A hierarchical precision adaptive nonlinear simulation iteration method

Abstract

The application discloses a layered precision self-adaptive nonlinear simulation iteration method, and relates to the field of nonlinear simulation.The method comprises the following steps: obtaining an element model set of a simulation system, and dividing the element model into a low-precision equivalent model layer and a high-precision detailed model layer; constructing a first solving matrix based on the low-precision equivalent model layer, and performing first-stage iteration by using a Newton-Raphson algorithm to obtain an initial solution vector, wherein the convergence condition of the first-stage iteration is that the solution vector satisfies a preset low-precision threshold; constructing a second solving matrix based on the high-precision detailed model layer and the initial solution vector, and performing second-stage iteration to obtain a target accurate solution vector, wherein the convergence condition of the second-stage iteration is that the solution vector satisfies a preset high-precision threshold.The application can effectively solve the problems of sensitivity of the traditional Newton-Raphson algorithm to an initial solution and sacrifice of simulation precision caused by a simplified model.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of nonlinear simulation, in particular to a layered precision adaptive nonlinear simulation iteration method. BACKGROUND

[0002] As the core tool for the design and analysis of complex physical systems such as aviation, aerospace, ships, weapons and rail transit, the simulation technology relies on the lumped parameter model which is simple in structure and suitable for system comprehensive analysis, and becomes the basis for accurate analysis. However, there are a large number of elements with strong nonlinear characteristics in the system, and the output characteristics cannot be ignored due to high-frequency operation, which must be included in the simulation model to ensure analysis accuracy. For solving nonlinear equations, the traditional method mostly uses Newton-Raphson iteration method, but this algorithm is extremely sensitive to the selection of initial solution, and when the initial solution deviates from the true solution, it is easy to appear slow convergence speed or even numerical overflow, which seriously affects the simulation efficiency and reliability.

[0003] The existing nonlinear iteration simulation method has two key defects: first, although the Newton-Raphson iteration method can accurately solve nonlinear equations, it requires high precision of the initial solution, and if the initial solution is set unreasonably, it will lead to a significant increase in the number of iterations, a sharp decline in convergence speed, and even termination of simulation due to numerical overflow; second, in order to improve convergence, some methods use simplified models such as piecewise linear models to replace detailed nonlinear models, which can quickly obtain the initial solution, but because the simplified model ignores the high-order nonlinear characteristics of the element, the simulation accuracy cannot meet the high-precision requirements of switch loss calculation and transient response analysis, and it is difficult to balance the simulation efficiency and accuracy. Therefore, based on the above problems, the present application proposes a layered precision adaptive nonlinear simulation iteration method. SUMMARY

[0004] PURPOSE OF THE INVENTION

[0005] In order to solve the above problems, the purpose of the present application is to provide a layered precision adaptive nonlinear simulation iteration method, which is sensitive to the initial solution when solving nonlinear element equations with Newton-Raphson algorithm, and is prone to slow convergence speed or even numerical overflow and non-convergence, and the traditional simplified model sacrifices the simulation accuracy, while ensuring the simulation accuracy, improving the iteration solving efficiency and convergence performance of the nonlinear solver.

[0006] TECHNICAL SCHEME

[0007] In order to achieve the above object, the application provides a hierarchical precision adaptive nonlinear simulation iteration method, which constructs a hierarchical model for an element with high-order nonlinear characteristics, adopts a two-stage iteration strategy: in the first stage, an initial solution vector close to the true solution is obtained through fast iteration based on a piecewise linear equivalent model by using Newton-Raphson algorithm; in the second stage, iteration is carried out based on the detailed model of the element G group with the initial solution vector as the initial value to obtain the accurate solution; meanwhile, in transient analysis, selective application of the process is realized according to the closeness of the initial solution and the accurate solution, so that efficient and accurate simulation of the nonlinear system is realized.

