A method for evaluating the health state of an RC circuit

Abstract

The present application relates to a kind of RC circuit health state evaluation method, belong to the circuit health management technical field of equipment, solve the technical problem of the inaccuracy of circuit health state evaluation, high computing cost caused by algebraic loop in prior art.The method of the present application is: constructing RC circuit device multi-physical field coupling degradation model and block diagram simulation model;Obtain the simulation module of block diagram simulation model;Convert simulation module into directed graph and obtain algebraic loop candidate set;Determine the solving execution order of simulation module;According to the algebraic loop solver of trust region broken line method;Using algebraic loop solver obtains the complete dynamic response result of RC circuit device multi-physical field coupling degradation model in entire simulation time, and the health state of RC circuit is evaluated.The present application can accurately identify and efficiently process the algebraic loop in degradation model, so as to ensure the physical authenticity of degradation mechanism, realize high-precision tracking of RC circuit performance and reliable evaluation of health state index.

Description

Technical Field

[0001] This invention belongs to the field of circuit health management technology for equipment, and specifically relates to a method for assessing the health status of RC circuits. Background Technology

[0002] The monitoring and management of the operating status, health status, and lifespan status of circuits are directly related to the normal operation of equipment. Failure to detect abnormalities in a timely manner will cause significant economic losses and safety hazards to enterprises and users. Existing technologies already contain a large amount of research on the operating status and health status of circuits, resistors, capacitors, and other devices.

[0003] Chinese invention patent application CN114091937A discloses a method and device for assessing the health status of a DC-DC circuit on an instrument control board. The method involves real-time acquisition of operational monitoring data of the DC-DC circuit on the instrument control board; inputting the operational monitoring data into a preset health assessment model to determine the assessment status of the DC-DC circuit on the instrument control board, thereby achieving the assessment of the health status of the DC-DC circuit on the instrument control board. The preset health assessment model includes standard health assessment indicators and standard health thresholds.

[0004] Chinese invention patent application CN115238927A discloses a method for assessing the condition of capacitive equipment based on the dielectric loss factor tgδ. The method organizes the historical tgδ data obtained from online monitoring of capacitive equipment into a vector form, calculates the correlation coefficient of the historical tgδ data of three-phase equipment on the same line, and uses it as the basis for assessment, making the condition assessment of capacitive equipment more quantitative.

[0005] Chinese invention patent application CN117853089A discloses an intelligent evaluation method based on capacitor operating status. This method acquires real-time capacitor compensation power factor information and average capacitor compensation power factor information; determines the undercompensation duration based on the real-time and average capacitor compensation power factor information; and compares the undercompensation duration information with the undercompensation duration threshold information to determine the operating status evaluation information of a specified capacitor. RC circuits, as the most basic circuit type in electronic engineering, consist of resistors (R) and capacitors (C) and are widely used in integrated circuit design, analog filters, signal conditioning circuits, power management, and other fields. In practical engineering applications, RC circuits inevitably experience degradation, severely affecting the reliability and performance of electronic systems.

[0006] The main degradation mechanisms of RC circuits are as follows.

[0007] (1) Resistance degradation: Due to factors such as electromigration, thermal stress, and time aging, the resistance value will drift over time, causing the circuit characteristic parameters to deviate from the design value;

[0008] (2) Capacitor degradation: Dielectric breakdown, dielectric aging, temperature cycling, etc. can lead to changes in capacitance and increased dielectric loss, affecting the frequency response characteristics of the circuit;

[0009] (3) Evolution of parasitic effects: Process deviations and environmental factors can cause changes in parasitic resistance and capacitance parameters, further deteriorating circuit performance.

[0010] As integrated circuit technology continues to advance towards higher integration levels and smaller feature sizes, the degradation problem of RC circuits is becoming increasingly prominent, posing a serious threat to the reliability of electronic systems. Therefore, accurate status and health assessments of RC circuits are crucial for ensuring the long-term stable operation of electronic systems, preventing failures, optimizing lifespan management, and achieving reliable design. The core of achieving such accurate health status assessment lies in establishing a circuit model that reflects the actual physical degradation mechanism and performing efficient simulation analysis.

[0011] However, a common and serious technical challenge hindering the evaluation of RC circuit health status assessments is the algebraic loop problem. When feedback loops or strong coupling relationships exist between parameters in the RC circuit model (e.g., changes in degradation resistance directly affect the capacitor's terminal voltage, which in turn affects the circuit through the charging and discharging of the degradation capacitor, thus feeding back to the resistor), cyclic dependencies form between variables in the model, making it impossible to obtain results through conventional methods. The algebraic loop problem directly leads to difficulty in model simulation convergence and decreased computational accuracy, making it extremely difficult to accurately obtain the dynamic degradation parameter trajectory and predict remaining lifetime.

