RC circuit health state assessment method

Abstract

The invention relates to an RC circuit health state assessment method, belongs to the technical field of circuit health management of equipment, and solves the technical problems of circuit health state assessment inaccuracy and high calculation cost caused by an algebraic ring in the prior art. The method comprises the following steps: constructing a multi-physics field coupling degradation model and a block diagram simulation model of the RC circuit device; the simulation module is used for acquiring a block diagram simulation model; converting the simulation module into a directed graph and obtaining an algebraic ring candidate set; determining a solving execution sequence of the simulation modules; establishing an algebraic ring solver according to a trust region broken line method; and obtaining a complete dynamic response result of the RC circuit device multi-physical field coupling degradation model in the whole simulation time by using an algebraic ring solver, and evaluating the health state of the RC circuit. According to the method, the algebraic ring in the degradation model can be accurately identified and efficiently processed, so that the physical authenticity of a degradation mechanism is ensured, and high-precision tracking of RC circuit performance and reliable evaluation of health state indexes are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of circuit health management of equipment, and particularly relates to a method for evaluating the health status of an RC circuit. Background Art

[0002] The monitoring and management of the operating status, health status and life status of circuits are directly related to the normal operation of equipment. If abnormal conditions are not discovered in time, it will cause significant economic losses and safety hazards to enterprises and users. In the existing technology, there are a lot of studies on the operating status and health status of circuits, resistors, capacitors and other device equipment.

[0003] Chinese invention patent application publication number CN114091937A discloses a method and device for assessing the health status of a DCDC circuit on an instrumentation and control board. The method collects operational monitoring data of the DCDC circuit on the instrumentation and control board in real time, inputs the operational monitoring data into a preset health assessment model, and determines the assessment status of the DCDC circuit on the instrumentation and control board, thereby enabling assessment of the health status of the DCDC circuit on the instrumentation and control board. The preset health assessment model includes standard health assessment indicators and standard health thresholds.

[0004] Chinese invention patent application publication number CN115238927A discloses a method for evaluating the status of capacitor-type equipment based on the dielectric loss factor tgδ. The method forms a vector of the historical tgδ data obtained through online monitoring of capacitor-type equipment, calculates the correlation coefficient of the historical tgδ data of three-phase equipment on the same line, and uses it as the basis for evaluation, making the capacitor-type equipment status evaluation more quantitative.

[0005] A Chinese invention patent application with publication number CN117853089A discloses an intelligent evaluation method based on the operating status of capacitors, which obtains real-time capacitor compensation power factor information and average capacitor compensation power factor information; determines undercompensation duration information based on the real-time capacitor compensation power factor information and the average capacitor compensation power factor information; and compares the undercompensation duration information with the undercompensation duration critical value information to determine the operating status evaluation information of the 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 actual engineering applications, RC circuits inevitably degrade, seriously 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 aging, the resistance value will drift over time, causing the circuit characteristic parameters to deviate from the design value; (2) Capacitor degradation: dielectric breakdown, dielectric aging, temperature cycling, etc. will cause capacitance value changes and dielectric loss to increase, affecting the frequency response characteristics of the circuit; (3) Parasitic effect evolution: Process deviations and environmental factors can cause parasitic resistance and capacitance parameters to change, further deteriorating circuit performance.

[0008] As integrated circuit technology continues to advance toward higher integration densities and smaller feature sizes, RC circuit degradation is becoming increasingly prominent, posing a serious threat to the reliability of electronic systems. Therefore, accurate RC circuit health assessment is crucial for ensuring long-term stable operation, preventing failures, optimizing lifespan management, and achieving reliability design. The key to achieving this precise health assessment lies in establishing circuit models that reflect real-world physical degradation mechanisms and conducting efficient simulation analysis.

[0009] However, when establishing physical degradation models for RC circuit health assessment and conducting simulation analysis, a common technical challenge that seriously hinders effective assessment is the algebraic loop problem. This problem arises when there are feedback loops or strong coupling relationships between parameters in the RC circuit model (for example, changes in the degradation resistor directly affect the voltage at the capacitor terminals, which in turn affects the circuit through the charging and discharging of the degraded capacitor and feeds back to the resistor). A circular dependency forms between the variables in the model, making it impossible to obtain results through a conventional sequence. This algebraic loop problem directly leads to difficulty in model simulation convergence and reduced computational accuracy, making it extremely difficult to accurately obtain dynamic degradation parameter trajectories and predict remaining life.

