A method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov

Abstract

This invention discloses a method for predicting the remaining life of aero-engines based on a multi-feature hidden Markov model, belonging to the field of aero-engine health management technology. The invention includes: collecting monitoring data from multiple sources of aero-engine sensors; discretizing the monitoring data from each sensor; aligning the discrete observation levels based on the degradation direction; constructing a multi-feature hidden Markov model and estimating the model parameters; dividing the observation space of each sensor into a non-alarm observation subset and an alarm observation subset, and deriving the probability distribution of multi-sensor observation counts under each hidden state condition; deriving the closed-form expression of the conditional reliability function of the multi-sensor model based on the parameter estimation; and constructing an adaptive remaining life prediction model based on the conditional reliability function, outputting the cumulative distribution function of the remaining life, the average remaining life, and the prediction interval. This invention integrates multi-source sensor signals to achieve accurate prediction of the remaining life of aero-engines.

Description

Technical Field

[0001] This invention relates to the field of engine health management technology, specifically to a method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model. Background Technology

[0002] As the core power plant of an aircraft, the operating status of the aero-engine directly affects flight safety and economic efficiency. Due to prolonged exposure to extreme conditions such as high temperature, high pressure, high speed, and alternating loads, the performance of various engine components inevitably degrades. If their health status is not identified and appropriate maintenance is not implemented in a timely manner, performance degradation will continue to accumulate, potentially leading to serious failures. Therefore, accurately predicting the remaining useful life (RUL) of aero-engines is a crucial foundation for implementing condition-based maintenance and predictive health management (PHM), and is of great significance for reducing maintenance costs and improving equipment utilization.

[0003] Currently, methods for predicting the remaining life of aero-engines are mainly divided into three categories: physical model-based methods, data-driven methods, and hybrid methods. Physical model-based methods rely on a precise mathematical description of the engine degradation mechanism, requiring the introduction of specific physical prior knowledge and operating conditions. The modeling process is complex and has limited generalization ability. Data-driven methods, on the other hand, directly learn the mapping relationship between degradation trends and remaining life from monitoring data through statistical learning or deep learning models, exhibiting strong adaptability under complex operating conditions. However, existing data-driven methods mostly focus on improving prediction accuracy and still have significant shortcomings in practical applications.

[0004] First, the actual degradation state is usually implicit and not directly observable to decision-makers, making engine remaining life prediction a partially observable problem. Hidden Markov Models (HMMs) can infer unobservable degradation states from observable sensor signals and have been applied in the field of health assessment. However, existing HMM-based methods do not fully utilize multi-sensor information in remaining life prediction, lacking systematic modeling of the probabilistic relationship between multi-sensor observation counts and degradation stages, making it difficult to fully extract degradation information from multi-source monitoring data.

[0005] Secondly, the required prediction accuracy varies significantly across different stages of engine degradation. When the system is in relatively good health, the degradation trend of sensor signals is weak, and available information is limited, leading to significant uncertainty in remaining life prediction. However, as the system enters a significant degradation phase, the changing trend of sensor signals strengthens, available information increases, and the uncertainty of the prediction results decreases. Most existing methods employ a single prediction strategy, which is insufficient to simultaneously adapt to these differentiated requirements. They cannot adaptively select a prediction strategy based on the system's current health status, resulting in significant fluctuations in prediction accuracy across different degradation stages.

[0006] Third, existing data-driven methods mostly employ black-box models, resulting in predictions that lack interpretable analytical expressions and struggle to provide theoretically sound confidence intervals. While some methods can provide point estimates of remaining lifespan, they fail to offer complete probability distribution information, hindering the quantitative assessment of risks in maintenance decisions.

[0007] Furthermore, while the hybrid approach of physical modeling and data-driven methods attempts to combine the advantages of both, it is still constrained by the dual limitations of insufficient accuracy in physical modeling and insufficient interpretability of data-driven methods, making it difficult to provide theoretically guaranteed closed-form analytical results.

[0008] Therefore, how to systematically integrate multi-sensor conditional monitoring signals, characterize the probabilistic relationship between implicit degradation states and multi-source observations, provide closed-form analytical expressions for conditional reliability and remaining lifetime distribution, and adaptively select prediction strategies based on the current health status of the system, so as to provide reliable point estimates and interval estimates at different degradation stages, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for predicting the remaining life of aero-engines based on a multi-feature hidden Markov model. This method constructs a multi-feature hidden Markov model to fuse multi-source heterogeneous sensor signals, employs K-means clustering and weighted Mann-Kendall test to discretize and align the observed data, and builds an adaptive prediction framework based on conditional reliability. It outputs closed-form analytical expressions for the cumulative distribution function of remaining life, the average remaining life, and the confidence interval, thereby achieving high-precision prediction and uncertainty quantification of remaining life under different degradation stages.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] This invention proposes a method for predicting the remaining life of aero-engines based on multi-feature hidden Markov models, comprising the following steps:

[0012] S1. Collect monitoring data from multiple sensors of the aero-engine throughout its entire life cycle. The monitoring data is used to characterize the degradation process of the engine. Discretize the monitoring data of each sensor to obtain the discrete observation level corresponding to each sensor. Align the discrete observation levels based on the degradation direction to obtain the multivariate discrete observation sequence of the aero-engine.

[0013] S2. Construct a multi-feature hidden Markov model. Based on the discrete observation sequences of each sensor, use the expectation-maximization algorithm to estimate the parameters of the multi-feature hidden Markov model to obtain the parameter-estimated multi-feature hidden Markov model.

[0014] S3. Divide the observation space of each sensor into a non-alarm observation subset and an alarm observation subset, and derive the probability distribution of multi-source sensor observation counts under each hidden state condition based on the probability generation function.