[0012] Currently, existing modeling and simulation technologies suffer from significant problems when dealing with algebraic loop problems, including technological limitations, algorithmic deficiencies, and methodological shortcomings. In particular, existing methods that avoid algebraic loops (such as introducing ideal assumptions, artificially delaying the loop by one frame, or using specific numerical techniques to force a solution) severely sacrifice the physical realism of the model and the integrity of the degradation mechanism. These methods cannot accurately characterize the parameter feedback mechanism, inevitably leading to estimation bias, misjudgment of health status indicators, and significant inaccuracies in the final lifetime prediction results, severely restricting the effectiveness of reliability analysis and health status assessment. Therefore, there is an urgent need to develop a technical method that can efficiently and realistically handle algebraic loops and achieve high-precision degradation status of RC circuits, in order to overcome existing technological bottlenecks and provide independent and controllable technical support for preventive maintenance, accurate lifetime prediction, and high-reliability design of integrated circuits. Summary of the Invention

[0013] In view of the severe challenges posed by the algebraic loop problem in the health status assessment of RC circuits and the resulting model distortion and assessment failure, this invention provides a method for assessing the health status of RC circuits. The core of this method lies in accurately identifying and efficiently processing algebraic loops in the degradation model, thereby ensuring the physical authenticity of the degradation mechanism and achieving high-precision tracking of RC circuit performance and reliable assessment of health status indicators.

[0014] This invention provides a method for assessing the health status of an RC circuit, the specific steps of which are as follows:

[0015] Step S1: Construct a multi-physics coupling degradation model for RC circuit devices; construct a block diagram simulation model based on the multi-physics coupling degradation model for RC circuit devices;

[0016] Step S2: Obtain all simulation modules of the block diagram simulation model; convert the simulation modules into a directed graph and identify and filter out the candidate set of algebraic rings;

[0017] Step S3: Based on the candidate set of algebraic rings, determine the solution execution order of the simulation module;

[0018] Step S4: Establish an algebraic ring solver based on the trust region piecewise linear method;

[0019] Step S5: Based on the candidate set of algebraic loops identified and screened in step S2; execute the simulation loop according to the execution order of the simulation modules obtained in step S3. When an algebraic loop is encountered, call the algebraic loop solver in step S4; obtain the complete dynamic response results of the multi-physics coupling degradation model of RC circuit devices throughout the entire simulation time.

[0020] Step S6: Based on the complete dynamic response results of the RC circuit device multi-physics coupling degradation model obtained in step S5 throughout the entire simulation time, evaluate the health status of the RC circuit.

[0021] Optionally, the multi-physics coupling degradation model for RC circuit devices includes a resistance degradation model and a capacitance degradation model.

[0022] Optionally, in step S2, the specific steps for converting the simulation module into a directed graph and identifying and filtering the candidate set of algebraic rings are as follows:

[0023] Identify and label the type of simulation module;

[0024] Identify the valid edges of the simulation module based on its type.

[0025] Construct the original adjacency list based on the identified valid edges;

[0026] Collect all strongly connected components in the original adjacency list;

[0027] Identify and filter algebraic rings in strongly connected components to form a candidate set of algebraic rings.

[0028] Optionally, the simulation module types include direct feedthrough modules and indirect feedthrough modules.

[0029] Optionally, depending on the type of simulation module, the specific steps for identifying the valid edges of the simulation module are as follows: if the endpoint module of the connection line between simulation modules is a direct feedthrough module, then the connection line is marked as a valid edge.

[0030] Optionally, the collected strongly connected components are filtered to remove those containing only one simulation module and identify those containing multiple simulation modules as algebraic rings.

[0031] Optionally, in step S3, based on the original adjacency list and the candidate set of algebraic rings, each valid edge in the original adjacency list is traversed, and a simplified adjacency list is established according to the belonging relationship between the starting simulation module and the ending simulation module of the valid edge; based on the simplified adjacency list, topological sorting is performed to determine the solution execution order of the simulation modules.

[0032] Optionally, the specific steps of step S4 are as follows:

[0033] Step S41: Initialize the parameters of the RC circuit;

[0034] Step S42: Construct a hash table for the algebraic rings in the candidate set of algebraic rings;

[0035] Step S43: Based on the hash table, construct the initial output state vector to be solved;

[0036] Step S44: Construct the residual vector corresponding to the initial output state vector to be solved;

[0037] Step S45: Calculate the Jacobian matrix of the initial output state vector and the corresponding residual vector to be solved;

[0038] Step S46: Based on the current output state vector and Jacobian matrix to be solved, establish an algebraic ring solver.

[0039] Optionally, in step S6, the health status of the RC circuit is assessed based on the health threshold and the proportion of abnormal moments.

[0040] Optionally, the complete dynamic response results of the multi-physics coupling degradation model of the RC circuit device throughout the simulation time include the voltage values ​​of each node, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors in the RC circuit.

