Bayesian-based aviation equipment residual life uncertainty prediction method and system

Abstract

The invention provides a Bayesian-based aviation equipment residual life uncertainty prediction method and system. The method comprises the following steps: S1, constructing an observation function equation and a state parameter description equation of residual life of key or important systems, modules and parts of aviation equipment; s2, constructing an agent model; s3, solving joint posterior probability distribution and performing residual life prediction; and S4, according to the prediction probability distribution of the remaining life of the aviation equipment, generating an optimization control instruction or a maintenance instruction for the aviation equipment, and acting the optimization control instruction or the maintenance instruction on the aviation equipment. The method provided by the invention not only provides a theoretical basis for solving the problem of prediction, analysis and prediction of the service life of the aviation equipment, but also clearly defines how information and uncertainty thereof flow and convert between a physical world and a digital world, and provides a brand new thought for prediction of the uncertainty of the residual service life of the aviation equipment.

Description

A Bayesian-based method and system for predicting the uncertainty of remaining service life of aerospace equipment Technical Field

[0001] This invention relates to the fields of digital twins, reliability engineering, and aviation equipment safety, specifically to a Bayesian-based method and system for predicting the uncertainty of the remaining life of aviation equipment. Background Technology

[0002] Ensuring the high reliability and safety of complex aerospace equipment systems is a core challenge facing modern industry. Traditional methods relying on static safety margins and offline simulations are no longer sufficient to address performance drift issues caused by dynamic loads, material degradation, and environmental changes during actual service.

[0003] Digital twin (DT) technology offers a revolutionary way to bridge the gap between the "design state" and the "actual state" by constructing dynamic virtual mappings of physical assets. However, most existing digital twins are deterministic, with their predictions being single numerical values ​​that cannot quantify the reliability of the prediction itself. This lack of reliability fundamentally stems from the neglect of various uncertainties within the system. These uncertainties can be categorized as follows: 1) Aleatoric uncertainty, arising from the inherent randomness of the system, such as measurement noise and measurement noise matrices, which are non-reducible; 2) Epistemic uncertainty, arising from a lack of knowledge, such as imperfections in the physical model and unknown model parameters, which can be reduced through the accumulation of data and knowledge.

[0004] If these two types of uncertainty cannot be formally addressed, the output of a digital twin will be a "black box" with unknown confidence levels, posing a significant risk when supporting high-risk decision-making. Currently, while there are attempts to apply uncertainty quantification to engineering analysis, most are one-off offline assessments, failing to form a closed loop of continuous learning and dynamic adaptation with physical assets. Therefore, there is an urgent need in this field for a theoretically sound and practically feasible framework to seamlessly integrate uncertainty quantification into the real-time operation of digital twins, elevating them from simple simulators to intelligent systems capable of probabilistic reasoning and autonomous learning. Summary of the Invention

[0005] To address the shortcomings of the existing technology, the present invention aims to provide a Bayesian-based method and system for predicting the uncertainty of the remaining lifespan of aviation equipment. This method and system are used to systematically and dynamically manage the uncertainty of the entire life cycle of complex aviation equipment systems, so as to achieve high-confidence prediction of the remaining lifespan of aviation equipment and output maintenance instructions in real time based on the lifespan prediction results to maintain or repair the aviation equipment.

