A method for reliability evaluation of a nuclear reactor control rod drive mechanism with an in-line mechanism

Abstract

The application discloses a kind of embedded mechanism nuclear reactor control rod drive mechanism reliability evaluation method, comprising the following steps: step 1: establishing coil electromagnetic force, armature movement water resistance, reset spring force calculation model, constructs and promotes armature movement coupling dynamics partial differential equation;Step 2: select the core index of the armature attraction time, clear failure criterion and establish reliability calculation model;Step 3: build the physical information bayesian neural network of three subnets structure, embed the physical law loss term and design phased training strategy, realize the uncertainty quantification of attraction time by combining variational inference and monte carlo discard mechanism;Step 4: based on Gaussian kernel density estimation fitting attraction time probability density function and solving reliability, through measured data, carry out ablation experiment and contrast verification, complete method engineering applicability verification.The application can provide accurate, efficient technical support for the reliability evaluation and operation and maintenance decision of nuclear reactor control rod drive mechanism.

Description

Technical Field

[0001] This invention is a reliability assessment method for nuclear reactor control rod drive mechanisms with embedded mechanisms. Background Technology

[0002] The Control Rod Drive Mechanism (CRDM), a core component of third-generation pressurized water reactors, plays a crucial role in reactor power regulation, normal shutdown, and accident shutdown. Its reliability under harsh operating conditions of high temperature, high pressure, and strong radiation directly determines reactor operational safety. The lifting unit, as the core actuator of the CRDM, relies heavily on the armature's engagement characteristics as a key indicator of the mechanism's reliability. Engagement times exceeding a threshold will directly trigger failure modes such as rod slippage and inability to lift. Therefore, accurate assessment of CRDM reliability is a critical requirement for nuclear power equipment operation and maintenance.

[0003] Traditional CRDM reliability assessment methods largely rely on multiphysics coupling simulations, requiring complex iterative calculations of multiple fields such as electromagnetics, water resistance, and mechanics. This involves numerous key parameters with random uncertainties, such as air gap length and gap magnetoresistance area. Furthermore, the nonlinear coupling characteristics make it difficult to obtain the pull-in time probability density function analytically, resulting in computational efficiency on the order of hours, which cannot meet the needs of rapid reliability assessment in practical engineering. Simultaneously, traditional machine learning methods rely solely on fitting monitoring data, lacking the embedding of physical mechanisms. Since only limited monitoring data such as vibration acceleration and coil current are available in actual CRDM service, key physical quantities such as displacement, velocity, and water resistance cannot be directly measured. Purely data-driven models are prone to poor convergence and large prediction biases, and cannot quantify the uncertainties of parameters, models, and data, making it difficult to achieve probabilistic representation of pull-in time and accurate reliability calculation.

[0004] Furthermore, existing methods are insufficient for analyzing the uncertainty propagation under multiphysics coupling in CRDM, failing to effectively combine physical constraints with probabilistic modeling methods. They are unable to accurately invert unmonitorable physical quantities, nor can they efficiently fit the probability density function of the absorption time and solve for reliability. This results in significant shortcomings in the accuracy, efficiency, and engineering applicability of CRDM reliability assessment. Therefore, there is an urgent need to develop a probabilistic modeling method that embeds physical mechanisms to achieve accurate inversion of key physical quantities in CRDM, characterization of the uncertainty of absorption time, and efficient quantification of reliability, thus overcoming the technical bottlenecks of traditional methods. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a reliability assessment method for nuclear reactor control rod drive mechanisms with embedded mechanisms. It integrates multi-physics field coupled dynamic modeling, physical information neural networks and probabilistic reasoning theory to achieve accurate prediction of armature engagement time, uncertainty characterization and efficient quantification of reliability of CRDM. It solves the problems of low computational efficiency, poor prediction accuracy and inability to quantify uncertainty in traditional methods, and improves the accuracy and engineering applicability of CRDM reliability assessment.

[0006] This invention is achieved through the following technical solution: a reliability assessment method for a nuclear reactor control rod drive mechanism with an embedded mechanism, comprising the following steps:

[0007] Step 1: Multiphysics Coupling Mechanism Analysis and Dynamic Modeling of CRDM. Based on the working principle of the third-generation pressurized water reactor magnetic lifting control rod drive mechanism (CRDM) and its high-temperature, high-pressure, and high-irradiation service environment, this study focuses on the lifting armature, the core actuator, and conducts an analysis of the electromagnetic-water resistance-mechanical multiphysics coupling effect. Calculation models for the coil electromagnetic force, armature motion water resistance, and reset spring force are established. Based on Newton's second law, a coupled dynamic partial differential equation for the lifting armature motion is constructed, clarifying key parameters with random uncertainties in the model (air gap length, gap magnetic reluctance area, additional magnetic reluctance, etc.), providing a theoretical basis for subsequent physical mechanism embedding.

[0008] Step 2: Construction of Core Indicators and Quantitative Model for CRDM Reliability Assessment. The armature pull-in time is selected as the core performance indicator for CRDM reliability. The physical definition of pull-in time is clarified (the time interval from the start of coil energization to the lowest point of the current waveform "return groove" corresponding to complete armature pull-in). Criteria for triggering failure modes such as slippage and failure to lift when pull-in time exceeds a threshold are determined. A CRDM reliability calculation model considering the propagation of input parameter uncertainties is established, clarifying the mathematical mapping relationship between reliability and the probability density function of pull-in time, thus completing the construction of the reliability assessment framework.

[0009] Step 3: Construct the CRDM-PINN-VI probabilistic neural network with embedded mechanism and complete the characterization of absorption time uncertainty. An embedded physical information Bayesian neural network (CRDM-PINN-VI) was constructed, comprising three subnetworks: displacement fitting, water resistance calculation, and current prediction. Utilizing the automatic differentiation characteristic of neural networks, the first and second order differential relationships of displacement, velocity, and acceleration were automatically solved. Using monitorable vibration acceleration and coil current data from the CRDM during service as training inputs, data fitting loss terms for acceleration and current were constructed respectively. Simultaneously, two major physical law loss terms—the non-negativity constraint of the lifting armature motion velocity and the multi-physics coupling dynamic equation—were embedded to form a weighted total loss function. A phased training strategy was designed to optimize the network, achieving accurate inversion of physical quantities that cannot be directly monitored, such as displacement, velocity, and water resistance, and deterministic point estimation of the pull-in time. Furthermore, variational inference theory and the Monte Carlo Dropout (MC-Dropout) mechanism were introduced into the three subnetworks. By enabling multiple rounds of forward propagation with MC-Dropout enabled, Monte Carlo sampling was achieved to obtain a large number of random samples of the pull-in time, quantifying the uncertainty of parameters, models, and data, and obtaining the sample set and distribution characteristics of the pull-in time.

[0010] Step 4: CRDM Reliability Measurement and Method Validation. Based on the Gaussian kernel density estimation (KDE) method, the absorption time sample set is fitted to obtain the probability density function (PDF) of the absorption time. Combined with the preset absorption time failure threshold, the reliability result of CRDM under specified service conditions is obtained by probability integration. Based on the measured data of the CRDM reliability test platform, ablation experiments are carried out to verify the effect of physical constraints on the model accuracy. The accuracy of the method is verified by comparing the nonparametric reliability estimation results. At the same time, the computational efficiency of the proposed method is verified by comparing it with the traditional multiphysics coupling simulation method, thus completing the engineering applicability verification of the method.

[0011] Furthermore, according to the method described in step 1, the characteristic is that, in step 1:

[0012] The magnetically lifted reactor core modulator (CRDM) is a crucial component of a pressurized water reactor (PWR), enabling functions such as reactor power regulation, normal shutdown, and accident shutdown. A typical CRDM topology primarily consists of coil assemblies (yoke, lifting coil, moving coil, and holding coil), claw assemblies (lifting pole, lifting armature, moving armature, holding pole, holding armature, moving claw, and holding claw), pressure vessel assemblies (sealing shell and magnetic ring), thermal insulation assemblies, and drive rod assemblies.

[0013] In the operation of a magnetically driven CRDM, the lifting coil, lifting pole, lifting armature, and corresponding yoke and magnetic ring constitute the lifting unit; the moving coil, moving armature, lifting armature, and corresponding yoke and magnetic ring constitute the moving unit; and the holding coil, holding pole, holding armature, and corresponding yoke and magnetic ring constitute the holding unit. When the coil is energized, the armature in the corresponding unit (such as the lifting armature, moving armature, or holding armature) will be subjected to electromagnetic force, thereby overcoming resistances such as gravity, water resistance, spring force, and load, and engaging with the corresponding magnetic pole. The lifting unit is the key actuator that drives the drive rod to perform lifting or lowering actions, therefore its health is particularly important. The moving unit engages or disengages with the drive rod's annular groove via a connecting rod and pawl. The holding unit has a similar structure to the moving unit, but its main function is to position the pawl into the drive rod's annular groove, keeping the drive rod in a designated position. Each unit requires its coil to be energized and de-energized according to a specific time and sequence to properly complete actions such as lifting, lowering, holding, or rapid rod drop.

[0014] Furthermore, according to the method described in step 1, the characteristic is that, in step 1:

[0015] Step 3.1: Electromagnetic force calculation model.

[0016] This is the equivalent resistance of the coil; This is an energy-dissipating resistor. Its function is to allow current to flow through the CRDM coil when the coil is de-energized, forming a closed loop and thus consuming all the energy in the coil, causing the current to drop rapidly to zero. I represents the current in the coil; x represents the length of the air gap for lifting the armature. The equivalent inductance of the coil can be expressed as a function of the air gap x. VT1 is an inverter switching transistor used to control the duration and sequence of the coil current; VT2 is a chopper switching transistor used to control the magnitude of the coil current.

[0017] During the pull-in phase of CRDM, the coil circuit equation is:

[0018]

[0019] During the movement of the CRDM, the air gap x can be written as time. function When the CRDM gap is fully open, x(t) = 0; when the gap is fully closed, The clearance during the lifting armature movement is... Therefore, during the armature attraction process, the inductance L can be expressed as a function of the air gap x and time t, that is:

[0020]

[0021] In the formula, S is the area at the gap reluctance; Let be the vacuum permeability, and take . ; It represents the sum of the magnetic reluctances of all parts except the air gap magnetic reluctance; The number of coil turns is 577.

[0022] Substituting equation (2) into equation (1), the current can be calculated. Then the electromagnetic force can be expressed as:

[0023]

[0024] Step 3.2: Water resistance calculation model.

[0025] When the CRDM lifting armature moves upward, the water gap between it and the lifting pole decreases. Part of the squeezed water flows along the gaps between the lifting armature, moving armature, and other parts and the sealing shell. The other part flows along the gaps between the lifting pole and the sealing shell, the radial holes of the lifting pole, and the gaps between the drive rod and the sleeve shaft. Due to the conservation of circuit voltage drop:

[0026]

[0027] In the formula, P 1i and P 2i Let represent the voltage drop at various points in the circuit. The voltage drop mainly consists of frictional voltage drop, inertial voltage drop, and local voltage drop, which can be calculated using the following formula:

[0028]

[0029] In the formula, These are the frictional pressure drop and the inertial pressure drop. and These are the drag coefficients for the inner and outer walls, respectively, which can be calculated using the Colebrook formula; The density of water; and These are the relative velocities of the inner and outer walls with the water, respectively. and. These are the wetted perimeters of the inner and outer walls, respectively. The lengths of the inner and outer walls; For localized pressure drop; The acceleration of water; This is the local drag coefficient; The velocity of the water.

[0030] The drive lever assembly and the control rod assembly it drives are The water resistance encountered during movement due to pressure drop:

[0031]

[0032] Analysis of the above model shows that the magnitude of water resistance is not only related to the structural characteristics and surface roughness of the CRDM, but also significantly affected by factors such as the armature movement speed, water flow velocity, and density.

[0033] However, due to the difficulty in directly measuring the drag coefficients of the inner and outer walls of the drive mechanism, and its complex and irregular shape, key parameters required for calculating water resistance, such as length and cross-sectional area, are difficult to obtain accurately. A PINN network will be used to learn the magnitude of water resistance in the future.

[0034] Step 3.3: Spring force calculation model.

[0035] Hooke's Law can be used to simulate the elastic force of the spring on the armature. Hooke's Law states that when a spring undergoes elastic deformation, the elastic force of the spring... Change in spring length A linear relationship, that is

[0036]

[0037] In the formula, The spring stiffness is determined by the material properties of the spring. The negative sign indicates that the elastic force generated by the spring is opposite to the direction of its elongation. This is the preload of the spring.

[0038] Step 3.4: Multiphysics coupling model.

[0039] Electromagnetic lifting force; It is the elastic force of the spring; To increase the weight of moving parts such as the armature, drive rod, and pawl; This refers to the load force, specifically the weight of the control rod assembly. For water resistance; Other resistance factors include gravity. and load capacity It is a constant; other resistances The value of is relatively small, and its influence on the armature's motion can be ignored. Based on the analysis, using Newton's second law, the dynamics of lifting the armature can be expressed as follows:

[0040]

[0041] In the formula, This represents the acceleration that lifts the armature; x is the displacement of the armature; and M is the total mass of the moving parts and the load.