[0041] Compared with the prior art, the present invention has at least the following beneficial effects:

[0042] This invention achieves accurate identification of algebraic ring structures in degradation models through the Tarjan strongly connected component algorithm based on effective edge identification, ensuring the reliability of the evaluation basis. Furthermore, it significantly improves parameter solution efficiency and greatly reduces computational resource consumption by leveraging algebraic ring vertex merging and topology sorting optimization techniques. Simultaneously, it employs the trust region piecewise linear method for numerical solution to ensure the accuracy of key performance parameters under coupled degradation feedback mechanisms, thus providing highly reliable support for core health status assessment results such as performance margin analysis, stability criteria, and lifetime assessment. Finally, this invention provides a complete processing scheme for RC circuit health status assessment in an autonomous block diagram modeling environment, successfully solving the mechanism distortion problem caused by avoidance methods, and achieving high-precision assessment of stable RC circuit health status while realistically reflecting the physical degradation process. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the accompanying drawings. The accompanying drawings are schematic and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart of the RC circuit health status assessment method of the present invention;

[0045] Figure 2 This is a schematic diagram of the input / output ports of the inner edge of the algebraic ring according to the present invention;

[0046] Figure 3 A circuit diagram of an RC circuit according to a specific embodiment of the present invention;

[0047] Figure 4 This is a schematic diagram of the block diagram simulation model of the multiphysics coupling degradation model of RC circuit devices, which is a specific embodiment of the present invention.

[0048] Figure 5 This is a schematic diagram comparing the simulation results of capacitor C with the simulation results of SIMULINK in a specific embodiment of the present invention;

[0049] Figure 6 The resistor is a specific embodiment of the present invention. A diagram showing the comparison between the simulation results and the SIMULINK simulation results;

[0050] Figure 7 The resistor is a specific embodiment of the present invention. A diagram showing the comparison between the simulation results and the SIMULINK simulation results;

[0051] Figure 8 Branch current in a specific embodiment of the present invention A diagram showing the comparison between the simulation results and the SIMULINK simulation results; Detailed Implementation

[0052] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0053] A specific embodiment of the present invention, such as Figures 1-8 A method for assessing the health status of an RC circuit is disclosed, with the following specific steps:

[0054] Step S1: Construct a multi-physics coupling degradation model for RC circuit devices. The specific steps are as follows:

[0055] Step S11, construct the resistance degradation model, the expression of which is:

[0056]

[0057] in, Indicates the resistance at time t. The resistance value; Indicates the initial nominal resistance value; , and The resistance degradation factor is related to the resistive material and process. is the degradation function of electromigration effect; This is the degradation function of the thermal stress effect; A time-dependent material aging function; Indicates current density; Indicates the ambient operating temperature; This indicates a temperature cycle.

[0058] Understandable Describing current density Ambient operating temperature Under the combined action, the resistance at time The change in resistance; Describe the temperature cycle The resulting resistance at time Thermomechanical stress degradation; For the resistance at time The material aging function describes the purely time-dependent material aging effect.

[0059] Step S12, calibrate the resistor parameters;

[0060] Specifically, the resistance degradation coefficient related to the resistive material and process is determined by fitting accelerated degradation experimental data. , , A quantitative mapping relationship between the resistance degradation coefficient and the operating conditions was established.

[0061] Step S13, construct the capacitance degradation model, the expression of which is:

[0062]

[0063] in, Indicates the capacitance at time t. The capacitance value; Indicates the initial nominal capacitance value of the capacitor; , These are the dielectric breakdown function and the dielectric aging function, respectively. , The degradation factor is related to the capacitor material; This represents the electric field strength across the capacitor. Indicates the ambient operating temperature; Indicates the operating frequency of the circuit.

[0064] Furthermore, Describe the dielectric of a capacitor under electric field strength and ambient operating temperature Under the action of the capacitor at time Performance degradation; Describe the capacitor dielectric at the circuit operating frequency Under the action of the capacitor at time The aging effect.

[0065] Step S14: Calibrate capacitor parameters;

[0066] Specifically, the degradation coefficient of capacitance related to the capacitor material is determined by fitting accelerated degradation experimental data. , A quantitative mapping relationship between capacitor degradation parameters and operating conditions was established.

[0067] Step S15: Combine the resistor degradation model, capacitor degradation model and RC circuit topology to construct a block diagram simulation model of the multi-physics coupling degradation model of RC circuit devices, realizing the conversion from circuit diagram to block diagram model.

[0068] Step S2: Obtain all simulation modules contained in the block diagram simulation model; convert the simulation modules into a directed graph and identify and filter the candidate set of algebraic rings. The specific steps are as follows:

[0069] Step S21: Identify and label the type of simulation module;

[0070] Specifically, all simulation modules in the block diagram simulation model are traversed, and all simulation modules are classified and marked into two types according to the characteristics of the module transfer function: direct feedthrough modules (such as gainers, adders, etc.) and non-direct feedthrough modules (such as integrators, transfer functions, and other dynamic elements).

[0071] Step S22: Identify the valid edges of the simulation module according to its type;

[0072] For each connection line of each simulation module, the validity is judged. If the terminal module of the connection line is a direct feedthrough module, the connection line is marked as a valid edge; otherwise, it is marked as an invalid edge.