[0006] Specifically, in a first aspect, the present invention provides a method for predicting the uncertainty of the remaining life of aerospace equipment based on Bayesian state space, which includes the following steps: S1, constructing the observation function equation: The observation function equation is as follows: ;in, For observation data, These are the status parameters representing the remaining lifespan of critical or important systems, modules, and components of aviation equipment. For uncertain cognitive parameters, To reduce noise in the measurement data; For observation functions; state parameters of the remaining lifespan of critical or important systems, modules, and components of aviation equipment. The describing equation is: ;in, For process noise, S2. Constructing a surrogate model: Historical state space observation data is collected by sensors and multi-source data is fused to construct a multi-source heterogeneous historical state dataset. A surrogate model of the state transition function is generated based on the multi-source heterogeneous historical state dataset. and surrogate models of observation functions S3, Solve for the joint posterior probability distribution, specifically: S31, For uncertain cognitive parameters Initial state parameters of the remaining life of critical or important systems, modules and components of aviation equipment. Set the prior probability distributions respectively and S32. Based on the observation function equation, a recursive Bayesian filtering algorithm is used at each time step. Received observation data Subsequently, through two stages of prediction and updating, the state parameters of the remaining lifespan of key or important systems, modules, and components of aviation equipment are recursively solved based on a surrogate model. With uncertain cognitive parameters joint posterior probability distribution S33, Based on joint posterior probability distribution S4. Calculate the predicted probability distribution of the remaining lifespan of the aircraft equipment; Based on the predicted probability distribution of the remaining lifespan of the aircraft equipment, generate optimized control commands for the aircraft equipment. Or maintenance instructions, and apply to aircraft equipment.

[0007] Preferably, in step S32, the sequential Monte Carlo method is used as the recursive Bayesian filtering algorithm, through a set of weighted particles. The joint posterior probability distribution is approximated, where Np represents the total number of particles drawn, and i represents an element in the set of the selected Np particles.

[0008] Preferably, the surrogate model is a physical information neural network, and the total loss function of the surrogate model is: ;in, The traditional data fitting loss; For physical residual loss, For traditional data fitting loss weights, This represents the weight of the physical residual loss.

[0009] Preferably, step S32 specifically includes the following sub-steps: S321, Initialization: Extracting from the prior distribution of parameters and initial state One particle; S322, Preliminary prediction: Invoke the proxy model S323, Preliminary prediction of the state of each particle: When new observation data is received, the surrogate model is invoked. Calculate the likelihood value for each particle state that produces the observation, and update the particle weights based on the likelihood value. S324, Output uncertain cognitive parameters and state Discrete representation of the joint posterior probability distribution.

[0010] Preferably, step S33 specifically involves: using the joint posterior probability distribution obtained in step S32 as a new sampling distribution, running a surrogate model on each sample to obtain a set of predicted trajectories of future performance as the predicted probability distribution of the remaining lifespan of the aviation equipment.

[0011] Preferably, step S33 further includes outputting a global sensitivity index to quantitatively assess the contribution of each input uncertainty parameter to the output uncertainty. The specific method for solving the global sensitivity index is as follows: the expansion coefficient is calculated by spectral projection or non-invasive regression method, the complete statistical information of the output is obtained in real time, and the global sensitivity index is calculated.

[0012] Preferably, the multi-source data in step S2 includes numerical simulation data, ground test data, flight test data, and service data.

[0013] Secondly, this invention provides a prediction system for the uncertainty of remaining service life of aviation equipment based on observation function equations, which includes a perception domain, a modeling domain, and a quantization engine domain; the perception domain is used to process observation data collected by sensors from aviation equipment. The modeling domain is used for data based on historical observations. A surrogate model is constructed, using remaining lifetime state parameters as input, and outputting remaining lifetime parameters for key / important systems, modules, and components. The quantization engine domain includes a recursive Bayesian filtering algorithm to store the prior probability distributions of cognitive parameters and initial remaining lifetime state parameters. Receive real-time observation data from the sensing domain. The proxy model of the modeling domain is invoked to recursively calculate the joint posterior probability distribution of the state and parameters; the decision domain is used to output control or maintenance instructions for key / important systems, modules and components based on the posterior probability distribution output by the quantization engine.

[0014] Preferably, the modeling domain includes a multi-fidelity hybrid modeling module, which uses a physical information neural network to construct a surrogate model and outputs a state transition function. The quantization engine domain includes an online Bayesian update module and an uncertainty propagation and analysis module. The online Bayesian update module is used to update the surrogate model based on real-time observation data and output uncertain cognitive parameters. and state The discrete representation of the joint posterior probability distribution is used. The uncertainty propagation and analysis module makes probabilistic predictions of the future behavior of the system based on the posterior probability distribution, and outputs the probability density function or cumulative distribution function of key performance indicators and the global sensitivity index.