[0042] Furthermore, according to the method described in step 1, step 2 includes the following sub-steps:

[0043] The lifting unit is a crucial motion unit of the CRDM, and its reliability directly impacts the overall performance of the CRDM. Under the coupling of multiple physical fields, the lifting armature moves relative to the bushing shaft, driving the hook assembly and load to move together until engagement is complete. However, during service, direct contact and friction between the lifting armature and the bushing shaft can generate debris or even foreign objects that can cause jamming, leading to variations in the lifting armature's speed and consequently, its engagement time. These variations in engagement time further disrupt the current timing of the holding and moving units, ultimately causing CRDM failures such as slippage and inability to lift. The current waveforms of the lifting unit under normal and fault conditions are shown. The completion time of the lifting armature engagement action is the lowest point of the current waveform's "return groove," and the process from zero current to this lowest point fully describes the change in coil current during armature engagement. Compared to the normal current waveform, the fault waveform of the CRDM shows the disappearance of the current engagement point and a severely delayed engagement time, posing a risk of slippage and inability to lift. Therefore, whether the armature pull-in time meets the requirements is a criterion for judging whether the CRDM exhibits failure modes such as slippage or inability to lift. Thus, efficiently and accurately assessing the armature pull-in time is crucial for evaluating the reliability of the CRDM.

[0044] The armature pull-in time was selected as a key performance indicator for the CRDM. If this indicator exceeds a certain threshold, the entire CRDM is considered to have malfunctions such as arm slippage or failure to lift. The pull-in time in the current waveform of the CRDM lifting unit is shown. Meaning, where c represents the current running step number. CRDM booster unit pull-in time. From The time interval is from 0 (the moment when energization begins) to the point where the current is at its lowest after the coil exhibits back electromotive force. The duration of the time interval. This is a fixed value, representing the start time of step c. The point where the current is lowest after the coil exhibits back EMF indicates that the armature is fully engaged.

[0045] It is worth noting that, due to the movement of the lifting armature under the influence of electromagnetic force, water resistance, spring force, and gravity, the current is at its lowest point. It is not a fixed value, but a value that changes continuously with the number of steps taken. First, This depends on the dynamic equation of the lifting armature, i.e., equation (8). Specifically, according to the CRDM dynamic analysis model in Section 2, if the values ​​of all electromagnetic forces, spring forces, gravity, load forces, water resistance, and other resistances are given, the displacement, velocity, and acceleration results of the CRDM motion process can be quickly calculated. When the CRDM armature is engaged, the current reaches its minimum value, and at this time, the displacement reaches its maximum value. Therefore, the engagement time of the CRDM lifting unit can be calculated by calculating the difference between the initial moment and the time when the displacement is maximum. Specifically, we will... The stepping bar process is decomposed into countless small time elements, and the time step is represented by... In other words, using... , Indicates the first Stepping stick The displacement, velocity, acceleration, and the water resistance, spring force, and electromagnetic force acting on the CRDM at any given moment can be used to calculate the acceleration value at that moment using equation (9). ,Right now:

[0046]

[0047] when Given the given information, substitute it into the following equation to iteratively calculate the next time step. The velocity and displacement values, namely:

[0048]

[0049] Continue Substituting the displacement and velocity values ​​at a given time into the corresponding electromagnetic force, spring force, and water resistance calculation models, we can obtain... At present , , .Will Water resistance at time Spring force Electromagnetic force Substituting back into equation (10), we can calculate... acceleration value at time t ,Right now:

[0050]

[0051] In the formula, express The combined efforts at any given moment; To improve the mass of the unit itself, the acceleration... Substituting these values ​​into equation (10) allows us to calculate the displacement and velocity at that moment. Repeating the above steps iteratively allows us to calculate the [missing value]. The acceleration, velocity, displacement, electromagnetic force, water resistance, and spring force of the stepping rod at any time during the process are recorded. When the displacement reaches its maximum value during iteration, that is, when it is just attracted, the displacement is set to no longer change. Then, according to equation (10), the velocity and acceleration at this moment are both zero. The time at this moment is recorded as _____. Then the absorption time can be further obtained. .

[0052] The above calculations were performed under the condition that relevant parameters such as electromagnetic force and water resistance were known. However, in actual engineering, the air gap length l... g Area S at the gap reluctance, reluctance Due to material variations and manufacturing process fluctuations, uncertainties are inevitable; that is, these parameters are not fixed constants but can only be described by distributions. The uncertainty of the input parameters, after the aforementioned calculation process, also leads to uncertainty in the CRDM pull-in time. This process is called uncertainty propagation, and its purpose is to analyze how the uncertainty of the lifter unit's input parameters affects the uncertainty of the system output. Without loss of generality, let's assume the uncertainty parameters of the lifter unit are... All follow a normal distribution, that is:

[0053]

[0054] In the formula, , , Let lg represent the air gap length, S represent the area at the air gap reluctance, and S represent the reluctance. The mean of the probability distribution, and , , Let represent the variances of the probability distribution, respectively. If the mean and variance are known, then the uncertainty parameters can be collected using the hyper-Latin square sampling method. middle Each parameter sample is used, and the pull-in time of the lifting unit is calculated for each sample using the above iterative process. . use Each suction time This allows for the estimation of the probability density function (PDF) that increases the unit's pull-in time. Based on the absorbance time PDF results and combined with the absorbance time threshold. The reliability of CRDM can be calculated. Without loss of generality, the reliability formula for CRDM at any number of running steps c can be expressed as:

[0055]

[0056] However, it is worth noting that due to the complexity and high nonlinearity of the armature attraction process under multiphysics coupling, the PDF of the attraction time varies with the number of running steps. It is difficult to estimate directly and cannot be solved analytically. Therefore, the reliability of CRDM cannot be directly calculated using equation (13). This paper proposes PINN

[24] to solve the CRDM booster unit pull-in time PDF. Then convert the absorption time PDF Substitute into equation (20) to calculate the reliability of CRDM under any number of running steps.

[0057] Furthermore, according to the method described in step 1, step 3 includes the following sub-steps:

[0058] Step 5.1: PINN and variational inference theory.

[0059] This invention utilizes PINN to continuously adjust network parameters. This paper aims to improve the armature engagement time under multiphysics coupling while ensuring the data satisfies the physical laws in the model. However, traditional PINN networks can only obtain point estimates of the output, not its probability distribution. This paper introduces Variation Inference (VI) into PINN, termed the PINN-VI model, to obtain the PDF of the engagement time. The implementation process of PINN-VI and how to achieve the posterior PDF approximation in VI using Monte Carlo Dropout (MC-Dropout) are described below.

[0060] VI method utilizes functions Posterior distribution of approximate parameters , As a prior distribution hypothesis for parameter θ, by Parameterization. Function The mean-field Gaussian approximation method is generally used, that is:

[0061]

[0062] In the formula, The mean Standard deviation PDFs with a normal distribution; The number of model parameters, i.e. The dimension. The approximation principle is to minimize and posterior distribution KL divergence between This is achieved by maximizing the Evidence Lower Bound (ELBO). ELBO can be expressed as:

[0063]

[0064] In the formula, Let be the loss function of the neural network. For parameter priors and posterior The KL divergence between them.

[0065] Executing the MC-Dropout method in a neural network can achieve the ELBO optimization process in VI. In the MC-Dropout method, a dropout probability is specified. The value of each network node during forward propagation has The probability is set to zero. Gal et al. theoretically proved that in ELBO... It is proportional to the L2 regularization of the neural network, that is:

[0066]

[0067] Therefore, optimizing the loss function of a neural network with MC-Dropout is consistent with optimizing ELBO. Based on the above theoretical derivation, we will apply MC-Dropout to PINN to obtain the posterior PDF of the absorption time.

[0068] Step 5.2: CRDM-PINN method.

[0069] The pull-in time index of the CRDM lifting unit reflects the reliability level of the mechanism's operation. The following will explain how to fit the CRDM pull-in time distribution based on PINN-VI. First, we will introduce how to use the PINN model to fit the CRDM pull-in time index. During the CRDM operation phase, some acceleration and current data can be obtained using vibration sensors and current signals. In this problem, acceleration data serves as the raw data, requiring the inversion of CRDM velocity and displacement data. The magnitude of the displacement is directly related to the CRDM lifting unit's pull-in time. Therefore, displacement is used as the antiderivative in this problem. Data for the antiderivative is scarce, while data representing physical information using the differential terms of the antiderivative (the differential of displacement is velocity, and the differential of velocity is acceleration) is readily available. Therefore, we can utilize PINN's automatic differentiation function to embed the differential relationship between acceleration, velocity, and displacement into the neural network, and fit the displacement as a function of time using only the CRDM-based acceleration data. Furthermore, as discussed in Section 2 regarding the multiphysics coupling model, electromagnetic force in reality is a displacement-related quantity, while water resistance is a velocity-related quantity, and both possess implicit characteristics. Therefore, an architecture as shown below can be used to combine the electromagnetic force and water resistance physical fields with the motion of the CRDM, forming a multiphysics coupling CRDM-PINN, which can be used to evaluate the pull-in time of the CRDM lifting unit.

[0070] The CRDM-PINN model comprises three sub-networks, which respectively fit the motion of the CRDM itself, the current in the coil, and the acceleration experienced by the CRDM. The reasons for designing this network architecture are as follows: First, we build a first neural network model to evaluate the displacement value. Since the velocity value can be obtained by differentiating the displacement output with respect to time, and this process can be automatically acquired within the neural network, the automatically obtained velocity value is input into the second neural network to solve the water resistance model. As analyzed in Section 2, water resistance is related to the mechanism's motion velocity; therefore, the velocity value automatically differentiated by the first network is input into the second neural network to solve for acceleration. The displacement of the first network can also be differentiated with respect to time, which is also obtained through automatic differentiation within the neural network. The acceleration value can be trained using acceleration data from the vibration sensor. On the other hand, as mentioned in step 1, the electromagnetic force calculation model is related to the armature air gap; therefore, a third network can be designed to input the displacement value (air gap) into the third neural network to predict the electromagnetic force, which will be obtained through training using current data. The specific details of the three networks in CRDM-PINN are shown.

[0071] Neural network 1 is used to train the displacement during the attraction process. Since displacement data is unavailable, the automatic differentiation function of the neural network is utilized to obtain the acceleration by calculating the second-order partial derivative between the output displacements. Acceleration can be directly obtained using an acceleration vibration sensor; therefore, vibration acceleration data can be used to train the first neural network in PINN. Secondly, current data is used to train the third neural network. This invention utilizes a dynamic model under multi-physics coupling to train the second neural network, namely the water resistance model. From the above analysis, it can be seen that the dynamic analysis model under multi-physics coupling in Section 2 is embedded through the automatic differentiation function of the first network in PINN, which is also the main manifestation of the embedded mechanism neural network proposed in this section. The training process of the three neural networks will be described in detail below.

[0072] Since the three outputs of the PINN proposed in this invention are all continuous values, all three neural networks belong to the regression problem. For regression problems, the loss function of PINN is generally the mean squared error. Let's represent this. The following will explain how to train the three neural networks mentioned above using the root mean square error. First, assume the training dataset from the CRDM service process... , representing the actual observed values ​​of acceleration and current, respectively, and relative to the input time. The time values ​​in the data correspond one-to-one. They are respectively used... Let represent the three sub-networks of CRDM-PINN. Then we have:

[0073]

[0074] In the formula, the function This represents the first neural network used to solve for the shift output, while This can be obtained automatically through differentiation using the first neural network. It can also be obtained automatically through differentiation using neural networks. This indicates that the second neural network is used to solve for water resistance. Since water resistance is related to velocity, the output of the first neural network is used instead. Also input into the network This represents the third neural network, which outputs the displacement because current and displacement are related. The input is fed into the neural network. Additionally, Indicate each The resultant force is calculated at the corresponding time point. With this information, the terms in PINN's loss function can be calculated. Assume... , Let represent the loss functions for the CRDM-PINN displacement and current neural networks, respectively. Then, the training dataset can be used. The following loss functions were obtained respectively:

[0075]

[0076] In equation (18), The loss function representing acceleration data, Indicates the size of the data. This represents the i-th acceleration training data; in equation (19), The loss function representing the current data. Let represent the i-th current training data. The two loss functions mentioned above are insufficient to achieve satisfactory results for the entire PINN training. Two additional loss functions based on physical laws are needed. First, for CRDM, its velocity cannot be negative. Therefore, the first piece of physical information is added to the CRDM-PINN loss function, expressed as:

[0077]

[0078] This means that a constraint is imposed on all outputs with velocities less than 0 for all CRDM displacement models, limiting the output velocity to be greater than or equal to 0. Secondly, the motion process of the CRDM lifting unit must satisfy the dynamic equation of equation (8), therefore, a second physical constraint needs to be added. This means that the motion process of the CRDM lifting unit must satisfy Newton's second law, that is:

[0079]

[0080] In the formula, Indicates resultant force; It represents the sum of forces other than electromagnetic force and water resistance, including the lifting force, elastic force, and load. The resultant force is the sum of forces calculated from the outputs of the water resistance model and the electromagnetic force model, as well as other given parameters. This indicates that when the current is The magnitude of the electromagnetic lifting force is calculated by substituting it into the equivalent magnetic circuit model.