[0073] Step S23: Construct the original adjacency table based on the identified valid edges. The expression is:

[0074]

[0075] in, Indicates from simulation module A list of terminal modules for all valid starting edges. , This represents the number of simulation modules.

[0076] Step S24: Collect the original adjacency list All strongly connected components in;

[0077] Furthermore, adopt Strongly connected component algorithm traversing the original adjacency list Collect the original adjacency list All strongly connected components in it.

[0078] It is understandable that a strongly connected component is a subset of simulation modules in an adjacency list, consisting of several simulation modules. Within this subset, there is a directed path that allows any two simulation modules to reach each other, and there is no larger subset that can contain the current subset while still maintaining bidirectional reachability.

[0079] Step S25: Identify and filter algebraic rings in the strongly connected components collected in step S24 to form a candidate set of algebraic rings. The expression is:

[0080]

[0081] in, Indicates the first One algebraic ring; denoted as the number of algebraic rings in the candidate set of algebraic rings.

[0082] Specifically, the strongly connected components collected in step S24 are filtered, removing those containing only one simulation module, and identifying those containing multiple simulation modules as candidate sets of algebraic rings. .

[0083] Step S3, based on the candidate set of algebraic rings The specific steps to determine the execution order of the simulation module are as follows:

[0084] Step S31: Establish a candidate set of algebraic rings A The mapping from the simulation module to its specific algebraic ring.

[0085] Step S32, based on the original adjacency list candidate sets of algebraic rings Based on the mapping of the algebraic ring, traverse the original adjacency list. For each valid edge in the simulation module, there is a corresponding starting point. and endpoint simulation module Simulation module based on the starting point of the effective edge and endpoint simulation module Establish a simplified adjacency list based on the attribution relationship. G 2.

[0086] Specifically, if the starting simulation module In the algebraic ring Inside, the endpoint simulation module In the algebraic ring In addition, the endpoint simulation module will be used. Add to simplified adjacency list (i.e., from the algebraic ring) (A list of all valid edge-reachable endpoint modules from the starting point), where... Representing candidate sets of algebraic rings A The Middle An algebraic ring, .

[0087] If the starting simulation module In the algebraic ring In addition, the endpoint simulation module In the algebraic ring Inside, the algebraic ring will be... Add to simplified adjacency list (i.e., from the starting simulation module) Simulation module for all reachable endpoints from the starting point. (list)

[0088] If the starting simulation module and endpoint simulation module Since both edges are within the same algebraic ring, this valid edge is an in-ring edge and is not included in the simplified adjacency list. Establish a connection in the middle;

[0089] If the starting simulation module and endpoint simulation module None of them are in the algebraic ring, so the endpoint simulation module will be used. Add to simplified adjacency list ;

[0090] Step S33, based on the simplified adjacency list Perform topological sorting to determine the solution execution order that satisfies the dependencies between simulation modules.

[0091] This can be understood as meaning that "the calculation result of one simulation module needs to be used as the input data of another simulation module". For example, there is a simulation module for power supply voltage and a simulation module for the voltage across a resistor. The simulation module for the voltage across the resistor needs to use the output result of the simulation module for the power supply voltage as input. Then the dependency relationship is that the simulation module for the power supply voltage is executed first, and after the simulation module for the power supply voltage outputs its result, the simulation module for the voltage across the resistor is executed.

[0092] Step S4: Establish an algebraic ring solver based on the trust region piecewise linear method.

[0093] The algebraic ring solver of the present invention is used to solve the system of algebraic ring equations encountered in the process of block diagram modeling and simulation. When an algebraic ring is detected during the simulation, it is automatically invoked by the system.

[0094] The algebraic loop solver calculates the instantaneous voltage and current balance state in an RC circuit due to the feedback loop, while also considering the impact of device parameter degradation on circuit behavior. In the feedback loop of an RC circuit, not only must the voltage at each node and the current in each branch simultaneously satisfy Kirchhoff's Voltage Law (KVL) and Current Law (KCL), but it also needs to calculate in real time the changes in resistance and capacitance due to factors such as temperature, aging, and stress, as well as the resulting impedance changes, time constant changes, and other derived physical parameters. These mutually coupled physical constraints and parameter degradation models together form a complex system of algebraic equations. The function of the algebraic loop solver in this invention is to find a unique physical parameter solution that satisfies all physical laws and degradation characteristics at each simulation moment.

[0095] Step S41: Initialize the parameters of the RC circuit;

[0096] Specifically, the initial trust region radius is set according to the physical characteristics of the RC circuit. Maximum trust region radius Maximum number of iterations Trust ratio lower limit threshold Trust ratio upper limit threshold Trust region reduction factor Trust region expansion factor Convergence threshold and improved threshold .

[0097] Step S42: Construct a candidate set of algebraic rings A Hash tables for algebraic rings in the algebraic ring;

[0098] Specifically, for the candidate set of algebraic rings A Algebraic rings in Each valid edge within the edge is numbered sequentially starting from 1. A hash table is created to store the mapping relationship between each valid edge and its number.

