning method can be applied to early fault early warning. The method not only can accurately judge the degradation stage of the current equipment, but also can carry out probabilistic prediction on the change trend of the future state, so that the evolution law of the nonlinear degradation process of the equipment is accurately described, and the prediction accuracy and adaptability are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of industrial equipment state monitoring, and particularly relates to a fault prediction system and method based on chaos theory and a hidden Markov model. BACKGROUND

[0002] In the modern industrial field, with the increasing complexity, automation and intelligentization of equipment, predictive maintenance technology has become a core means to ensure production safety, reduce operation and maintenance costs, and improve equipment operation efficiency. The goal is to analyze the operation data of the equipment, identify early fault signs, and accurately predict the remaining useful life of the equipment, so as to change the traditional "after-maintenance" or "periodic maintenance" into active "condition-based maintenance".

[0003] At present, the fault prediction methods in the industry can be mainly divided into the following categories: 1. Physical model-based method: This method relies on a deep understanding of the mechanism of the equipment, and establishes an accurate mathematical model to describe the degradation process. Although this method has good interpretability under the premise of accurate model, it is extremely difficult, even impossible, to establish an accurate physical model for a complex nonlinear system. At the same time, this method has poor universality and is difficult to adapt to changes in different types of equipment or operating conditions.

[0004] 2. Data-driven method: This method does not rely on a physical model, but directly learns the degradation law of the equipment from the historical data and real-time data of the equipment operation.

[0005] However, the core problems and difficulties existing in the prior art are that the single HMM method is limited by the quality of feature extraction and the linear assumption, and is not sensitive to early faults of systems with strong nonlinearity and chaotic characteristics; and the single chaos theory method lacks the ability to probabilistically model and predict the degradation process of the equipment throughout its life cycle. Therefore, there is a lack of an effective means to deeply integrate the deep features of a nonlinear dynamic system with a probabilistic state evolution model to achieve earlier, more accurate and more reliable fault prediction of complex industrial equipment. SUMMARY

[0006] The purpose of the present application is to solve the above-mentioned problems, and to provide a fault prediction system and method based on chaos theory and a hidden Markov model.

[0007] The technical solution adopted by the present application is as follows: a fault prediction system based on chaos theory and a hidden Markov model, comprising: a data acquisition module, a signal preprocessing module, a chaos feature extraction module, an HMM training and prediction module, and a man-machine interaction and early warning module; The chaos feature extraction module is internally provided with: Phase space reconstruction unit: using time delay coordinates method, according to the determined embedding dimension m and time delay τ, the one-dimensional time series signal is reconstructed into an m-dimensional phase space orbit to reproduce the topological properties of the original dynamic system.

[0008] Chaotic characteristic quantity calculation unit: on the basis of the reconstructed phase space, quantitative indexes capable of representing the dynamic characteristics of the system are calculated. The HMM training and prediction module is internally provided with: HMM training unit: using the chaotic characteristic sequence extracted from the historical data as the training set, a plurality of HMM models are trained, and each model corresponds to a preset health state stage. State recognition and prediction unit: for online monitoring data, the chaotic characteristic sequence thereof is extracted in real time and input into the trained HMM model.

[0009] In a preferred embodiment, a fault prediction method based on chaos theory and hidden Markov model comprises the following steps: Step S100: starting the fault prediction system; Step S101: data acquisition and preprocessing: acquiring the original time series signal x(t) through the sensor installed on the device. The acquired signal is preprocessed, including denoising and normalization, to obtain the clean signal sequence x'(t).

[0010] Step S102: phase space reconstruction: mapping the one-dimensional signal to a high-dimensional phase space to recover the dynamic characteristics of the system.

[0011] Step S103: calculating chaotic characteristic quantities to form observation sequences: in the reconstructed phase space, quantitative characteristics representing the nonlinear dynamic behavior of the system are calculated to form observation vectors. Step S200: model training and online prediction judgment. Determine the current data processing mode. If it is historical full life cycle data used for training, execute the offline model training process: steps S201-S203; if it is window data for real-time monitoring, execute the online prediction process: steps S301-S303.

