Digital twin modeling method for methanol fuel supply system based on dynamic bayesian network

Abstract

This invention discloses a digital twin modeling method for a methanol fuel supply system based on a dynamic Bayesian network. Based on the laws of mass conservation, momentum conservation, and energy conservation, a modular mechanistic model of the methanol fuel supply system is established. For key components in the system prone to performance degradation, correction parameters that vary with operating conditions are introduced into the mechanistic model to construct an enhanced physical model that includes performance degradation characteristics. The system state variables and correction parameter vectors are defined as random variables and embedded within a dynamic Bayesian network framework to establish a probabilistic state-space model containing state equations and observation equations. A particle filtering algorithm is used to recursively update the mechanistic model, achieving joint estimation and online calibration of the system state and correction parameters. Based on the posterior estimation of the updated correction parameters, the calibrated predicted system state value is output, and the health status of key components is accurately assessed based on parameter drift.

Description

Technical Field

[0001] This invention relates to the fields of marine power engineering and digital twin technology, specifically to a digital twin modeling method for a methanol fuel supply system based on dynamic Bayesian networks. Background Technology

[0002] Methanol, due to its clean combustion properties and relatively mature storage and transportation technologies, is becoming an important alternative fuel for marine propulsion. The methanol fuel supply system, as the core link between the fuel tank and the main engine, primarily functions to provide the engine with methanol fuel at pressure, temperature, and flow rates that meet specific requirements. The operational stability of this system directly affects the ship's navigation safety and power efficiency.

[0003] However, the methanol fuel supply system is a typical complex electromechanical-hydraulic coupled system, facing multiple uncertainties in actual marine operation. First, methanol fuel has unique physicochemical properties, and the system's operating conditions (such as load changes and sea state fluctuations) change frequently. Second, key components in the system (such as high-pressure pumps, regulating valves, and heat exchangers) may experience performance degradation, wear, or internal leakage after long-term operation, leading to time-varying system characteristics. Finally, data collected by shipboard sensors is often accompanied by various environmental noises and interferences.

[0004] Traditional physical mechanism models are typically built based on fixed design parameters (such as rated efficiency and theoretical heat transfer coefficient). When the physical entity degrades, the static mechanism model cannot automatically sense and adjust its internal parameters, causing the error between the model output and the actual observation value to increase over time, thus losing the ability to monitor and predict the true state of the system.

[0005] Existing solutions sometimes employ purely data-driven methods, but these methods lack physical interpretability and are difficult to generalize in the absence of sample data. Others attempt to modify the physical model, but often only use simple error feedback correction, failing to quantify the uncertainty of model parameters from a probabilistic and statistical perspective, and also making it difficult to achieve a quantitative assessment of equipment health status.

[0006] Therefore, there is an urgent need for a digital twin modeling method for methanol fuel supply systems that can maintain physical interpretability, dynamically correct model parameters using real-time data, and effectively handle multi-source uncertainties. Summary of the Invention

[0007] To address the limitations of existing methanol fuel supply system modeling methods, this invention provides a digital twin modeling method for methanol fuel supply systems based on dynamic Bayesian networks, characterized by the following steps: S1. Based on the laws of conservation of mass, momentum and energy, a modular mechanism model of the methanol fuel supply system is established to describe the dynamic evolution of pressure, temperature and flow state variables within the system. S2. For key components in the system that are prone to performance degradation, including booster pumps, heat exchangers, valves and filters, a correction parameter that varies with operating conditions is introduced into the mechanism model to construct an enhanced physical model that includes performance degradation characterization. S3. Define the system state variables and the modified parameter vector as random variables, embed them into a dynamic Bayesian network framework, establish a probabilistic state space model containing state equations and observation equations, construct an augmented state vector containing system state variable vectors, degenerate state quantities and deviation term parameter vectors, and explicitly characterize process noise and observation noise. S4. Based on real-time sensor observation data, the system's state input variables and the state output variables obtained from the mechanism model are acquired. The particle filter algorithm is used to perform recursive Bayesian updates on the mechanism model to achieve joint estimation and online calibration of the system state and correction parameters. The degenerate state variables satisfy the non-negative increment accumulation form, and the transfer prior of the degenerate increment is explicitly incorporated into the particle weight update process. S5. Based on the updated corrected parameter posterior estimation, output the calibrated system state prediction value, and assess the health status of key components based on parameter drift.