[0010] Currently, existing modeling and simulation technologies face significant challenges when addressing such algebraic loops, including technical blockades, algorithmic deficiencies, and methodological flaws. In particular, existing evasive approaches to handling algebraic loops (e.g., introducing ideality assumptions, artificially delaying the loop by one frame, or using specialized numerical techniques to force the solution) severely compromise the model's physical realism and the integrity of the degradation mechanism. These methods fail to accurately characterize the feedback mechanisms of parameters, inevitably leading to estimation biases, misjudgments of health indicators, and significant inaccuracies in the final life prediction results, severely limiting the effectiveness of reliability analysis and health assessment. Therefore, there is an urgent need to develop a technical approach that can efficiently and realistically handle algebraic loops and achieve high-precision prediction of RC circuit degradation states. This approach will overcome existing technical bottlenecks and provide independent and controllable technical support for preventive maintenance, accurate life prediction, and high-reliability design of integrated circuits. Summary of the Invention

[0011] In light of the aforementioned severe challenges of algebraic loops in RC circuit health assessment, and the resulting model distortion and assessment failure, this paper provides a method for RC circuit health assessment. The core of this method lies in accurately identifying and efficiently processing algebraic loops in degradation models, thereby ensuring the physical authenticity of degradation mechanisms, enabling high-precision tracking of RC circuit performance, and reliable assessment of health indicators.

[0012] The present invention provides a method for evaluating the health status of an RC circuit, the specific steps of which are as follows: Step S1, constructing a multi-physics field coupling degradation model of an RC circuit device; constructing a block diagram simulation model based on the multi-physics field coupling degradation model of the RC circuit device; Step S2, obtaining all simulation modules of the block diagram simulation model; converting the simulation modules into a directed graph and identifying and screening algebraic ring candidate sets; Step S3, determining the execution order of solving the simulation modules based on the algebraic ring candidate set; Step S4, establishing an algebraic ring solver based on the trust region broken line method; Step S5, based on the algebraic loop candidate set identified and screened in step S2; executing the simulation loop according to the execution order of the simulation modules obtained in step S3, and calling the algebraic loop solver in step S4 when an algebraic loop is encountered; obtaining the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device during the entire simulation time; Step S6: evaluating the health status of the RC circuit according to the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device obtained in step S5 during the entire simulation time.

[0013] Optionally, the multi-physics field coupling degradation model of the RC circuit device includes a resistance degradation model and a capacitance degradation model.

[0014] Optionally, in step S2, the specific steps of converting the simulation module into a directed graph and identifying and screening the algebraic ring candidate set are: Identify and label the type of simulation module; According to the type of simulation module, identify the valid edges of the simulation module; Construct the original adjacency list based on the identified valid edges; Collect all strongly connected components in the original adjacency list; Identify and screen algebraic rings in strongly connected components to form a candidate set of algebraic rings.

[0015] Optionally, types of the simulation modules include direct feedthrough modules and indirect feedthrough modules.

[0016] Optionally, according to the type of the simulation module, the specific step of identifying the valid edge of the simulation module is: if the end point module of the connection line between the simulation modules is a direct feedthrough module, then the connection line is marked as a valid edge.

[0017] Optionally, the collected strongly connected components are screened to remove the strongly connected components containing only one simulation module, and the strongly connected components containing multiple simulation modules are identified as algebraic rings.

[0018] Optionally, in step S3, based on the original adjacency list and the algebraic ring candidate set, each valid edge in the original adjacency list is traversed, and a simplified adjacency list is established according to the affiliation relationship between the starting point simulation module and the end point simulation module of the valid edge; topological sorting is performed based on the simplified adjacency list to determine the solution execution order of the simulation modules.

[0019] Optionally, the specific steps of step S4 are: Step S41, initializing the parameters of the RC circuit; Step S42, constructing a hash table of algebraic rings in the algebraic ring candidate set; Step S43: constructing an initial output state vector to be solved based on the hash table; Step S44, constructing a residual vector corresponding to the initial output state vector to be solved; Step S45, calculating the Jacobian matrix of the initial output state vector to be solved and the corresponding residual vector; Step S46: Establish an algebraic loop solver based on the output state vector and Jacobian matrix to be solved.