[0012] Step S201: initializing HMM parameters: Step S202: using the Baum-Welch algorithm to iteratively train the HMM.

[0013] Step S203: saving the trained HMM model parameters, storing the final model parameters λ=(A, B, π) obtained after convergence into the system database for calling by the online prediction module.

[0014] Step S301: real-time state recognition.

[0015] Step S302: Failure prediction and remaining useful life (RUL) estimation, based on the identified current state and HMM model: Step S303: Result Output and Decision Support: The status identification results (e.g., "Currently in a slightly degraded state"), prediction information (e.g., "The probability of failure in the next 24 hours is 15%), and RUL estimates (e.g., "Remaining useful life is approximately 50 hours") are visualized on the human-machine interface. If the predicted risk is high, the system triggers an audible and visual alarm or sends a notification to maintenance personnel.

[0016] Step S400: Loop Monitoring. After completing the prediction for the current window, the system returns to step S101 to collect data for the next time period, realizing continuous, real-time status monitoring and fault prediction of the equipment.

[0017] In a preferred embodiment, in step S101, the raw time-series signal x(t) is acquired by a sensor (such as a vibration acceleration sensor) installed on the device. The acquired signal is preprocessed, including denoising (such as using wavelet thresholding) and normalization, to obtain a clean signal sequence x′(t).

[0018] In a preferred embodiment, step S102 specifically includes: Determining the time delay τ: The autocorrelation function method is used. Calculate the autocorrelation function of x′(t), and take the delay corresponding to its first zero crossing or when it drops to the initial value 1 / e as the optimal time delay τ.

[0019] Determine the embedding dimension m: Use the pseudo nearest neighbor method. Gradually increase the embedding dimension m. When the proportion of pseudo nearest neighbors is less than 5% or tends to stabilize, the corresponding minimum m is the optimal embedding dimension.

[0020] Reconstructing the phase space: Using the given τ and m, according to the formula Reconstructing the phase space yields the point set { (i)}.

[0021] In a preferred embodiment, step S103 specifically includes: Calculations are performed continuously in units of a sliding time window to form an observation sequence. Specifically, calculate at least two of the following characteristics: Correlation dimension D2: The Grassberger-Procaccia algorithm (GP algorithm) is used to calculate the correlation integral C(r) and find the slope of the scale-free region in double logarithmic coordinates.

[0022] Maximum Lyapunov exponent λ1: Using the small data method proposed by Wolf et al., the average divergence rate of adjacent trajectories in phase space is tracked. λ1>0 indicates that the system has chaotic characteristics.

[0023] Kolmogorov entropy K is calculated by correlation integrals under different embedding dimensions, and characterizes the information generation rate of the system.

[0024] In a preferred embodiment, step S201 specifically includes: Define the HMM model as λ=(A,B,π).

[0025] State set Q: Preset N health states such as {normal, slight degradation, severe degradation, fault}.

[0026] Observation probability B: Since the observed values ​​are continuous chaotic eigenvectors, B is set as a Gaussian mixture model (GMM), that is: The state transition matrix A and the initial state distribution π are initialized.

[0027] In a preferred embodiment, step S202 specifically includes: Based on the current model parameters λ(n) and the observation sequence O, the forward variable αt(i) and the backward variable βt(i) are calculated, and then the probability γt(i) of being in state i at time t and the state transition probability ξt(i,j) are obtained.

[0028] M-Step (Parameter Reestimation): Using the results of E-Step, update the model parameters through the reestimation formula. ; The revaluation formula is: The parameters cjk, μjk, Σjk of the GMM are also re-estimated by weighted γt(j); Convergence criterion: Calculate the likelihood function If the change in the value is less than a preset threshold, it is considered convergent, and step S203 is executed; otherwise, it is used... Alternative Return to E-Step to continue iteration.

[0029] In a preferred embodiment, in step S301, for the observation sequence Ocurrent obtained after processing the real-time data segment by S101-S103, the forward algorithm is used to calculate the probability P=Ocurrent|λi generated by each trained HMM model λi. =argmaxi[P(Ocurrent∣λi].