[0008] Furthermore, the process of establishing the modular mechanism model of the methanol fuel supply system described in S1 includes: S11. Based on the laws of conservation of mass, momentum, and energy, and the characteristic parameters of components, a modular mechanism model including fuel tank, booster pump, heat exchanger, valve and filter is established to describe the state change process of methanol in each component in the methanol fuel supply system. S12. The outlet pressure and temperature of the first-stage booster pump, the outlet pressure and temperature of the second-stage booster pump, the outlet pressure and temperature of the heat exchanger of the methanol fuel supply system are calculated using the aforementioned mechanism model.

[0009] Furthermore, the enhanced physics model described in S2 includes: The first-stage booster pump is at a constant time Correction pressure head Represented as: in, This indicates the degree of efficiency degradation of the primary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the primary booster pump. This refers to the actual speed of the primary booster pump. This represents the leakage / slippage additional loss coefficient of the first-stage booster pump; The secondary booster pump is at a certain time Correction pressure head Represented as: in, This indicates the degree of efficiency degradation of the secondary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the secondary booster pump. This refers to the actual speed of the secondary booster pump. This represents the leakage / slippage additional loss coefficient of the secondary booster pump.

[0010] The heat exchanger is constantly Corrected outlet temperature Represented as: in, This refers to the heat exchanger inlet temperature. The heat transfer efficiency coefficient, For reference temperature, This is a temperature-based systematic bias term; and in, The nominal heat transfer efficiency coefficient, Indicates the amount of fouling and degradation in the heat exchanger. It is a smoothing constant. This represents the mass flow rate of methanol.

[0011] The valve is at all times Corrected flow Represented as: in, The nominal flow coefficient, This represents the actual valve opening. This indicates the degree of degradation in the valve's flow coefficient. The pressure difference across the valve. For the density of the medium, Add a flow term for internal leakage.

[0012] Filter at time Corrected pressure drop Represented as: in, Nominal flow resistance coefficient Indicates the amount of filter clogging and degradation. This is a systematic bias term for voltage drop.

[0013] Furthermore, S3 specifically includes the following steps: S31. Construct the state vector of DBN This vector contains the system's state variables and the aforementioned correction parameters: in Let be the system's physical state vector. , , , Let these represent the pressure, flow rate, and temperature at time t, respectively. To correct the parameter vector, it is defined as: ; S32. Given the augmented state at the previous time step System Input and the correction parameter vector Under the given conditions, the predicted prior distribution of the enhanced physics model is constructed, and its state transition equation is expressed as: in, This is a combined prediction function of a modular mechanistic model and an enhanced physical model based on the conservation of mass, momentum, and energy. For the evolution model of degradation and deviation parameters, This includes process noise caused by unmodeled errors and random disturbances. Indicates parameter evolution noise; Therefore, the state transition probability distribution of the augmented state is obtained as follows: .

[0014] Furthermore, S4 specifically includes the following steps: S41. Obtain the initial state of the particles based on the system state and prior distribution. For all particles... , , in, This represents the initial physical state of the system and the degradation / deviation parameters of the i-th particle. As a prior distribution, is the initial particle weight, and N is the number of particles; S42. At that moment Based on the particle state at the previous moment and input By performing forward prediction on all particles using the state transition equation, the particle state at time t is obtained. and correction parameter vector ; Degenerate state variables are represented by a non-negative incremental cumulative form: in ; For degenerate incremental random variables; S43. Particles Calculate the predicted values ​​of observations using an enhanced physical model. : in, The observation function is composed of the combined physical models of the key components in S2. During the particle filter update process, based on the observation data Update particle weights: The observation consistency term uses Gaussian likelihood; a degenerate consistency term is also introduced. The non-negative increment of degradation is used as the transition prior and explicitly incorporated into the weight update: in, , For degradation increment; The Gamma distribution is used to characterize the irreversible degradation process; The vector of deviation terms; Used to constrain the slow drift of the deviation term; Normalize the weights: ; S44. Calculate the number of valid samples. If the number of valid samples is lower than a preset threshold, perform a resampling operation and reset the particle weights to: ; S45. Finally, the posterior estimate of the model is calculated using a weighted average: in, These are the normalized weights. Let t be the posterior expected estimate of the system state and model correction parameters at time t.

[0015] Furthermore, S5 includes, at each time t, taking a weighted average of the system state based on the posterior particle set obtained by particle filtering to obtain a calibrated system state prediction value, which is used to characterize the actual operating state of the system under the current operating conditions.

