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CN-121997723-A - Residual life prediction method based on nonlinear wear and random jump

CN121997723ACN 121997723 ACN121997723 ACN 121997723ACN-121997723-A

Abstract

A residual life prediction method based on nonlinear abrasion and random jump comprises the steps of firstly constructing health indexes fused by multi-source information, constructing a composite degradation model integrating a power law time scale function and a non-homogeneous poisson process to simultaneously represent progressive accelerated abrasion and time-varying burst impact characteristics of equipment, then designing an improved two-stage parameter estimation strategy, processing impact frequency hidden variables by using an expected condition maximization algorithm, combining maximum likelihood estimation to identify time-varying intensity parameters, realizing robust identification of complex model parameters, deducing an approximate probability density function of residual life based on a first time frame and Gaussian approximation theory, realizing probabilistic prediction through numerical integration, and finally establishing a sliding window updating mechanism to realize online self-adaptive adjustment and dynamic prediction of model parameters. The method has the advantages of strong nonlinear fitting capability, sensitive impact capturing, high prediction precision and accurate uncertainty quantification under the conditions of complex working conditions and limited observation data.

Inventors

  • FU ZHEHAO
  • ZHOU CHUCHU
  • FU LEI

Assignees

  • 浙江工业大学

Dates

Publication Date
20260508
Application Date
20260107

Claims (8)