[0081] The total loss of CRDM-PINN is obtained by weighted summation of all terms, where This represents the weight corresponding to each loss term. That is:

[0082]

[0083] In the formula, This ensures that the model's predictions do not incorrectly assume that the CRDM will move in a downward direction; It includes a dynamic model under CRDM multiphysics coupling, which can connect the information between the three sub-networks and achieve the most accurate absorption time assessment.

[0084] Step 5.3: CRDM-PINN-VI Method

[0085] The CRDM-PINN model can only evaluate the deterministic value of the absorption time, without considering the uncertainty of input parameters, data, and neural network. Therefore, this section proposes a PINN-VI-based CRDM absorption time distribution evaluation. Based on the absorption time distribution and the threshold of absorption time, the reliability of CRDM can be evaluated. The proposed CRDM-PINN-VI architecture is presented. The only difference is that all three networks use Bayesian neural networks, and the MC-Dropout method is used to implement the PINN-VI probability distribution output. The model structure, data, loss function, and other details are consistent with CRDM-PINN. With MC-Dropout, the gradient descent of the model is less stable, and the training convergence speed is slower. Therefore, more training epochs are required, followed by a small number of training epochs with MC-Dropout disabled to further adjust the model accuracy.

[0086] After training, the model's output mean and standard deviation can be obtained with MC-Dropout disabled. To evaluate the uncertainty of the suction time, the displacement function curve needs to be analyzed. Specifically, with MC-Dropout enabled, the model's displacement prediction over time is output to obtain the minimum time. make The adsorption time is the time required to complete the adsorption process. By sampling the adsorption time multiple times using the Monte Carlo method, the PDF of the CRDM adsorption time can be obtained, which is the value in equation (13). .

[0087] Furthermore, according to the method described in step 1, step 4 includes the following example verification process:

[0088] This invention uses CRDM current and acceleration test data to verify the correctness and effectiveness of the proposed method. The CRDM reliability test platform mainly consists of three parts: an ML-CRDM mounting platform, an electromagnetic loading unit, and a data acquisition and control unit. Current data is acquired from the data acquisition and control system of the three sets of CRDM coils. A CRDM displacement sensor is mounted on the drive rod, indirectly characterizing the displacement characteristics of the lifting armature by detecting the displacement of the drive rod during dynamic operation. An acceleration vibration sensor is fixed to the flange base to collect the vibration acceleration signals generated during the operation of the CRDM lifting unit.

[0089] As revealed by the CRDM reliability test platform, only acceleration and current data are available for CRDM condition monitoring; displacement, velocity, and water resistance data are unavailable. Therefore, this invention ingeniously designs a loss function based on a multiphysics-coupled dynamic model, simultaneously incorporating the prediction of CRDM water resistance, displacement, and velocity into the training of the PINN. Using only the CRDM's acceleration and current data, the changes in these three physical quantities can be accurately estimated. Thus, the multiphysics-coupled CRDM dynamic model is an essential physical loss function for the designed network. This underscores the necessity of the CRDM-PINN designed in this invention.

[0090] Two networks, PINN and PINN-VI, are used to evaluate the armature engagement time and engagement time probability distribution of CRDM. The network hyperparameters are set as follows: Due to the inconsistent units of physical quantities and the different orders of magnitude among the terms in the loss function, selecting appropriate weight parameters is crucial for the model's training performance and final convergence. In this example, , , , Each sub-network is a fully connected neural network with four hidden layers and node counts of [50, 100, 100, 50]. The training data consists of current and acceleration data from the CRDM over 12 million runs. Regarding the training strategy, although incorporating physical information into the loss function is theoretically optimal, in practice, the gradient of the differential term in the loss function is unstable at the beginning of training when the error is large, making model convergence difficult. Accordingly, Although equivalent to numerical regression, it converges quickly for loss terms without differentiation. Therefore, a strategy of training the first neural network first is adopted to increase... The weights are adjusted until the displacement model essentially converges, at which point the model switches to the next loss function. The specific training hyperparameters are: and Using learning rate and 10,000 training sessions; and Using learning rate and 30,000 training sessions.

[0091] Furthermore, the training data for current and acceleration are explained as follows: First, the state monitoring data is divided into training, validation, and test sets in an 8:1:1 ratio. All data is randomly divided into three datasets according to this ratio. 80% of the data is used to train the proposed PINN and PINN-VI networks. The trained model is then used to validate its generalization ability and optimize its hyperparameters using the remaining 10% of the dataset. Finally, the remaining 10% of the dataset is used for testing. We also compared cross-testing with other ratios and found that the 8:1:1 cross-testing performed best. Therefore, this invention only presents the analysis results of the 8:1:1 cross-testing.

[0092] use That is, training and simultaneous use of data and physical information are completed solely based on data, without introducing the physical information contained in equations (20) and (21). , The prediction results of the trained model are shown in the following sub-figures: prediction of displacement; prediction of velocity; prediction of acceleration; prediction of current in the coil; prediction of water resistance; and comparison of the resultant force calculated based on the prediction values ​​with mass × acceleration. The results show that the prediction results of the model based solely on the data differ significantly from the actual values. This is because CRDM can only collect acceleration and current data. For neural network 3, the network uses the CRDM's motion velocity to predict water resistance, but there is no training data for water resistance. Therefore, without the data from equation (21), the prediction results are significantly different. If the motion law of the CRDM booster unit is not known, then there is no loss function available for training the neural network 3. Therefore, the convergence effect of the entire PINN network is poor. On the other hand, due to the lack of equation (21) Accurate predictions of displacement and velocity using only acceleration and current data are difficult because there is no directly observable data for training these physical quantities, and indirect data lacks physical laws to guide convergence. Therefore, the predictions of models based solely on data show a significant discrepancy with the actual values. It can be seen that, except for the relatively accurate prediction of current physical quantity using CRDM (due to the existence of directly measurable current data), the predictions of other physical quantities have large deviations. The CRDM-PINN model proposed in this invention, however, incorporates… and After two physical laws, all three networks were Therefore, the prediction of CRDM motion physical quantities is also relatively accurate.

[0093] Table 1 presents the ablation experimental results based on PINN-based estimation of CRDM motion parameters. Experiment 1: MSE of CRDM motion parameters using only CRDM status monitoring data; Experiment 2: Ablation using CRDM status monitoring data plus... (i.e., motion velocity is not negative) MSE of CRDM motion parameters; Experiment 3: Using CRDM state monitoring data to add (i.e., the MSE of CRDM motion parameters under the CRDM dynamic equations under multiphysics coupling); Experiment 4: Using CRDM state monitoring data to... and The MSE of the CRDM motion parameters was calculated. The results show that both physical loss parameters can improve the accuracy of CRDM motion parameter estimation. The second physical loss parameter has the greatest impact on the accuracy, resulting in an order-of-magnitude improvement in the error index. This demonstrates the necessity and novelty of the designed physical loss parameter based on the dynamic equations under multi-physics coupling. Furthermore, the correlation coefficient between the resultant force and mass and acceleration is 0.68, indicating good consistency between these two predicted physical quantities and suggesting that the model better satisfies the laws of the CRDM dynamic equations under multi-physics coupling.

[0094]

[0095] Furthermore, according to the method described in step 1, step 4 further includes the following example verification process:

[0096] PINN-VI is used to characterize the uncertainty of the output, thereby evaluating the reliability of CRDM. In this section, firstly, CRDM-PINN-VI is trained based on MC-Dropout with a dropout rate of 1%. The model, training data, loss function, and other details are the same as CRDM-PINN. Since the model gradient is noisy with dropout, training using gradient descent is less stable. Therefore, a relatively large number of training epochs are performed, followed by a small number of training epochs with dropout disabled to adjust the model accuracy. The training results of CRDM-PINN-VI using MC-Dropout are shown. It can be seen that the output mean still provides accurate predictions for the relevant indicators. In addition, the MC Dropout method also provides the standard deviation of the output. The semi-transparent area represents the interval of ±2 standard deviations of the output mean. It can be seen that the represented uncertainty is stable in the region of the function with gentle changes; in the region with large changes and steeper slopes, such as when velocity and acceleration change abruptly, the standard deviation is large. This phenomenon is consistent with the understanding of numerical regression in deep learning methods.

[0097] The pull-in time was sampled using MC-Dropout, and the PDF of the boosting unit pull-in time and the frequency histogram of the samples were estimated using Gaussian kernel density estimation (KDE).

[0098] Combined with a given time threshold Based on equation (13), the reliability assessment result of CRDM at 12 million running steps is calculated to be 0.9015. To verify the above reliability, the absorption time data of 10 CRDMs at 12 million running steps were obtained using a multiphysics coupling platform, as shown in Table 2:

[0099]

[0100] Based on the reliability nonparametric estimation method, we have:

[0101]

[0102] In the formula, n=10 represents the total number of samples, i=1 represents the number of failure samples, and c represents 12 million steps. Statistical data shows that the nonparametric reliability estimate for 10 CRDM units at 12 million steps is 0.9091, while the result given in this example is 0.9015. Compared to the nonparametric estimate, the absolute reliability error is 0.0091, which is smaller. Furthermore, the reliability estimate is lower than the nonparametric estimate, making it more conservative and more suitable for practical engineering applications.

[0103] It is worth noting that the CRDM-PINN-VI proposed in this invention exhibits very high efficiency in reliability calculation after model training, with an average response time of 0.25 milliseconds. In contrast, the absorption time calculated using the CRDM multiphysics coupling simulation platform is extremely time-consuming due to the iterative calculations involved in multiphysics coupling models under different scenarios, resulting in an average response time on the order of hours. The above comparison of computational efficiency demonstrates that the method proposed in this invention is more suitable for practical engineering applications and can more quickly respond to CRDM reliability results in multiphysics coupling environments for subsequent operation and maintenance decisions.

[0104] Furthermore, based on the method described in step 1, steps 1-4 are summarized as follows:

[0105] (1) Starting from the working principle of CRDM, the dynamic model of CRDM under multi-physics coupling is analyzed in detail, and a reliability assessment method of CRDM based on improving armature engagement time is proposed.

[0106] (2) A CRDM reliability assessment method based on PINN is introduced, which can make full use of the data and dynamic model within the CRDM working cycle and improve the limitations of traditional machine learning models.

[0107] (3) Numerical examples show that the proposed method has a small relative error compared with the statistical reliability assessment results, verifying the accuracy of the reliability assessment results in CRDM. On the other hand, compared with the dynamic model under multi-physics coupling, the proposed PINN model has an order-of-magnitude improvement in computational efficiency, which is more in line with the requirements of practical engineering for rapid reliability assessment. Attached Figure Description

[0108] Figure 1 Diagram of the basic components of CRDM;

[0109] Figure 2 This is the circuit diagram for the CRDM coil.

[0110] Figure 3 To improve the calculation model for armature water resistance;

[0111] Figure 4 Force analysis diagram for improving the armature lifting process;

[0112] Figure 5 Waveform diagram of contact friction and fault between the armature and sleeve shaft of CRDM lifting;

[0113] Figure 6 Improve CRDM unit pull-in time meaning;

[0114] Figure 7The CRDM-PINN model under multiphysics coupling;

[0115] Figure 8 For specific details of CRDM-PINN;

[0116] Figure 9 The model is CRDM-PINN-VI.

[0117] Figure 10 It serves as a CRDM reliability testing platform;

[0118] Figure 11 This is a comparison chart of CRDM motion parameter results and actual values ​​using only the data;

[0119] Figure 12 A comparison chart of CRDM motion parameter results and actual values ​​driven by both data and physical information;

[0120] Figure 13 The CRDM-PINN-VI results using the MC-Dropout method are shown in the image.

[0121] Figure 14 PDF estimation and frequency histogram for absorption time; Detailed Implementation

[0122] The technical solution of the present invention will be further described below with reference to the accompanying drawings:

[0123] Step 1: Multiphysics Coupling Mechanism Analysis and Dynamic Modeling of CRDM. Based on the working principle of the third-generation pressurized water reactor magnetic lifting control rod drive mechanism (CRDM) and its high-temperature, high-pressure, and high-irradiation service environment, this study focuses on the lifting armature, the core actuator, and conducts an analysis of the electromagnetic-water resistance-mechanical multiphysics coupling effect. Calculation models for the coil electromagnetic force, armature motion water resistance, and reset spring force are established. Based on Newton's second law, a coupled dynamic partial differential equation for the lifting armature motion is constructed, clarifying key parameters with random uncertainties in the model (air gap length, gap magnetic reluctance area, additional magnetic reluctance, etc.), providing a theoretical basis for subsequent physical mechanism embedding.