[0030] In a preferred embodiment, step S302, state prediction includes calculating the probability P(St+k=qfault|Ocurrent,λ) of being in a fault state after k time steps. When this probability exceeds a safety threshold, an early warning is triggered.

[0031] RUL estimation includes setting the device to state i. Based on the state transition probability matrix A, the expected time to first reach the fault state N from the current state i is calculated. The simplified RUL point estimation formula is as follows: .

[0032] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. In this invention, features extracted through chaos theory are extremely sensitive to minute changes in the initial state of equipment, enabling precise identification of early nonlinear dynamic anomalies. This allows maintenance personnel to detect potential problems before they become apparent, effectively preventing serious downtime caused by missed early fault reports. Chaotic features deeply explore the hidden nonlinear dynamic behavior of the system within monitoring signals, capturing even the faintest fault signs, providing a reliable basis for very early fault warnings.

[0033] 2. In this invention, chaotic features are used as input to a Hidden Markov Model (HMM). Leveraging the powerful temporal modeling capabilities of HMMs, the dynamic changes of chaotic features are transformed into a probabilistic evolution path of the equipment's health state. This not only accurately determines the current degradation stage of the equipment but also probabilistically predicts future trends, making the predictions more closely aligned with the actual operating conditions of the equipment. The probabilistic reasoning capabilities of HMMs enable a precise description of the evolutionary patterns of the equipment's nonlinear degradation process, significantly improving the accuracy and adaptability of the predictions.

[0034] 3. This invention, by combining chaotic analysis and hidden Markov models, provides richer predictive information. It not only indicates the possible timing of a failure but also clarifies the probability of the equipment being in each health state and the likelihood of transitioning to a more severe state. Maintenance personnel can clearly understand the current health status distribution of the equipment and the probability trend of future state changes, making the estimation of remaining useful life more reliable. This information provides a quantitative basis for maintenance decisions, avoiding resource waste caused by over-maintenance and preventing failures due to untimely maintenance, making condition-based maintenance more precise and efficient. Attached Figure Description

[0035] Fig. 1 This is a schematic diagram of the overall system block structure of the present invention; Fig. 2 This is a schematic diagram illustrating the principle of the method flow in this invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] Reference Figs. 1-2 The fault prediction system based on chaos theory and hidden Markov model includes: a data acquisition module, a signal preprocessing module, a chaotic feature extraction module, an HMM training and prediction module, and a human-computer interaction and early warning module. The data acquisition module is responsible for acquiring physical signals that reflect the operating status of the equipment, such as vibration acceleration signals, sound signals, and temperature signals, either in real time or offline. This module includes hardware devices such as sensors and data acquisition cards.

[0038] The signal preprocessing module receives the raw monitoring signal and performs preprocessing operations such as denoising, filtering, and detrending to eliminate environmental noise and irrelevant interference and improve the signal-to-noise ratio.

[0039] The chaotic feature extraction module is the innovative core module of this invention. It receives the preprocessed signal and performs the following key operations: ① Phase space reconstruction unit: Using the time delay coordinate method, based on the determined embedding dimension m and time delay τ, the one-dimensional time series signal is reconstructed into an m-dimensional phase space trajectory to reproduce the topological characteristics of the original dynamic system.

[0040] ② Chaotic characteristic quantity calculation unit: Based on the reconstructed phase space, calculates quantitative indicators that can characterize the dynamic properties of the system, such as:  Correlation dimension: used to quantify the complexity and degrees of freedom of a system.

[0041]  Maximum Lyapunov exponent: Used to determine whether a system is sensitive to initial conditions, i.e. whether it has chaotic characteristics. Its value turning from negative to positive or increasing significantly indicates the loss of system stability and is a strong sign of early failure.

[0042] Kolmogorov entropy: used to measure the information production rate of a system, reflecting the degree of disorder in the system; The internal settings of the HMM training and prediction module include: ① HMM training unit: The chaotic feature sequence extracted from historical data (covering the entire lifecycle data from normal to fault) is used as the training set. Multiple HMM models are trained using algorithms such as Baum-Welch. Each model corresponds to a preset health state stage (such as "healthy", "slightly degraded", "severely degraded" and "faulty").