  1. 1. A method for predicting remaining life based on nonlinear wear and random jump, the method comprising the steps of: Step 1, vibration signal acquisition and health index construction, namely acquiring vibration signals by utilizing an acceleration sensor arranged on mechanical equipment, preprocessing an original signal by adopting a Z-score standardization method, extracting the maximum amplitude MA as a health index, and providing high-quality input data for subsequent modeling by constructing a degradation sequence and an increment sequence thereof; Step 2, constructing a composite degradation model, namely providing the composite degradation model fused with nonlinear time scale abrasion and random jump effects, capturing nonlinear characteristics of a degradation process by introducing a time scale function, and describing a law of the change of the impact occurrence rate along with time by combining with a non-homogeneous poisson process; step 3, two-stage parameter estimation, namely, processing hidden variables by adopting an expected condition maximizing algorithm in the first stage, regarding the occurrence times of impact as the hidden variables, calculating posterior probability in an expected step, and respectively maximizing each condition expectation in the condition maximizing step so as to iteratively update drift coefficients Diffusion parameter Nonlinear index The second stage adopts maximum likelihood estimation method, and on the basis of fixing the degradation and impact amplitude parameters obtained in the first stage, the strength parameters of non-homogeneous Poisson process are aimed at Performing maximum likelihood estimation, and accurately capturing a time-varying rule of impact occurrence by constructing and solving a log-likelihood function; step 4, deducing residual life distribution, namely defining a system failure threshold value as based on a first-pass time frame Solving RUL distribution by adopting a method combining approximate analysis and numerical integration aiming at a composite degradation model containing random jump items to obtain a prediction distribution curve of the residual life and a quantized uncertainty interval.
  2. 2. The method for predicting remaining life based on nonlinear wear and random jump according to claim 1, further comprising the steps of: And 5, establishing a sliding window updating mechanism to realize online self-adaptive adjustment of model parameters, setting an updating period and collecting new monitoring data, adding the new data into a historical data set when acquiring the new data, and re-triggering a parameter estimation algorithm, updating the model parameters in real time, repeating the step 4 to realize dynamic tracking prediction based on the updated parameters, and simultaneously adopting a multi-index verification system to evaluate performance, wherein the method comprises the steps of measuring absolute errors of instantaneous prediction deviation, evaluating root mean square errors of integral precision and inspecting accumulated relative precision of trend tracking capability, so that the model can adapt to dynamic change in the degradation process of equipment.
  3. 3. The method for predicting the remaining life based on nonlinear wear and random jump according to claim 1 or 2, wherein in the step 1, the raw signal is preprocessed by using a Z-score normalization method to eliminate the sensor dimension difference, and the calculation formula is as follows Wherein Is the characteristic average value of the characteristic, Is the standard deviation.
  4. 4. The method for predicting remaining life based on nonlinear wear and random jump according to claim 3, wherein in said step 1, a degradation state sequence is constructed in time series , wherein, Is the first Maximum amplitude values at each monitoring moment are calculated, and first-order differences of the maximum amplitude values are calculated to obtain an increment sequence Wherein The incremental sequence eliminates the effect of the cumulative trend, directly reflecting the instantaneous rate of change and random fluctuations of the degradation process.
  5. 5. The method for predicting remaining life based on nonlinear wear and random jump according to claim 1 or 2, wherein the procedure of step 2 is: 2.1 Nonlinear wiener process modeling based on power law transformation, namely introducing a time scale transformation strategy and adopting a time scale function in a power law form The drift term is subjected to nonlinear correction, and a constructed continuous degradation part model is as follows: ; Wherein, the As an initial amount of degradation, As a result of the drift coefficient, For the diffusion coefficient, in this model, the nonlinear index Plays a key role in adjusting the curvature of the degenerated track when When the degradation rate monotonically increases with time, the performance acceleration degradation phenomenon of the equipment caused by fatigue accumulation can be accurately fitted, when When the model is degenerated into a linear form, so that universality and flexibility of the model to different degenerated modes are ensured; 2.2 Time-varying impact modeling based on non-homogeneous poisson process using non-homogeneous poisson process To describe the occurrence times of impact events and to introduce a time-varying intensity function Cut-off to time Is derived from the cumulative impact expected times by a cumulative intensity function A decision, defined as the integral of the instantaneous intensity over the time domain: ; Setting the damage amplitude caused by each impact Obeying mean value of Variance is The independent same-distribution normal distribution of the system is realized, so that a random jump item capable of reflecting an aging-vulnerable mechanism is constructed; 2.3 The Gaussian approximation and continuous processing of the composite model is to put forward a two-step Gaussian approximation strategy, firstly, based on the central limit theorem, the accumulated jump damage is decomposed into a deterministic mean shift part and a random fluctuation part, namely Wherein Is a zero-mean normal variable, and further, the non-homogeneous poisson process Approximately as a continuous process driven by brownian motion: ; Wherein, the Substituting the approximation into the original model to obtain an approximation analytical model for subsequent parameter estimation and life prediction, wherein the approximation analytical model is a standard normal random variable: 。
  6. 6. The method for predicting remaining life based on nonlinear wear and random jump according to claim 1 or 2, wherein in the step 3, in the first stage, based on hidden variable processing and distribution parameter estimation of expected condition maximizing algorithm, a degradation incremental sequence is obtained first by using first order difference And (3) carrying out iterative solution by adopting an expected condition maximization algorithm: the expected step is to calculate the posterior probability of hidden variables, calculate the time when the first is observed based on the current parameter estimation value Incremental data Under conditions of (1) within the time period Posterior probability of secondary impact ; And a condition maximization step, namely constructing a log likelihood function expectation of the complete data by utilizing the posterior probability obtained in the step, and decomposing the log likelihood function expectation into four sub-optimization problems for alternate updating: (3.1) fixed variance and nonlinear index, updating drift coefficients by maximizing the number likelihood function expectation function And the mean value of the impact amplitude ; (3.2) Fixed mean class parameter, updating variance of impact amplitude ; (3.3) Updating the scale factor related to the diffusion coefficient To adjust the adaptation of the model to background noise; (3.4) updating the nonlinear index Using the one-dimensional search Algorithm To match precisely the curvature characteristics of the degraded track; The above process is cyclically executed until the variation of the parameter estimation value is smaller than the preset threshold value.
  7. 7. The method for predicting remaining life based on nonlinear wear and random jump as recited in claim 6, wherein in said step 3, in the second stage, based on non-uniform intensity parameter optimization of maximum likelihood estimation algorithm, convergence degradation and amplitude parameters are obtained in the first stage The remaining unknowns of the model are then only the intensity parameters of the non-homogeneous poisson process Constructing an edge likelihood function for the mild parameter: ; in the case of the likelihood function, A cutoff threshold value representing the number of impacts; Indicating that this occurs within the assumed current time period Secondary impact and known first stage parameters Under the condition of (1) observation data Conditional probability density of (2); representing the probability of impact occurrence determined by the integral intensity function of a non-homogeneous poisson process, the value of which directly accepts the intensity parameter Control, since the function eliminates hidden variables And other parameters, the likelihood function can be quickly obtained by using a quasi-Newton method Thereby realizing the accurate identification of time-varying impact strength.
  8. 8. The method for predicting remaining life based on nonlinear wear and random jump according to claim 1 or 2, wherein in said step 4, the remaining life of the system is defined based on the first pass time, i.e. the system degradation state reaches a preset failure threshold for the first time By combining approximate analysis and numerical integration, firstly, gaussian approximation of jump terms, approximation of the complex poisson process to a continuous process including drift and diffusion using the central limit theorem, and secondly, deriving a conditional probability density function of remaining life based on the approximated model, the function describing the time when current monitoring is known Current state of degradation In the future, the device experiences a length of time Probability density of post failure, its approximate expression form is as follows: ; Wherein, the Representing random variables with respect to standard normal Each intermediate parameter in the above formula is expressed as follows: Intermediate variable And (3) with Reflecting the statistical characteristics of random jump items and their rate of change: ; drift and diffusion related terms The influence of nonlinear wear trend, current degradation state and random impact is integrated: ; ; ; Jump process moment approximation term And (3) with Respectively, the cumulative impact strength approximation and its derivative over the prediction interval: ; ; Wherein, the In order to accumulate the function of the impact strength, Is a transient intensity function of a non-homogeneous poisson process; finally, the numerical integration method is utilized to integrate the expected items And (3) calculating the probability density function of the residual life, thereby obtaining a predicted distribution curve, an expected value and a confidence interval of the residual life.