[0016] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1) For key components in the system that are prone to performance degradation, correction parameters that vary with operating conditions are introduced into the mechanism model to build an enhanced physical model. A dynamic Bayesian network is used for continuous online updates, enabling the model to automatically follow the performance degradation of the equipment and compensate for parameter drift, effectively suppressing model drift and ensuring high-fidelity state prediction at all stages of the equipment's life cycle.

[0017] 2) In the process of recursive Bayesian update of the mechanism model using the particle filter algorithm, the transfer prior of the degradation increment is introduced into the particle weight update, so that the weight update considers both observation consistency and degradation consistency. The degradation consistency changes with the operating load, reducing the error accumulation caused by fixed process noise under variable operating conditions. This is conducive to maintaining a stable online calibration effect during load switching and operating condition fluctuations, suppressing the non-physical regression of degradation caused by observation noise, so that the obtained degradation state sequence is more consistent with the irreversible degradation mechanism of component wear, scaling, blockage, etc., and improving the interpretability and usability of health indicators. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is an overall flowchart of the modeling method of the present invention; Figure 2 A schematic diagram of the physical structure of a methanol fuel supply system; Figure 3 This is a schematic diagram of the operating principle of a methanol fuel supply system. Figure 4 This is a schematic diagram illustrating the principle of joint parameter and state update based on particle filtering. Figure 5 The time-series prediction results of the digital twin models for each channel; Figure 6 This is a diagram showing the evolution of parameter distribution for key components. Detailed Implementation

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

[0021] Please see Figure 1-4 This invention provides a technical solution: a digital twin modeling method for a methanol fuel supply system based on dynamic Bayesian networks, comprising the following steps: S1. Based on the laws of conservation of mass, momentum and energy, a modular mechanism model of the methanol fuel supply system is established to describe the dynamic evolution of pressure, temperature and flow state variables within the system. The process of establishing the modular mechanism model of the methanol fuel supply system described in S1 includes: S11. Based on the laws of conservation of mass, momentum, and energy, and the characteristic parameters of components, a modular mechanism model including fuel tank, booster pump, heat exchanger, and valves is established to describe the state change process of methanol in each component in the methanol fuel supply system; S12. The outlet pressure and temperature of the first-stage booster pump, the outlet pressure and temperature of the second-stage booster pump, the outlet pressure and temperature of the heat exchanger of the methanol fuel supply system are calculated through the aforementioned mechanism model, providing a model basis for subsequent identification and optimization of unknown parameters.

[0022] The first-stage booster pump of the booster pump is based on the inlet methanol temperature. ,pressure And combined with the set export flow Based on the booster pump characteristic curve, calculate the methanol state change during the boosting process and output the outlet pressure of the first-stage booster pump. Primary booster pump outlet temperature ; The secondary booster pump of the booster pump is based on the inlet methanol temperature. ,pressure And combined with the set export flow Based on the booster pump characteristic curve, calculate the methanol state change during the boosting process, and output the outlet pressure of the secondary booster pump. Secondary booster pump outlet temperature ; The heat exchanger is based on the outlet temperature TIT1504, pressure PT1505, and outlet flow rate of the booster pump. Based on the heat exchanger design parameters and the set heat exchange medium operating conditions, the heat exchange process is solved using a heat transfer model based on energy conservation, and the heat exchanger outlet pressure PT1506 and heat exchanger outlet temperature TIT1503 are output.

[0023] Based on the above mechanism model, and according to the state input variable: inlet methanol temperature ,pressure Export flow The system obtains the pressure, temperature, and flow rate changes of methanol in various components of the methanol fuel supply system, including the frequency of the booster pump inverter, the hot-side inlet temperature of the heat exchanger, and the hot-side inlet flow rate of the heat exchanger. Primary booster pump outlet temperature Secondary booster pump outlet pressure Secondary booster pump outlet temperature Heat exchanger outlet pressure Heat exchanger outlet temperature This provides a model foundation for subsequent identification and optimization of unknown parameters.