[0099] Step S43: Based on the hash table, construct the initial output state vector to be solved. ,in, Represents the first digit within the algebraic ring. i The output signal value of the output port of each valid edge at the initial solution time. i =1,2,..., m , This represents the total number of valid edges within the algebraic ring.

[0100] For example, the output state vector to be solved contains all physical quantities to be solved in the algebraic loop at the current simulation moment, covering basic electrical parameters (voltage, current), device characteristic parameters (resistance value, capacitance value), and derivative physical parameters generated by the degradation of multi-physics coupling.

[0101] It is understandable that the output port of the edge is: such as Figure 2 If there is an algebraic ring, the first i Valid edge The simulation module corresponding to the starting point With output port Connect the simulation module corresponding to the endpoint of that edge. input port So, the input port That is, the th in the algebraic ring i Valid edge The output port, the output port That is, the th in the algebraic ring i Valid edge The input port.

[0102] Furthermore, if the th in the algebraic ring i Valid edge To obtain the output signal value of its output port at the current solution time, it is necessary to retrieve the value of the nth signal within the algebraic ring using a hash table. i Valid edge Numbering in the algebraic ring i Then the output state vector to be solved The first algebraic ring i The output signal value of the output port of the effective edge at the current solution time. That is, the th in the algebraic ring i Valid edge The value of the output port.

[0103] Step S44: Construct the residual vector corresponding to the initial output state vector, with the expression:

[0104]

[0105] in, Represents the first digit within the algebraic ring. i The initial residual of the corresponding output port of each valid edge.

[0106] Furthermore, the first in the algebraic ring i The initial residual of the corresponding output port of each valid edge The expression is:

[0107]

[0108] in, The first one in the algebraic ring i The output signal value of the output port of each valid edge at the initial solution time; Indicates the first i Signal processing functions for the input ports of a valid edge; Used to measure the first algebraic ring to be solved i Signal processing function for the input port of a valid edge The degree to which the conditions are met.

[0109] Step S45: Calculate the Jacobian matrix of the initial output state vector to be solved and the corresponding residual vector of the initial output state vector to be solved. The expression is:

[0110] .

[0111] Furthermore, the Jacobian matrix The expression for the element is:

[0112]

[0113] in, Represents the Jacobian matrix The Line number Column elements, , ; Represents the first digit within the algebraic ring. The output signal value of the output port of the active edge at the initial moment.

[0114] Furthermore, The solution method is as follows:

[0115] Search the hash table for the first... Valid edge and the Valid edge ;

[0116] Judge the first The simulation module corresponding to the starting point and the first Valid edge Whether the simulation module corresponding to the endpoint is the same simulation module, and based on the judgment result, the number of simulation modules in the algebraic ring is obtained. The output signal value of the output port of the active edge at the initial time Is it the first Signal processing function for the input port of a valid edge The basis for actual input;

[0117] If the th in the algebraic ring The output signal value of the output port of the active edge at the initial time Not the first Signal processing function for the input port of a valid edge The actual input, The value is 0;

[0118] If the th in the algebraic ring The output signal value of the output port of the active edge at the initial time It is the first Signal processing function for the output port of a valid edge The actual input, determine the first i Signal processing function for the input port of a valid edge Is there an interface that can directly obtain the corresponding partial derivative based on the input port number? If so, then pass the first... Valid edge The port number of the connected input port can be used to obtain the information. The value; if there is no interface, then the partial derivative is obtained by perturbation, by applying the value of the first... Valid edge Apply a small perturbation value to the output port (e.g., 1e-7), the resulting algebraic ring of the th The output signal value of the input port of the active edge at the initial time. Difference divided by small perturbation value That is The value of .

[0119] Step S46: Based on the current output state vector and Jacobian matrix, establish an algebraic loop solver to obtain the final output signal value.

[0120] Step S461, based on the current output state vector to be solved Perform residual calculations to obtain the updated residual vector. And construct the gradient vector ;

[0121] Specifically, based on updating the residual vector and the Jacobian matrix Obtain the gradient vector .

[0122] It is understandable that when entering the loop for the first time, the current output state vector to be solved is... =The initial output state vector to be solved .

[0123] Step S462, pre-convergence judgment;

[0124] The residual vector is updated in step S461 using the cost function value evaluation. The degree of closeness to 0 is considered. If the degree of closeness is less than the convergence threshold, it indicates that the trust region piecewise linear method has converged and the iteration is complete. The current output state vector is used as the final output signal value to obtain the final output signal value. Its components correspond to the specific values ​​of each physical quantity in the algebraic loop at the current simulation time. If it does not converge, proceed to step S463.

[0125] Furthermore, the expression for the cost function is:

[0126]

[0127] in, Represents the first digit within the algebraic ring. i The update residual of the corresponding output port of each valid edge.

[0128] Step S463, based on updating the residual vector and Jacobian matrix To obtain the Gaussian-Newton step size, the expression is:

[0129]

[0130] in, The step length is Gauss-Newton.