[0124] Step 2: Construction of Core Indicators and Quantitative Model for CRDM Reliability Assessment. The armature pull-in time is selected as the core performance indicator characterizing CRDM reliability. The physical definition of pull-in time is clarified (the time interval from the start of coil energization to the lowest point of the current waveform "return groove" corresponding to complete armature pull-in). Criteria for triggering failure modes such as slippage and failure to lift when pull-in time exceeds a threshold are determined. A CRDM reliability calculation model considering the propagation of input parameter uncertainties is established, clarifying the mathematical mapping relationship between reliability and the probability density function of pull-in time, thus completing the construction of the reliability assessment framework.

[0125] Step 3: Construct the CRDM-PINN-VI probabilistic neural network with embedded mechanism and complete the characterization of absorption time uncertainty. An embedded physical information Bayesian neural network (CRDM-PINN-VI) was constructed, comprising three subnetworks: displacement fitting, water resistance calculation, and current prediction. Utilizing the automatic differentiation characteristic of neural networks, the first and second order differential relationships of displacement, velocity, and acceleration were automatically solved. Using monitorable vibration acceleration and coil current data during CRDM service as training inputs, data fitting loss terms for acceleration and current were constructed respectively. Simultaneously, two major physical law loss terms—the non-negativity constraint of the lifting armature motion velocity and the multi-physics coupling dynamic equation—were embedded to form a weighted total loss function. A phased training strategy was designed to optimize the network, achieving accurate inversion of physical quantities that cannot be directly monitored, such as displacement, velocity, and water resistance, and deterministic point estimation of the pull-in time. Furthermore, variational inference theory and the Monte Carlo Dropout (MC-Dropout) mechanism were introduced into the three subnetworks. By enabling multiple rounds of forward propagation with MC-Dropout enabled, Monte Carlo sampling was achieved to obtain a large number of random samples of the pull-in time, quantifying the uncertainty of parameters, models, and data, and obtaining the sample set and distribution characteristics of the pull-in time.

[0126] Step 4: CRDM Reliability Measurement and Method Validation. Based on the Gaussian kernel density estimation (KDE) method, the absorption time sample set is fitted to obtain the probability density function (PDF) of the absorption time. Combined with the preset absorption time failure threshold, the reliability result of CRDM under specified service conditions is obtained by probability integration. Based on the measured data of the CRDM reliability test platform, ablation experiments are carried out to verify the effect of physical constraints on improving model accuracy. The accuracy of the method is verified by comparing the nonparametric reliability estimation results. At the same time, the computational efficiency of the proposed method is verified by comparing it with the traditional multiphysics coupling simulation method, thus completing the engineering applicability verification of the method.

[0127] Furthermore, according to the method described in step 1, the characteristic is that, in step 1:

[0128] The magnetically lifted reactor core modulator (CRDM) is a crucial component of a pressurized water reactor (PWR), enabling functions such as reactor power regulation, normal shutdown, and accident shutdown. A typical CRDM topology is shown below. Figure 1 As shown, it mainly consists of a coil assembly (magnetic yoke, lifting coil, moving coil and holding coil), a claw assembly (lifting magnetic pole, lifting armature, moving armature, holding magnetic pole, holding armature, moving claw and holding claw, etc.), a pressure-resistant shell assembly (sealing shell and magnetic ring, etc.), a heat insulation sleeve assembly and a drive rod assembly.

[0129] In the operation of a magnetically driven CRDM, the lifting coil, lifting pole, lifting armature, and corresponding yoke and magnetic ring constitute the lifting unit; the moving coil, moving armature, lifting armature, and corresponding yoke and magnetic ring constitute the moving unit; and the holding coil, holding pole, holding armature, and corresponding yoke and magnetic ring constitute the holding unit. When the coil is energized, the armature in the corresponding unit (such as the lifting armature, moving armature, or holding armature) will be subjected to electromagnetic force, thereby overcoming resistances such as gravity, water resistance, spring force, and load, and engaging with the corresponding magnetic pole. The lifting unit is the key actuator that drives the drive rod to perform lifting or lowering actions, therefore its health is particularly important. The moving unit engages or disengages with the drive rod's annular groove via a connecting rod and pawl. The holding unit has a similar structure to the moving unit, but its main function is to position the pawl into the drive rod's annular groove, keeping the drive rod in a designated position. Each unit requires its coil to be energized and de-energized according to a specific time and sequence to properly complete actions such as lifting, lowering, holding, or rapid rod drop.

[0130] Furthermore, according to the method described in step 1, the characteristic is that, in step 1:

[0131] Step 3.1: Electromagnetic force calculation model.

[0132] This is the equivalent resistance of the coil; This is an energy-dissipating resistor. Its function is to allow current to flow through the CRDM coil when the coil is de-energized, forming a closed loop and thus consuming all the energy in the coil, causing the current to drop rapidly to zero. I represents the current in the coil; x represents the length of the air gap for lifting the armature. The equivalent inductance of the coil can be expressed as a function of the air gap x. VT1 is an inverter switching transistor used to control the duration and sequence of the coil current; VT2 is a chopper switching transistor used to control the magnitude of the coil current.

[0133] During the pull-in phase of CRDM, the coil circuit equation is:

[0134]

[0135] During the movement of the CRDM, the air gap x can be written as time. function When the CRDM gap is fully open, x(t) = 0; when the gap is fully closed, The clearance during the lifting armature movement is... Therefore, during the armature attraction process, the inductance L can be expressed as a function of the air gap x and time t, that is:

[0136]

[0137] In the formula, S is the area at the gap reluctance; Let be the vacuum permeability, and take . ; It represents the sum of the magnetic reluctances of all parts except the air gap magnetic reluctance; The number of coil turns is 577.

[0138] Substituting equation (2) into equation (1), the current can be calculated. Then the electromagnetic force can be expressed as:

[0139]

[0140] Step 3.2: Water resistance calculation model.

[0141] When the CRDM lifting armature moves upward, the water gap between it and the lifting pole decreases. Part of the squeezed water flows along the gaps between the lifting armature, moving armature, and other parts and the sealing shell. The other part flows along the gaps between the lifting pole and the sealing shell, the radial holes of the lifting pole, and the gaps between the drive rod and the sleeve shaft. Due to the conservation of circuit voltage drop:

[0142]

[0143] In the formula, P 1i and P 2i Let represent the voltage drop at various points in the circuit. The voltage drop mainly consists of frictional voltage drop, inertial voltage drop, and local voltage drop, which can be calculated using the following formula:

[0144]

[0145] In the formula, These are the frictional pressure drop and the inertial pressure drop. and These are the drag coefficients for the inner and outer walls, respectively, which can be calculated using the Colebrook formula; The density of water; and These are the relative velocities of the inner and outer walls with the water, respectively. and. These are the wetted perimeters of the inner and outer walls, respectively. The lengths of the inner and outer walls; For localized pressure drop; The acceleration of water; This is the local drag coefficient; The velocity of the water.

[0146] The drive lever assembly and the control rod assembly it drives are The water resistance encountered during movement due to pressure drop:

[0147]

[0148] Analysis of the above model shows that the magnitude of water resistance is not only related to the structural characteristics and surface roughness of the CRDM, but also significantly affected by factors such as the armature movement speed, water flow velocity, and density.

[0149] However, due to the difficulty in directly measuring the drag coefficients of the inner and outer walls of the drive mechanism, and its complex and irregular shape, key parameters required for calculating water resistance, such as length and cross-sectional area, are difficult to obtain accurately. A PINN network will be used to learn the magnitude of water resistance in the future.

[0150] Step 3.3: Spring force calculation model.

[0151] Hooke's Law can be used to simulate the elastic force of the spring on the armature. Hooke's Law states that when a spring undergoes elastic deformation, the elastic force of the spring... Change in spring length A linear relationship, that is

[0152]

[0153] In the formula, The spring stiffness is determined by the material properties of the spring. The negative sign indicates that the elastic force generated by the spring is opposite to the direction of its elongation. This is the preload of the spring.

[0154] Step 3.4: Multiphysics coupling model.

[0155] Figure 4 middle, Electromagnetic lifting force; It is the elastic force of the spring; To increase the weight of moving parts such as the armature, drive rod, and pawl; This refers to the load force, specifically the weight of the control rod assembly. For water resistance; Other resistance factors include gravity. and load capacity It is a constant; other resistances The value is relatively small, and its effect on the armature's motion state can be ignored. According to Figure 4 Analysis shows that, using Newton's second law, the dynamics of lifting the armature can be expressed by the following equation:

[0156]

[0157] In the formula, This represents the acceleration that lifts the armature; x is the displacement of the armature; and M is the total mass of the moving parts and the load.

[0158] Furthermore, according to the method described in step 1, step 2 includes the following sub-steps:

[0159] The lifting unit is a crucial motion unit of the CRDM, and its reliability directly impacts the overall performance of the CRDM. Under the coupling of multiple physical fields, the lifting armature undergoes relative motion with the sleeve shaft, driving the hook assembly and load to move together until engagement is achieved. Figure 5 As shown. However, due to the direct contact and friction between the lifting armature and the bushing shaft during service, debris or even foreign objects may become stuck, causing changes in the lifting armature's movement speed. Consequently, the lifting armature's engagement time will also change. These changes in engagement time will further cause the current timing of the holding and moving units to interleave, ultimately leading to CRDM failure modes such as slippage and inability to lift. Figure 5 The current waveforms of the lifting unit under normal and fault modes are shown. The completion point of the lifting armature engagement action is the lowest point of the current waveform "return groove," and the process from zero current to this lowest point fully describes the change in coil current during armature engagement. Figure 5 It is evident that, compared to the normal current waveform, the current pull-in point disappears in the CRDM fault waveform, and the pull-in time is severely delayed, posing a risk of faults such as armature slippage and inability to lift. Therefore, whether the armature pull-in time meets the requirements is the criterion for judging whether the CRDM exhibits fault modes such as armature slippage or inability to lift. Thus, efficiently and accurately assessing the armature pull-in time is crucial for evaluating the reliability of the CRDM.

[0160] The armature engagement time was selected as the key performance indicator for the CRDM. If this indicator exceeds a certain threshold, the entire CRDM is considered to be prone to malfunctions such as arm slippage or failure to lift. Figure 5 The pull-in time in the current waveform of the CRDM booster unit is shown. Meaning, where c represents the current running step number. CRDM booster unit pull-in time. From The time interval is from 0 (the moment when energization begins) to the point where the current is at its lowest after the coil exhibits back electromotive force. The duration of the time interval. This is a fixed value, representing the start time of step c. The point where the current is lowest after the coil exhibits back EMF indicates that the armature is fully engaged.

[0161] It is worth noting that, due to the movement of the lifting armature under the influence of electromagnetic force, water resistance, spring force, gravity, etc., Figure 6 The lowest point of current in It is not a fixed value, but a value that changes continuously with the number of steps taken. First, This depends on the dynamic equation of the lifting armature, i.e., equation (8). Specifically, according to the CRDM dynamic analysis model in Section 2, if the values ​​of all electromagnetic forces, spring forces, gravity, load forces, water resistance, and other resistances are given, the displacement, velocity, and acceleration results of the CRDM motion process can be quickly calculated. When the CRDM armature is engaged, the current reaches its minimum value, and at this time, the displacement reaches its maximum value. Therefore, the engagement time of the CRDM lifting unit can be calculated by calculating the difference between the initial moment and the time when the displacement is maximum. Specifically, we will... The stepping bar process is decomposed into countless small time elements, and the time step is represented by... In other words, using... , Indicates the first Stepping stick The displacement, velocity, acceleration, and the water resistance, spring force, and electromagnetic force acting on the CRDM at any given moment can be used to calculate the acceleration value at that moment using equation (9). ,Right now:

[0162]

[0163] when Given the given information, substitute it into the following equation to iteratively calculate the next time step. The velocity and displacement values, namely:

[0164]

[0165] Continue Substituting the displacement and velocity values ​​at a given time into the corresponding electromagnetic force, spring force, and water resistance calculation models, we can obtain... At present , , .Will Water resistance at time Spring force Electromagnetic force Substituting back into equation (10), we can calculate... acceleration value at time t ,Right now:

[0166]

[0167] In the formula, express The combined efforts at any given moment; To improve the mass of the unit itself, the acceleration... Substituting these values ​​into equation (10) allows us to calculate the displacement and velocity at that moment. Repeating the above steps iteratively allows us to calculate the [missing value]. The acceleration, velocity, displacement, electromagnetic force, water resistance, and spring force of the stepping rod at any time during the process are recorded. When the displacement reaches its maximum value during iteration, that is, when it is just attracted, the displacement is set to no longer change. Then, according to equation (10), the velocity and acceleration at this moment are both zero. The time at this moment is recorded as _____. Then the absorption time can be further obtained. .