[0008] In the first aspect, the application provides a hierarchical precision adaptive nonlinear simulation iteration method, which comprises the following steps:

[0009] S1, a netlist file, simulation parameters and a current step length of a simulation system are obtained, elements with high-order nonlinear characteristics are classified into an element G group based on the time-varying characteristics of the nonlinear characteristics of the elements and the sensitivity of simulation target parameters to the precision of the element model, and a low-precision equivalent model layer and a high-precision detailed model layer are constructed for the element G group;

[0010] Further, the time-varying characteristics of the nonlinear characteristics of the elements include the change of nonlinear coefficients caused by temperature drift;

[0011] Further, the sensitivity of the simulation target parameters to the precision of the element model includes that the precision sensitivity of the switch element model for switch loss calculation is higher than that of the passive element;

[0012] S2, first-stage iteration is carried out based on the low-precision equivalent model layer by using Newton-Raphson algorithm: the Jacobian matrix and the right end item are updated according to the step length, the matrix equation is solved to obtain an initial solution vector, and the iteration is continued until the low-precision threshold value based on the first-stage convergence speed is met, if the convergence speed is faster than the preset value, the threshold value is reduced to reduce the iteration times of the subsequent high-precision layer;

[0013] Further, the updating frequency of the Jacobian matrix according to the step length is based on the linearization error threshold value of the low-precision model, and the updating is carried out when the linearization error exceeds the threshold value;

[0014] S3, second-stage iteration is carried out based on the high-precision detailed model layer with the initial solution vector as the initial solution: the Jacobian matrix and the right end item are updated according to the nonlinear strength of the high-precision model, the iteration is carried out by using the nonlinear strength adaptive step length adjustment strategy, and the iteration is continued until the high-precision threshold value set based on the nonlinear strength of the high-precision model is met;

[0015] Further, the nonlinear strength of the high-precision model includes the slope change rate of the exponential model;

[0016] Further, the higher the nonlinearity strength of the non-linear strength adaptive step adjustment strategy, the smaller the iteration step.

[0017] S4, updating the simulation step and repeating the above steps to realize the transient simulation of the non-linear system according to the target accurate solution vector obtained by the second stage iteration.

[0018] Further, the element model in the low-precision equivalent model layer is selected from a segmented linear approximation model, a low-order polynomial fitting model, a simplified model based on neural network compression, a fuzzy logic simplified model or an adaptive segmented linear model, wherein the training data of the neural network compression model comes from the historical simulation data of the high-precision detailed model.

[0019] Further, the simplified model based on neural network compression reduces the computational complexity through pruning or quantization.

[0020] Further, the adaptive segmented linear model dynamically adjusts the number and position of the segmented points based on the nonlinearity strength index of the element nonlinearity function; wherein the higher the nonlinearity strength of the region, the denser the segmented points, and the lower the nonlinearity strength of the region, the sparser the segmented points.

[0021] Further, the classification of the element G group also includes the functional priority of the element in the simulation system and the non-negligibility of the nonlinearity characteristics.

[0022] Further, in the Newton-Raphson algorithm of the first stage iteration, the update logic of the Jacobian matrix is to calculate the linearization error of the low-precision model, that is, the deviation of the low-precision model output from the high-precision model output, and when the deviation exceeds the linearization error threshold, the Jacobian matrix is updated; in the Newton-Raphson algorithm of the second stage iteration, the update logic of the Jacobian matrix is to calculate the nonlinearity derivative change rate of the high-precision model, such as the change rate of the derivative of the exponential model with respect to the input variable, and when the change rate exceeds the derivative change threshold, the Jacobian matrix is updated.

[0023] Further, the linearization error threshold is preset by a user or a simulation system.

[0024] Further, the adaptive adjustment formula of the low-precision threshold is:

[0025]

[0026] In the formula, is the adjusted low-precision threshold; is the initial low-precision threshold; is the first adjustment coefficient, ; a preset convergence speed for the first stage iteration; a preset convergence speed;

[0027] The adaptive adjustment formula of the high-precision threshold is:

[0028]

[0029] In the formula, is the adjusted high-precision threshold; is the initial high-precision threshold; is the second adjustment coefficient, ; is the nonlinear strength of the high-precision model; is a preset nonlinear strength.