[0015] S4. Based on the multi-feature hidden Markov model after parameter estimation, derive the closed-form expression of the conditional reliability function of the multi-source sensor;

[0016] S5. Based on the conditional reliability function of multi-source sensors, construct an adaptive remaining lifetime prediction model; based on the monitoring data to be measured of the aero-engine, recursively obtain the posterior state occupancy probability at the current moment through a multi-feature hidden Markov model after parameter estimation, and calculate the conditional reliability accordingly; the adaptive remaining lifetime prediction model determines the observation counting conditions to be adopted according to the conditional reliability, and outputs the cumulative distribution function of the remaining lifetime, the average remaining lifetime, and the prediction interval under the condition.

[0017] Furthermore, the process of discretizing the monitoring data of each sensor is as follows: the monitoring data is pooled, and the K-means clustering algorithm is used to cluster the pooled monitoring data under multiple candidate cluster numbers to obtain the preliminary discrete label sequence corresponding to the monitoring data under each candidate cluster number. The weighted Mann-Kendall statistic of the preliminary discrete label sequence under each candidate cluster number is calculated respectively. The minimum number of clusters that makes the monotonicity of the preliminary discrete label sequence tend to be stable is determined according to the absolute value of the weighted Mann-Kendall statistic. The minimum number of clusters is used as the optimal number of discrete levels of the sensor, and the monitoring data is mapped to discrete observation levels according to the optimal number of discrete levels.

[0018] The process of aligning the discrete observation levels based on the degradation direction is as follows: the degradation direction of the monitoring data is determined according to the sign of the weighted Mann-Kendall statistic. If the sign is positive, the discrete observation levels are arranged in ascending order according to the cluster centroid. If the sign is negative, the discrete observation levels are arranged in descending order according to the cluster centroid. The discrete observation sequences of each sensor are then time-aligned to obtain the multivariate discrete observation sequence of the aero-engine.

[0019] Furthermore, the parameters of the multi-feature hidden Markov model include the hidden state transition probability matrix, the emission probability matrix of each sensor, and the initial state distribution;

[0020] Furthermore, the process of estimating the parameters of the multi-feature hidden Markov model using the expectation-maximization algorithm includes:

[0021] S201. Based on the parameters of the current multi-feature hidden Markov model, for each multivariate discrete observation sequence, the forward variable is calculated by forward recursion, and the backward variable is calculated by backward recursion. The posterior state occupancy probability at each time step and the posterior state transition probability between adjacent time steps are calculated based on the forward and backward variables.

[0022] S202. Update the parameters of the current multi-feature hidden Markov model based on the posterior state occupancy probability and the posterior state transition probability:

[0023] Each dimension of the initial state distribution is updated to the mean of the posterior state occupancy probability at the start time of each multivariate discrete observation sequence, resulting in the updated state distribution.

[0024] The hidden state transition probability matrix is ​​constrained into an upper triangular form, and the updated hidden state transition probability matrix is ​​obtained by dividing the posterior state transition probability statistic by the sum of all non-zero transition statistics of the corresponding hidden state.

[0025] Based on the posterior state occupancy probability, the frequency of each sensor at each discrete observation level is counted to obtain the updated emission probability matrix of each sensor.

[0026] S201 and S202 are executed alternately until the increment of the log-likelihood function of each discrete observation sequence is less than a preset threshold or the number of iterations reaches a preset number, thus obtaining the multi-feature hidden Markov model after parameter estimation.

[0027] Furthermore, S3 specifically includes:

[0028] S301. Divide the observation space of each sensor into a non-alarm observation subset and an alarm observation subset that do not overlap, wherein the discrete observation level contained in the alarm observation subset is greater than the discrete observation level contained in the non-alarm observation subset.

[0029] S302. Calculate the probability that the discrete observation level of each sensor falls into the non-alarm observation subset and the alarm observation subset under each hidden state based on the emission probability matrix.

[0030] S303. Based on the Bernoulli distribution of each sensor falling into the non-alarm observation subset or alarm observation subset and the conditional independence under a given hidden state, construct the probability generation function of the multi-source sensor observation count in each hidden state.

[0031] S304. Expand the probability generation function into a polynomial form to obtain the conditional probability mass function of the number of sensors falling into the non-alarm observation subset or the alarm observation subset in each hidden state.

[0032] Furthermore, the closed-form expression of the multi-source sensor conditional reliability function is:

[0033]

[0034] In the formula, This represents the total number of hidden states. This is the hidden state transition probability matrix. Based on the current time Multi-source sensor joint observation history The updated system is in Always in a hidden state The probability of the posterior state occupies, For the system at time The probability of a posterior state being in a completely invalid state. For the process Step from hidden state Transition to hidden state The probability, From the current moment The initial prediction step size.

[0035] Furthermore, methods for constructing adaptive remaining life prediction models include:

[0036] Set a conditional reliability threshold and a threshold for the number of non-alarm features;

[0037] At the current moment, the conditional reliability after a preset number of steps is calculated based on the multi-feature hidden Markov model after parameter estimation, and the conditional reliability is compared with the conditional reliability threshold.

[0038] When the conditional reliability is greater than or equal to the conditional reliability threshold, the aero-engine is determined to be in a relatively healthy state. The remaining lifetime cumulative distribution function is set with the condition that the number of sensors falling into the non-alarm observation subset of each sensor is not less than the first non-alarm feature number threshold.

[0039] When the conditional reliability is less than the conditional reliability threshold, the aero-engine is determined to be in a degraded state. The remaining lifetime cumulative distribution function is set with the condition that the number of sensors falling into the non-alarm observation subset of each sensor does not exceed the second non-alarm feature number threshold.