[0131] Step S464, calculate the steepest descent step size, the expression is:

[0132]

[0133] in, The step size coefficient is the steepest descent step size. This is the search step size vector in the steepest descent direction; This represents the gradient vector.

[0134] Step S465: Determine the piecewise linear step size based on the Gauss-Newton step size, the steepest descent step size, and the trust region radius;

[0135] Specifically, if the L2 norm of the Gauss-Newton step size does not exceed the radius of the trust region, the Gauss-Newton step size is used as the piecewise linear step size; if the steepest descent step size exceeds the radius of the trust region, the steepest descent step size is scaled proportionally according to the ratio of the trust region radius to the L2 norm of the steepest descent step size to obtain the piecewise linear step size; otherwise, the piecewise linear step size is obtained by interpolating between the Gauss-Newton step size and the steepest descent step size by solving the quadratic constraint equation. .

[0136] Step S466, based on the piecewise linear step size and the current output state vector to be solved Obtain the trial solution vector And calculate the trial solution vector. The corresponding residual vector Exploratory solution vector Cost function value .

[0137] Specifically, probing solution vectors The expression is:

[0138]

[0139] in, Represents the first digit within the algebraic ring. The trial output signal value of the input port of a valid edge at the current solution time.

[0140] Specifically, probing solution vectors The corresponding residual vector The expression is:

[0141]

[0142] in, Represents the first digit within the algebraic ring. The trial output signal value of the input port of the valid edge at the current solution time. The residual.

[0143] Furthermore, the first in the algebraic ring The trial output signal value of the input port of the valid edge at the current solution time. residual The expression is:

[0144] .

[0145] Furthermore, explore the solution vector Cost function value The expression is:

[0146]

[0147] Step S467, calculate the confidence ratio To evaluate the step size of the broken line The improvement effect is expressed as:

[0148]

[0149] in, This represents the actual reduction in the cost function; This represents the predicted reduction in the cost function.

[0150] Step S468: Adjust the trust region radius according to the trust ratio;

[0151] Specifically, if Or the actual reduction in cost function A negative value indicates poor improvement; the trust region radius should be reduced to its original value. The algorithm doubles the output state vector and simultaneously refuses to update the current output state vector to be solved. ;like And the step size of the broken line Approaching the trust region boundary indicates a significant improvement; therefore, the trust region radius should be expanded to the original value. The radius of the expanded trust region can be increased by a factor of 1, but the radius of the expanded trust region cannot exceed the maximum trust region radius set in step S41. The constraints, while accepting the current trial solution vector, i.e. In other cases, the step size of the broken line is accepted. However, the trust region radius remains unchanged.

[0152] Step S469: Check if the current iteration number is greater than or equal to the maximum iteration number. If the current iteration number is greater than the maximum iteration number If the simulation model fails to meet the convergence condition, it indicates an error, and the loop should be terminated. Researchers need to readjust the simulation model before re-executing the method of this invention. If the current iteration number is less than or equal to the maximum iteration number... However, it does not meet the convergence condition, so a trial solution vector is used. The output state vector to be solved in the next iteration step Return to step S461; if the current iteration number is less than or equal to the maximum iteration number. And satisfying the convergence condition, an algebraic ring solver is obtained, using trial solution vectors. The final output signal value is obtained as the final output signal value.

[0153] Among them, the trial solution vector The components are the specific values ​​of each physical quantity in the corresponding algebraic loop at the current simulation moment, including node voltage, branch current, resistance value of resistive devices, capacitance value of capacitor devices, degradation characteristic parameters, and other derivative circuit characteristic parameters generated by multi-physics coupling.

[0154] Specifically, the convergence condition is:

[0155] .

[0156] It is understandable that if the following condition is met, it indicates that the trust region piecewise linear method has converged, and the current trial solution vector... The values ​​of each component are the final output signal values ​​of the corresponding valid edge's output port; otherwise, a trial solution vector is used. The current output state vector to be solved in the next iteration step Return to step S461.

[0157] Step S5: Based on the candidate set of algebraic loops identified and filtered in Step S2; execute the simulation loop according to the execution order of the simulation modules in the simulation model obtained in Step 3. When an algebraic loop is encountered, the algebraic loop solver from Step 4 is automatically called; obtain the complete dynamic response results of the multi-physics coupling degradation model of RC circuit devices throughout the entire simulation time. The specific steps are as follows:

[0158] Step S51: Set an appropriate simulation time range and simulation time step according to the parameter degradation rate of the RC circuit under test.

[0159] Step S52: Perform algebraic ring identification and screening on the simulation model according to step S2, and obtain a candidate set of algebraic rings; obtain the execution order of the simulation modules in the simulation model according to step S3.

[0160] Step S53, the simulation is executed in a loop;

[0161] For each time step, the simulation modules are executed sequentially according to the execution order obtained in step S52: for non-algebraic loop simulation modules, the pre-designed signal processing functions (such as basic operations like addition, subtraction, multiplication, division, integration, etc.) are executed; when an algebraic loop is encountered, the algebraic loop solver from step 4 is called to solve the loop and obtain the specific values ​​of each physical quantity at the current simulation time; after all simulation modules have been executed, the simulation data of the current time step is saved, including physical quantities such as the voltage values ​​of each node, the current values ​​of branches, the resistance values ​​of resistive devices, and the capacitance values ​​of capacitors; then the process is repeated until the simulation ends, thus forming the complete dynamic response result of the multi-physics coupling degradation model of RC circuit devices throughout the entire simulation time.