[0168] The above calculations were performed under the condition that relevant parameters such as electromagnetic force and water resistance were known. However, in actual engineering, the air gap length l... g Area S at the gap reluctance, reluctance Due to material variations and manufacturing process fluctuations, uncertainties are inevitable; that is, these parameters are not fixed constants but can only be described by distributions. The uncertainty of the input parameters, after the aforementioned calculation process, also leads to uncertainty in the CRDM pull-in time. This process is called uncertainty propagation, and its purpose is to analyze how the uncertainty of the lifter unit's input parameters affects the uncertainty of the system output. Without loss of generality, let's assume the uncertainty parameters of the lifter unit are... All follow a normal distribution, that is:

[0169]

[0170] In the formula, , , Let lg represent the air gap length, S represent the area at the air gap reluctance, and S represent the reluctance. The mean of the probability distribution, and , , Let represent the variances of the probability distribution, respectively. If the mean and variance are known, then the uncertainty parameters can be collected using the hyper-Latin square sampling method. middle Each parameter sample is used, and the pull-in time of the lifting unit is calculated for each sample using the above iterative process. . use Each suction time This allows for the estimation of the probability density function (PDF) that increases the unit's pull-in time. Based on the absorbance time PDF results and combined with the absorbance time threshold. The reliability of CRDM can be calculated. Without loss of generality, the reliability formula for CRDM at any number of running steps c can be expressed as:

[0171]

[0172] However, it is worth noting that due to the complexity and high nonlinearity of the armature attraction process under multiphysics coupling, the PDF of the attraction time varies with the number of running steps. It is difficult to estimate directly and cannot be solved analytically. Therefore, the reliability of CRDM cannot be directly calculated using equation (13). This paper proposes PINN

[24] to solve the CRDM booster unit pull-in time PDF. Then convert the absorption time PDF Substitute into equation (20) to calculate the reliability of CRDM under any number of running steps.

[0173] Furthermore, according to the method described in step 1, step 3 includes the following sub-steps:

[0174] Step 5.1: PINN and variational inference theory.

[0175] This invention utilizes PINN to continuously adjust network parameters. This paper aims to improve the armature engagement time under multiphysics coupling while ensuring the data satisfies the physical laws in the model. However, traditional PINN networks can only obtain point estimates of the output, not its probability distribution. This paper introduces Variation Inference (VI) into PINN, termed the PINN-VI model, to obtain the PDF of the engagement time. The implementation process of PINN-VI and how to achieve the posterior PDF approximation in VI using Monte Carlo Dropout (MC-Dropout) are described below.

[0176] VI method utilizes functions Posterior distribution of approximate parameters , As a prior distribution hypothesis for parameter θ, by Parameterization. Function The mean-field Gaussian approximation method is generally used, that is:

[0177]

[0178] In the formula, The mean Standard deviation PDFs with a normal distribution; The number of model parameters, i.e. The dimension. The approximation principle is to minimize and posterior distribution KL divergence between This is achieved by maximizing the Evidence Lower Bound (ELBO). ELBO can be expressed as:

[0179]

[0180] In the formula, Let be the loss function of the neural network. For parameter priors and posterior The KL divergence between them.

[0181] Executing the MC-Dropout method in a neural network can achieve the ELBO optimization process in VI. In the MC-Dropout method, a dropout probability is specified. The value of each network node during forward propagation has The probability is set to zero. Gal et al. theoretically proved that in ELBO... It is proportional to the L2 regularization of the neural network, that is:

[0182]

[0183] Therefore, optimizing the loss function of a neural network with MC-Dropout is consistent with optimizing ELBO. Based on the above theoretical derivation, we will apply MC-Dropout to PINN to obtain the posterior PDF of the absorption time.

[0184] Step 5.2: CRDM-PINN method.

[0185] The pull-in time index of the CRDM lifting unit reflects the reliability level of the mechanism's operation. The following will explain how to fit the CRDM pull-in time distribution based on PINN-VI. First, we will introduce how to use the PINN model to fit the CRDM pull-in time index. During the CRDM operation phase, some acceleration and current data can be obtained using vibration sensors and current signals. In this problem, acceleration data serves as the raw data, requiring the inversion of CRDM velocity and displacement data. The magnitude of the displacement is directly related to the CRDM lifting unit's pull-in time. Therefore, displacement is used as the antiderivative in this problem. Data for the antiderivative is scarce, while data representing physical information using the differential terms of the antiderivative (the differential of displacement is velocity, and the differential of velocity is acceleration) is readily available. Therefore, we can utilize PINN's automatic differentiation function to embed the differential relationship between acceleration, velocity, and displacement into the neural network, and fit the displacement as a function of time using only the CRDM-based acceleration data. Furthermore, as discussed in Section 2 regarding the multiphysics coupling model, electromagnetic force in practice is a displacement-related quantity, while water resistance is a velocity-related quantity, and both exhibit implicit characteristics. Therefore, an architecture can be used, as shown below, to combine the electromagnetic force and water resistance physical fields with the motion of the CRDM, forming a multiphysics-coupled CRDM-PINN, used to evaluate the pull-in time of the CRDM lifting unit, such as... Figure 7 As shown.

[0186] Figure 7 In the model, the CRDM-PINN contains three sub-networks, which respectively fit the motion of the CRDM itself, the current in the coil, and the acceleration experienced by the CRDM. The reasons for designing this network architecture are as follows: First, we build a first neural network model to evaluate the displacement value. Since the velocity value can be obtained by differentiating the displacement output with respect to time, and this process can be automatically obtained in the neural network, the automatically solved velocity value is input into the second neural network to solve the water resistance model. As analyzed in Section 2, water resistance is related to the motion speed of the mechanism, so the velocity value automatically differentiated by the first network is input into the second neural network to solve the acceleration. The displacement of the first network can also be differentiated with respect to time, which is also obtained through automatic differentiation in the neural network, and the acceleration value can be trained using the acceleration data from the vibration sensor. On the other hand, as mentioned in step 1, the electromagnetic force calculation model is related to the armature air gap, so a third network can be designed to input the displacement value (air gap) into the third neural network to predict the electromagnetic force, which will be obtained by training using the current data. Figure 9 The specific details of the three networks in CRDM-PINN are shown.

[0187] from Figure 8 It can be seen from this that Figure 7The first neural network in PINN is used to train the displacement during the attraction process. Since displacement data is unavailable, the automatic differentiation function of the neural network is utilized to obtain the acceleration by taking the second-order partial derivative between the output displacements. Acceleration can be directly obtained using an acceleration vibration sensor; therefore, vibration acceleration data can be used to train the first neural network in PINN. Secondly, current data is used to train the third neural network. This invention utilizes a dynamic model under multi-physics coupling to train the second neural network, namely the water resistance model. From the above analysis, it can be seen that the dynamic analysis model under multi-physics coupling in Section 2 is embedded through the automatic differentiation function of the first network in PINN, which is also the main manifestation of the embedded mechanism neural network proposed in this section. The training process of the three neural networks will be described in detail below.

[0188] Since the three outputs of the PINN proposed in this invention are all continuous values, all three neural networks belong to the regression problem. For regression problems, the loss function of PINN is generally the mean squared error. Let's represent this. The following will explain how to train the three neural networks mentioned above using the root mean square error. First, assume the training dataset from the CRDM service process... , representing the actual observed values ​​of acceleration and current, respectively, and relative to the input time. The time values ​​in the data correspond one-to-one. They are respectively used... Let represent the three sub-networks of CRDM-PINN. Then we have:

[0189]

[0190] In the formula, the function This represents the first neural network used to solve for the shift output, while This can be obtained automatically through differentiation using the first neural network. It can also be obtained automatically through differentiation using neural networks. It can also be obtained automatically through differentiation using a neural network. This indicates that the second neural network is used to solve for water resistance. Since water resistance is related to velocity, the output of the first neural network is used instead. Also input into the network This represents the third neural network, which outputs the displacement because current and displacement are related. The input is fed into the neural network. Additionally, Indicate each The resultant force is calculated at the corresponding time point. With this information, the terms in PINN's loss function can be calculated. Assume... , Let represent the loss functions for the CRDM-PINN displacement and current neural networks, respectively. Then, the training dataset can be used. The following loss functions were obtained respectively:

[0191]

[0192]

[0193] In equation (18), The loss function representing acceleration data, Indicates the size of the data. This represents the i-th acceleration training data; in equation (19), The loss function representing the current data. Let represent the i-th current training data. The two loss functions mentioned above are insufficient to achieve satisfactory results for the entire PINN training. Two additional loss functions based on physical laws are needed. First, for CRDM, its velocity cannot be negative. Therefore, the first piece of physical information is added to the CRDM-PINN loss function, expressed as:

[0194]

[0195] This means that a constraint is imposed on all outputs with velocities less than 0 for all CRDM displacement models, limiting the output velocity to be greater than or equal to 0. Secondly, the motion process of the CRDM lifting unit must satisfy the dynamic equation of equation (8), therefore, a second physical constraint needs to be added. This means that the motion process of the CRDM lifting unit must satisfy Newton's second law, that is:

[0196]

[0197] In the formula, Indicates resultant force; It represents the sum of forces other than electromagnetic force and water resistance, including the lifting force, elastic force, and load. The resultant force is the sum of forces calculated from the outputs of the water resistance model and the electromagnetic force model, as well as other given parameters. This indicates that when the current is The magnitude of the electromagnetic lifting force is calculated by substituting it into the equivalent magnetic circuit model.

[0198] The total loss of CRDM-PINN is obtained by weighted summation of all terms, where This represents the weight corresponding to each loss term. That is:

[0199]

[0200] In the formula, This ensures that the model's predictions do not incorrectly assume that the CRDM will move in a downward direction; It includes a dynamic model under CRDM multiphysics coupling, which can connect the information between the three sub-networks and achieve the most accurate absorption time assessment.

[0201] Step 5.3: CRDM-PINN-VI Method

[0202] Figure 7 The CRDM-PINN model shown can only evaluate a fixed value of the absorption time, without considering the uncertainty of input parameters, data, and neural network. Therefore, this section proposes a PINN-VI-based CRDM absorption time distribution evaluation. Based on the absorption time distribution and a threshold for absorption time, the reliability of the CRDM can be evaluated. The proposed CRDM-PINN-VI architecture is as follows: Figure 9 As shown. With Figure 7 The only difference is that all three networks use Bayesian neural networks and employ the MC-Dropout method to implement the PINN-VI probability distribution output. The model structure, data, loss function, and other details are consistent with CRDM-PINN. With MC-Dropout, the model's gradient descent is less stable, resulting in slower convergence during training. Therefore, more training epochs are required, followed by a small number of training epochs with MC-Dropout disabled to further refine the model's accuracy.

[0203] After training, the model's output mean and standard deviation can be obtained with MC-Dropout disabled. To evaluate the uncertainty of the suction time, the displacement function curve needs to be analyzed. Specifically, with MC-Dropout enabled, the model's displacement prediction over time is output to obtain the minimum time. make The adsorption time is the time required to complete the adsorption process. By sampling the adsorption time multiple times using the Monte Carlo method, the PDF of the CRDM adsorption time can be obtained, which is the value in equation (13). .

[0204] Furthermore, according to the method described in step 1, step 4 includes the following example verification process:

[0205] This invention uses CRDM current and acceleration test data to verify the correctness and effectiveness of the proposed method. The CRDM reliability test platform is as follows: Figure 10As shown, the test platform mainly consists of three parts: the ML-CRDM mounting platform, the electromagnetic loading unit, and the data acquisition and control unit. Current data is acquired from the data acquisition and control system of the three sets of CRDM coils. The CRDM displacement sensor is mounted on the drive rod, indirectly characterizing the displacement characteristics of the lifting armature by detecting the displacement of the drive rod during dynamic operation; the acceleration vibration sensor is fixed to the flange base and is used to collect the vibration acceleration signals generated during the operation of the CRDM lifting unit.

[0206] As revealed by the CRDM reliability test platform, only acceleration and current data are available for CRDM condition monitoring; displacement, velocity, and water resistance data are unavailable. Therefore, this invention ingeniously designs a loss function based on a multiphysics-coupled dynamic model, simultaneously incorporating the prediction of CRDM water resistance, displacement, and velocity into the training of the PINN. Using only the CRDM's acceleration and current data, the changes in these three physical quantities can be accurately estimated. Thus, the multiphysics-coupled CRDM dynamic model is an essential physical loss function for the designed network. This underscores the necessity of the CRDM-PINN designed in this invention.

[0207] use Figure 7 and Figure 9 Two networks, PINN and PINN-VI, are used to evaluate the CRDM's armature engagement time and engagement time probability distribution. The network hyperparameters are set as follows: Due to the inconsistent units of physical quantities and the different orders of magnitude among the terms in the loss function, choosing appropriate weight parameters is crucial for the model's training performance and final convergence. In this example, , , , Each sub-network is a fully connected neural network with four hidden layers and node counts of [50, 100, 100, 50]. The training data consists of current and acceleration data from the CRDM over 12 million runs. Regarding the training strategy, although incorporating physical information into the loss function is theoretically optimal, in practice, the gradient of the differential term in the loss function is unstable at the beginning of training when the error is large, making model convergence difficult. Accordingly, Although equivalent to numerical regression, it converges quickly for loss terms without differentiation. Therefore, a strategy of training the first neural network first is adopted to increase... The weights are adjusted until the displacement model essentially converges, at which point the model switches to the next loss function. The specific training hyperparameters are: and Using learning rate and 10,000 training sessions; and Using learning rate and 30,000 training sessions.