[0043] ② State Recognition and Prediction Unit: For online monitoring data, the chaotic feature sequence is extracted in real time and input into the trained Hidden Markov Model (HMM). The probability of this sequence being generated by each HMM model is calculated using forward algorithms, and the state corresponding to the model with the highest probability is the most likely current state of the device. Furthermore, the Viterbi algorithm is used to analyze state transition paths, or the forward algorithm is used to predict the probability of future observation sequences, thereby achieving early warning of faults and probabilistic estimation of remaining useful life.

[0044] The human-computer interaction and early warning module presents the status recognition results, prediction information, remaining lifespan, etc. to the user in a visual manner (such as dashboard, trend chart), and issues audible and visual alarms or remote notifications when a dangerous state is identified or an impending failure is predicted.

[0045] This invention breaks free from the limitations of traditional time-domain and frequency-domain features, creatively using chaotic features (such as correlation dimension D2 and maximum Lyapunov exponent λ1) characterizing the nonlinear dynamics of equipment as core indicators of equipment health status. It directly addresses the problems of "traditional features being insensitive to early, minor faults" and "HMM being strongly dependent on the initial observation sequence." By introducing chaotic features that are extremely sensitive to changes in the system's initial state, HMM can "see" early signs of degradation that were previously "unseen."

[0046] This invention presents a deeply integrated architecture that works collaboratively and complements each other's functions. Chaos theory acts as a high-performance "feature extractor," specifically responsible for mining deep degradation information from nonlinear signals; while Hidden Markov Models (HMMs) act as a "state predictor," specifically responsible for time-series modeling and probabilistic prediction of these feature sequences with clear physical meaning. This addresses the limitations of single-technology approaches. This integrated model allows the results of chaos analysis to be effectively utilized by HMMs, while also ensuring that the predictive power of HMMs is based on more reliable and earlier-emerging feature changes.

[0047] A fault prediction method based on chaos theory and hidden Markov models includes the following steps: Step S100: Start the fault prediction system; Step S101: Data Acquisition and Preprocessing: The raw time-series signal x(t) is acquired through sensors installed on the device. The acquired signal is preprocessed, including denoising and normalization, to obtain a clean signal sequence x′(t).

[0048] Step S102: Phase space reconstruction: Map the one-dimensional signal to a high-dimensional phase space to recover the dynamic characteristics of the system.

[0049] Step S103: Calculate chaotic characteristic quantities and form an observation sequence: On the reconstructed phase space, calculate the quantitative characteristics that characterize the nonlinear dynamic behavior of the system and form an observation vector; Step S200: Model Training and Online Prediction Assessment. Determine the current data processing mode. If it is historical full-lifecycle data used for training, execute the offline model training process: steps S201-S203; if it is real-time monitored window data, execute the online prediction process: steps S301-S303.

[0050] Step S201: Initialize HMM parameters: Step S202: Iteratively train the HMM using the Baum-Welch algorithm.

[0051] Step S203: Save the trained HMM model parameters and store the final model parameters λ=(A,B,π) obtained after convergence into the system database for use by the online prediction module.

[0052] Step S301: Real-time status recognition.

[0053] Step S302: Failure prediction and remaining useful life (RUL) estimation, based on the identified current state and HMM model: Step S303: Result Output and Decision Support: The status identification results (e.g., "Currently in a slightly degraded state"), prediction information (e.g., "The probability of failure in the next 24 hours is 15%), and RUL estimates (e.g., "Remaining useful life is approximately 50 hours") are visualized on the human-machine interface. If the predicted risk is high, the system triggers an audible and visual alarm or sends a notification to maintenance personnel.

[0054] Step S400: Loop Monitoring. After completing the prediction for the current window, the system returns to step S101 to collect data for the next time period, realizing continuous, real-time status monitoring and fault prediction of the equipment.

[0055] In step S101, the raw time-series signal x(t) is acquired by a sensor (such as a vibration acceleration sensor) installed on the device. The acquired signal is preprocessed, including denoising (such as using wavelet thresholding) and normalization, to obtain a clean signal sequence x′(t).