[0040] Furthermore, the closed-form expression of the remaining lifetime cumulative distribution function is:

[0041]

[0042] In the formula, For the current moment, To predict the step size, To preset the inspection interval, For conditional reliability threshold, The threshold for the number of non-alarm features. This is the threshold for the number of the second non-alarm feature. The total number of sensors, This represents the total number of hidden states. For the current moment The set of hidden states for Remaining lifespan at any given moment Let m be the probability of being in state m at the initial moment. Let be the hidden state transition probability matrix. For the process Step state transition from hidden state Reaching the hidden state The probability, For the process Step state from hidden state Transition to a completely failed state The probability, In the hidden state The number of sensors falling into the non-alarm observation subset is The conditional probability mass function. In the hidden state The number of sensors falling into the alarm observation subset is The conditional probability mass function.

[0043] Further, the expected value of the remaining lifetime is calculated based on the cumulative distribution function of the remaining lifetime, which is used as the average remaining lifetime; the inverse of the cumulative distribution function of the remaining lifetime is obtained at a given confidence level to obtain the lower and upper bounds of the prediction interval.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] (1) This invention constructs the emission probability of a multi-feature hidden Markov model as a product of the edge emission probabilities of each sensor, enabling each sensor to independently associate with a unified hidden state through its own emission probability matrix, thus establishing a structured probability generation relationship between the hidden state and multi-sensor observations. Based on this, the invention divides the observation space of each sensor into a non-alarm subset and an alarm subset, and uses a probability generation function to transform the multi-sensor observation pattern into a probability counting distribution of the number of sensors. This distribution is the convolution result of independent Bernoulli trials of each sensor under a given hidden state. This fusion strategy of first establishing a structured probability generation relationship and then performing count compression enables the multi-sensor observation information to be compressed from high-dimensional vectors to low-dimensional count statistics within a probabilistic framework, providing observational features with clear physical meaning for subsequent reliability calculations and remaining lifetime predictions.

[0046] (2) This invention utilizes the recursive update property of the posterior distribution of the hidden states in a multi-feature hidden Markov model to express the conditional reliability function as the ratio of the posterior state occupancy probability to the power operation of the state transition matrix. The power operation of the state transition matrix only involves discrete matrix multiplication, without the need to solve differential equations or perform high-dimensional numerical integration. The closed-form expression of the conditional reliability function is calculated online with the flight cycle as the time unit, making the remaining lifetime prediction feasible for real-time engineering deployment. At the same time, the probability transition between non-failure states in the numerator and the non-failure probability at the current moment in the denominator form a complete probability normalization structure, giving the reliability assessment results good probabilistic semantic interpretability between 0 and 1.

[0047] (3) This invention uses the conditional reliability function value as the state discrimination index. The conditional reliability itself contains all the probabilistic inference information under the current observation history, including the latent state posterior distribution, state transition probability, and collective pattern of sensor observations. Based on this, this invention conditions the remaining lifetime cumulative distribution function for events with sufficient non-alarm feature numbers in the healthy state branch, and conditions it for events with insufficient non-alarm feature numbers in the degraded state branch. Both branches have closed-form analytical expressions and are mutually exclusive by the conditional reliability threshold. This adaptive probabilistic prediction mechanism automatically switches to the matching information conditions based on the current health state of the system to infer the remaining lifetime distribution, so that the prediction results maintain statistical optimality throughout the entire life cycle, providing a basis for risk quantification assessment and maintenance timing decision-making in condition-based maintenance.

[0048] (4) This invention derives a complete closed-form solution to the cumulative distribution function of remaining lifetime from the discretization of multi-sensor observation data, parameter estimation of multi-feature hidden Markov models, probability generation of observation counts, and closed-form expression of conditional reliability. This cumulative distribution function covers all possible values ​​of remaining lifetime, and its mathematical expectation provides a point estimate of remaining lifetime. The prediction interval can be directly obtained by analytically inverting the cumulative distribution function at any given confidence level. The entire calculation process only involves matrix multiplication and series summation, without relying on any numerical simulation or approximate sampling, and has a significant advantage in computational efficiency. The existence of the closed-form solution gives the prediction results strict probabilistic semantics. The confidence interval is no longer an empirical value, but a statistic with strict probability coverage guarantee, which provides a reliable theoretical basis for risk quantification assessment in condition-based maintenance of aero-engines. Attached Figure Description

[0049] Figure 1 A flowchart illustrating the remaining life prediction method for aero-engines based on multi-feature hidden Markov model provided by this invention.

[0050] Figure 2 This is a graph showing the relationship between the number of hidden states and the BIC value in an embodiment of the present invention.

[0051] Figure 3 This is a visual schematic diagram of the emission probability matrix of each sensor in an embodiment of the present invention;

[0052] Figure 4 The graphs showing the variation of conditional reliability of a centralized engine with operating cycles in this embodiment of the invention are shown; where (a) to (d) each correspond to one representative engine.

[0053] Figure 5 The diagram shows the predicted remaining life of the engines in the embodiment of the present invention, where (a) to (d) each correspond to one engine. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Example

[0056] refer to Figure 1 This embodiment provides a method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model, which is performed according to the following steps:

[0057] S1. Collect monitoring data from multiple sources of sensors on the aero-engine throughout its entire life cycle. The monitoring data is used to characterize the degradation process of the engine. The entire life cycle refers to the complete process of the engine from the start of operation to complete failure. The multiple sources of sensors include temperature sensors, pressure sensors, speed sensors, etc., arranged on the aero-engine. The monitoring data includes temperature data, pressure data, speed data, etc.