[0024] S2. For key components in the system that are prone to performance degradation, including booster pumps, heat exchangers, valves and filters, a correction parameter that varies with operating conditions is introduced into the mechanism model to construct an enhanced physical model that includes performance degradation characterization. The enhanced physical model includes: The first-stage booster pump is at a constant time Correction pressure head Represented as: in, This indicates the degree of efficiency degradation of the primary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the primary booster pump. This refers to the actual speed of the primary booster pump. This represents the leakage / slippage additional loss coefficient of the first-stage booster pump; The secondary booster pump is at a certain time Correction pressure head Represented as: in, This indicates the degree of efficiency degradation of the secondary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the secondary booster pump. This refers to the actual speed of the secondary booster pump. This represents the leakage / slippage additional loss coefficient of the secondary booster pump.

[0025] The heat exchanger is constantly Corrected outlet temperature Represented as: in, This refers to the heat exchanger inlet temperature. The heat transfer efficiency coefficient, For reference temperature, This is a temperature-based systematic bias term; and in, The nominal heat transfer efficiency coefficient, Indicates the amount of fouling and degradation in the heat exchanger. It is a smoothing constant. This represents the mass flow rate of methanol.

[0026] The valve is at all times Corrected flow Represented as: in, The nominal flow coefficient, This represents the actual valve opening. This indicates the degree of degradation in the valve's flow coefficient. The pressure difference across the valve. For the density of the medium, Add a flow term for internal leakage.

[0027] Filter at time Corrected pressure drop Represented as: in, Nominal flow resistance coefficient Indicates the amount of filter clogging and degradation. This is a systematic bias term for voltage drop.

[0028] S3. Define the system state variables and the modified parameter vector as random variables, embed them into a dynamic Bayesian network framework, establish a probabilistic state space model containing state equations and observation equations, construct an augmented state vector containing system state variable vectors, degenerate state quantities and deviation term parameter vectors, and explicitly characterize process noise and observation noise. S3 specifically includes the following steps: S31. Construct the state vector of DBN This vector contains the system's state variables and the aforementioned correction parameters: in Let be the system's physical state vector. , , , Let these represent the pressure, flow rate, and temperature at time t, respectively. To correct the parameter vector, it is defined as: ; S32. Given the augmented state at the previous time step System Input and the correction parameter vector Under the given conditions, the predicted prior distribution of the enhanced physics model is constructed, and its state transition equation is expressed as: in, This is a combined prediction function of a modular mechanistic model and an enhanced physical model based on the conservation of mass, momentum, and energy. For the evolution model of degradation and deviation parameters, This includes process noise caused by unmodeled errors and random disturbances. Indicates parameter evolution noise; Therefore, the state transition probability distribution of the augmented state is obtained as follows: .

[0029] S4. Based on real-time sensor observation data, the system's state input variables and the state output variables obtained from the mechanism model are acquired. The particle filter algorithm is used to perform recursive Bayesian updates on the mechanism model to achieve joint estimation and online calibration of the system state and correction parameters. The degenerate state variables satisfy the non-negative increment accumulation form, and the transfer prior of the degenerate increment is explicitly incorporated into the particle weight update process. S4 specifically includes the following steps: S41. Obtain the initial state of the particles based on the system state and prior distribution. For all particles... , , in, This represents the initial physical state of the system and the degradation / deviation parameters of the i-th particle. As a prior distribution, is the initial particle weight, and N is the number of particles; S42. At that moment Based on the particle state at the previous moment and input By performing forward prediction on all particles using the state transition equation, the particle state at time t is obtained. and correction parameter vector ; Degenerate state variables are represented by a non-negative incremental cumulative form: in ; For degenerate incremental random variables; S43. Particles Calculate the predicted values ​​of observations using an enhanced physical model. : in, The observation function is composed of the combined physical models of the key components in S2. During the particle filter update process, based on the observation data Update particle weights: The observation consistency term is calculated using Gaussian likelihood: To reflect the irreversible evolution of degradation parameters, a degradation consistency term is introduced. The non-negative increment of degradation is used as the transition prior and explicitly incorporated into the weight update: in, , For degradation increment; The Gamma distribution is used to characterize the irreversible degradation process; The vector of deviation terms; Used to constrain the slow drift of the deviation term; Normalize the weights: ; S44. Calculate the number of valid samples. If the number of valid samples is lower than a preset threshold, perform a resampling operation and reset the particle weights to: ; S45. Finally, the posterior estimate of the model is calculated using a weighted average: in, These are the normalized weights. Let t be the posterior expected estimate of the system state and model correction parameters at time t.

[0030] S5. Based on the updated corrected parameter posterior estimation, output the calibrated system state prediction value, and assess the health status of key components based on parameter drift.