[0020] Optionally, in step S6, the health status of the RC circuit is evaluated based on the health threshold and the abnormal time ratio.

[0021] Optionally, the complete dynamic response results of the multi-physics field coupling degradation model of the RC circuit device during the entire simulation time include the voltage values ​​of each node in the RC circuit, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors.

[0022] Compared with the prior art, the present invention has at least the following beneficial effects: The present invention realizes the 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; further with the help of algebraic ring vertex merging and topological sorting optimization technology, the parameter solution efficiency is significantly improved and the consumption of computing resources is greatly reduced; at the same time, the trust region broken line method numerical solution technology is adopted to ensure the solution accuracy of key performance parameters under the coupled degradation feedback mechanism, thereby providing high-reliability support for core health status assessment results such as performance margin analysis, stability criteria and life assessment; finally, the present invention provides a complete RC circuit health status assessment processing solution for the autonomous block diagram modeling environment, successfully solves the mechanism distortion problem caused by the avoidance method, and can achieve high-precision assessment of the stable RC circuit health status under the premise of truly reflecting the physical degradation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention can be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0024] Figure 1 is a flow chart of the RC circuit health status assessment method of the present invention; Figure 2 A schematic diagram of the input and output ports of the inner edge of the algebraic ring of the present invention; Figure 3 A circuit diagram of an RC circuit according to a specific embodiment of the present invention; Figure 4 Schematic diagram of a block diagram simulation model of a multi-physics field coupled degradation model of an RC circuit device according to a specific embodiment of the present invention; Figure 5 Schematic diagram comparing the simulation results of the capacitor C of a specific embodiment of the present invention and the SIMULINK simulation results; Figure 6 The resistor of the specific embodiment of the present invention Schematic diagram of the comparison between the simulation results and the SIMULINK simulation results; Figure 7 The resistor of the specific embodiment of the present invention Schematic diagram of the comparison between the simulation results and the SIMULINK simulation results; Figure 8 The branch current of the specific embodiment of the present invention is Schematic diagram of the comparison between the simulation results and the SIMULINK simulation results; DETAILED DESCRIPTION In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0025] A specific embodiment of the present invention, as Figures 1-8 , discloses a method for evaluating the health status of an RC circuit, the specific steps of which are as follows: Step S1: Construct a multi-physics field coupled degradation model of an RC circuit device. The specific steps are as follows: Step S11: construct a resistance degradation model, the expression is:

[0026] in, The resistance at time resistance value; Indicates the initial nominal resistance of the resistor; 、 and is the resistance degradation coefficient related to the resistor material and process; is the degradation function of the electromigration effect; is the degradation function of thermal stress effect; is the time-dependent material aging function; represents the current density; Indicates the ambient operating temperature; Represents temperature cycling.

[0027] It is understandable that Describing current density , ambient operating temperature Under the combined effect of the resistance at the moment Resistance change; Describing temperature cycles The resistance caused by thermal mechanical stress degradation; The resistance at time The material aging function describes the purely time-related material aging effect.

[0028] Step S12, calibrating resistance parameters; Specifically, the resistance degradation coefficient related to the resistor material and process is determined by fitting the accelerated degradation experimental data. 、 、 , a quantitative mapping relationship between the resistance degradation coefficient and the working conditions is established.

[0029] Step S13: construct a capacitor degradation model, expressed as:

[0030] in, Indicates the capacitance at time The capacitance value; Indicates the initial nominal capacitance value of the capacitor; 、 are dielectric breakdown function and dielectric aging function respectively; 、 is the degradation coefficient related to the capacitor material; Indicates the electric field strength across the capacitor; Indicates the ambient operating temperature; Indicates the circuit operating frequency.

[0031] Further, Describe the electric field strength of the capacitor medium and ambient operating temperature Under the action of the capacitor at the moment performance degradation; Describe the working frequency of the capacitor dielectric at the circuit Under the action of the capacitor at the moment aging effects.

[0032] Step S14, calibrating capacitance parameters; Specifically, the degradation coefficient of capacitance related to the capacitor material is determined by fitting the accelerated degradation experimental data. 、 , establish a quantitative mapping relationship between capacitor degradation parameters and working conditions.

[0033] Step S15 , combining the resistance degradation model, the capacitance degradation model and the RC circuit topology structure to construct a block diagram simulation model of the multi-physics field coupled degradation model of the RC circuit device, thereby realizing the conversion from the circuit diagram to the block diagram model.