[0058] The monitoring data from each sensor is discretized to obtain the discrete observation level corresponding to each sensor. The specific process is as follows:

[0059] Pool the monitoring data from each sensor. For the first... The sensor is recorded as the [number]th sensor. The continuous monitoring data collected throughout the entire life cycle of each engine is ,in , This represents the total number of engines. Sampling time, For the first The lifespan of each engine.

[0060] The K-means clustering algorithm is used to cluster the pooled monitoring data under multiple candidate cluster numbers. For the first... Number of sensors and candidate clusters After pooling the continuous monitoring data of all engines, K-means clustering is performed according to the following objective function:

[0061]

[0062] in For the division of measurement space, For the first Clusters The centroid. Each continuous monitoring data point. An initial discrete label is assigned based on the cluster to which it belongs. The preliminary discrete label sequences corresponding to the monitoring data under each candidate cluster number are obtained.

[0063] To determine the number of discrete ranks, this invention employs a weighted Mann-Kendall test to assess the degree to which the discrete sequence preserves the monotonically degenerate trend of the original data. For the number of discrete ranks... Number of sensors and candidate clusters Define the aggregation monotonicity index:

[0064]

[0065] in and The first The first engine The and the first At each measurement time, It is a symbolic function. For the first The sensor at the first Under the number of candidate clusters, the th The engine in the first Preliminary discrete labels for each measurement time. The larger the value, the stronger the monotonic correlation between discrete observations and runtime. The absolute value of the weighted Mann-Kendall statistic is used to determine the... The minimum number of clusters that no longer significantly improves is used as the optimal number of discrete levels for the sensor. For example, a tolerance of 0.01 can be set when... The number of clusters will stop increasing when the increment is below the tolerance.

[0066] The monitoring data is mapped to discrete observation levels according to the optimal number of discrete levels. The observation space of each sensor is denoted as .

[0067] Since different sensors may exhibit different degradation directions—for example, temperature and vibration increase with increasing degradation, while pressure and efficiency may decrease—this invention, based on the principle that the monotonic likelihood ratio property of the emission probability matrix is ​​effective for heterogeneous sensors, aims to ensure that this property is valid for heterogeneous sensors. The sign determines the first The degradation direction of each sensor: if Then, the discrete observation levels are arranged in ascending order of cluster centroid; if Then, the discrete observation levels are arranged in descending order of cluster centroid. Under this convention, level 1 represents the best observable state, and level... This represents the worst observable state, from which the discrete observation sequences of each sensor are obtained.

[0068] Time alignment of the discrete observation levels in the discrete observation sequences of each sensor yields a multivariate discrete observation sequence for each airborne engine. The multivariate discrete observation sequence corresponding to each engine is: ,in For a moment The K-dimensional discrete observation vector.

[0069] S2. Construct a multi-feature hidden Markov model. Based on the discrete observation sequences of each sensor, estimate the parameters of the multi-feature hidden Markov model using the expectation-maximization algorithm to obtain the parameter-estimated multi-feature hidden Markov model. This specifically includes the following sub-steps:

[0070] S201. Construct a multi-feature hidden Markov model.

[0071] Suppose the hidden state degradation process of an aero-engine is a discrete-time Markov chain. The state space is State 1 represents perfect health. Indicates complete failure, intermediate state. This indicates the degree of degradation, from mild to severe. Total number of hidden states. These are the key structural parameters of the model, and their values ​​can be determined on the validation set using the Bayesian information criterion.

[0072] The parameters of the multi-feature hidden Markov model include the hidden state transition probability matrix. Emission probability matrix of each sensor and initial state distribution .in:

[0073] Hidden state transition probability matrix ,in ,express The time system is in a hidden state Under the conditions, Transition to hidden state at any time The probability of;

[0074] No. Emission probability matrix of each sensor ,in ,express The time system is in a hidden state Under the conditions, the first Each sensor observed discrete observation levels. The probability of;

[0075] Initial state distribution ,in This indicates that the system is in a hidden state at the initial moment. The probability of.

[0076] Given a hidden state Under these conditions, the discrete observation sequences of each sensor are conditionally independent of each other, therefore the multivariate observation vectors The joint emission probability can be decomposed into the product of the emission probabilities at the edges of each sensor:

[0077]

[0078] in This indicates that the system is in a hidden state. At that time, the multi-source sensor outputs the observation vector. The probability of; observation vector In the Components on each sensor, For joint observation space, Indicates the first Each sensor at time Discrete observation level.

[0079] The multivariate discrete observation sequences of each engine are independent of each other, and the log-likelihood function of the observation data is:

[0080]

[0081] in, This is the set of model parameters.

[0082] Since the hidden state sequence cannot be directly observed, this invention employs the expectation-maximization algorithm for parameter estimation. This algorithm iterates alternately through steps S202 and S203 until convergence.

[0083] S202. Based on the current model parameters, for each multivariate discrete observation sequence, calculate the forward variable through forward recursion and the backward variable through backward recursion. Calculate the posterior state occupancy probability at each time step and the posterior state transition probability between adjacent time steps based on the forward and backward variables.

[0084] Define forward variables , indicating that given model parameters Under the conditions, the first Each engine from the start time to The observation sequence at time and The hidden state at any time is The joint probability. The recursive calculation process for the forward variable is as follows:

[0085] initialization: ;

[0086] Recursion: ;

[0087] termination: .

[0088] Define backward variables , indicating that in a given The hidden state at any time is and model parameters Under the conditions, the first One engine from The conditional probability from time point to the end. The recursive calculation process for the backward variable is as follows:

[0089] initialization: ;

[0090] Recursion: .

[0091] Calculate the posterior state occupancy probability based on the forward and backward variables. and the posterior state transition probability between adjacent time points :

[0092]

[0093]

[0094] in, For a moment The observation vector in the hidden state The probability of joint launch under the following conditions.