[0031] S5 specifically includes the following steps: S51 system status calibration output; At each time t, the system state is weighted and averaged based on the posterior particle set obtained by particle filtering to obtain the calibrated system state prediction value, which is used to characterize the actual operating state of the system under the current conditions.

[0032] To verify the effectiveness of the method of the present invention in state prediction, the key measurement points of the system were predicted using both the traditional physical mechanism model and the digital twin model of the present invention, and the prediction error index was calculated.

[0033] Table 1. Calculation accuracy of the physical mechanism model for each channel Table 2. Calculation accuracy of digital twin models for each channel Comparing Table 1 and Table 2, it can be seen that the digital twin modeling method of this invention significantly reduces RMSE, MAE, and MAPE at most measurement points, and improves R... 2 The value indicates that by introducing an online parameter calibration mechanism, the accumulation of model bias can be effectively suppressed, and the accuracy of system state prediction can be improved.

[0034] Furthermore, such as Figure 5 As shown in (a)–(f), a comparison of the time-series prediction results for each key measurement point is presented. The results show that, compared with the uncalibrated physical model, the digital twin modeling method of this invention can better track the sensor's measured data during sudden changes in operating conditions and non-steady-state stages, and the predicted curves have higher consistency with the measured curves.

[0035] S52 Corrected parameter posterior distribution analysis; While completing the state update, the particle filter algorithm simultaneously outputs the posterior probability distribution of the corrected parameters. For example... Figure 6 As shown in (a)-(b), the probability distribution evolution of the correction parameters for the first-stage and second-stage booster pumps is presented, respectively. By comparing the prior and posterior distributions, it can be seen that as observation data is continuously introduced, the posterior distribution of the correction parameters gradually converges, and the variance of the distribution decreases significantly, indicating that the uncertainty of parameter estimation is effectively reduced.

[0036] S53 Critical Component Health Status Assessment The health status of the primary and secondary booster pumps is assessed based on the posterior mean of the corrected parameters and their trend over time. By simultaneously analyzing the changes in parameter mean and the convergence characteristics of their distributions, potential faults can be predicted in advance before significant deterioration in system performance, providing a quantitative basis for equipment operation and maintenance decisions.

[0037] In this specification, the same or similar parts between the various embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the descriptions of the embodiments described later are relatively simple, and relevant parts can be referred to the descriptions of the foregoing embodiments.

[0038] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A digital twin modeling method for a methanol fuel supply system based on dynamic Bayesian networks, characterized in that, Includes the following steps: S1. Based on the laws of conservation of mass, momentum and energy, a modular mechanism model of the methanol fuel supply system is established to describe the dynamic evolution of pressure, temperature and flow state variables within the system. S2. For key components in the system that are prone to performance degradation, including booster pumps, heat exchangers, valves and filters, a correction parameter that varies with operating conditions is introduced into the mechanism model to construct an enhanced physical model that includes performance degradation characterization. S3. Define the system state variables and the modified parameter vector as random variables, embed them into a dynamic Bayesian network framework, establish a probabilistic state space model containing state equations and observation equations, construct an augmented state vector containing system state variable vectors, degenerate state quantities and deviation term parameter vectors, and explicitly characterize process noise and observation noise. S4. Based on real-time sensor observation data, the system's state input variables and the state output variables obtained from the mechanism model are acquired. The particle filter algorithm is used to perform recursive Bayesian updates on the mechanism model to achieve joint estimation and online calibration of the system state and correction parameters. The degenerate state variables satisfy the non-negative increment accumulation form, and the transfer prior of the degenerate increment is explicitly incorporated into the particle weight update process. S5. Based on the updated corrected parameter posterior estimation, output the calibrated system state prediction value, and assess the health status of key components based on parameter drift.

2. The method according to claim 1, characterized in that, The process of establishing the modular mechanism model of the methanol fuel supply system described in S1 includes: S11. Based on the laws of conservation of mass, momentum, and energy, and the characteristic parameters of components, a modular mechanism model including fuel tank, booster pump, heat exchanger, valve and filter is established to describe the state change process of methanol in each component in the methanol fuel supply system. S12. The outlet pressure and temperature of the first-stage booster pump, the outlet pressure and temperature of the second-stage booster pump, the outlet pressure and temperature of the heat exchanger of the methanol fuel supply system are calculated using the aforementioned mechanism model.