[0030] The strategy reduces the low-precision threshold, makes the low-precision layer convergence condition more difficult to meet, sacrifices a small amount of calculation cost of the low-precision layer, makes the initial solution of the high-precision layer closer to the real solution, and greatly reduces the calculation cost of the high-precision layer.

[0031] Further, before inputting the initial solution vector to the second stage iteration, the system further comprises a cross-layer error compensation step: establishing an error compensation model based on historical iteration error data of the low-precision equivalent model layer and the high-precision detailed model layer, and correcting the initial solution vector by using the model to reduce the initial solution deviation from the low-precision layer to the high-precision layer.

[0032] Further, the nonlinear system simulation is a high-frequency switching simulation of a power electronic converter, wherein:

[0033] The low-precision equivalent model layer adopts an ideal switching model of a switching tube, ignores the conduction voltage drop and the switching time, and is used for quickly tracking the conduction and cutoff states of the switching tube;

[0034] The high-precision detailed model layer adopts a SPICE model of the switching tube, contains the conduction voltage drop, the switching time and the parasitic parameters, and is used for accurately calculating the conduction loss and the cutoff loss of the switching tube.

[0035] In a second aspect, the application further provides a layered precision adaptive nonlinear simulation iteration system, which is based on the method of the first aspect and comprises:

[0036] A model layering module is used for classifying elements with high-order nonlinear characteristics into an element G group and constructing a low-precision equivalent model layer and a high-precision detailed model layer based on the time-varying characteristics of the nonlinear characteristics of the elements and the precision sensitivity of the simulation target parameters.

[0037] a first iteration module configured to perform a first-stage iteration based on the low-precision equivalent model layer using a Newton-Raphson algorithm to obtain an initial solution vector, wherein the update frequency of the Jacobian matrix is based on a linearization error threshold of the low-precision model;

[0038] a second iteration module configured to perform a second-stage iteration based on the high-precision detailed model layer using the initial solution vector as an initial value to obtain a target accurate solution vector, wherein the update frequency of the Jacobian matrix is based on the nonlinearity strength of the high-precision model, and the iteration step is adaptively adjusted based on the nonlinearity strength;

[0039] a threshold adjustment module configured to adaptively adjust the low-precision threshold based on the first-stage convergence speed and adjust the high-precision threshold based on the nonlinearity strength of the high-precision model;

[0040] an error compensation module configured to establish an error compensation model based on historical iteration error data of the low-precision layer and the high-precision layer, and correct the initial solution vector to reduce the cross-layer deviation.

[0041] a resource scheduling unit configured to dynamically adjust the number of high-performance computing nodes of the second iteration module according to the convergence speed of the first-stage iteration, and increase the number of computing nodes of the second iteration module if the first-stage convergence speed is fast to speed up the iteration speed of the high-precision layer.

[0042] Further, the model layering module further comprises a time-varying characteristic monitoring unit configured to monitor the time-varying characteristics of the nonlinear characteristics of the elements in real time and dynamically adjust the classification of the element G group.

[0043] Further, the first iteration module and the second iteration module adopt a hybrid parallel computing architecture:

[0044] The first iteration module adopts a data parallel mode to distribute the iteration tasks of the low-precision model to a plurality of low-performance computing nodes, and each node processes the low-precision model calculation of a group of elements.

[0045] The second iteration module adopts a task parallel mode to distribute the iteration tasks of the high-precision model to high-performance computing nodes, and each node processes the calculation of one high-precision model.

[0046] The application discloses a layered precision adaptive nonlinear simulation iteration method, constructs a hierarchical model system of a segmented linear equivalent model and a detailed model, and adopts a two-stage iteration strategy: first, for elements with high-order nonlinear characteristics, an initial solution vector close to a true solution is obtained through a Newton-Raphson algorithm based on a segmented linear equivalent model; then, the detailed model of the element G group is called to perform iteration using the initial solution vector as an initial value to obtain an accurate solution; in transient analysis, according to the closeness of the initial solution and the accurate solution, a flow is adaptively selected to realize efficient transient simulation of a nonlinear system.