[0095] S203. Update the parameters of the current multi-feature hidden Markov model based on the posterior state occupancy probability and the posterior state transition probability.

[0096] Each dimension of the initial state distribution is updated to the mean of the posterior state occupancy probability corresponding to the start time of each sequence:

[0097]

[0098] The hidden state transition probability matrix is ​​constrained to an upper triangular form, i.e., when hour, This ensures that each hidden state can only maintain its current level or transition to a more severe degradation level, and also disables the completely ineffective state. For the absorbing state, divide the posterior state transition probability statistic by the sum of all non-zero posterior state transition statistics for the corresponding hidden state to obtain the updated hidden state transition probability matrix:

[0099]

[0100] for , .

[0101] Based on the posterior state occupancy probability, the frequency of each sensor at each discrete observation level is statistically analyzed to obtain the updated emission probability matrix for each sensor:

[0102]

[0103] in, This is an indicator function; it takes the value 1 when the condition within the parentheses is true, and 0 otherwise.

[0104] S202 and S203 are executed alternately until the increment of the log-likelihood function of each multivariate discrete observation sequence is less than a preset threshold or the number of iterations reaches a preset upper limit, thus obtaining the estimated parameters of the multi-feature hidden Markov model. In this embodiment, the convergence threshold is set to a log-likelihood increment of less than 10 between two adjacent iterations. -4 The maximum number of iterations is 500.

[0105] S3. Divide the observation space of each sensor into a non-alarm observation subset and an alarm observation subset, and derive the probability distribution of multi-source sensor observation counts under each hidden state condition based on the probability generation function; specifically including the following sub-steps:

[0106] S301, The observation space of each sensor Divided into disjoint non-alarm observation subsets and alarm observation subset ,satisfy and The alarm observation subset contains a higher discrete observation level than the non-alarm observation subset. In this embodiment, the observation space for each sensor... Divide the non-alarm observation subset With alarm observation subset This involves classifying the worst-case observation level of each sensor into a separate alarm subset, and classifying the remaining levels into a non-alarm subset. The classification method in this embodiment is merely an example; in practical applications, the thresholds for the non-alarm and alarm subsets of each sensor can be flexibly adjusted based on the engine model, sensor type, and engineering experience.

[0107] S302. Calculate the probability that the discrete observation level of each sensor falls into the non-alarm observation subset and the alarm observation subset under each hidden state, based on the emission probability matrix:

[0108]

[0109]

[0110] in, Indicates the hidden state Next, the The discrete observation levels of each sensor fall into the non-alarm observation subset. The probability of; Indicates the hidden state Next, the The discrete observation levels of each sensor fall into the alarm observation subset. The probability of.

[0111] S303. Based on the Bernoulli distribution of each sensor falling into the non-alarm observation subset or the alarm observation subset, and the conditional independence under a given hidden state, construct the probability generation function for the multi-source sensor observation counts in each hidden state. Definition for The number of sensors that fall into the non-alarm observation subset at any given time. for The number of sensors falling into the alarm observation subset at any given time, and the combination of these two factors, reflect the collective pattern of multi-sensor observations. In the hidden state... Under these conditions, whether each sensor falls into the non-alarm observation subset follows a Bernoulli distribution, and the conditions for each sensor are independent. Therefore, The conditional probability generating function is:

[0112]

[0113] S304. Expand the probability generation function into a polynomial form to obtain the conditional probability mass function of the number of sensors falling into the non-alarm observation subset or the alarm observation subset in each hidden state:

[0114]

[0115] in, In the hidden state The number of sensors falling into the non-alarm observation subset is The conditional probability mass function. Similarly, for a subset of alarm observations, we have And because ,have Therefore, at least The probability that a sensor falls into the non-alarm observation subset is .

[0116] S4. Based on the parameter estimation, derive the closed-form expression of the conditional reliability function of the multi-source sensor using the multi-feature hidden Markov model.

[0117] Reliability is a fundamental indicator characterizing a system's ability to perform its intended functions under specified conditions. Within the framework of this invention, since the actual degradation state is implicit to the decision-maker, the decision-maker can only rely on... The joint observations of multiple sensors are used to infer the health status of the system, therefore the definition of classical conditional reliability needs to be extended to multi-sensor scenarios.

[0118] Let the current running time be As of The history of multi-source sensor joint observation is ,in System lifespan Defined as the first time entering the absorption failure state The moment: Conditional reliability function for multi-source sensors This indicates that the observation history has been obtained. And the system is Assuming the time frame has not expired, the system in the future The probability that the device has not failed after a certain number of steps is expressed in closed form as follows:

[0119]

[0120] In the formula, This represents the total number of hidden states. This is the hidden state transition probability matrix. Based on the current time Multi-source sensor joint observation history The updated system is in Always in a hidden state The probability of the posterior state occupies, , For the system at time In a state of complete failure The probability of the posterior state occupies, For the process Step from hidden state Transition to hidden state The probability, From the current moment The initial prediction step size.

[0121] The physical meaning of this closed expression is: the molecular computing system in Always in any non-failure state Under the conditions, after The system remains in a non-failure state after the step transfer. The joint probability for all possible and Perform a weighted summation; denominator For the system in The total probability that the system has not yet failed at the current time. Dividing the numerator by the denominator gives the probability that, given the current observation history and the system has not yet failed, the system will fail in the future. The conditional probability that the condition has not failed after a certain number of steps.

[0122] Real-time updates are achieved through Bayesian recursion. The belief vector is denoteed. Its update process starts from the current time. Multivariate observation vector The hidden state transition probability matrix The recursive formula is determined jointly by the emission probability matrices of each sensor, as follows:

[0123]

[0124] in, To observe the launch diagonal array, A vector consisting entirely of 1s. Initial belief vector. The initial state distribution is given by estimation.