[0034] Step S2: Obtain all simulation modules included in the block diagram simulation model; convert the simulation modules into a directed graph and identify and screen algebraic ring candidate sets. The specific steps are as follows: Step S21, identifying and marking the type of the simulation module; Specifically, all simulation modules in the block diagram simulation model are traversed, and all simulation modules are classified and marked as direct feedthrough modules (such as gainers, adders, etc.) and indirect feedthrough modules (such as integrators, transfer functions and other dynamic links) according to the module transfer function characteristics.

[0035] Step S22, identifying valid edges of the simulation module according to the type of the simulation module; The validity of each connection line of each simulation module 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.

[0036] Step S23: construct the original adjacency table based on the identified valid edges , the expression is:

[0037] in, Indicates that the simulation module The list of endpoint modules of all valid starting edges, , is the number of simulation modules.

[0038] Step S24: Collect the original adjacency list All strongly connected components in ; Further, using Strongly connected component algorithm traverses the original adjacency list , collect the original adjacency list All strongly connected components in .

[0039] It can be understood that a strongly connected component is a subset of simulation modules in the adjacency list, which is composed of several simulation modules. There is a mutually reachable directed path between any two simulation modules in this subset, and there is no larger subset that can contain the current subset and still maintain the bidirectional reachability.

[0040] Step S25: Identify and filter the algebraic rings in the strongly connected components collected in step S24 to form a candidate set of algebraic rings. , the expression is:

[0041] in, Indicates the an algebraic ring; is the number of algebraic rings in the candidate set of algebraic rings.

[0042] Specifically, the strongly connected components collected in step S24 are screened, and the strongly connected components containing only one simulation module are removed, and the strongly connected components containing multiple simulation modules are identified as algebraic ring candidate sets. .

[0043] Step S3, based on the algebraic ring candidate set , determine the execution order of the simulation module solution, the specific steps are as follows: Step S31: Establish an algebraic ring candidate set AThe mapping of the simulation module to the algebraic ring in which it is located.

[0044] Step S32: Based on the original adjacency table and algebraic ring candidate sets , according to the mapping of the algebraic ring, traverse the original adjacency list For each valid edge in, there is a corresponding starting point simulation module and endpoint simulation module , according to the starting point simulation module of the effective edge and endpoint simulation module The simplified adjacency table is established based on the ownership relationship G 2. Specifically, if the starting simulation module In algebraic rings Endpoint simulation module In algebraic rings In addition, the endpoint simulation module Add to simplified adjacency list (i.e. from the algebraic ring The list of endpoint modules of all valid edges that can be reached from the start), where Represents a candidate set of algebraic rings A Middle an algebraic ring, .

[0045] If the starting simulation module In algebraic rings In addition, the endpoint simulation module In algebraic rings Inside, the algebraic ring Add to simplified adjacency list (i.e., simulation module from the starting point The endpoint simulation module of all valid edges that can be reached list); If the starting simulation module and endpoint simulation module They are all in the same algebraic ring. The valid edge is an inner edge of the ring and is not in the simplified adjacency list. Establish a connection in If the starting simulation module and endpoint simulation module Are not in the algebraic loop, the end point simulation module Add to simplified adjacency list ; Step S33, based on the simplified adjacency table Perform topological sorting to determine the solution execution order that satisfies the dependencies between simulation modules.

[0046] It can be understood that the dependency here means "the calculation result of one simulation module needs to be used as input data of another simulation module". For example, there is a simulation module for power supply voltage and a simulation module for voltage across resistor. The simulation module for voltage across resistor needs to use the output result of the simulation module for power supply voltage as input. Then the dependency is to execute the simulation module for power supply voltage first, and after the simulation module for power supply voltage outputs the result, execute the simulation module for voltage across resistor.

[0047] Step S4: establishing an algebraic loop solver based on the trust region broken line method.

[0048] The algebraic loop solver of the present invention is used to solve algebraic loop equations encountered in a block diagram modeling simulation process, and is automatically called by the system when an algebraic loop is detected during the simulation process.