[0056] Step S102 specifically includes: Determining the time delay τ: The autocorrelation function method is used. Calculate the autocorrelation function of x′(t), and take the delay corresponding to its first zero crossing or when it drops to the initial value 1 / e as the optimal time delay τ.

[0057] Determine the embedding dimension m: Use the pseudo nearest neighbor method. Gradually increase the embedding dimension m. When the proportion of pseudo nearest neighbors is less than 5% or tends to stabilize, the corresponding minimum m is the optimal embedding dimension.

[0058] Reconstructing the phase space: Using the given τ and m, according to the formula Reconstructing the phase space yields the point set { (i)}.

[0059] Step S103 specifically includes: Calculations are performed continuously in units of a sliding time window to form an observation sequence. Specifically, calculate at least two of the following characteristics: Correlation dimension D2: The Grassberger-Procaccia algorithm (GP algorithm) is used to calculate the correlation integral C(r) and find the slope of the scale-free region in double logarithmic coordinates.

[0060] Maximum Lyapunov exponent λ1: Using the small data method proposed by Wolf et al., the average divergence rate of adjacent trajectories in phase space is tracked. λ1>0 indicates that the system has chaotic characteristics.

[0061] Kolmogorov entropy K is calculated by correlation integrals under different embedding dimensions, and characterizes the information generation rate of the system.

[0062] Step S201 specifically includes: Define the HMM model as λ=(A,B,π).

[0063] State set Q: Preset N health states such as {normal, slight degradation, severe degradation, fault}.

[0064] Observation probability B: Since the observed values ​​are continuous chaotic eigenvectors, B is set as a Gaussian mixture model (GMM), that is: The state transition matrix A and the initial state distribution π are initialized.

[0065] Step S202 specifically includes: Based on the current model parameters λ(n) and the observation sequence O, the forward variable αt(i) and the backward variable βt(i) are calculated, and then the probability γt(i) of being in state i at time t and the state transition probability ξt(i,j) are obtained.

[0066] M-Step (Parameter Reestimation): Using the results of E-Step, update the model parameters through the reestimation formula. ; The revaluation formula is: The parameters cjk, μjk, Σjk of the GMM are also re-estimated by weighted γt(j); Convergence criterion: Calculate the likelihood function If the change in the value is less than a preset threshold, it is considered convergent, and step S203 is executed; otherwise, it is used... Alternative Return to E-Step to continue iteration.

[0067] In step S301, for the observation sequence Ocurrent obtained after processing the real-time data segment by S101-S103, the forward algorithm is used to calculate the probability P=Ocurrent|λi generated by each trained HMM model λi. =argmaxi[P(Ocurrent∣λi].

[0068] In step S302, state prediction includes calculating the probability P(St+k=qfault|Ocurrent,λ) of being in a fault state after k time steps. When this probability exceeds a safety threshold, an early warning is triggered.

[0069] RUL estimation includes setting the device to state i. Based on the state transition probability matrix A, the expected time to first reach the fault state N from the current state i is calculated. The simplified RUL point estimation formula is as follows: .

[0070] From the above, we can conclude that: In this invention, features extracted using chaos theory are extremely sensitive to minute changes in the initial state of equipment, enabling precise identification of early nonlinear dynamic anomalies. This allows maintenance personnel to detect potential problems before they become apparent, effectively preventing serious downtime caused by missed early fault reports. Chaotic features delve into the hidden nonlinear dynamic behavior of the system within monitoring signals, capturing even the faintest fault signs and providing a reliable basis for very early fault warnings.

[0071] In this invention, chaotic features are used as input to a Hidden Markov Model (HMM). Leveraging the powerful temporal modeling capabilities of HMMs, the dynamic changes of chaotic features are transformed into a probabilistic evolution path of the equipment's health state. This not only accurately determines the current degradation stage of the equipment but also probabilistically predicts future trends, making the predictions more closely aligned with the actual operating conditions of the equipment. The probabilistic reasoning capabilities of HMMs enable a precise description of the evolutionary patterns of the equipment's nonlinear degradation process, significantly improving the accuracy and adaptability of the predictions.