[0015] Preferably, the online Bayesian update module uses the sequential Monte Carlo algorithm to approximate the posterior probability distribution using weighted random samples.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The method of the present invention abstracts and formalizes aviation equipment and digital systems into a Bayesian observation function equation. This not only provides a theoretical basis for solving the RUL analysis and prediction problem of aviation equipment, but also clearly defines how information and its uncertainty flow and transform between the physical world and the digital world. Under this framework, the process of reducing cognitive uncertainty is interpreted as a Bayesian recursive estimation problem of model parameters, while random uncertainty is used as the accurate probability propagation of system and measurement noise.

[0017] (2) The method of this invention innovatively integrates an online Bayesian update mechanism, breaking through the technical bottleneck of traditional modeling methods that rely on general data and are difficult to adapt to individual differences in aviation equipment. This method can deeply mine the unique data throughout the entire life cycle of aviation equipment, and through a dynamic iterative learning process, continuously optimize the structural parameters and predictive performance of the surrogate model, systematically reducing the model output bias and the estimation uncertainty of key performance parameters. By continuously reducing uncertainty, the surrogate model can stably output highly reliable equipment status representation results, providing accurate data support for key aspects such as fault prediction and health management, performance optimization, and maintenance decisions of aviation equipment.

[0018] (3) The method of this invention breaks through the technical limitation of traditional prediction methods that only output single-point prediction values. By outputting complete probability distribution results, it not only achieves accurate quantitative representation of prediction results, but also intuitively presents the confidence interval, fluctuation range, and probability of occurrence of various risk events of the prediction values. This fundamentally solves the core problem that traditional single-point prediction cannot reflect uncertainty and leads to a lack of risk reference for decision-making. It enables decision-makers to fully grasp the reliability boundary and potential risk dimensions of prediction results, no longer relying on empirical judgment or fuzzy assessment, but instead conducting risk trade-offs and decision optimization based on quantified uncertainty information. This effectively reduces the probability of decision-making errors caused by insufficient information, significantly improves the rationality, foresight, and feasibility of decisions, and has broad practical application value and promotion prospects. Attached Figure Description

[0019] Figure 1 is a schematic diagram of the overall method flow of the aviation equipment remaining life uncertainty prediction method based on Bayesian state space according to the present invention; Figure 2 is a schematic diagram of the PMQD loop under PDTF proposed in the present invention; Figure 3 is a schematic diagram of the PDTF technology implementation path proposed in the present invention; Figure 4 is a probability density function evolution diagram of the remaining life of the aero-engine turbine disk in the embodiment of the present invention. Detailed Implementation

[0020] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings and specific application examples.

[0021] As shown in Figures 1-4, specifically, on one hand, this invention provides a method for predicting the uncertainty of the remaining life of aerospace equipment based on Bayesian state space, which includes the following steps: S1, constructing the observation function equation: The observation function equation is as follows: ;in, The equation for the observation function is... State parameter description equations for the remaining lifespan of critical or important systems, modules, and components of aviation equipment. For uncertain cognitive parameters, To measure the noise matrix.

[0022] State parameter description equations for the remaining life of critical / important systems, modules, and components of aviation equipment It can describe the evolution of hidden states within aircraft equipment related to their remaining service life. The evolution of hidden states generally includes changes in temperature, vibration, thrust, and geometric deformation. , This is the process noise matrix. Critical systems, modules, and components refer to those whose failures would endanger personal safety and prevent the aircraft equipment from completing its primary missions. Important systems, modules, and components refer to those whose failures would prevent the aircraft equipment from completing its primary missions.