[0049] The algebraic loop solver calculates the instantaneous voltage and current equilibrium state generated by the feedback loop in an RC circuit, while also considering the impact of device parameter degradation in the RC circuit 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 Kirchhoff's current law (KCL), but it also requires real-time calculation of resistance changes and capacitance drift under the influence of 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 set of algebraic equations. The purpose of the algebraic loop solver of the present invention is to find a unique physical parameter solution that satisfies all physical laws and degradation characteristics at each simulation moment.

[0050] Step S41, initializing the parameters of the RC circuit; Specifically, according to the physical characteristics of the RC circuit, the initial trust region radius is set , the maximum trust region radius , maximum number of iterations , the lower limit threshold of the confidence ratio , upper threshold of trust ratio , trust region reduction factor , trust region expansion factor , convergence threshold and improvement threshold .

[0051] Step S42: Construct an algebraic ring candidate set A Hash tables for algebraic rings in ; Specifically, the candidate set of algebraic rings A Algebraic rings in The valid edges in the network are numbered sequentially starting from 1, and a hash table is established. The hash table will save the mapping relationship between each valid edge and its number.

[0052] Step S43: construct the initial output state vector to be solved based on the hash table ,in, Indicates the first i The output signal value of the output port of the valid edge at the initial solution time, i =1,2,..., m , is the total number of valid edges in the algebraic ring.

[0053] Exemplarily, 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 multi-physical field coupling degradation.

[0054] It is understandable that the output port of the edge is: Figure 2 , if there is an algebraic ring i Valid edges The simulation module corresponding to the starting point Output port Connect to the simulation module corresponding to the end point of the edge Input port , then the input port That is the first i Valid edges Output port, output port That is the first i Valid edges Input port.

[0055] Furthermore, if the algebraic ring i Valid edges To obtain the output signal value of its output port at the current solution time, the hash table is used to obtain the first i Valid edges Numbering in algebraic rings i , then the output state vector to be solved is The algebraic ring of i The output signal value of the output port of the valid edge at the current solution time That is the first i Valid edges The value of the output port.

[0056] Step S44: construct the residual vector corresponding to the initial output state vector, which is expressed as:

[0057] in, Indicates the first i The initial residuals of the corresponding output ports of the valid edges.

[0058] Furthermore, the algebraic ring i The initial residuals of the corresponding output ports of the valid edges The expression is:

[0059] in, is the first i The output signal value of the output port of the valid edge at the initial solution time; Indicates the i The signal processing function of the input port of the valid edge; Used to measure the number of algebraic rings to be solved i Signal processing function for the input port of valid edges the degree to which the conditions are met.

[0060] Step S45, calculate the Jacobian matrix of the initial output state vector to be solved and the residual vector corresponding to the initial output state vector to be solved , the expression is: .

[0061] Furthermore, the Jacobian matrix The expression for the elements of is:

[0062] in, Represents the Jacobian matrix No. Rank Column elements, , ; Indicates the first The output signal value of the output port of the valid edge at the initial moment.

[0063] Further, The solution is: Look up the first Valid edges Hedi Valid edges ; Judge the The simulation module corresponding to the starting point is Valid edges The simulation module corresponding to the end point is the same simulation module, and the first simulation module in the algebraic loop is obtained based on the judgment result. The output signal value of the output port of the valid edge at the initial moment Is it the first Signal processing function for the input port of valid edges The basis for the actual input; If the algebraic ring The output signal value of the output port of the valid edge at the initial moment Not the first Signal processing function for the input port of valid edges The actual input, The value of is 0; If the algebraic ring The output signal value of the output port of the valid edge at the initial moment It is Signal processing function of the output port of the valid edge The actual input of i Signal processing function for the input port of valid edges Is there an interface that can directly get the corresponding partial derivative according to the input port number? If there is an interface, then the first Valid edges The port number of the connected input port can be obtained If there is no interface, the perturbation partial derivative method is used to find the value of Valid edges Apply a small disturbance value to the output port (such as 1e-7), the obtained algebraic ring The output signal value of the input port of the valid edge at the initial moment The difference is divided by the small perturbation value That is value.

[0064] Step S46: Based on the output state vector and Jacobian matrix to be solved, an algebraic loop solver is established to obtain the final output signal value: Step S461: Based on the output state vector to be solved Calculate the residual and obtain the updated residual vector , and construct the gradient vector ; Specifically, based on the updated residual vector and Jacobian matrix , get the gradient vector .

[0065] It is understandable that when the loop is first entered, the output state vector to be solved is = the initial output state vector to be solved .