[0072] This invention combines chaos analysis and hidden Markov models to provide richer predictive information. It not only indicates the potential time of failure but also clarifies the probability of the equipment being in various health states and the likelihood of transitioning to a more severe state. Maintenance personnel can clearly understand the current health status distribution of the equipment and the probability trend of future state changes, making the estimation of remaining useful life more reliable. This information provides a quantitative basis for maintenance decisions, avoiding resource waste caused by over-maintenance and preventing failures due to untimely maintenance, making condition-based maintenance more precise and efficient.

[0073] In this invention, based on the chaotic feature quantity extracted from real-time monitoring signals, the system compares it with the preset hidden Markov model of health status in the system database. The system intelligently judges the current degradation stage of the equipment and predicts its future state evolution trend, so that the fault prediction system can achieve early warning and accurate remaining life estimation when facing individual differences of equipment and complex working conditions. In this invention, the matching probability of real-time chaotic feature sequences is compared with that of a standard health HMM model, thereby intelligently identifying the current health status of the equipment, such as normal or slightly degraded, and dynamically adjusting the prediction conclusions. Compared with traditional methods that use fixed thresholds or single model prediction, this method is more intelligent and adaptive, and can effectively avoid problems such as missed faults, false alarms, and inaccurate predictions caused by fluctuations in equipment operating conditions or individual differences. In this invention, when the dynamic stability of the real-time chaotic feature display device begins to decline, indicating the early onset of a fault, the system uses HMM probability calculation to provide an early warning of potential fault risks, thus significantly advancing the maintenance window. When the matching probability between the feature sequence and the severe degradation state model increases, the system can accurately estimate the remaining useful life, providing a quantitative basis for formulating precise maintenance plans, thereby avoiding accidents and enabling condition-based maintenance.

[0074] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the term "comprising" or any other variations thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0075] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault prediction system based on chaos theory and hidden Markov model, characterized in that: The system comprises a data acquisition module, a signal preprocessing module, a chaotic feature extraction module, an HMM training and prediction module, and a human-computer interaction and early warning module. The chaotic feature extraction module is internally provided with: a phase space reconstruction unit: a time delay coordinate method is adopted to reconstruct a one-dimensional time series signal into an m-dimensional phase space orbit according to a determined embedding dimension m and time delay τ, so as to reproduce the topological properties of the original dynamic system; a chaotic feature quantity calculation unit: on the basis of the reconstructed phase space, quantitative indexes capable of representing the dynamic characteristics of the system are calculated; The HMM training and prediction module is internally provided with: an HMM training unit: using the chaotic feature sequence extracted from the historical data as a training set, a plurality of HMM models are trained, and each model corresponds to a preset health state stage; a state recognition and prediction unit: for online monitoring data, the chaotic feature sequence thereof is extracted in real time and input into the trained HMM model. The method comprises the following steps when in use:

2. A fault prediction method based on chaos theory and hidden Markov model, characterized in that: Step S100: starting the fault prediction system; Step S101: data acquisition and preprocessing: acquiring original time series signals x(t) through sensors installed on the equipment; and performing preprocessing on the acquired signals, including denoising and normalization, to obtain clean signal sequences x'(t); Step S102: phase space reconstruction: mapping a one-dimensional signal to a high-dimensional phase space to restore the dynamic characteristics of the system; Step S103: calculating chaotic feature quantities to form observation sequences: calculating quantitative features representing the nonlinear dynamic behavior of the system on the reconstructed phase space to form observation vectors; Step S200: model training and online prediction judgment; judging the current data processing mode; if it is historical full-life cycle data for training, executing an offline model training process: steps S201-S203; if it is window data for real-time monitoring, executing an online prediction process: steps S301-S303; Step S201: initializing HMM parameters: Step S202: iteratively training the HMM using the Baum-Welch algorithm; Step S203: saving the trained HMM model parameters, storing the final model parameters λ=(A, B, π) obtained after convergence into a system database for calling by the online prediction module; Step S301: real-time state recognition; Step S302: fault prediction and remaining useful life RUL estimation, predicting based on the recognized current state and the HMM model: Step S303: result output and decision support: visualizing the state recognition result, prediction information, and RUL estimation value on a human-computer interaction interface; if the prediction risk is high, the system triggers an audible and light alarm or sends a notification to maintenance personnel; Step S400: cyclic monitoring; after completing the prediction of the current window, the system returns to step S101 to acquire data of the next time period, realizing continuous and real-time state monitoring and fault prediction of the equipment. ​ 3. The method of claim 1, wherein the method is based on a combination of chaos theory and a hidden Markov model. In the step S101, the original time series signal x(t) is collected by the sensor installed on the equipment; the collected signal is preprocessed, including denoising and normalization, to obtain the clean signal sequence x'(t).