[0047] The method can effectively solve the problems of sensitivity of initial solution of traditional Newton-Raphson algorithm and loss of simulation precision due to simplification of model. High-quality initial solution is quickly obtained through the piecewise linear equivalent model, which provides an optimal initial condition for iteration of the detailed model, significantly reduces the total iteration number of nonlinear solution, and improves the solving efficiency; application of the detailed model ensures the simulation precision and avoids loss of precision of the simplified model; the transient adaptive process further realizes dynamic balance of efficiency and precision, enhances the convergence performance and numerical stability of nonlinear iteration, and is suitable for high-precision and efficient simulation of complex electrical systems.

[0048] Advantages

[0049] By implementing the layered precision adaptive nonlinear simulation iteration method provided by the application, the following technical effects are achieved:

[0050] (1) A two-stage nonlinear iteration framework is proposed, which quickly obtains an initial solution through a low-precision piecewise linear model and accurately solves a real solution through a high-precision detailed model. The first stage quickly converges through the low-complexity characteristic of the piecewise linear model to obtain an initial solution close to the real solution; the second stage solves the real solution through the high-precision characteristic of the detailed model starting from the initial solution. This strategy combines the advantages of fast convergence of the simplified model and high precision of the detailed model, solves the defects of a single model, significantly reduces the total iteration number of nonlinear solution while ensuring the simulation precision, and improves the solving efficiency.

[0051] (2) In transient simulation, an adaptive iteration process is selected according to the closeness of the initial solution to the accurate solution: when the initial solution is close enough to the accurate solution, the high-precision detailed model process is directly called; when the deviation is large, the complete two-stage process is used. This mechanism avoids unnecessary low-precision stage calculation when the initial solution is close to the real solution, optimizes the calculation efficiency of transient simulation; at the same time, for the case where the deviation is large, the two-stage process is used to ensure the satisfaction of high-precision requirement, realizing dynamic balance of efficiency and precision in transient simulation.

[0052] (3) The density of the segmentation point is dynamically adjusted through the nonlinear strength of the nonlinear function of the element, solving the problem of imbalance between linearization error and calculation overhead caused by fixed segmentation of the traditional piecewise linear model. The model maintains high linearization precision in the strong nonlinear region and reduces the calculation complexity in the weak nonlinear region, so that the solution of the low-precision stage is closer to the real solution of the high-precision model, providing a better initial condition for subsequent high-precision iteration, and realizing the balance between precision and efficiency of the low-precision model.

[0053] (4) Using the historical iteration deviation data of the low-precision model and the high-precision model, a linear feedback model is established to correct the solution of the low-precision model as the initial solution of the high-precision model in real time. This strategy reduces the initial deviation between the low-precision solution and the high-precision true solution, reduces the number of iterations in the high-precision stage; at the same time, the reduction of the initial deviation reduces the risk of Newton-Raphson iteration divergence or numerical overflow caused by the initial value deviating too far, and improves the numerical stability and solving efficiency of nonlinear iteration. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to make the above-mentioned layered precision adaptive nonlinear simulation iteration method of the application more obvious and easy to understand, the drawings needed in the specific embodiments of the application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0055] Figure 1 The method flowchart of the present application is shown;

[0056] Figure 2 The iteration flowchart of the piecewise linear model is shown;

[0057] Figure 3 The iteration flowchart of the detailed model is shown;

[0058] Figure 4 The system parallel architecture flowchart is shown. DETAILED DESCRIPTION

[0059] Embodiment 1:

[0060] A layered precision adaptive nonlinear simulation iteration method is provided, and the method flowchart is as shown in Figure 1 , which comprises:

[0061] S1, obtaining the netlist file, simulation parameters and current step length of the simulation system, based on the time-varying characteristics of the nonlinear characteristics of the elements and the sensitivity of the simulation target parameters to the element model precision, classifying the elements with high-order nonlinear characteristics into element group G, and constructing a low-precision equivalent model layer and a high-precision detailed model layer for the element group G;