[0066] Step S462, pre-convergence judgment; Update the residual vector in step S461 using the cost function value evaluation The degree of closeness to 0, if the degree of closeness is less than the convergence threshold, it means that the trust region broken line method converges, the iteration is completed, and the current output state vector is used as the final output signal value to obtain the final output signal value, whose components correspond to the specific values ​​of each physical quantity in the algebraic loop at the current simulation moment; if it does not converge, go to step S463.

[0067] Furthermore, the cost function is expressed as:

[0068] in, Indicates the first i The updated residuals of the corresponding output ports of the valid edges.

[0069] Step S463, based on the updated residual vector and the Jacobian matrix , get the Gauss-Newton step size, the expression is:

[0070] in, is the Gauss-Newton step size.

[0071] Step S464: Calculate the steepest descent step length, expressed as:

[0072] in, is the step size coefficient of the steepest descent step size, is the search step vector in the steepest descent direction; represents the gradient vector.

[0073] Step S465, determining the broken line step length based on the Gauss-Newton step length, the steepest descent step length, and the trust region radius; Specifically, if the second norm of the Gauss-Newton step length does not exceed the trust region radius, the Gauss-Newton step length is used as the broken line step length; if the steepest descent step length exceeds the trust region radius, the steepest descent step length is scaled proportionally according to the ratio of the trust region radius to the second norm of the steepest descent step length to obtain the broken line step length; otherwise, the quadratic constraint equation is solved to interpolate between the Gauss-Newton step length and the steepest descent step length to obtain the broken line step length. .

[0074] Step S466, based on the broken line step length and the current output state vector to be solved , and obtain the trial solution vector , and calculate the trial solution vector The corresponding residual vector , trial solution vector The cost function value .

[0075] Specifically, the trial solution vector The expression is:

[0076] in, Indicates the first The tentative output signal value of the input port of the valid edge at the current solution time.

[0077] Specifically, the trial solution vector The corresponding residual vector The expression is:

[0078] in, Indicates the first The tentative output signal value of the input port of the valid edge at the current solution time The residual.

[0079] Furthermore, the algebraic ring The tentative output signal value of the input port of the valid edge at the current solution time The residual The expression is: .

[0080] Furthermore, the solution vector The cost function value The expression is:

[0081] Step S467, calculate the confidence ratio , to evaluate the polyline step size The improvement effect is expressed as:

[0082] in, represents the actual reduction in the cost function; Represents the reduction in the predicted cost function.

[0083] Step S468, adjusting the trust region radius according to the trust ratio; Specifically, if Or the actual cost function reduction If it is negative, it means that the improvement effect is poor, and the trust region radius is reduced to the original times, and refuse to update the current output state vector to be solved ;like And the broken line step length Close to the trust region boundary, indicating that the effect is improved, the trust region radius is expanded to the original times, but the enlarged trust region radius cannot exceed the maximum trust region radius set in step S41 , while accepting the current trial solution vector, i.e. ; In other cases, the polyline step size is accepted But the trust region radius remains unchanged.

[0084] Step S469: Check whether the current number of iterations is greater than or equal to the maximum number of iterations , if the current number of iterations is greater than the maximum number of iterations , and the convergence condition is not met, it means that the simulation model is wrong, exit the loop, and the R&D personnel need to readjust the simulation model before executing the method of the present invention; if the current number of iterations is less than or equal to the maximum number of iterations , but does not meet the convergence conditions, use the trial solution vector As the output state vector to be solved in the next iteration step , return to step S461; if the current number of iterations is less than or equal to the maximum number of iterations , and meet the convergence conditions, obtain the algebraic loop solver, use the trial solution vector As the final output signal value, the final output signal value is obtained.

[0085] Among them, the trial solution vector The components of are the specific values ​​of the physical quantities in the corresponding algebraic loop at the current simulation time, including node voltages, branch currents, resistance values ​​of resistors, capacitance values ​​of capacitors, degradation characteristic parameters, and other derived circuit characteristic parameters generated by multi-physics field coupling; Specifically, the convergence condition is: .

[0086] It can be understood that if it satisfies, it means that the trust region broken line method converges, and the current trial solution vector The component values ​​of are the final output signal values ​​of the output ports of the corresponding valid edges; otherwise, the trial solution vector is used As the current output state vector to be solved in the next iteration step , return to step S461.