Description

Residual life prediction method based on nonlinear wear and random jump Technical Field The invention belongs to the technical field of mechanical equipment Prediction and Health Management (PHM), and particularly relates to a residual life prediction method based on nonlinear abrasion and random jump. Background Predictive and Health Management (PHM) techniques optimize equipment maintenance strategies and reduce operational risk by monitoring performance degradation throughout the life cycle of the equipment in real time, assessing reliability and predicting Remaining Useful Life (RUL). In modern industry, mechanical components, particularly rotating components such as bearings and turbines, inevitably degrade over time and are often subject to sudden load changes, environmental disturbances, and other impact events, which if mismanaged can lead to unexpected failure, increased maintenance costs, and safety risks. Therefore, PHM technology becomes critical, with RUL prediction as a core function of predictive maintenance, with important theoretical and engineering value. The current RUL prediction method is mainly divided into a physical model-based method, an artificial intelligence-based method and a data driving-based method. Among them, wiener process models in data-driven based methods are attracting attention due to their good mathematical theoretical basis and practicality, and the methods implement RUL prediction by building a random process model between performance degradation and time. However, in the practical application process, the following problems still exist in the existing method, which are to be solved: (1) The traditional wiener process model adopts a linear drift assumption, so that nonlinear degradation characteristics cannot be accurately described, and the nonlinear degradation characteristics are not enough in coupling with random impact effects, so that degradation process modeling deviation is caused. (2) The existing random impact model is mostly based on a homogeneous poisson process, ignores the time change characteristic of the impact occurrence rate, or assumes that the impact and the degradation are independent, and cannot effectively capture the combined effect of the impact and the degradation. (3) The hidden variables under partial observation cause the parameter estimation method to be easy to be in local optimum, and the parameter estimation method is not optimized for a time-varying impact process, so that the estimation precision is insufficient. Disclosure of Invention In order to overcome the defects of insufficient nonlinear degradation modeling, limitation of random impact description and limitation of parameter estimation precision under partial observation conditions in the prior art, the invention provides a residual life prediction method based on nonlinear abrasion and random jump, the method integrates a nonlinear wiener process and a non-homogeneous poisson jump process, establishes a composite degradation model capable of simultaneously describing progressive wear and sudden impact, adopts an improved two-stage parameter estimation strategy, and realizes accurate parameter estimation and reliable RUL prediction under partial observation data. The problem that a single degradation model is poor in adaptability in a complex industrial environment is effectively solved, and powerful theoretical support and technical support are provided for the condition-dependent maintenance of mechanical equipment. The technical scheme adopted for solving the technical problems is as follows: A method of predicting remaining life based on nonlinear wear and random jump, the method comprising the steps of: step 1, vibration signal acquisition and health index construction, namely acquiring vibration signals by using an acceleration sensor arranged on mechanical equipment, wherein the vibration signals generated by the rotating machinery in the running process are often influenced by various factors such as working condition change, sensor noise and the like, so that the signal-to-noise ratio of the original data is low, and the characteristic extraction is difficult. In order to overcome the dependence of the traditional feature construction method on priori knowledge and improve the data distribution stability, the invention firstly adopts a Z-score standardization method to preprocess the original signal so as to eliminate the sensor dimension difference, and the calculation formula is as follows WhereinIs the characteristic average value of the characteristic,Is the standard deviation, and on the basis of the standard deviation, the Maximum Amplitude (MA) with higher sensitivity to the early failure and impact of the bearing is extracted as a health index, and finally a degradation sequence is constructedAnd delta sequence thereofProviding high-quality input data for subsequent modeling, ensuring that the input signal effectively suppresses interference of environment