[0023] S2. Constructing a surrogate model: Historical state space observation data is collected by sensors and multi-source data is fused to construct a multi-source heterogeneous historical state dataset. In a specific embodiment, the multi-source data includes numerical simulation data, ground test data, flight test data, and service data. After obtaining the multi-source data, the data is cleaned and used to construct the multi-source heterogeneous historical state dataset. Then, a surrogate model of the state transition function is generated based on the multi-source heterogeneous historical state dataset. and surrogate models of observation functions The real-time remaining lifespan of the aircraft equipment is obtained by solving the observation function equation using a surrogate model. The surrogate equation enables efficient computation of the state equation. and / or observation equations .

[0024] In a specific embodiment, the proxy model is a physical information neural network, and the total loss function of the proxy model is... for: ;in, It is a traditional data fitting loss (such as mean square error), used to fit existing high-fidelity simulation data or sparse sensor data. This is the Physical Residual Loss (PDE). It uses automatic differentiation to calculate the derivative of the network output with respect to the input (time and spatial coordinates) and substitutes this derivative into the PDE. This ensures that the network, during training, not only fits the data but also adheres to known physical laws. This method allows the model to make reasonable inferences consistent with physical laws even in sparse data regions, greatly improving the model's generalization ability and data efficiency.

[0025] S3, Probability Quantification, specifically: S31, Cognitive Parameters for Uncertainty. Description of initial state parameters for the remaining lifespan of critical or important systems, modules, and components of aviation equipment. Set the prior probability distributions respectively and Prior probability distribution and The settings are based on existing experience and the results of statistical data analysis from existing experiments / uses.

[0026] S32. Based on the observation function equation, a recursive Bayesian filtering algorithm is used at each time step. Received observations Then, through two stages of prediction and update, the relevant state parameters of RUL are recursively solved. With uncertain cognitive parameters joint posterior probability distribution In a specific embodiment, the sequential Monte Carlo method is used as the recursive Bayesian filtering algorithm, through a set of weighted particles. The joint posterior probability distribution is approximated. Here, Np represents the total number of particles drawn, and i represents an element in the set of the selected Np particles.

[0027] Step S32 specifically includes the following sub-steps: S321, Initialization: Extract from the prior distribution of parameters and initial state One particle.

[0028] S322, Preliminary prediction: Invoke the proxy model of module one. This allows for a preliminary prediction of the state of each particle.

[0029] S323, Weight Update: When new observation data is received, the surrogate model is invoked. Calculate the likelihood value that produced the observation for each particle state. And update the particle weights based on the likelihood values. This yields a set of weighted particles. .

[0030] S324, Utilizing weighted particles Output uncertain cognitive parameters and state Discrete representation of the joint posterior probability distribution. Obtain the joint posterior probability distribution. Then, this is used as a new prior, and Monte Carlo simulation or multinomial chaotic expansion is performed through a surrogate model to quantify the uncertainty of future RUL performance indicators. The discretization step is specifically represented as follows: after updating the weights of the examples based on the observations, the surrogate model updates the posterior probability distribution of the initial state parameters of the remaining lifetime based on the prior probability distribution of the initial state parameters of the remaining lifetime. Subsequently, based on the generated posterior distribution, it is discretized using sampling methods represented by the Monte Carlo method.

[0031] S33, Based on joint posterior probability distribution The predicted probability distribution of the remaining lifespan of the aviation equipment and the global sensitivity index are calculated. Specifically, the predicted probability distribution of the remaining lifespan of the aviation equipment is calculated as follows: the joint posterior probability distribution obtained in step S32 is used as a new sampling distribution, and a surrogate model is run on each sample to obtain a set of predicted trajectories of future performance as the predicted probability distribution of the remaining lifespan of the aviation equipment.

[0032] The specific method for solving the global sensitivity index is as follows: the expansion coefficient is calculated by spectral projection or non-invasive regression method, the complete statistical information of the output is obtained in real time, and the global sensitivity index is calculated.

[0033] S4. Based on the predicted probability distribution of the remaining lifespan of the aviation equipment, generate optimized control commands for the aviation equipment. Control or maintenance instructions, and applied to aircraft equipment. These instructions are generated by, but are not limited to: expert systems, machine learning and deep learning, knowledge graphs, and generative large model techniques / methods in vertical fields.