[0087] Step S5, based on the algebraic loop candidate set identified and screened in step S2; executing the simulation loop according to the execution order of the simulation modules in the simulation model obtained in step 3, automatically calling the algebraic loop solver in step 4 when an algebraic loop is encountered; obtaining the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device during the entire simulation time, the specific steps are as follows: Step S51 : setting a suitable simulation time range and simulation time step according to the parameter degradation rate of the RC circuit to be tested.

[0088] Step S52: perform algebraic ring identification and screening on the simulation model according to step S2, and obtain an algebraic ring candidate set; and obtain the execution order of the simulation modules in the simulation model according to step S3.

[0089] Step S53, simulation loop execution; For each time step, each simulation module is executed in sequence according to the execution order obtained in step S52: for non-algebraic loop simulation modules, the simulation module is executed according to the pre-designed signal processing function (such as addition, subtraction, multiplication, division, integration and other basic operations); when an algebraic loop is encountered, the algebraic loop solver of step 4 is called to solve and obtain the specific value of each physical quantity in the algebraic loop at the current simulation moment; after all simulation modules are executed, the simulation data of the current time step is saved, including physical quantities such as the voltage value of each node, the branch current value, the resistance value of the resistor device, the capacitance value of the capacitor device, etc.; then the simulation is advanced to the next time step, and the above process is repeated until the simulation is completed, and finally the complete dynamic response result of the multi-physical field coupling degradation model of the RC circuit device is formed during the entire simulation time.

[0090] Furthermore, the complete dynamic response results of the multi-physics field coupling degradation model of the RC circuit device during the entire simulation time include the voltage values ​​of each node in the RC circuit, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors.

[0091] Step S6, evaluating the health status of the RC circuit based on the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device obtained in step S5 during the entire simulation time, the specific steps are as follows: 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 the voltage parameter allowable deviation range of ±5%, the current parameter allowable deviation range of ±10%, the electric power parameter allowable deviation range of ±15%, the device resistance value deviation range of ±10%, etc.; when any key physical parameter exceeds its corresponding allowable deviation range at a certain moment, record this moment as an abnormal moment.

[0092] Step S62, fixed window local health assessment: The entire simulation time is divided into several fixed time windows (e.g., each window length is 10% of the total simulation time), and the proportion of abnormal moments in each time window is counted. When the proportion of abnormal moments in the window exceeds a preset threshold (e.g., 30%), the RC circuit is determined to be in an unhealthy state during this time period.

[0093] 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.

[0094] In order to illustrate the effectiveness of the method proposed in the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment, which is as follows: Use Figure 3 The passive RC filter circuit shown in the figure verifies the effect of the present invention. The operating temperature of the RC circuit is 45-70℃. is a DC voltage source with a ripple voltage of 100 Hz frequency, is the resistor The voltage across the terminals; Through the resistor The current, Through the resistor Current; is the current through capacitor C; Further, C The capacitance value is 10 Aluminum electrolytic capacitors, A metal film resistor of 5000Ω, It is a 150Ω metal film resistor.

[0095] The block diagram simulation model of the device multi-physics field coupling degradation model of the RC circuit established in step 1 is as follows Figure 4 .

[0096] Based on step S2 of the method of the present invention, the algebraic ring structure (i.e. Figure 4 in ), confirm that the feedback loop does not contain an integrator or delay unit, the identification time is 0.5m, the accuracy is 100%, and the correct execution order of the simulation modules is obtained. The algebraic loop solver established based on step 4 of the present invention maintains stable convergence under various degenerate parameter conditions, with an average number of iterations of 2-5 times, a convergence accuracy of 1e-8, and an average single time step algebraic loop solution time of 0.23m. Compared with the traditional delay method, the present invention avoids the artificially introduced phase distortion, and the current solved by the algebraic loop is The accuracy reaches 99.8%, fully maintaining the physical authenticity of the RC circuit.

[0097] In order to further verify the correctness of the simulation results of the present invention, a group of the same block diagram simulation models were established in SIMULINK software, and the same simulation end time was set to 80600, the simulation step size was 50, and the solver was ode4. C 、 、 、 The specific comparison diagrams of the simulation results are as follows Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 , the simulation results are in line with expectations.