[0125] S5. Based on the conditional reliability function of multi-source sensors, an adaptive remaining lifetime prediction model is constructed. Based on the monitoring data to be measured of the aero-engine, the corresponding posterior state occupancy probability is obtained through a multi-feature hidden Markov model after parameter estimation. The adaptive remaining lifetime prediction model outputs the cumulative distribution function of the remaining lifetime, the average remaining lifetime, and the prediction interval according to the posterior state occupancy probability.

[0126] Define remaining lifetime as That is, at time The remaining time until system failure under certain conditions.

[0127] Methods for constructing adaptive remaining lifetime prediction models include:

[0128] Set conditional reliability threshold First non-alarm feature quantity threshold and the threshold for the number of second non-alarm features .

[0129] At the present moment The number of future preset steps is calculated based on the multi-feature hidden Markov model after parameter estimation. Conditional reliability And compare the conditional reliability with the conditional reliability threshold. Comparison, among which This is the preset inspection interval.

[0130] When the condition reliability When the aircraft engine is determined to be in a relatively healthy state, the number of sensors falling into the non-alarm observation subset of each sensor is not less than the first non-alarm feature quantity threshold. As a condition, the cumulative distribution function of the remaining lifetime is defined. :

[0131]

[0132] When the condition reliability When an aircraft engine is determined to be in a degraded state, the number of sensors falling into the non-alarm observation subset of each sensor is no more than the second non-alarm feature quantity threshold. As a condition, the cumulative distribution function of the remaining lifetime is defined. :

[0133]

[0134] Therefore, the cumulative distribution function of the remaining lifetime has the following closed-form expression:

[0135]

[0136] In the formula, For the current moment, To predict the step size, To preset the inspection interval, For conditional reliability threshold, The threshold for the number of non-alarm features. This is the threshold for the number of the second non-alarm feature. The total number of sensors, This represents the total number of hidden states. For the current moment The set of hidden states For the current moment In hidden state The posterior probability, Let be the hidden state transition probability matrix. For the process Step state transition from hidden state Reaching the hidden state The probability, For the process Step from hidden state Transition to a completely failed state The probability, In the hidden state The number of sensors falling into the non-alarm observation subset is The conditional probability mass function. In the hidden state The number of sensors falling into the alarm observation subset is The conditional probability mass function.

[0137] The derivation logic of the closed-form expression of the remaining lifetime cumulative distribution function is as follows: ,because exist The event was established. Equivalent to That is, the system is The moment or before the first time entering a complete failure state Molecules are the system in Always in a non-failure state, The joint probability of entering a complete failure state at time t is given by the given condition, where the denominator is the probability of satisfying the corresponding observation counting conditions, and the numerator divided by the denominator is the conditional cumulative distribution function. Depicting from Hidden state at time Departure, Passage Step transition to complete failure state The probability, and These characteristics depict the collective patterns of multi-sensor observations under different health states.

[0138] Based on the closed-form expression of the cumulative distribution function of remaining lifetime, the point estimate and interval estimate of remaining lifetime at the current moment can be obtained, which are used to quantify the average level of the prediction and the prediction uncertainty, respectively.

[0139] Point estimation: Calculate the expected value of the remaining lifetime based on the cumulative distribution function of the remaining lifetime, and output it as the average remaining lifetime.

[0140]

[0141] Interval estimation: at a given confidence level The lower bound of the prediction interval is obtained by inverting the cumulative distribution function of the remaining lifetime. and the Upper Realm :

[0142]

[0143]

[0144] Make .

[0145] To verify the effectiveness of the proposed method, the FD001 subset of the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset, publicly available from NASAAmes Laboratory, was used for experimental verification. The FD001 subset contains 100 training trajectories and 100 test trajectories.

[0146] The training trajectory in the FD001 subset records the engine's full lifecycle monitoring data from start to finish, while the test trajectory records the monitoring data interrupted at a certain point before the engine failure, and includes a corresponding label for the actual remaining life. Each sample contains monitoring data from 21 sensors.

[0147] The monitoring data of 14 sensors were selected from the monitoring data of 21 sensors. The monitoring data of these 14 sensors can characterize the engine degradation process and serve as the input features of the multi-feature hidden Markov model.

[0148] The 100 training trajectories in the FD001 subset were randomly divided in a 6:2:2 ratio. 60 trajectories formed the training set for model training; 20 formed the validation set for determining the number of hidden states; and 20 formed the evaluation set for evaluating prediction performance. For the monitoring data of each selected sensor, K-means clustering was performed within the candidate cluster number range of 2 to 30. The optimal number of discrete levels was determined using a weighted Mann-Kendall test. The discrete observation levels were then aligned according to the sign of the statistical measure, ensuring that level 1 for each sensor represents the best observable state and the highest level represents the worst observable state. The degradation direction and optimal number of discrete levels for each sensor are shown in Table 1.

[0149] Table 1. Optimal Discreteness Number and Degradation Direction for Each Sensor

[0150]

[0151] Total number of hidden states Determined on the validation set using Bayesian information criteria. Within the candidate range. Within the model, the model parameters are estimated on the training set for each candidate hidden state number, and then the BIC value is calculated on the validation set. A higher BIC value indicates a better trade-off between goodness of fit and model complexity. The value corresponding to the maximum BIC value is taken. As the optimal number of hidden states. Figure 2 This shows the BIC values ​​corresponding to the number of candidate hidden states. The BIC value is highest at position 6, therefore the optimal number of hidden states is determined to be 6.