[0034] Secondly, the present invention provides a prediction system for the uncertainty of the remaining life of aviation equipment based on observation function equations, which includes a perception domain, a modeling domain, and a quantization engine domain.

[0035] The sensing domain is used to process observation data collected by sensors from aviation equipment. .

[0036] Modeling domain is used for historical observation data Construct a proxy model, using the remaining lifetime state parameters as input, and output the remaining lifetime parameters of key / important systems, modules and components.

[0037] The quantization engine domain is equipped with a recursive Bayesian filtering algorithm to store the prior probability distributions of cognitive parameters and initial remaining lifetime state parameters. Receive real-time observation data from the sensing domain. ; Invoke the proxy model of the modeling domain and recursively calculate the joint posterior probability distribution of the state and parameters.

[0038] The decision domain is used to output control or maintenance commands for critical / important systems, modules, and components based on the posterior probability distribution output by the quantization engine. The decision domain optimizes maintenance intervals based on the calculated Probability Density Function (PDF) of the Remaining Useful Life (RUL). Maintenance commands are triggered when the preset quantile of the PDF (e.g., 5%) falls below a safety threshold. Control or maintenance commands in the decision domain are generated by, but are not limited to, expert systems, machine learning and deep learning, knowledge graphs, and generative large-scale model techniques / methods in vertical fields.

[0039] The modeling domain includes a multi-fidelity hybrid modeling module, which uses a physical information neural network to construct a surrogate model and outputs a near-realistic state transition function. In specific applications of this invention, the Physical Information Neural Network (PINN) is preferably used as a surrogate model for remaining lifetime analysis and prediction. PINN is a deep neural network whose innovation lies in incorporating the residuals of the physical governing equations, which are typically partial differential equations, as a term into the network's loss function. Its total loss function... It can be represented as: ;in, It is a traditional data fitting loss (such as mean square error), used to fit existing high-fidelity simulation data or sparse sensor data. This is the Physical Residual Loss (PDE). It uses automatic differentiation to calculate the derivative of the network output with respect to the input (time and spatial coordinates) and substitutes this derivative into the PDE. This ensures that the network, during training, not only fits the data but also adheres to known physical laws. This method allows the model to make reasonable inferences consistent with physical laws even in sparse data regions, greatly improving the model's generalization ability and data efficiency.

[0040] In other embodiments, a multi-fidelity Gaussian process regression Co-Kriging model is employed as an alternative or supplementary method for the surrogate model in remaining lifetime analysis and prediction. The Co-Kriging model can integrate data sources of different fidelities. It learns the correlation structure between high-fidelity and low-fidelity data—for example, the difference or ratio between them—and uses a large number of low-fidelity model calculations to enhance a small number of high-fidelity model calculations, thereby constructing a relatively accurate surrogate model across the entire design space.

[0041] The quantization engine domain includes an online Bayesian update module and an uncertainty propagation and analysis module. The online Bayesian update module is used to update the surrogate model based on real-time observation data, outputting uncertain cognitive parameters. and state The discrete representation of the joint posterior probability distribution is used. The uncertainty propagation and analysis module makes probabilistic predictions of the system's future behavior based on the posterior probability distribution, outputting the probability density function or cumulative distribution function of key performance indicators and the global sensitivity index. The online Bayesian update module uses the sequential Monte Carlo algorithm to approximate the posterior probability distribution using weighted random samples.

[0042] The implementation methods of the uncertainty propagation and analysis module include, but are not limited to: For scenarios requiring rapid forward prediction of a large number of variables, embodiments of the present invention may employ polynomial chaotic expansion (PCE). PCE represents the model output as a linear combination of a set of orthogonal polynomial bases with respect to the input random variables. Once the expansion coefficients are calculated using spectral projection or non-intrusive regression methods, complete statistical information of the output, such as mean, variance, PDF, etc., can be obtained almost in real time, and the global sensitivity index can be analytically calculated.