[0208] Furthermore, the training data for current and acceleration are explained as follows: First, the state monitoring data is divided into training, validation, and test sets in an 8:1:1 ratio. All data is randomly divided into three datasets according to this ratio. 80% of the data is used to train the proposed PINN and PINN-VI networks. The trained model is then used to validate its generalization ability and optimize its hyperparameters using the remaining 10% of the dataset. Finally, the remaining 10% of the dataset is used for testing. We also compared cross-testing with other ratios and found that the 8:1:1 cross-testing performed best. Therefore, this invention only presents the analysis results of the 8:1:1 cross-testing.

[0209] Figure 11 and Figure 12 They respectively demonstrated the use of That is, training and simultaneous use of data and physical information are completed solely based on data, without introducing the physical information contained in equations (20) and (21). , The prediction results of the trained model are shown in the following sub-figures: prediction of displacement; prediction of velocity; prediction of acceleration; prediction of current in the coil; prediction of water resistance; and comparison of the resultant force calculated based on the prediction values ​​with mass × acceleration. The results show that the prediction results of the model based solely on the data differ significantly from the actual values. This is because CRDM can only collect acceleration and current data. For neural network 3, the network uses the CRDM's motion velocity to predict water resistance, but there is no training data for water resistance. Therefore, without the data from equation (21), the prediction results are significantly different. If the motion law of the CRDM booster unit is not known, then there is no loss function available for training the neural network 3. Therefore, the convergence effect of the entire PINN network is poor. On the other hand, due to the lack of equation (21) Even using only acceleration and current data, it's difficult to accurately predict displacement and velocity results. This is because there's no directly observable data for these physical quantities to use for training, and indirect data lacks physical laws to guide convergence. Therefore, the predictions of models based solely on data often differ significantly from the actual values. Figure 11 As can be seen, apart from the relatively accurate prediction results of the CRDM current physical quantity (due to the existence of directly measurable quantities—current data), the prediction results of other physical quantities have large deviations. The CRDM-PINN model proposed in this invention, however, incorporates... and After two physical laws, all three networks were Therefore, the prediction of CRDM motion physical quantities is also relatively accurate.

[0210] Table 1 presents the ablation experimental results based on PINN-based estimation of CRDM motion parameters. Experiment 1: MSE of CRDM motion parameters using only CRDM status monitoring data; Experiment 2: Ablation using CRDM status monitoring data plus... (i.e., motion velocity is not negative) MSE of CRDM motion parameters; Experiment 3: Using CRDM state monitoring data to add (i.e., the MSE of CRDM motion parameters under the CRDM dynamic equations under multiphysics coupling); Experiment 4: Using CRDM state monitoring data to... and The MSE of the CRDM motion parameters was calculated. The results show that both physical information can improve the accuracy of CRDM motion parameter estimation. Among them, the second physical loss has the greatest improvement on the accuracy of CRDM motion parameter estimation, and the error index is improved by an order of magnitude. This demonstrates the necessity and novelty of the physical loss based on the dynamic equation under multi-physics coupling.

[0211]

[0212] Furthermore, according to the method described in step 1, step 4 further includes the following example verification process:

[0213] PINN-VI is used to characterize the uncertainty of the output, thereby evaluating the reliability of CRDM. In this section, firstly, CRDM-PINN-VI is trained based on MC-Dropout with a dropout rate of 1%. The model, training data, loss function, and other details are the same as CRDM-PINN. Since the model gradient is noisy with dropout, training using gradient descent is less stable. Therefore, a relatively large number of training epochs are performed. Then, a small number of training epochs are performed with dropout disabled to adjust the model accuracy. Figure 13 The training results of CRDM-PINN-VI using MC-Dropout are shown. It can be seen that the output mean still provides accurate predictions for the relevant metrics. Furthermore, the MC Dropout method also provides the standard deviation of the output. Figure 13 In the diagram, the semi-transparent region represents the interval between the output mean and 2 standard deviations. It can be seen that the uncertainty it represents is stable in regions where the function is relatively flat; however, in regions with larger and steeper changes, such as when velocity and acceleration undergo abrupt changes, the standard deviation is large. This phenomenon is consistent with the understanding of numerical regression in deep learning methods.

[0214] The pull-in time was sampled using MC-Dropout, and the PDF of the boosted unit pull-in time and the frequency histogram of the samples were estimated using Gaussian kernel density estimation (KDE), as shown below. Figure 14 As shown.

[0215] Combined with a given time threshold Based on equation (13), the reliability assessment result of CRDM at 12 million running steps is calculated to be 0.9015. To verify the above reliability, the absorption time data of 10 CRDMs at 12 million running steps were obtained using a multiphysics coupling platform, as shown in Table 2:

[0216]

[0217] Based on the reliability nonparametric estimation method, we have:

[0218]

[0219] In the formula, n=10 represents the total number of samples, i=1 represents the number of failure samples, and c represents 12 million steps. Statistical data shows that the nonparametric reliability estimate for 10 CRDM units at 12 million steps is 0.9091, while the result given in this example is 0.9015. Compared to the nonparametric estimate, the absolute reliability error is 0.0091, which is smaller. Furthermore, the reliability estimate is lower than the nonparametric estimate, making it more conservative and more suitable for practical engineering applications.

[0220] It is worth noting that the CRDM-PINN-VI proposed in this invention exhibits very high efficiency in reliability calculation after model training, with an average response time of 0.25 milliseconds. In contrast, the absorption time calculated using the CRDM multiphysics coupling simulation platform is extremely time-consuming due to the iterative calculations involved in multiphysics coupling models under different scenarios, resulting in an average response time on the order of hours. The above comparison of computational efficiency demonstrates that the method proposed in this invention is more suitable for practical engineering applications and can more quickly respond to CRDM reliability results in multiphysics coupling environments for subsequent operation and maintenance decisions.

[0221] Furthermore, based on the method described in step 1, steps 1-4 are summarized as follows:

[0222] (1) Starting from the working principle of CRDM, the dynamic model of CRDM under multi-physics coupling is analyzed in detail, and a reliability assessment method of CRDM based on improving armature engagement time is proposed.

[0223] (2) A CRDM reliability assessment method based on PINN is introduced, which can make full use of the data and dynamic model within the CRDM working cycle and improve the limitations of traditional machine learning models.

[0224] (3) Numerical analysis shows that the proposed method has a small relative error with the statistical reliability assessment results, verifying the accuracy of the reliability assessment results in CRDM. On the other hand, compared with the dynamic model under multi-physics coupling, the proposed PINN model has an order-of-magnitude improvement in computational efficiency, which is more in line with the further requirements of practical engineering for rapid reliability assessment.

Claims

1. A reliability assessment method for a nuclear reactor control rod drive mechanism with an embedded mechanism, the specific steps of which are as follows: Step 1: Multiphysics Coupling Mechanism Analysis and Dynamic Modeling of CRDM. Based on the working principle of the third-generation pressurized water reactor magnetic lifting control rod drive mechanism (CRDM) and its high-temperature, high-pressure, and high-irradiation service environment, this study focuses on the lifting armature, the core actuator, and conducts an analysis of the electromagnetic-water resistance-mechanical multiphysics coupling effect. Calculation models for the coil electromagnetic force, armature motion water resistance, and reset spring force are established. Based on Newton's second law, a coupled dynamic partial differential equation for the lifting armature motion is constructed, clarifying key parameters with random uncertainties in the model (air gap length, gap magnetic reluctance area, additional magnetic reluctance, etc.), providing a theoretical basis for subsequent physical mechanism embedding. Step 2: Construction of Core Indicators and Quantitative Model for CRDM Reliability Assessment. The armature pull-in time is selected as the core performance indicator characterizing CRDM reliability. The physical definition of pull-in time is clarified (the time interval from the start of coil energization to the lowest point of the current waveform "return groove" corresponding to complete armature pull-in). Criteria for triggering failure modes such as slippage and failure to lift when pull-in time exceeds a threshold are determined. A CRDM reliability calculation model considering the propagation of input parameter uncertainties is established, clarifying the mathematical mapping relationship between reliability and the probability density function of pull-in time, thus completing the construction of the reliability assessment framework. Step 3: Construct the CRDM-PINN-VI probabilistic neural network with embedded mechanism and complete the characterization of absorption time uncertainty. An embedded physical information Bayesian neural network (CRDM-PINN-VI) was constructed, comprising three subnetworks: displacement fitting, water resistance calculation, and current prediction. Utilizing the automatic differentiation characteristic of neural networks, the first and second order differential relationships of displacement, velocity, and acceleration were automatically solved. Using monitorable vibration acceleration and coil current data from the CRDM during service as training inputs, data fitting loss terms for acceleration and current were constructed respectively. Simultaneously, two major physical law loss terms—the non-negativity constraint of the lifting armature motion velocity and the multi-physics coupling dynamic equation—were embedded to form a weighted total loss function. A phased training strategy was designed to optimize the network, achieving accurate inversion of physical quantities that cannot be directly monitored, such as displacement, velocity, and water resistance, and deterministic point estimation of the pull-in time. Furthermore, variational inference theory and the Monte Carlo dropout mechanism were introduced into the three subnetworks. By enabling multiple rounds of forward propagation with MC-Dropout enabled, Monte Carlo sampling was achieved to obtain a large number of random samples of the pull-in time, quantifying the uncertainty of parameters, models, and data, and obtaining the sample set and distribution characteristics of the pull-in time. Step 4: CRDM Reliability Measurement and Method Validation. Based on the Gaussian kernel density estimation (KDE) method, the absorption time sample set is fitted to obtain the probability density function (PDF) of the absorption time. Combined with the preset absorption time failure threshold, the reliability result of CRDM under specified service conditions is obtained by probability integration. Based on the measured data of the CRDM reliability test platform, ablation experiments are carried out to verify the effect of physical constraints on improving model accuracy. The accuracy of the method is verified by comparing the nonparametric reliability estimation results. At the same time, the computational efficiency of the proposed method is verified by comparing it with the traditional multiphysics coupling simulation method, thus completing the engineering applicability verification of the method.

2. The method according to claim 1, characterized in that, In step 1: The magnetically lifted reactor core modulator (CRDM) is a crucial component of a pressurized water reactor (PWR), enabling functions such as reactor power regulation, normal shutdown, and accident shutdown. A typical CRDM topology primarily consists of coil assemblies (yoke, lifting coil, moving coil, and holding coil), claw assemblies (lifting pole, lifting armature, moving armature, holding pole, holding armature, moving claw, and holding claw), pressure vessel assemblies (sealing shell and magnetic ring), thermal insulation assemblies, and drive rod assemblies. In the operation of a magnetically driven CRDM, the lifting coil, lifting pole, lifting armature, and corresponding yoke and magnetic ring constitute the lifting unit; the moving coil, moving armature, lifting armature, and corresponding yoke and magnetic ring constitute the moving unit; and the holding coil, holding pole, holding armature, and corresponding yoke and magnetic ring constitute the holding unit. When the coil is energized, the armature in the corresponding unit (such as the lifting armature, moving armature, or holding armature) will be subjected to electromagnetic force, thereby overcoming resistances such as gravity, water resistance, spring force, and load, and engaging with the corresponding magnetic pole. The lifting unit is the key actuator that drives the drive rod to perform lifting or lowering actions, therefore its health is particularly important. The moving unit engages or disengages with the drive rod's annular groove via a connecting rod and pawl. The holding unit has a similar structure to the moving unit, but its main function is to position the pawl into the drive rod's annular groove, keeping the drive rod in a designated position. Each unit requires its coil to be energized and de-energized according to a specific time and sequence to properly complete actions such as lifting, lowering, holding, or rapid rod drop.