[0062] The time-varying characteristics of the nonlinear characteristics of the elements include the change of the nonlinear coefficient caused by the temperature drift;

[0063] The sensitivity of the simulation target parameters to the element model precision includes that the sensitivity of the switch loss calculation to the model precision of the switching element is higher than that of the passive element;

[0064] S2, based on the low-precision equivalent model layer, using Newton-Raphson algorithm for first-stage iteration, as Figure 2The Jacobian matrix and the right end item are updated according to the step length, and the initial solution vector is obtained by solving the matrix equation until a low-precision threshold based on the convergence speed of the first stage is met, and if the convergence speed is faster than a preset value, the threshold is reduced to reduce the number of iterations of the subsequent high-precision layer;

[0065] The updating frequency of the Jacobian matrix according to the step length is based on a linearization error threshold of the low-precision model, and the Jacobian matrix is updated when the linearization error exceeds the threshold.

[0066] S3, based on the high-precision detailed model layer, the initial solution vector is used as the initial solution for the second stage iteration, as Figure 3 The Jacobian matrix and the right end item are updated according to the step length, and the initial solution vector is obtained by solving the matrix equation until a low-precision threshold based on the convergence speed of the first stage is met, and if the convergence speed is faster than a preset value, the threshold is reduced to reduce the number of iterations of the subsequent high-precision layer;

[0067] The nonlinearity of the high-precision model includes the rate of change of the slope of the exponential model.

[0068] The nonlinearity of the high-precision model includes the rate of change of the slope of the exponential model.

[0069] S4, according to the target accurate solution vector obtained by the second stage iteration, the simulation step is updated and the above steps are repeated to realize the transient simulation of the nonlinear system.

[0070] The element model in the low-precision equivalent model layer is selected from: a piecewise linear approximation model, a low-order polynomial fitting model, a simplified model based on neural network compression, or a fuzzy logic simplified model, wherein the training data of the neural network compression model comes from the historical simulation data of the high-precision detailed model.

[0071] The simplified model based on neural network compression reduces the computational complexity by pruning or quantization.

[0072] The classification of the element G group also includes the functional priority of the element in the simulation system and the non-negligibility of the nonlinear characteristics.

[0073] In the Newton-Raphson algorithm of the first stage iteration, the updating logic of the Jacobian matrix is: calculating the linearization error of the low-precision model, i.e. the deviation of the low-precision model output from the high-precision model output, and when the deviation exceeds the linearization error threshold, the Jacobian matrix is updated; in the Newton-Raphson algorithm of the second stage iteration, the updating logic of the Jacobian matrix is: calculating the rate of change of the derivative of the high-precision model, such as the rate of change of the derivative of the exponential model with respect to the input variable, and when the rate of change exceeds the derivative change threshold, the Jacobian matrix is updated.

[0074] The linearization error threshold is preset by a user or a simulation system.

[0075] The adaptive adjustment formula of the low-precision threshold is:

[0076]

[0077] In the formula, is the adjusted low-precision threshold; is the initial low-precision threshold; is an adjustment coefficient, is the actual convergence speed of the first-stage iteration; is a preset convergence speed;

[0078] The adaptive adjustment formula of the high-precision threshold is:

[0079]

[0080] In the formula, is the adjusted high-precision threshold; is the initial high-precision threshold; is an adjustment coefficient, is the nonlinearity strength of the high-precision model; is a preset nonlinearity strength.

[0081] Before the initial solution vector is input to the second-stage iteration, a cross-layer error compensation step is further included: an error compensation model is established based on historical iteration error data of the low-precision equivalent model layer and the high-precision detailed model layer, and the initial solution vector is corrected by using the model to reduce the initial solution deviation from the low-precision layer to the high-precision layer.

[0082] The nonlinear system simulation is a high-frequency switching simulation of a power electronic converter, wherein:

[0083] The low-precision equivalent model layer adopts an ideal switching model of a switching tube, ignoring the conduction voltage drop and the switching time, and is used for fast tracking of the conduction and cutoff states of the switching tube;

[0084] The high-precision detailed model layer adopts a SPICE model of the switching tube, containing the conduction voltage drop, the switching time and the parasitic parameters, and is used for accurate calculation of the conduction loss and the cutoff loss of the switching tube.