[0043] The output parameter posterior distribution is used as a new sampling distribution for large-scale Monte Carlo simulation. That is, a large number of parameter samples are drawn from this posterior distribution, and the surrogate model of Module 1 is run on each sample to obtain a set of predicted trajectories for future performance.

[0044] This embodiment takes the probabilistic life prediction of an aero-engine turbine disk as an example to provide a detailed and reproducible description of the complete implementation process of the present invention.

[0045] Application Scenario: The turbine disk, a critical component of a certain type of aero-engine, primarily fails through low-cycle fatigue crack propagation. The goal is to create a dedicated probabilistic digital twin for each turbine disk in the winged aircraft fleet, dynamically track its health status, and provide quantifiable confidence-based RUL predictions to support condition-based maintenance.

[0046] S1. State space construction and uncertainty representation instantiate the theoretical model.

[0047] Equation of State: The Paris-Erdogan law is chosen as the physical model to describe crack propagation. This law represents the crack increment per flight cycle. With stress intensity factor range Related.

[0048] Hidden state Defined as the first Crack size at the end of the cycle .

[0049] State transition function : ;in, C represents the amplitude of the unit stress intensity factor (i.e., The basic crack propagation rate at (t) time. m represents the sensitivity of the material's crack propagation rate to stress changes.

[0050] It is a shape factor related to cracks and component geometry. It is the equivalent stress range for each cycle.

[0051] Cognitive uncertainty parameters Defined as a material property parameter These two parameters are fixed for a specific turbine disk, but vary between manufacturing and material batches, and are therefore unknown to maintenance engineers.

[0052] Process noise This assumes the model is perfect. In more complex models, it can represent unmodeled measurement noise matrices, etc.

[0053] Observation equation: During ground maintenance, NDT techniques such as eddy current testing are used to measure crack size.

[0054] Observations In the 1st The results of NDT measurements performed in one cycle.

[0055] Observation function : ; Measurement noise : Represents the inherent measurement error of NDT equipment, which is usually assumed to follow a Gaussian distribution.

[0056] Uncertainty Prior Distribution Setting: Based on historical test data and expert knowledge of the turbine disk material of this model, the prior probability distribution of the parameters is set to a normal distribution. .

[0057] Cognitive parameter priors: ; .

[0058] Random uncertainty distribution: initial crack size Assume that there may be minor initial defects at the time of manufacture, and that the size of these defects follows a log-normal distribution.

[0059] This represents an average size of approximately 0.69 mm.

[0060] Noise measurement : .

[0061] S2. Constructing the proxy model. This embodiment uses a physical information neural network as the proxy model.

[0062] S3. Probabilistic quantization based on the SMC algorithm.

[0063] This step will demonstrate how PDTF uses data from two NDT measurements to continuously learn and update predictions. We use particle number... The SMC algorithm.

[0064] Phase 0: Initial prediction (t=0, zero-flight cycle).

[0065] Initialization: Generation Each particle. Sampling from the prior distribution: , .

[0066] Sampling from the initial crack size distribution: .

[0067] Set initial weights .

[0068] Forward uncertainty propagation (initial RUL prediction): for each particle , using its parameters and initial state By integrating the state equation forward, the crack size is increased until it reaches a preset critical threshold. mm. Record the total number of iterations required to reach this threshold. These 5000 The values ​​constitute the prior probability distribution of RUL.

[0069] Results: As shown by the broad blue curve in Figure 4, this distribution range is wide, reflecting a high degree of uncertainty when no actual observational data is available. For example, its 95% confidence interval may be a secondary cycle.

[0070] Initial decision: Based on this highly uncertain prediction, in order to ensure safety, only an extremely conservative maintenance strategy can be adopted, such as stipulating that all turbine disks must be replaced after 6,000 cycles.

[0071] Phase 1: The first data assimilation is performed during the N=2000 loop.

[0072] Sensing: Obtaining the first NDT measurement data and the first observation data. mm.

[0073] Quantization (SMC Update): Prediction / Propagation: For each particle initialized in Phase 0 Its state from the initial crack size Propagation continues to the 2000th cycle to obtain the predicted crack size. .