4. The method of claim 1, wherein the method is based on a combination of chaos theory and a hidden Markov model. In the step S102, the following steps are included: Determining the time delay τ: using the autocorrelation function method; calculating the autocorrelation function of x'(t), and taking the first zero-crossing point or the delay corresponding to the time when the autocorrelation function decreases to 1 / e as the optimal time delay τ; Determining the embedding dimension m: using the pseudo nearest neighbor method; gradually increasing the embedding dimension m, and when the proportion of pseudo nearest neighbors is less than 5% or tends to be stable, the minimum m corresponding thereto is the optimal embedding dimension; Reconstruction of phase space: With the determined τ and m, the phase space is reconstructed according to the formula Reconstruct the phase space to get the point set (i)}.

5. The method of claim 1, wherein the method is based on a combination of chaos theory and a hidden Markov model. In the step S103, the following steps are included: are continuously computed in a sliding time window, forming an observation sequence ; the following at least two features are specifically computed: Correlation dimension D2: using the Grassberger-Procaccia algorithm, the correlation integral C(r) is calculated and the slope in the log-log coordinate is obtained in the scale-free region; Maximum Lyapunov exponent λ1: using the small data method, the average divergence rate of adjacent trajectories in the phase space is tracked, and λ1>0 indicates that the system has chaotic characteristics; Kolmogorov entropy K is calculated by the correlation integral under different embedding dimensions, which represents the information generation rate of the system.

6. The method of claim 1, wherein the method is based on a combination of chaos theory and hidden Markov models. In the step S201, the following steps are included: Defining the HMM model λ=(A, B, π); State set Q: preset health states such as {normal, slight degradation, severe degradation, and fault}; Observation probability B: Since the observation value is a continuous chaotic feature vector, B is set as a Gaussian mixture model (GMM), i.e.: Initializing and assigning the state transition matrix A and the initial state distribution π.

7. The method of claim 1, wherein the method is based on a combination of chaos theory and hidden Markov model. In the step S202, the following steps are included: Based on the current model parameters λ(n) and the observation sequence O, the forward variable αt(i), the backward variable βt(i), the probability γt(i) of being in state i at time t, and the state transition probability ξt(i,j) are calculated; Parameter re-estimation M-Step: update model parameters by re-estimation formula using the result of E-Step ; The re-estimation formula is: The parameters cjk, μjk, and Σjk of the GMM are also re-estimated by weighted average of γt(j); Convergence judgment: calculate the change of likelihood function If the change is less than a preset threshold, it is judged as convergence, and step S203 is executed; otherwise, replace with , and return to E-Step to continue iteration.

8. The method of claim 1, wherein the method is based on a combination of chaos theory and a hidden Markov model. In the step S301, for the observation sequence Ocurrent obtained after the real-time data segment is processed by S101-S103, the forward algorithm is used to calculate the probability P=Ocurrent∣λi generated by each trained HMM model λi; = argmaxi[P(Ocurrent | λi).

9. The method of claim 1, wherein the method is based on a combination of chaos theory and a hidden Markov model. In the step S302, state prediction includes calculating the probability P(St+k=qfault∣Ocurrent, λ) of being in the fault state after k time steps in the future; when the probability exceeds the safety threshold, a warning is triggered; RUL estimation includes setting: the equipment is currently in state i; based on the state transition probability matrix A, the expected time from the current state i to the fault state N for the first time is calculated. The simplified RUL point estimate formula is: .

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