[0085] A layered precision adaptive nonlinear simulation iteration system is also provided, and a parallel architecture flowchart of the system is as shown in Figure 4 The system includes:

[0086] ​​The model layering module is configured to classify elements with high-order nonlinear characteristics into an element G group based on time-varying characteristics of the nonlinear characteristics of the elements and precision sensitivity of a simulation target parameter, and to construct a low-precision equivalent model layer and a high-precision detailed model layer.

[0087] The first iteration module is configured to perform first-stage iteration on the low-precision equivalent model layer by using a Newton-Raphson algorithm to obtain an initial solution vector, wherein the update frequency of a Jacobian matrix is based on a linearization error threshold of the low-precision model.

[0088] The second iteration module is configured to perform second-stage iteration on the high-precision detailed model layer by using the initial solution vector as an initial solution to obtain a target precise solution vector, wherein the update frequency of the Jacobian matrix is based on the nonlinear strength of the high-precision model, and the iteration step length is adaptively adjusted based on the nonlinear strength.

[0089] The threshold adjustment module is configured to adaptively adjust the low-precision threshold based on the first-stage convergence speed, and to adjust the high-precision threshold based on the nonlinear strength of the high-precision model.

[0090] The error compensation module is configured to establish an error compensation model based on historical iteration error data of the low-precision layer and the high-precision layer, and to correct the initial solution vector to reduce cross-layer deviation.

[0091] The model layering module further includes a time-varying characteristic monitoring unit configured to monitor the time-varying characteristics of the nonlinear characteristics of the elements in real time, and to dynamically adjust the classification of the element G group.

[0092] The first iteration module and the second iteration module adopt a hybrid parallel computing architecture.

[0093] The first iteration module adopts a data parallel mode, and the iteration tasks of the low-precision model are distributed to multiple low-performance computing nodes, and each node processes low-precision model calculation of a group of elements.

[0094] The second iteration module adopts a task parallel mode, and the iteration tasks of the high-precision model are distributed to high-performance computing nodes, and each node processes calculation of a high-precision model.

[0095] The resource scheduling unit is configured to dynamically adjust the number of high-performance computing nodes of the second iteration module according to the convergence speed of the first-stage iteration, and if the first-stage convergence speed is fast, the number of computing nodes of the second iteration module is increased to speed up the iteration speed of the high-precision layer.

[0096] Embodiment 2:

[0097] To solve the problem of large linearization error and the inability to adapt to the dynamic changes of nonlinear characteristics of components caused by fixed segmentation points in traditional piecewise linear model, an adaptive piecewise linear model based on nonlinear strength is proposed. By calculating the second derivative of the nonlinear function of the component, the number and position of the segmentation points are dynamically adjusted. The stronger the nonlinearity of the region, the denser the segmentation, in order to minimize the linearization error; the weaker the nonlinearity of the region, the sparser the segmentation, in order to reduce the amount of calculation. This model not only ensures the linearization accuracy, but also avoids unnecessary computational overhead caused by fixed segmentation.

[0098] Take the exponential nonlinear model of diode as an example, its current and voltage characteristics are:

[0099]

[0100] In the formula, is the current and voltage characteristics; is the reverse saturation current; is the ideal factor, reflecting the non-ideal characteristics of PN junction; is the thermal voltage; is the voltage across the diode; is the temperature.

[0101] Calculate the second derivative to reflect the nonlinearity strength:

[0102]

[0103] Take the maximum value of the second derivative in the simulation interval:

[0104]

[0105] In the formula, is the nonlinear strength quantization index; is the lower limit value of the simulation voltage interval; is the upper limit value of the simulation voltage interval; is the lower limit value of the working temperature interval; is the upper limit value of the working temperature interval.

[0106] Calculate the number of segmentation points:

[0107]

[0108] In the formula, is the number of segmentation points; is the minimum segmentation number; is the voltage variation range; is the temperature sensitivity coefficient; is the temperature variation range.