[0152] On the training set, using the discretized 14-dimensional observation sequence as input, the parameters of the multi-feature hidden Markov model are iteratively estimated using the constrained Baum-Welch algorithm. The convergence threshold is set to a log-likelihood increment of less than 10 between two consecutive iterations. -4 The maximum number of iterations is set to 500. The resulting initial state distribution is as follows: The hidden state transition probability matrix is:

[0153]

[0154] The visualization results of the emission probability matrices of each sensor are as follows: Figure 3 As shown.

[0155] When dividing the observation space, the observation space for each sensor is... Set the non-alarm subset as The alarm subset is set as This involves classifying the worst-case observation level of each sensor into a separate alarm subset, and classifying the remaining levels into a non-alarm subset. The inspection interval is then set. =20, the threshold for the number of first non-alarm features. =9, the threshold for the number of second non-alarm features. =13, conditional reliability threshold =0.5.

[0156] For each engine in the evaluation set, at each operating cycle, the posterior state occupancy probability is first recursively derived using the belief vector update formula, and then the conditional reliability at each cycle time is calculated based on the closed-form expression of conditional reliability. Figure 4 The curves showing the change of conditional reliability of four engines in the evaluation set over operating cycles are presented. In the initial stage of engine operation, the conditional reliability remains stable at a level close to 1 for a long period. As the number of operating cycles increases, the conditional reliability decreases in a stepwise manner, and rapidly drops to 0 near the moment of failure. This demonstrates that the conditional reliability function can effectively characterize the complete degradation process of an aero-engine from health to failure.

[0157] The remaining lifetime of each engine is predicted at each operating cycle throughout its entire lifespan on the evaluation set. At each cycle, the system state is determined by comparing the current conditional reliability with a threshold, and the cumulative distribution function of the remaining lifetime is calculated. Based on this, the average remaining lifetime point estimate and the prediction interval at a 95% confidence level are given. Figure 5 The remaining life prediction results for the four engines in the assessment focus are presented, from... Figure 5 It can be seen that the prediction interval is relatively wide in the early stage of degradation and the point estimate deviates from the true value relatively large, reflecting the inherent uncertainty of the remaining lifespan in the healthy state. As the number of operating cycles increases, the point estimate gradually approaches the true remaining lifespan, and the true value always falls within the 95% confidence interval, indicating that the adaptive prediction framework can provide reliable point estimates and interval estimates at different stages of degradation.

[0158] To quantitatively assess the prediction accuracy, the method proposed in this invention (the method of this invention), comparison method 1, and comparison method 2 were compared on a test set. The evaluation metrics included three items: score, root mean square error (RMSE), and mean absolute error (MAE). The test set consisted of 100 test trajectories from the FD001 subset.

[0159] The only difference between Comparison Method 1 and the method of the present invention is that Comparison Method 1 does not perform state discrimination, and always calculates the remaining lifetime cumulative distribution function based on the condition that the number of sensors falling into the non-alarm observation subset of each sensor is not less than the first non-alarm feature quantity threshold.

[0160] The only difference between Comparison Method 2 and the method of the present invention is that Comparison Method 2 does not perform state discrimination, and always calculates the remaining lifetime cumulative distribution function based on the condition that the number of sensors falling into the non-alarm observation subset of each sensor is less than the second non-alarm feature quantity threshold.

[0161] The formula for calculating the score is:

[0162]

[0163] in For the number of test samples, It is the difference between the actual remaining lifetime and the predicted remaining lifetime (actual value minus predicted value).

[0164] The formula for calculating RMSE is:

[0165]

[0166] The formula for calculating MAE is:

[0167]

[0168] The comparison results of various indicators of different methods are shown in Table 2.

[0169] Table 2 Comparison of metrics for different methods on the test set

[0170]

[0171] As can be seen from Table 2, the method of the present invention is significantly better than the two single strategies in all three indicators, indicating that the adaptive switching of prediction strategies based on conditional reliability can effectively utilize the information characteristics of different degradation stages and significantly improve the accuracy and robustness of remaining lifetime prediction.

[0172] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0173] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model, characterized in that, Includes the following steps: S1. Collect monitoring data from multiple sensors of the aero-engine throughout its entire life cycle, and the monitoring data is used to characterize the degradation process of the engine; The monitoring data of each sensor is discretized to obtain the discrete observation level corresponding to each sensor. The discrete observation levels are aligned based on the degradation direction to obtain the multivariate discrete observation sequence of the aero-engine. S2. Construct a multi-feature hidden Markov model. Based on the discrete observation sequences of each sensor, use the expectation-maximization algorithm to estimate the parameters of the multi-feature hidden Markov model to obtain the parameter-estimated multi-feature hidden Markov model. S3. Divide the observation space of each sensor into a non-alarm observation subset and an alarm observation subset, and derive the probability distribution of multi-source sensor observation counts under each hidden state condition based on the probability generation function. S4. Based on the multi-feature hidden Markov model after parameter estimation, derive the closed-form expression of the conditional reliability function of the multi-source sensor; S5. Based on the conditional reliability function of multi-source sensors, construct an adaptive remaining lifetime prediction model; based on the monitoring data to be measured of the aero-engine, recursively obtain the posterior state occupancy probability at the current moment through a multi-feature hidden Markov model after parameter estimation, and calculate the conditional reliability accordingly; the adaptive remaining lifetime prediction model determines the observation counting conditions to be adopted according to the conditional reliability, and outputs the cumulative distribution function of the remaining lifetime, the average remaining lifetime, and the prediction interval under the condition.

2. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The process of discretizing the monitoring data of each sensor is as follows: the monitoring data is pooled, and the K-means clustering algorithm is used to cluster the pooled monitoring data under multiple candidate cluster numbers to obtain the preliminary discrete label sequence corresponding to the monitoring data under each candidate cluster number. The weighted Mann-Kendall statistic of the preliminary discrete label sequence under each candidate cluster number is calculated. The minimum number of clusters that makes the monotonicity of the preliminary discrete label sequence tend to be stable is determined according to the absolute value of the weighted Mann-Kendall statistic. The minimum number of clusters is used as the optimal number of discrete levels of the sensor, and the monitoring data is mapped to discrete observation levels according to the optimal number of discrete levels. The process of aligning the discrete observation levels based on the degradation direction is as follows: the degradation direction of the monitoring data is determined according to the sign of the weighted Mann-Kendall statistic. If the sign is positive, the discrete observation levels are arranged in ascending order according to the cluster centroid. If the sign is negative, the discrete observation levels are arranged in descending order according to the cluster centroid. The discrete observation sequences of each sensor are then time-aligned to obtain the multivariate discrete observation sequence of the aero-engine.

3. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The parameters of the multi-feature hidden Markov model include the hidden state transition probability matrix, the emission probability matrix of each sensor, and the initial state distribution.

4. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The process of estimating the parameters of the multi-feature hidden Markov model using the expectation-maximization algorithm includes: S201. Based on the parameters of the current multi-feature hidden Markov model, for each multivariate discrete observation sequence, the forward variable is calculated by forward recursion, and the backward variable is calculated by backward recursion. The posterior state occupancy probability at each time step and the posterior state transition probability between adjacent time steps are calculated based on the forward and backward variables. S202. Update the parameters of the current multi-feature hidden Markov model based on the posterior state occupancy probability and the posterior state transition probability: Each dimension of the initial state distribution is updated to the mean of the posterior state occupancy probability at the start time of each multivariate discrete observation sequence, resulting in the updated state distribution. The hidden state transition probability matrix is ​​constrained into an upper triangular form, and the updated hidden state transition probability matrix is ​​obtained by dividing the posterior state transition probability statistic by the sum of all non-zero transition statistics of the corresponding hidden state. Based on the posterior state occupancy probability, the frequency of each sensor at each discrete observation level is counted to obtain the updated emission probability matrix of each sensor. S201 and S202 are executed alternately until the increment of the log-likelihood function of each discrete observation sequence is less than a preset threshold or the number of iterations reaches a preset number, thus obtaining the multi-feature hidden Markov model after parameter estimation.

5. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, S3 specifically includes: S301. Divide the observation space of each sensor into a non-alarm observation subset and an alarm observation subset that do not overlap, wherein the discrete observation level contained in the alarm observation subset is greater than the discrete observation level contained in the non-alarm observation subset. S302. Calculate the probability that the discrete observation level of each sensor falls into the non-alarm observation subset and the alarm observation subset under each hidden state based on the emission probability matrix. S303. Based on the Bernoulli distribution of each sensor falling into the non-alarm observation subset or alarm observation subset and the conditional independence under a given hidden state, construct the probability generation function of the multi-source sensor observation count in each hidden state. S304. Expand the probability generation function into a polynomial form to obtain the conditional probability mass function of the number of sensors falling into the non-alarm observation subset or the alarm observation subset in each hidden state.

6. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The closed-form expression for the conditional reliability function of the multi-source sensor is: In the formula, This represents the total number of hidden states. This is the hidden state transition probability matrix. Based on the current time Multi-source sensor joint observation history The updated system is in Always in a hidden state The probability of the posterior state occupies, For the system at time The probability of a posterior state being in a completely invalid state. The hidden state transition probability matrix From the hidden state in the power of Transition to hidden state The probability, From the current moment The initial prediction step size.

7. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, Methods for constructing adaptive remaining lifetime prediction models include: Set a conditional reliability threshold and a threshold for the number of non-alarm features; At the current moment, the conditional reliability after a preset number of steps is calculated based on the multi-feature hidden Markov model after parameter estimation, and the conditional reliability is compared with the conditional reliability threshold. When the conditional reliability is greater than or equal to the conditional reliability threshold, the aero-engine is determined to be in a relatively healthy state. The remaining lifetime cumulative distribution function is set with the condition that the number of sensors falling into the non-alarm observation subset of each sensor is not less than the first non-alarm feature number threshold. When the conditional reliability is less than the conditional reliability threshold, the aero-engine is determined to be in a degraded state. The remaining lifetime cumulative distribution function is set with the condition that the number of sensors falling into the non-alarm observation subset of each sensor does not exceed the second non-alarm feature number threshold.

8. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The closed-form expression for the cumulative distribution function of remaining lifetime is: In the formula, For the current moment, To predict the step size, To preset the inspection interval, For conditional reliability threshold, The threshold for the number of non-alarm features. This is the threshold for the number of the second non-alarm feature. The total number of sensors, This represents the total number of hidden states. For the current moment The set of hidden states for Remaining lifespan at any given moment The state at the initial moment The probability, Let be the hidden state transition probability matrix. For the process Step state transition from hidden state Reaching the hidden state The probability, For the process Step state from hidden state Transition to a completely failed state The probability, In the hidden state The number of sensors falling into the non-alarm observation subset is The conditional probability mass function. In the hidden state The number of sensors falling into the alarm observation subset is The conditional probability mass function.

9. The method for predicting the remaining life of an aero-engine based on multi-feature hidden Markov model according to claim 1, characterized in that, The expected value of the remaining lifetime is calculated based on the cumulative distribution function of the remaining lifetime, which is used as the average remaining lifetime. The inverse of the cumulative distribution function of the remaining lifetime is obtained at a given confidence level to obtain the lower and upper bounds of the prediction interval.

Images