[0162] Furthermore, the complete dynamic response results of the multi-physics coupling degradation model of RC circuit devices throughout the simulation time include the voltage values ​​of each node, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors in the RC circuit.

[0163] Step S6: Based on the complete dynamic response results of the RC circuit device multi-physics coupling degradation model obtained in step S5 throughout the entire simulation time, the health status of the RC circuit is evaluated. The specific steps are as follows:

[0164] Step S61, Parameter Comparison and Anomaly Detection: Compare the simulation data at each simulation moment with the corresponding standard parameter values; set corresponding health thresholds according to the characteristics of different parameters, such as ±5% tolerance range for voltage parameters, ±10% tolerance range for current parameters, ±15% tolerance range for power parameters, and ±10% tolerance range for device resistance values; when any key physical parameter exceeds its corresponding tolerance range at a certain moment, record that moment as an abnormal moment.

[0165] Step S62, Fixed window local health assessment: Divide the entire simulation time into several fixed time windows (e.g., the length of each window is 10% of the total simulation time). Calculate the percentage of abnormal moments in each time window. When the percentage of abnormal moments in a window exceeds a preset threshold (e.g., 30%), it is determined that the RC circuit is in an unhealthy state during that time period.

[0166] Step S63, Overall health status determination: When the cumulative proportion of unhealthy time periods exceeds 5% of the total simulation time, the RC circuit is determined to be in an unhealthy state; otherwise, it is determined to be in a healthy state.

[0167] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment:

[0168] Adopting such Figure 3The passive RC filter circuit shown verifies the effectiveness of this invention. The operating temperature of this RC circuit is 45-70℃. A DC voltage source with ripple voltage at a frequency of 100Hz. For resistors The voltage across the two ends; To pass through resistor The current, To pass through resistor The current; The current flowing through capacitor C;

[0169] Furthermore, C The capacitance value is 10. Aluminum electrolytic capacitors, It is a 5000Ω metal film resistor. It is a 150Ω metal film resistor.

[0170] The block diagram simulation model of the RC circuit's multiphysics coupling degradation model established in step 1 is as follows: Figure 4 .

[0171] Based on step S2 of the method of the present invention, the algebraic ring structure (i.e.) was successfully identified. Figure 4 In The feedback loop was confirmed to contain no integrator or delay unit, with an identification time of 0.5m, an accuracy of 100%, and the correct execution order of the simulation modules was obtained. Based on step 4 of this invention, the algebraic loop solver maintains stable convergence under various degenerate parameter conditions, with an average of 2-5 iterations, a convergence accuracy of 1e-8, and an average single-time-step algebraic loop solution time of 0.23m. Compared to traditional delay methods, this invention avoids artificially introduced phase distortion, and the current in the algebraic loop solution... With an accuracy of 99.8%, it fully maintains the physical authenticity of the RC circuit.

[0172] To further verify the correctness of the simulation results of this invention, a set of identical block diagram simulation models were established in the SIMULINK software. The same simulation termination time was set to 80600, the simulation step size to 50, and the solver to ode4. The results regarding... C , , , The specific comparison charts of the simulation results are as follows: Figure 5 , Figure 6 , Figure 7 , Figure 8 The simulation results are in line with expectations.

[0173] Based on accurate algebraic loop solver results, the health status of the circuit under different degrees of degradation is evaluated and verified. Under normal operating conditions, all physical parameters are stable, and the system determines that the circuit is generally healthy. When circuit degradation occurs, the capacitance decreases and the resistance increases. The algebraic loop solver remains convergent and stable, and the system accurately determines that the circuit is in an unhealthy state based on the proportion of abnormal moments and time window analysis. Under severe degradation conditions, the system clearly identifies it as a seriously unhealthy state, and the evaluation results are in high agreement with the theoretical analysis.

[0174] Verification results show that this invention achieves high-precision simulation of RC circuits through accurate algebraic loop detection and solution techniques, and establishes a reliable health status assessment method based on this. This technical solution not only solves the core technical challenge of algebraic loops but also achieves practical engineering application goals, providing a complete technical solution for the design, analysis, and maintenance of RC circuits.