[0109] Divide the simulation interval into segments, each segment is a linear function fitting, wherein, is the approximation function of the i-th linear segment in the piecewise linear model; is the slope of the i-th segment; is the intercept.

[0110] Verification shows that in the case of obtaining similar average error as the above-mentioned embodiment, compared with fixed segmentation, the linearization error of adaptive segmentation is reduced by 45%, the number of first-stage iterations is reduced by 30%, the convergence time is shortened by 25%, and the deviation of the initial solution of the second stage from the high-precision solution is reduced by 50%. The results show that by dynamically adjusting the number and position of the segmentation points according to the nonlinearity, the linearization error of the low-precision model is significantly reduced, the accuracy of the first-stage iterative solution is improved, the more nonlinear the region, the more dense the segmentation, and the linearization accuracy of the key region is ensured; the less nonlinear the region, the sparser the segmentation, and unnecessary calculation overhead is avoided. This adaptive strategy makes the solution of the low-precision model closer to the true solution of the high-precision model, lays a better initial condition for the second-stage high-precision iteration, effectively shortens the overall iteration period, and at the same time, takes into account the calculation efficiency and solution quality of the low-precision stage.

[0111] Embodiment 3:

[0112] In view of the problem of large initial deviation and many iterations in the second stage caused by directly using the solution of the low-precision model as the initial solution of the high-precision model in the traditional two-stage iteration, an initial solution optimization strategy based on cross-layer error feedback is proposed. The deviation between the solutions of the low-precision model and the high-precision model in the first few iterations is used to establish a linear feedback model to correct the solution of the current low-precision model in real time, so that the corrected initial solution is closer to the true solution of the high-precision model, thereby reducing the number of iterations in the second stage and the risk of numerical overflow.

[0113] In the i-th iteration, record the low-precision model solution , , the corresponding high-precision model solution , , calculate the deviation: , ,

[0114]

[0115]

[0116]

[0117] The relationship between the error and the change amount of the low-precision solution is fitted by linear regression:​​​

[0118]

[0119] wherein, is the initial solution correction; is the error adjustment coefficient; is the current low-precision model solution; is the previous low-precision model solution; is the offset.

[0120] Substitute the current low-precision solution into the above formula to obtain the corrected initial solution: , and take as the initial solution of the high-precision model to perform the second-stage iteration.

[0121] The low-precision solution is directly used as the initial solution of the high-precision model, and the performance index of the optimized initial solution through the error feedback model is compared as shown in Table 1.

[0122] Table 1, performance index comparison summary

[0123]

[0124] Verification shows that in the case of obtaining an average error similar to the above-mentioned embodiment, compared with the uncorrected initial solution, the deviation of the corrected initial solution from the high-precision solution is reduced by 60%, the number of second-stage iterations is reduced by 40%, the convergence time is shortened by 35%, and the numerical overflow probability is reduced from 15% to 3%. The results show that by establishing a linear feedback model to correct the low-precision model solution in real time according to the solution deviation between the low-precision model and the high-precision model in the first few iterations, the initial deviation between the low-precision solution and the high-precision solution is greatly reduced. The corrected initial solution is closer to the true solution of the high-precision model, so that the second-stage iteration can start with a better initial value, significantly reducing the number of high-precision iterations; at the same time, the reduction of the initial deviation reduces the risk of numerical overflow caused by the initial value deviating too far from the true solution, improves the numerical stability of the nonlinear iteration, and further balances the simulation accuracy and solving efficiency.