3. The method according to claim 2, characterized in that, The enhanced physics model described in S2 includes: The first-stage booster pump is at a constant time Correction pressure head Represented as: ； in, This indicates the degree of efficiency degradation of the primary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the primary booster pump. This refers to the actual speed of the primary booster pump. This represents the leakage / slippage additional loss coefficient of the first-stage booster pump; The secondary booster pump is at a certain time Correction pressure head Represented as: ； in, This indicates the degree of efficiency degradation of the secondary booster pump. The theoretical pressure head is calculated from the basic physical mechanism model of the secondary booster pump. This refers to the actual speed of the secondary booster pump. This represents the leakage / slippage additional loss coefficient of the secondary booster pump.

4. The method according to claim 3, characterized in that, The enhanced physics model described in S2 also includes: The heat exchanger is constantly Corrected outlet temperature Represented as: ； in, This refers to the heat exchanger inlet temperature. The heat transfer efficiency coefficient, For reference temperature, This is a temperature-based systematic bias term; and ; in, The nominal heat transfer efficiency coefficient, Indicates the amount of fouling and degradation in the heat exchanger. It is a smoothing constant. This represents the mass flow rate of methanol.

5. The method according to claim 4, characterized in that, The enhanced physics model described in S2 also includes: The valve is at all times Corrected flow Represented as: ； in, The nominal flow coefficient, This represents the actual valve opening. This indicates the degree of degradation in the valve's flow coefficient. The pressure difference across the valve. For the density of the medium, Add a flow term for internal leakage.

6. The method according to claim 5, characterized in that, The enhanced physics model described in S2 also includes: Filter at time Corrected pressure drop Represented as: ； in, Nominal flow resistance coefficient Indicates the amount of filter clogging and degradation. This is a systematic bias term for voltage drop.

7. The method according to claim 6, characterized in that, S3 specifically includes the following steps: S31. Construct the state vector of DBN This vector contains the system's state variables and the aforementioned correction parameters: ； in Let be the system's physical state vector. , , , Let these represent the pressure, flow rate, and temperature at time t, respectively. To correct the parameter vector, it is defined as: ； S32. Given the augmented state at the previous time step System Input and the correction parameter vector Under the given conditions, the predicted prior distribution of the enhanced physics model is constructed, and its state transition equation is expressed as: ； ； in, This is a combined prediction function of a modular mechanistic model and an enhanced physical model based on the conservation of mass, momentum, and energy. For the evolution model of degradation and deviation parameters, This includes process noise caused by unmodeled errors and random disturbances. Indicates parameter evolution noise; Therefore, the state transition probability distribution of the augmented state is obtained as follows: 。 8. The method according to claim 7, characterized in that, S4 specifically includes the following steps: S41. Obtain the initial state of the particles based on the system state and prior distribution. For all particles... , ， ； in, This represents the initial physical state of the system and the degradation / deviation parameters of the i-th particle. As a prior distribution, is the initial particle weight, and N is the number of particles; S42. At that moment Based on the particle state at the previous moment and input By performing forward prediction on all particles using the state transition equation, the particle state at time t is obtained. and correction parameter vector ; Degenerate state variables are represented by a non-negative incremental cumulative form: ； in ; For degenerate incremental random variables; S43. Particles Calculate the predicted values ​​of observations using an enhanced physical model. : ； in, The observation function is composed of the combined physical models of the key components in S2. During the particle filter update process, based on the observation data Update particle weights: ； The observation consistency term uses Gaussian likelihood; a degenerate consistency term is also introduced. The non-negative increment of degradation is used as the transition prior and explicitly incorporated into the weight update: ； in, , For degradation increment; The Gamma distribution is used to characterize the irreversible degradation process; The vector of deviation terms; Used to constrain the slow drift of the deviation term; Normalize the weights: ； S44. Calculate the number of valid samples. If the number of valid samples is lower than a preset threshold, perform a resampling operation and reset the particle weights to: ; S45. Finally, the posterior estimate of the model is calculated using a weighted average: ； in, These are the normalized weights. Let t be the posterior expected estimate of the system state and model correction parameters at time t.

9. The method according to claim 8, characterized in that, S5 includes, at each time t, taking a weighted average of the system state based on the posterior particle set obtained by particle filtering to obtain a calibrated system state prediction value, which is used to characterize the actual operating state of the system under the current operating conditions.

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