[0175] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for assessing the health status of an RC circuit, characterized in that, The specific steps are as follows: Step S1: Construct a multi-physics coupling degradation model for RC circuit devices; construct a block diagram simulation model based on the multi-physics coupling degradation model for RC circuit devices; the multi-physics coupling degradation model for RC circuit devices includes a resistance degradation model and a capacitance degradation model; the expression for the resistance degradation model is: ,in, Indicates the resistance at time t. The resistance value; Indicates the initial nominal resistance value; , and The resistance degradation factor is related to the resistive material and process. Represents current density Ambient operating temperature Under the combined action, the resistance at time The change in resistance; Indicates temperature cycle The resulting resistance at time Thermomechanical stress degradation; For the resistance at time Material aging function; The expression for the capacitance degradation model is: ,in, Indicates the capacitance at time t. The capacitance value; Indicates the initial nominal capacitance value of the capacitor; Indicates the dielectric of the capacitor in the electric field strength and ambient operating temperature Under the action of the capacitor at time Performance degradation; Indicates the capacitor dielectric at the circuit operating frequency Under the action of the capacitor at time The aging effect; , The degradation factor is related to the capacitor material; Step S2: Obtain all simulation modules of the block diagram simulation model; convert the simulation modules into a directed graph and identify and filter out the candidate set of algebraic rings; Step S3: Based on the candidate set of algebraic rings, determine the solution execution order of the simulation module; Step S4: Establish an algebraic ring solver based on the trust region piecewise linear method; the specific steps of step S4 are as follows: Step S41: Initialize the parameters of the RC circuit; Step S42, construct a hash table for the algebraic rings in the candidate algebraic ring set; specifically, this includes creating a hash table for the candidate algebraic ring set. A Algebraic rings in Each valid edge within the simulation module is numbered sequentially starting from 1. A hash table is created to store the mapping relationship between each valid edge and its number. If the endpoint module of the connection line between simulation modules is a direct feedthrough module, then the connection line is marked as a valid edge. Step S43: Based on the hash table, construct the initial output state vector to be solved; the initial output state vector is represented as... ,in, Represents the first digit within the algebraic ring. k The output signal value of the output port of each valid edge at the initial solution time. k =1,2,..., m , The total number of valid edges within the algebraic ring; Step S44: Construct the residual vector corresponding to the initial output state vector to be solved; Step S45: Calculate the Jacobian matrix of the initial output state vector and the corresponding residual vector to be solved. , The expression for the element is: Represents the Jacobian matrix The Line number Column elements, , ; Represents the first digit within the algebraic ring. The output signal value of the output port of the active edge at the initial moment; Indicates the first i Signal processing functions for the input ports of a valid edge; The solution method is as follows: query the hash table for the first... Valid edge and the Valid edge ;judge The starting point and Are the simulation modules corresponding to the endpoints the same? If not, The value is 0; if so, check if the simulation module has an interface that can directly obtain the corresponding partial derivative based on the input port number. If there is an interface, then pass the input to that interface. The port number of the connected input port is obtained. The value; if there is no interface, through the value; if there is no interface, through the A small perturbation value is applied to the output port, and the result is calculated. The value; Step S46: Based on the current output state vector and Jacobian matrix to be solved, establish an algebraic ring solver; Step S5: Based on the candidate set of algebraic loops identified and screened in step S2; execute the simulation loop according to the execution order of the simulation modules obtained in step S3. When an algebraic loop is encountered, call the algebraic loop solver in step S4; obtain the complete dynamic response results of the multi-physics coupling degradation model of RC circuit devices throughout the entire simulation time. Step S6: Based on the complete dynamic response results of the RC circuit device multi-physics coupling degradation model obtained in step S5 throughout the entire simulation time, the health status of the RC circuit is evaluated; the evaluation includes parameter comparison and anomaly detection, fixed-window local health evaluation, and overall health status determination.

2. The method for assessing the health status of an RC circuit according to claim 1, characterized in that, In step S2, the specific steps for converting the simulation module into a directed graph and identifying and filtering the candidate set of algebraic rings are as follows: Identify and label the type of simulation module; Identify the valid edges of the simulation module based on its type. Construct the original adjacency list based on the identified valid edges; Collect all strongly connected components in the original adjacency list; Identify and filter algebraic rings in strongly connected components to form a candidate set of algebraic rings.

3. The RC circuit health status assessment method according to claim 2, characterized in that, The simulation modules include direct feedthrough modules and indirect feedthrough modules.

4. The method for assessing the health status of an RC circuit according to claim 3, characterized in that, The collected strongly connected components are filtered out, and those containing only one simulation module are removed. Strongly connected components containing multiple simulation modules are identified as algebraic rings.

5. The method for assessing the health status of an RC circuit according to claim 4, characterized in that, In step S3, based on the original adjacency list and the candidate set of algebraic rings, each valid edge in the original adjacency list is traversed. A simplified adjacency list is established according to the ownership relationship of the start and end points of the valid edges. Based on the simplified adjacency list, a topological sort is performed to determine the solution execution order of the simulation module.

6. The method for assessing the health status of an RC circuit according to any one of claims 1-5, characterized in that, In step S6, the health status of the RC circuit is assessed based on the health threshold and the proportion of abnormal moments.

7. The method for assessing the health status of an RC circuit according to any one of claims 1-5, characterized in that, The complete dynamic response results of the multiphysics coupling degradation model of RC circuit devices throughout the simulation time include the voltage values ​​of each node, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors in the RC circuit.

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