3. The method according to claim 1, characterized in that, In step 1: Step 3.1: Electromagnetic force calculation model. This is the equivalent resistance of the coil; This is an energy-dissipating resistor. Its function is to allow current to flow through the CRDM coil when the coil is de-energized, forming a closed loop and thus consuming all the energy in the coil, causing the current to drop rapidly to zero. I represents the current in the coil; x represents the length of the air gap for lifting the armature. The equivalent inductance of the coil can be expressed as a function of the air gap x. VT1 is an inverter switching transistor used to control the duration and sequence of coil current; VT2 is a chopper switching transistor used to control the magnitude of coil current. During the pull-in phase of CRDM, the coil circuit equation is: During the movement of the CRDM, the air gap x can be written as time. function When the CRDM gap is fully open, x(t) = 0; when the gap is fully closed, The clearance during the lifting armature movement is... Therefore, during the armature attraction process, the inductance L can be expressed as a function of the air gap x and time t, that is: In the formula, S is the area at the gap reluctance; Let be the vacuum permeability, and take . ; It represents the sum of the magnetic reluctances of all parts except the air gap magnetic reluctance; The number of coil turns is 577. Substituting equation (2) into equation (1), the current can be calculated. Then the electromagnetic force can be expressed as: Step 3.2: Water resistance calculation model. When the CRDM lifting armature moves upward, the water gap between it and the lifting pole decreases. Part of the squeezed water flows along the gaps between the lifting armature, moving armature, and other parts and the sealing shell. The other part flows along the gaps between the lifting pole and the sealing shell, the radial holes of the lifting pole, and the gaps between the drive rod and the sleeve shaft. Due to the conservation of circuit voltage drop: In the formula, P 1i and P 2i Let represent the voltage drop at various points in the circuit. The voltage drop mainly consists of frictional voltage drop, inertial voltage drop, and local voltage drop, which can be calculated using the following formula: In the formula, These are the frictional pressure drop and the inertial pressure drop. and These are the drag coefficients for the inner and outer walls, respectively, which can be calculated using the Colebrook formula; The density of water; and These are the relative velocities of the inner and outer walls with the water, respectively. and. These are the wetted perimeters of the inner and outer walls, respectively. The lengths of the inner and outer walls; For localized pressure drop; The acceleration of water; This is the local drag coefficient; The velocity of the water. The drive lever assembly and the control rod assembly it drives are The water resistance encountered during movement due to pressure drop: Analysis of the above model shows that the magnitude of water resistance is not only related to the structural characteristics and surface roughness of the CRDM, but also significantly affected by factors such as the armature movement speed, water flow velocity, and density. However, due to the difficulty in directly measuring the drag coefficients of the inner and outer walls of the drive mechanism, and its complex and irregular shape, key parameters required for calculating water resistance, such as length and cross-sectional area, are difficult to obtain accurately. A PINN network will be used to learn the magnitude of water resistance in the future. Step 3.3: Spring force calculation model. Hooke's Law can be used to simulate the elastic force of the spring on the armature. Hooke's Law states that when a spring undergoes elastic deformation, the elastic force of the spring... Change in spring length A linear relationship, that is In the formula, The spring stiffness is determined by the material properties of the spring. The negative sign indicates that the elastic force generated by the spring is opposite to the direction of its elongation. This is the preload of the spring. Step 3.4: Multiphysics coupling model. Electromagnetic lifting force; It is the elastic force of the spring; To increase the weight of moving parts such as the armature, drive rod, and pawl; This refers to the load force, specifically the weight of the control rod assembly. For water resistance; Other resistance factors include gravity. and load capacity It is a constant; other resistances The value is relatively small, and its influence on the motion state of the armature can be ignored. Analysis shows that, using Newton's second law, the dynamics of lifting the armature can be expressed by the following equation: In the formula, This represents the acceleration that lifts the armature; x is the displacement of the armature; and M is the total mass of the moving parts and the load.

4. The method according to claim 1, characterized in that, Step 2 includes the following sub-steps: The lifting unit is a crucial motion unit of the CRDM, and its reliability directly impacts the overall performance of the CRDM. Under the coupling of multiple physical fields, the lifting armature moves relative to the bushing shaft, driving the hook assembly and load to move together until engagement is complete. However, during service, direct contact and friction between the lifting armature and the bushing shaft can generate debris or even foreign objects that can cause jamming, leading to variations in the lifting armature's speed and consequently, its engagement time. These variations in engagement time further disrupt the current timing of the holding and moving units, ultimately causing CRDM failures such as slippage and inability to lift. The current waveforms of the lifting unit under normal and fault conditions are shown. The completion time of the lifting armature engagement action is the lowest point of the current waveform's "return groove," and the process from zero current to this lowest point fully describes the change in coil current during armature engagement. Compared to the normal current waveform, the fault waveform of the CRDM shows the disappearance of the current engagement point and a severely delayed engagement time, posing a risk of slippage and inability to lift. Therefore, whether the armature pull-in time meets the requirements is a criterion for judging whether the CRDM exhibits failure modes such as slippage or inability to lift. Thus, efficiently and accurately assessing the armature pull-in time is crucial for evaluating the reliability of the CRDM. The armature pull-in time was selected as a key performance indicator for the CRDM. If this indicator exceeds a certain threshold, the entire CRDM is considered to have malfunctions such as arm slippage or failure to lift. The pull-in time in the current waveform of the CRDM lifting unit is shown. Meaning, where c represents the current running step number. CRDM booster unit pull-in time. From The time interval is from 0 (the moment when energization begins) to the point where the current is at its lowest after the coil exhibits back electromotive force. The duration of the time interval. This is a fixed value, representing the start time of step c. The point where the current is lowest after the coil exhibits back EMF indicates that the armature is fully engaged. It is worth noting that, due to the movement of the lifting armature under the influence of electromagnetic force, water resistance, spring force, and gravity, the current is at its lowest point. It is not a fixed value, but a value that changes continuously with the number of steps taken. First, This depends on the dynamic equation of the lifting armature, i.e., equation (8). Specifically, according to the CRDM dynamic analysis model in Section 2, if the values ​​of all electromagnetic forces, spring forces, gravity, load forces, water resistance, and other resistances are given, the displacement, velocity, and acceleration results of the CRDM motion process can be quickly calculated. When the CRDM armature is engaged, the current reaches its minimum value, and at this time, the displacement reaches its maximum value. Therefore, the engagement time of the CRDM lifting unit can be calculated by calculating the difference between the initial moment and the time when the displacement is maximum. Specifically, we will... The stepping bar process is decomposed into countless small time elements, and the time step is represented by... In other words, using... , Indicates the first Stepping stick The displacement, velocity, acceleration, and the water resistance, spring force, and electromagnetic force acting on the CRDM at any given moment can be used to calculate the acceleration value at that moment using equation (9). ,Right now: when Given the given information, substitute it into the following equation to iteratively calculate the next time step. The velocity and displacement values, namely: Continue Substituting the displacement and velocity values ​​at a given time into the corresponding electromagnetic force, spring force, and water resistance calculation models, we can obtain... At present , , .Will Water resistance at time Spring force Electromagnetic force Substituting back into equation (10), we can calculate... acceleration value at time t ,Right now: In the formula, express The combined efforts at any given moment; To improve the mass of the unit itself, the acceleration... Substituting these values ​​into equation (10) allows us to calculate the displacement and velocity at that moment. Repeating the above steps iteratively allows us to calculate the [missing value]. The acceleration, velocity, displacement, electromagnetic force, water resistance, and spring force of the stepping rod at any time during the process are recorded. When the displacement reaches its maximum value during iteration, that is, when it is just attracted, the displacement is set to no longer change. Then, according to equation (10), the velocity and acceleration at this moment are both zero. The time at this moment is recorded as _____. Then the absorption time can be further obtained. . The above calculations were performed under the condition that relevant parameters such as electromagnetic force and water resistance were known. However, in actual engineering, the air gap length l... g Area S at the gap reluctance, reluctance Due to material variations and manufacturing process fluctuations, uncertainties are inevitable; that is, these parameters are not fixed constants but can only be described by distributions. The uncertainty of the input parameters, after the aforementioned calculation process, also leads to uncertainty in the CRDM pull-in time. This process is called uncertainty propagation, and its purpose is to analyze how the uncertainty of the lifter unit's input parameters affects the uncertainty of the system output. Without loss of generality, let's assume the uncertainty parameters of the lifter unit are... All follow a normal distribution, that is: In the formula, , , Let lg represent the air gap length, S represent the area at the air gap reluctance, and S represent the reluctance. The mean of the probability distribution, and , , Let represent the variances of the probability distribution, respectively. If the mean and variance are known, then the uncertainty parameters can be collected using the hyper-Latin square sampling method. middle Each parameter sample is used, and the pull-in time of the lifting unit is calculated for each sample using the above iterative process. . use Each suction time This allows for the estimation of the probability density function (PDF) that increases the unit's pull-in time. Based on the absorbance time PDF results and combined with the absorbance time threshold. The reliability of CRDM can be calculated. Without loss of generality, the reliability formula for CRDM at any number of running steps c can be expressed as: However, it is worth noting that due to the complexity and high nonlinearity of the armature attraction process under multiphysics coupling, the PDF of the attraction time varies with the number of running steps. It is difficult to estimate directly and cannot be solved analytically. Therefore, the reliability of CRDM cannot be directly calculated using equation (13). This paper proposes PINN[24] to solve the CRDM booster unit pull-in time PDF. Then convert the absorption time PDF Substitute into equation (20) to calculate the reliability of CRDM under any number of running steps.

5. The method according to claim 1, characterized in that, Step 3 includes the following sub-steps: Step 5.1: PINN and variational inference theory. This invention utilizes PINN to continuously adjust network parameters. The goal is to find a way to increase the armature engagement time under multi-physics coupling while ensuring that the data meets the physical laws in the model. However, traditional PINN networks can only obtain point estimates of the output, not its probability distribution. This paper introduces Variation Inference (VI) into PINN, termed the PINN-VI model, to obtain the PDF of the absorption time. The following describes the implementation process of PINN-VI and how to approximate the posterior PDF in VI using Monte Carlo Dropout (MC-Dropout). VI method utilizes functions Posterior distribution of approximate parameters , As a prior distribution hypothesis for parameter θ, by Parameterization. Function The mean-field Gaussian approximation method is generally used, that is: In the formula, The mean Standard deviation PDFs with a normal distribution; The number of model parameters, i.e. The dimension. The approximation principle is to minimize and posterior distribution KL divergence between This is achieved by maximizing the Evidence Lower Bound (ELBO). ELBO can be expressed as: In the formula, Let be the loss function of the neural network. For parameter priors and posterior The KL divergence between them. Executing the MC-Dropout method in a neural network can achieve the ELBO optimization process in VI. In the MC-Dropout method, a dropout probability is specified. The value of each network node during forward propagation has The probability is set to zero. Gal et al. theoretically proved that in ELBO... It is proportional to the L2 regularization of the neural network, that is: Therefore, optimizing the loss function of a neural network with MC-Dropout is consistent with optimizing ELBO. Based on the above theoretical derivation, we will apply MC-Dropout to PINN to obtain the posterior PDF of the absorption time. Step 5.2: CRDM-PINN method. The pull-in time index of the CRDM lifting unit reflects the reliability level of the mechanism's operation. The following will explain how to fit the CRDM pull-in time distribution based on PINN-VI. First, we will introduce how to use the PINN model to fit the CRDM pull-in time index. During the CRDM operation phase, some acceleration and current data can be obtained using vibration sensors and current signals. In this problem, acceleration data serves as the raw data, requiring the inversion of CRDM velocity and displacement data. The magnitude of the displacement is directly related to the CRDM lifting unit's pull-in time. Therefore, displacement is used as the antiderivative in this problem. Data for the antiderivative is scarce, while data representing physical information using the differential terms of the antiderivative (the differential of displacement is velocity, and the differential of velocity is acceleration) is readily available. Therefore, we can utilize PINN's automatic differentiation function to embed the differential relationship between acceleration, velocity, and displacement into the neural network, and fit the displacement as a function of time using only the CRDM-based acceleration data. Furthermore, as discussed in Section 2 regarding the multiphysics coupling model, electromagnetic force in reality is a displacement-related quantity, while water resistance is a velocity-related quantity, and both possess implicit characteristics. Therefore, an architecture as shown below can be used to combine the electromagnetic force and water resistance physical fields with the motion of the CRDM, forming a multiphysics coupling CRDM-PINN, which can be used to evaluate the pull-in time of the CRDM lifting unit. The CRDM-PINN model comprises three sub-networks, which respectively fit the motion of the CRDM itself, the current in the coil, and the acceleration experienced by the CRDM. The reasons for designing this network architecture are as follows: First, we build a first neural network model to evaluate the displacement value. Since the velocity value can be obtained by differentiating the displacement output with respect to time, and this process can be automatically acquired within the neural network, the automatically obtained velocity value is input into the second neural network to solve the water resistance model. As analyzed in Section 2, water resistance is related to the mechanism's motion velocity; therefore, the velocity value automatically differentiated by the first network is input into the second neural network to solve for acceleration. The displacement of the first network can also be differentiated with respect to time, which is also obtained through automatic differentiation within the neural network. The acceleration value can be trained using acceleration data from the vibration sensor. On the other hand, as mentioned in step 1, the electromagnetic force calculation model is related to the armature air gap; therefore, a third network can be designed to input the displacement value (air gap) into the third neural network to predict the electromagnetic force, which will be obtained through training using current data. The specific details of the three networks in CRDM-PINN are shown. Neural network 1 is used to train the displacement during the attraction process. Since displacement data is unavailable, the automatic differentiation function of the neural network is utilized to obtain the acceleration by taking the second-order partial derivative between the output displacements. Acceleration can be directly obtained using an acceleration vibration sensor; therefore, vibration acceleration data can be used to train the first neural network in PINN. Secondly, current data is used to train the third neural network. This invention utilizes a dynamic model under multi-physics coupling to train the second neural network, namely the water resistance model. From the above analysis, it can be seen that the dynamic analysis model under multi-physics coupling in Section 2 is embedded through the automatic differentiation function of the first network in PINN, which is also the main manifestation of the embedded mechanism of the neural network proposed in this section. The training process of the three neural networks will be described in detail below. Since the three outputs of the PINN proposed in this invention are all continuous values, all three neural networks belong to the regression problem. For regression problems, the loss function of PINN is generally the mean squared error. Let's represent this. The following will explain how to train the three neural networks mentioned above using the root mean square error. First, assume the training dataset from the CRDM service process... , representing the actual observed values ​​of acceleration and current, respectively, and relative to the input time. The time values ​​in the data correspond one-to-one. They are respectively used... Let represent the three sub-networks of CRDM-PINN. Then we have: In the formula, the function This represents the first neural network used to solve for the shift output, while This can be obtained automatically through differentiation using the first neural network. It can also be obtained automatically through differentiation using neural networks. It can also be obtained automatically through differentiation using a neural network. This indicates that the second neural network is used to solve for water resistance. Since water resistance is related to velocity, the output of the first neural network is used instead. Also input into the network This represents the third neural network, which outputs the displacement because current and displacement are related. The input is fed into the neural network. Additionally, Indicate each The resultant force is calculated at the corresponding time point. With this information, the terms in PINN's loss function can be calculated. Assume... , Let represent the loss functions for the CRDM-PINN displacement and current neural networks, respectively. Then, the training dataset can be used. The following loss functions were obtained respectively: In equation (18), The loss function representing acceleration data, Indicates the size of the data. This represents the i-th acceleration training data; In equation (19), The loss function representing the current data. Let represent the i-th current training data. The two loss functions mentioned above are insufficient to achieve satisfactory results for the entire PINN training. Two additional loss functions based on physical laws are needed. First, for CRDM, its velocity cannot be negative. Therefore, the first piece of physical information is added to the CRDM-PINN loss function, expressed as: This means that a constraint is imposed on all outputs with velocities less than 0 for all CRDM displacement models, limiting the output velocity to be greater than or equal to 0. Secondly, the motion process of the CRDM lifting unit must satisfy the dynamic equation of equation (8), therefore, a second physical constraint needs to be added. This means that the motion process of the CRDM lifting unit must satisfy Newton's second law, that is: In the formula, Indicates resultant force; It represents the sum of forces other than electromagnetic force and water resistance, including the lifting force, elastic force, and load. The resultant force is the sum of forces calculated from the outputs of the water resistance model and the electromagnetic force model, as well as other given parameters. This indicates that when the current is The magnitude of the electromagnetic lifting force is calculated by substituting it into the equivalent magnetic circuit model. The total loss of CRDM-PINN is obtained by weighted summation of all terms, where This represents the weight corresponding to each loss term. That is: In the formula, This ensures that the model's predictions do not incorrectly assume that the CRDM will move in a downward direction; It includes a dynamic model under CRDM multiphysics coupling, which can connect the information between the three sub-networks and achieve the most accurate absorption time assessment. Step 5.3: CRDM-PINN-VI Method The CRDM-PINN model can only evaluate the deterministic value of the absorption time, without considering the uncertainty of input parameters, data, and neural network. Therefore, this section proposes a PINN-VI-based CRDM absorption time distribution evaluation. Based on the absorption time distribution and the threshold of absorption time, the reliability of CRDM can be evaluated. The proposed CRDM-PINN-VI architecture is presented. The only difference is that all three networks use Bayesian neural networks, and the MC-Dropout method is used to implement the PINN-VI probability distribution output. The model structure, data, loss function, and other details are consistent with CRDM-PINN. With MC-Dropout, the gradient descent of the model is less stable, and the training convergence speed is slower. Therefore, more training epochs are required, followed by a small number of training epochs with MC-Dropout disabled to further adjust the model accuracy. After training, the model's output mean and standard deviation can be obtained with MC-Dropout disabled. To evaluate the uncertainty of the suction time, the displacement function curve needs to be analyzed. Specifically, with MC-Dropout enabled, the model's displacement prediction over time is output to obtain the minimum time. make The adsorption time is the time required to complete the adsorption process. By sampling the adsorption time multiple times using the Monte Carlo method, the PDF of the CRDM adsorption time can be obtained, which is the value in equation (13). .