[0074] Weight Update: Calculate the likelihood of each particle relative to the observation data. The likelihood function is determined by the observation equations and the distribution of measurement noise. .

[0075] Update weights: .

[0076] Normalization: .

[0077] Resampling: Calculate the effective number of particles If lower Then according to the weight Perform resampling, then reset the weights of all particles to... After resampling, particles that better explain the observed data (i.e., predicted values ​​close to 1.2 mm) are replicated, while particles with poor explanatory power are discarded.

[0078] Updated RUL prediction: For the resampled particle set, from the current state and cycle number Begin, continue integrating forward until the [number]th ... When the cycle ends mm, to obtain the new failure cycle number RUL is .

[0079] Results: As shown by the green curve in Figure 4, the PDF of RUL becomes narrower, and the uncertainty decreases. The statistic of the posterior distribution of the cognitive parameters (applied by weighted particles) becomes: (Standard deviation decreased to 0.12) That is, the standard deviation drops to 0.06.

[0080] Decision Update: At this point, the maintenance engineer has a more certain understanding of the turbine disk's lifespan and can postpone the maintenance schedule.

[0081] Phase 2: Second Data Assimilation (at N=4000 cycles) Sensing: Obtain the second NDT measurement data. mm.

[0082] Quantization (SMC Update Again): Prediction / Propagation: For each particle after Phase 1 update change its state from Propagation to the 4000th cycle yields... .

[0083] Weight update: Using new observations mm calculates the new likelihood and updates the weights.

[0084] Normalization and resampling.

[0085] Final RUL prediction and decision: Perform forward integration on the latest particle set to obtain the final RUL posterior distribution.

[0086] Results: As shown by the red curve in Figure 4, the PDF of RUL becomes highly concentrated. The posterior distribution of cognitive parameters further converges. (Standard deviation decreased to 0.07) (Standard deviation decreased to 0.03). This indicates that, through two data assimilation processes, our understanding of the material properties of this particular turbine disk is already very accurate.

[0087] S4. Final Decision: Based on this highly confident RUL distribution, such as a 95% confidence interval as the subcycle, a precise CBM plan can be developed. For example, a decision rule can be set: when the 5th percentile of the RUL distribution is below 1000 safety margin cycles, a maintenance work order is triggered. This achieves a maximum balance between safety and economic benefits.

[0088] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space, characterized in that: It includes the following steps: S1. Construct the observation function equations and the descriptive equations for the state parameters of the remaining lifespan of key or important systems, modules, and components of the aviation equipment: The observation function equations are as follows: ;in, For observation data, These are the status parameters representing the remaining lifespan of critical or important systems, modules, and components of aviation equipment. For uncertain cognitive parameters, To reduce noise in the measurement data; For observation functions; state parameters of the remaining lifespan of critical or important systems, modules, and components of aviation equipment. The describing equation is: ;in, For process noise, S2. Constructing a surrogate model: Historical state space observation data is collected by sensors and multi-source data is fused to construct a multi-source heterogeneous historical state dataset. A surrogate model of the state transition function is generated based on the multi-source heterogeneous historical state dataset. and surrogate models of observation functions S3. Solve for the joint posterior probability distribution and predict remaining lifespan, specifically: S31. For uncertain cognitive parameters... Initial state parameters of the remaining life of critical or important systems, modules and components of aviation equipment. Each sets a prior probability distribution. and S32. Based on the observation function equation, a recursive Bayesian filtering algorithm is used at time step 1~ Received observation data Subsequently, through two stages of prediction and updating, the state parameters of the remaining lifespan of key or important systems, modules, and components of aviation equipment are recursively solved based on a surrogate model. With uncertain cognitive parameters joint posterior probability distribution S33, Based on joint posterior probability distribution S4. Calculate the predicted probability distribution of the remaining lifespan of the aircraft equipment; Based on the predicted probability distribution of the remaining lifespan of the aircraft equipment, generate optimized control commands for the aircraft equipment. Or maintenance instructions, and apply to aircraft equipment.

2. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 1, characterized in that: In step S32, the sequential Monte Carlo method is used as the recursive Bayesian filtering algorithm, through a set of weighted particles. The joint posterior probability distribution is approximated, where Np represents the total number of particles drawn, and i represents an element in the set of the selected Np particles.

3. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 1, characterized in that: surrogate model of state transition function and surrogate models of observation functions For a physical information neural network, the total loss function of the surrogate model is: ;in, The traditional data fitting loss; For physical residual loss, For traditional data fitting loss weights, This represents the weight of the physical residual loss.

4. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 2, characterized in that: Step S32 specifically includes the following sub-steps: S321, Initialization: Starting from uncertain cognitive parameters Initial state parameters of the remaining life of critical or important systems, modules and components of aviation equipment. Drawing from the prior distribution One particle; S322, Preliminary prediction: surrogate model calling state transition function. and surrogate models of observation functions S323, Weight Update: When new observation data is received, the surrogate model of the observation function is called. Calculate the likelihood value for each particle state that generated the observation data, and update the particle weights based on the likelihood value. S324. A discrete representation of the joint posterior probability distribution of the output uncertain cognitive parameters and the initial state parameters of the remaining lifespan of key or important systems, modules and components of aviation equipment.

5. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 2, characterized in that: Step S33 specifically involves: using the joint posterior probability distribution obtained in step S32 as a new sampling distribution, running a surrogate model on each sample to obtain a set of predicted trajectories of future performance as the predicted probability distribution of the remaining lifespan of the aviation equipment.

6. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 2, characterized in that: Step S33 also includes outputting a global sensitivity index to quantitatively assess the contribution of each input uncertainty parameter to the output uncertainty. The specific method for solving the global sensitivity index is as follows: calculate the expansion coefficient through spectral projection or non-invasive regression methods, obtain complete statistical information of the output in real time, and calculate the global sensitivity index.

7. The method for predicting the uncertainty of remaining service life of aerospace equipment based on Bayesian state space according to claim 2, characterized in that: The multi-source data in step S2 includes numerical simulation data, ground test data, flight test data, and service data.

8. A system for predicting the remaining life uncertainty of aviation equipment based on observation function equations, used in the Bayesian state-space-based method for predicting the remaining life uncertainty of aviation equipment as described in claim 1, characterized in that: It includes the perception domain, the modeling domain, and the quantization engine domain; the perception domain is used to process observation data collected by sensors from airborne equipment. ； Modeling domain is used for historical observation data A surrogate model is constructed, using remaining lifetime state parameters as input, and outputting remaining lifetime parameters for key / important systems, modules, and components. The quantization engine domain includes a recursive Bayesian filtering algorithm to store the prior probability distributions of cognitive parameters and initial remaining lifetime state parameters. Receive real-time observation data from the sensing domain. ； The proxy model of the modeling domain is invoked to recursively calculate the joint posterior probability distribution of the state and parameters; the decision domain is used to output control or maintenance instructions for key / important systems, modules and components based on the posterior probability distribution output by the quantization engine.

9. The aviation equipment remaining life uncertainty prediction system based on observation function equations according to claim 8, characterized in that: The modeling domain includes a multi-fidelity hybrid modeling module, which uses a physical information neural network to construct a surrogate model and outputs a near-realistic state transition function. The quantization engine domain includes an online Bayesian update module and an uncertainty propagation and analysis module. The online Bayesian update module is used to update the surrogate model based on real-time observation data and output uncertain cognitive parameters. and state The discrete representation of the joint posterior probability distribution is used. The uncertainty propagation and analysis module makes probabilistic predictions of the future behavior of the system based on the posterior probability distribution, and outputs the probability density function or cumulative distribution function of key performance indicators and the global sensitivity index.

10. The airborne equipment remaining life uncertainty prediction system based on observation function equations according to claim 9, characterized in that: The online Bayesian update module uses the sequential Monte Carlo algorithm to approximate the posterior probability distribution using weighted random samples.

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