Claims

1. A hierarchical accuracy adaptive nonlinear simulation iterative method, characterized in that, include: Obtain the component model set of the simulation system, and divide the component model into a low-precision equivalent model layer and a high-precision detailed model layer. The low-precision equivalent model layer is used to simplify the high-order nonlinear characteristics of the components, and the high-precision detailed model layer is used to describe the precise nonlinear characteristics of the components. The first solution matrix is ​​constructed based on the low-precision equivalent model layer, and the Newton-Rafaelson algorithm is used for the first stage of iteration to obtain the initial solution vector. The convergence condition of the first stage of iteration is that the solution vector satisfies the preset low-precision threshold. An error compensation model is established based on the historical iteration error data of the low-precision equivalent model layer and the high-precision detailed model layer, and the initial solution vector is corrected using the error compensation model. Based on the high-precision detailed model layer and the initial solution vector, a second solution matrix is ​​constructed, and a second-stage iteration is performed to obtain the target accurate solution vector. The convergence condition of the second-stage iteration is that the solution vector satisfies a preset high-precision threshold. The preset low-precision threshold is dynamically adjusted based on the convergence speed of the first-stage iteration; the preset high-precision threshold is dynamically adjusted based on the nonlinear intensity of the high-precision detailed model layer; the convergence speed of the first-stage iteration is faster than that of the second-stage iteration, and the solution vector accuracy of the second-stage iteration is higher than that of the first-stage iteration.

2. The method according to claim 1, characterized in that: The criteria for dividing the component model into a low-precision equivalent model layer and a high-precision detailed model layer include the nonlinear characteristic order of the component, the sensitivity of the simulation results to the component parameters, or the functional weight of the component in the simulation system.

3. The method according to claim 1, characterized in that: The component models in the low-precision equivalent model layer are piecewise linear approximation models, low-order polynomial fitting models, fuzzy logic simplification models, or adaptive piecewise linear models.

4. The method according to claim 3, characterized in that: The adaptive piecewise linear model dynamically adjusts the number and position of segmentation points based on the nonlinearity index of the element's nonlinear function; where regions with higher nonlinearity have denser segmentation points, and regions with lower nonlinearity have sparser segmentation points.

5. The method according to claim 1, characterized in that: In the first stage of the Newton-Rafaelson algorithm iteration, the Jacobian matrix is ​​updated based on the linearization error of the low-precision model. When the deviation between the output of the low-precision model and the output of the high-precision model exceeds the linearization error threshold, the Jacobian matrix is ​​updated. In the second-stage iterative Newton-Rafaelson algorithm, the Jacobian matrix is ​​updated based on the rate of change of the nonlinear derivative of the high-precision model. When the rate of change of the nonlinear derivative exceeds the derivative change threshold, the Jacobian matrix is ​​updated.

6. The method according to claim 1, characterized in that: The dynamic adjustment is achieved through an adaptive formula, which calculates the threshold adjustment amount based on the degree to which the convergence speed deviates from the preset value or the degree to which the nonlinear intensity deviates from the preset intensity.

7. A hierarchical accuracy adaptive nonlinear simulation iterative system, characterized in that: The system is implemented based on the method of any one of claims 1-6, comprising: The model layering module is used to obtain the set of component models of the simulation system and divide the component models into a low-precision equivalent model layer and a high-precision detailed model layer. The low-precision equivalent model layer is used to simplify the high-order nonlinear characteristics of the components, and the high-precision detailed model layer is used to describe the precise nonlinear characteristics of the components. The first iteration module is used to construct a first solution matrix based on the low-precision equivalent model layer, and to perform a first-stage iteration using the Newton-Rafaelson algorithm to obtain an initial solution vector. The convergence condition of the first-stage iteration is that the solution vector satisfies a preset low-precision threshold. The second iteration module is used to construct a second solution matrix based on the high-precision detailed model layer and the initial solution vector, and to perform a second-stage iteration to obtain the target accurate solution vector. The convergence condition of the second-stage iteration is that the solution vector satisfies a preset high-precision threshold. The convergence judgment module is used to determine whether the solution vectors of the first stage iteration and the second stage iteration satisfy the corresponding preset thresholds respectively. The first iteration module and the second iteration module adopt a parallel computing architecture, wherein the computing tasks of the first iteration module are allocated to low-performance computing nodes, and the computing tasks of the second iteration module are allocated to high-performance computing nodes.

8. The system according to claim 7, characterized in that: The model layering module is also used to receive model accuracy preference parameters input by the user and adjust the granularity of the division of the low-precision equivalent model layer and the high-precision detailed model layer.

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