6. The method according to claim 1, characterized in that, Step 4 includes the following example verification process: This invention uses CRDM current and acceleration test data to verify the correctness and effectiveness of the proposed method. The CRDM reliability test platform mainly consists of three parts: an ML-CRDM mounting platform, an electromagnetic loading unit, and a data acquisition and control unit. Current data is acquired from the data acquisition and control system of the three sets of CRDM coils. A CRDM displacement sensor is mounted on the drive rod, indirectly characterizing the displacement characteristics of the lifting armature by detecting the displacement of the drive rod during dynamic operation. An acceleration vibration sensor is fixed to the flange base to collect the vibration acceleration signals generated during the operation of the CRDM lifting unit. As revealed by the CRDM reliability test platform, only acceleration and current data are available for CRDM condition monitoring; displacement, velocity, and water resistance data are unavailable. Therefore, this invention ingeniously designs a loss function based on a multiphysics-coupled dynamic model, simultaneously incorporating the prediction of CRDM water resistance, displacement, and velocity into the training of the PINN. Using only the CRDM's acceleration and current data, the changes in these three physical quantities can be accurately estimated. Thus, the multiphysics-coupled CRDM dynamic model is an essential physical loss function for the designed network. This underscores the necessity of the CRDM-PINN designed in this invention. Two networks, PINN and PINN-VI, are used to evaluate the armature engagement time and engagement time probability distribution of CRDM. The network hyperparameters are set as follows: Due to the inconsistent units of physical quantities and the different orders of magnitude among the terms in the loss function, selecting appropriate weight parameters is crucial for the model's training performance and final convergence. In this example, , , , Each sub-network is a fully connected neural network with four hidden layers and node counts of [50, 100, 100, 50]. The training data consists of current and acceleration data from the CRDM over 12 million runs. Regarding the training strategy, although incorporating physical information into the loss function is theoretically optimal, in practice, the gradient of the differential term in the loss function is unstable at the beginning of training when the error is large, making model convergence difficult. Accordingly, Although equivalent to numerical regression, it converges quickly for loss terms without differentiation. Therefore, a strategy of training the first neural network first is adopted to increase... The weights are adjusted until the displacement model essentially converges, at which point the model switches to the next loss function. The specific training hyperparameters are: and Using learning rate and 10,000 training sessions; and Using learning rate and 30,000 training sessions. Furthermore, the training data for current and acceleration are explained as follows: First, the state monitoring data is divided into training, validation, and test sets in an 8:1:1 ratio. All data is randomly divided into three datasets according to this ratio. 80% of the data is used to train the proposed PINN and PINN-VI networks. The trained model is then used to validate its generalization ability and optimize its hyperparameters using the remaining 10% of the dataset. Finally, the remaining 10% of the dataset is used for testing. We also compared cross-testing with other ratios and found that the 8:1:1 cross-testing performed best. Therefore, this invention only presents the analysis results of the 8:1:1 cross-testing. use That is, training and simultaneous use of data and physical information are completed solely based on data, without introducing the physical information contained in equations (20) and (21). , The prediction results of the trained model are shown in the following sub-figures: prediction of displacement; prediction of velocity; prediction of acceleration; prediction of current in the coil; prediction of water resistance; and comparison of the resultant force calculated based on the prediction values ​​with mass × acceleration. The results show that the prediction results of the model based solely on the data differ significantly from the actual values. This is because CRDM can only collect acceleration and current data. For neural network 3, the network uses the CRDM's motion velocity to predict water resistance, but there is no training data for water resistance. Therefore, without the data from equation (21), the prediction results are significantly different. If the motion law of the CRDM booster unit is not known, then there is no loss function available for training the neural network 3. Therefore, the convergence effect of the entire PINN network is poor. On the other hand, due to the lack of equation (21) Accurate predictions of displacement and velocity using only acceleration and current data are difficult because there is no directly observable data for training these physical quantities, and indirect data lacks physical laws to guide convergence. Therefore, the predictions of models based solely on data show a significant discrepancy with the actual values. It can be seen that, except for the relatively accurate prediction of current physical quantity using CRDM (due to the existence of directly measurable current data), the predictions of other physical quantities have large deviations. The CRDM-PINN model proposed in this invention, however, incorporates… and After two physical laws, all three networks were Therefore, the prediction of CRDM motion physical quantities is also relatively accurate. Table 1 presents the ablation experimental results based on PINN-based estimation of CRDM motion parameters. Experiment 1: MSE of CRDM motion parameters using only CRDM status monitoring data; Experiment 2: Ablation using CRDM status monitoring data plus... (i.e., motion velocity is not negative) MSE of CRDM motion parameters; Experiment 3: Using CRDM state monitoring data to add (i.e., the MSE of CRDM motion parameters under the CRDM dynamic equations under multiphysics coupling); Experiment 4: Using CRDM state monitoring data to... and The MSE of the CRDM motion parameters was calculated. The results show that both physical loss parameters can improve the accuracy of CRDM motion parameter estimation. The second physical loss parameter has the greatest impact on the accuracy, resulting in an order-of-magnitude improvement in the error index. This demonstrates the necessity and novelty of the designed physical loss parameter based on the dynamic equations under multi-physics coupling. Furthermore, the correlation coefficient between the resultant force and mass and acceleration is 0.68, indicating good consistency between these two predicted physical quantities and suggesting that the model better satisfies the laws of the CRDM dynamic equations under multi-physics coupling.

7. The method according to claim 1, characterized in that, Step 4 also includes the following example verification process: PINN-VI is used to characterize output uncertainty, thereby evaluating the reliability of CRDM. In this section, firstly, CRDM-PINN-VI is trained based on MC-Dropout with a dropout rate of 1%. The model, training data, loss function, and other details are the same as CRDM-PINN. Since the model's gradients are noisy with dropouts, training using gradient descent is less stable; therefore, a relatively large number of training epochs are performed. Then, a small number of training epochs are performed with dropouts disabled to adjust the model accuracy. The training results of CRDM-PINN-VI using MC-Dropout are shown. It can be seen that the output mean still provides accurate predictions for the relevant metrics. Furthermore, the MC Dropout method also provides the standard deviation of the output, with the semi-transparent region representing the interval between the output mean and 2 standard deviations. It can be seen that the represented uncertainty is stable in regions with gentle function changes; however, in regions with larger and steeper changes, such as when velocity and acceleration undergo abrupt changes, the standard deviation is large. This phenomenon is consistent with the understanding of numerical regression in deep learning methods. The pull-in time was sampled using MC-Dropout, and the PDF of the boosting unit pull-in time and the frequency histogram of the samples were estimated using Gaussian kernel density estimation (KDE). Combined with a given time threshold Based on equation (13), the reliability assessment result of CRDM at 12 million running steps is calculated to be 0.9015. To verify the above reliability, the absorption time data of 10 CRDMs at 12 million running steps were obtained using a multiphysics coupling platform, as shown in Table 2: Based on the reliability nonparametric estimation method, we have: In the formula, n=10 represents the total number of samples, i=1 represents the number of failure samples, and c represents 12 million steps. Statistical data shows that the nonparametric reliability estimate for 10 CRDM units at 12 million steps is 0.9091, while the result given in this example is 0.9015. Compared to the nonparametric estimate, the absolute reliability error is 0.0091, which is smaller. Furthermore, the reliability estimate is lower than the nonparametric estimate, making it more conservative and more suitable for practical engineering applications. It is worth noting that the CRDM-PINN-VI proposed in this invention exhibits very high efficiency in reliability calculation after model training, with an average response time of 0.25 milliseconds. In contrast, the absorption time calculated using the CRDM multiphysics coupling simulation platform is extremely time-consuming due to the iterative calculations involved in multiphysics coupling models under different scenarios, resulting in an average response time on the order of hours. The above comparison of computational efficiency demonstrates that the method proposed in this invention is more suitable for practical engineering applications and can more quickly respond to CRDM reliability results in multiphysics coupling environments for subsequent operation and maintenance decisions.

8. The method according to claim 1, steps 1-4 are summarized as follows: (1) Starting from the working principle of CRDM, the dynamic model of CRDM under multi-physics coupling is analyzed in detail, and a reliability assessment method of CRDM based on improving armature engagement time is proposed. (2) A CRDM reliability assessment method based on PINN is introduced, which can make full use of the data and dynamic model within the CRDM working cycle and improve the limitations of traditional machine learning models. (3) Numerical analysis shows that the proposed method has a small relative error with the statistical reliability assessment results, verifying the accuracy of the reliability assessment results in CRDM. On the other hand, compared with the dynamic model under multi-physics coupling, the proposed PINN model has an order-of-magnitude improvement in computational efficiency, which is more in line with the further requirements of practical engineering for rapid reliability assessment.

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