[0098] Based on the precise algebraic loop solution results, the circuit health status is evaluated and verified under different levels of degradation. Under normal operating conditions, all physical parameters are stable, and the system determines that the circuit is healthy overall. When the circuit degrades, the capacitance value decreases and the resistance value increases. The algebraic loop solver maintains convergence and stability. The system accurately determines that the circuit is in an unhealthy state based on the abnormal moment ratio and time window analysis. Under severe degradation conditions, the system clearly identifies a critically unhealthy state, and the evaluation results are highly consistent with theoretical analysis.

[0099] Verification results demonstrate that this method, through precise algebraic loop detection and solution techniques, achieves high-precision simulation of RC circuits and establishes a reliable health assessment method based on this. This technical solution not only addresses the core technical challenge of algebraic loops but also achieves practical engineering applications, providing a complete technical solution for the design, analysis, and maintenance of RC circuits.

[0100] The above description is only a preferred specific 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 thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for evaluating the health status of an RC circuit, characterized in that: The specific steps are as follows: Step S1, constructing a multi-physics field coupling degradation model of an RC circuit device; constructing a block diagram simulation model based on the multi-physics field coupling degradation model of the RC circuit device; Step S2, obtaining all simulation modules of the block diagram simulation model; converting the simulation modules into a directed graph and identifying and screening algebraic ring candidate sets; Step S3, determining the execution order of solving the simulation modules based on the algebraic ring candidate set; Step S4, establishing an algebraic ring solver based on the trust region broken line method; Step S5, based on the algebraic ring candidate set identified and screened in step S2; Execute the simulation loop according to the execution order of the simulation modules obtained in step S3, and when an algebraic loop is encountered, call the algebraic loop solver in step S4; obtain the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device during the entire simulation time; Step S6: evaluating the health status of the RC circuit according to the complete dynamic response results of the multi-physics field coupled degradation model of the RC circuit device obtained in step S5 during the entire simulation time.

2. The RC circuit health status assessment method according to claim 1, characterized in that: The multi-physics field coupling degradation model of RC circuit devices includes resistance degradation model and capacitance degradation model.

3. The RC circuit health status assessment method according to claim 1, characterized in that: In step S2, the specific steps of converting the simulation module into a directed graph and identifying and screening the algebraic ring candidate set are: Identify and label the type of simulation module; According to the type of simulation module, identify the valid edges of the simulation module; Construct the original adjacency list based on the identified valid edges; Collect all strongly connected components in the original adjacency list; Identify and screen algebraic rings in strongly connected components to form a candidate set of algebraic rings.

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

5. The RC circuit health status assessment method according to claim 4, characterized in that: If the endpoint of a connection line between simulation blocks is a direct feedthrough block, the connection line is marked as a valid edge.

6. The RC circuit health status assessment method according to claim 5, characterized in that: The collected strongly connected components are screened to remove those containing only one simulation module, and those containing multiple simulation modules are identified as algebraic rings.

7. The RC circuit health status assessment method according to claim 6, characterized in that: In step S3, based on the original adjacency list and the algebraic ring candidate set, each valid edge in the original adjacency list is traversed, a simplified adjacency list is established according to the affiliation relationship between the starting point and the end point of the valid edge, and a topological sorting is performed based on the simplified adjacency list to determine the solution execution order of the simulation module.

8. The RC circuit health status assessment method according to claim 7, characterized in that: The specific steps of step S4 are: Step S41, initializing the parameters of the RC circuit; Step S42, constructing a hash table of algebraic rings in the algebraic ring candidate set; Step S43: constructing an initial output state vector to be solved based on the hash table; Step S44, constructing a residual vector corresponding to the initial output state vector to be solved; Step S45, calculating the Jacobian matrix of the initial output state vector to be solved and the corresponding residual vector; Step S46: Establish an algebraic loop solver based on the output state vector and Jacobian matrix to be solved.

9. The RC circuit health status assessment method according to any one of claims 1 to 8, characterized in that: In step S6, the health status of the RC circuit is evaluated based on the health threshold and the abnormal time ratio.

10. The RC circuit health status assessment method according to any one of claims 1 to 8, characterized in that: The complete dynamic response results of the multi-physics field coupling degradation model of the RC circuit device during the entire simulation time include the voltage values ​​of each node in the RC circuit, the branch current values, the resistance values ​​of the resistors, and the capacitance values ​​of the capacitors.

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