A complex system simulation solving method based on hybrid gradient search

Abstract

The application discloses a complex system simulation solving method based on a hybrid gradient search, and aims at the high-performance simulation solving demand of a system model under a mixed modeling strategy of an explicit mechanism and an implicit model. Under a mechanism description specification based on data and mechanism mixing, three main steps of an automatic optimization step of a solving path based on constraint qualitative information, an automatic transformation step of a differential term based on a robust Euler method and a gray-box system solving step based on a hybrid gradient search are adopted to adaptively establish a solving path of a system-level mechanism model, and high-precision gray-box solving guarantee is provided for a simulation task of the mixed modeling strategy.

Description

Technical Field

[0001] This invention relates to a method for simulating and solving complex systems, and more particularly to a method for simulating and solving complex systems based on hybrid gradient search. Background Technology

[0002] With the increasing scale and continuity of equipment operation in fields such as aviation, aerospace, and nuclear power, the high-quality operation capability of equipment is becoming increasingly important. Digital twins based on mechanistic models have provided a highly interpretable and reliable strategy for monitoring the operational status of equipment. However, as the boundary conditions of different mechanistic units within the equipment become increasingly coupled, the construction of the high-fidelity models upon which digital twins rely becomes significantly more difficult.

[0003] Specifically, there are currently two main strategies for mechanistic modeling of complex equipment: simplified modeling methods based on explicit mechanisms and surrogate modeling methods based on implicit models. Simplified modeling methods based on explicit mechanisms, represented by bond graphs, aim to standardize the representation structure of multi-domain mechanisms through fundamental laws such as energy conservation. They further integrate the explicit / implicit constraints of each mechanism unit using common variables from multiple domains, such as generalized energy, to construct a simplified mechanistic model at the equipment system level. Surrogate monitoring methods based on implicit models, represented by Kriging interpolation modeling, aim to collect sufficient data through unit experiments or equivalent simulations to construct a numerical model based on polynomial modal interpolation.

[0004] However, while simplified models based on explicit mechanisms can effectively achieve system-level modeling of signals and mechanisms across multiple domains, they struggle to accurately characterize strongly nonlinear units at the local detail level. This is especially true for complex mechanisms such as motor torque and output efficiency, and battery charge state and open-circuit voltage, where it is difficult to directly construct explicit mechanistic representations. While surrogate models based on implicit models can achieve high-fidelity characterization of local mechanisms, data-driven modeling methods still cannot directly meet the modeling needs of complex equipment at the system-level digital twin level due to the scarcity of actual equipment operating data and the limited sensor layout. Therefore, combining the advantages of explicit multi-domain modeling and implicit high-precision modeling to construct a generalized simulation and solution framework that integrates data and mechanism modeling is a key task in overcoming the current bottlenecks in the application of digital twins for complex equipment. Furthermore, the hybrid strategy also prevents modeling methods from requiring complex mechanistic constraints to be transformed into recursive relationships from signal input to output, further limiting the generalizability of the hybrid modeling strategy across different complex equipment. Therefore, compared to the technical issues at the modeling level, the real core of breaking through the high-quality digital twin technology for complex equipment lies in how to construct an autonomous solution mechanism for hybrid models and improve the autonomy of hybrid modeling strategies at the simulation level, thereby eliminating the stringent requirements for the modeling process.

[0005] Based on the engineering requirements of the above-mentioned data and mechanism hybrid simulation solution, this invention proposes a complex system simulation solution method based on a hybrid gradient search strategy. The aim is to standardize the information input mechanism of local mechanisms under different strategies, adaptively establish the solution path of the system-level mechanism model, and provide high-precision gray-box solution guarantee for simulation tasks of hybrid modeling strategies. Summary of the Invention

[0006] To address the challenge of simulating and solving system models under a hybrid modeling strategy combining explicit mechanisms and implicit models, this invention proposes a method for simulating and solving complex equipment based on a hybrid gradient search strategy. By enhancing the autonomous solution capability at the simulation level and reducing the constraint characterization requirements at the modeling level, this method provides a more generalized mechanism model guarantee for digital twin tasks of complex equipment based on a hybrid data-mechanism modeling strategy.

[0007] The aforementioned simulation solution method for complex equipment is primarily aimed at medium to large-sized equipment with complex internal mechanisms and high twin accuracy requirements. Specifically, the complex equipment simulation solution method based on a hybrid gradient search strategy is mainly based on a mechanism characterization specification that combines data and mechanism, including an automatic optimization step for the solution path based on constraint qualitative information, an automatic transformation step for differential terms based on the robust Euler method, and a gray-box system solution step based on hybrid gradient search.

[0008] The features of this invention are:

[0009] (1) The complex equipment simulation solution method described above is oriented towards the task characteristics of the hybrid modeling strategy at the simulation level. It can achieve high-performance solution of internal simulation signals based on positive definite gray box constraint relationship, thereby reducing the recursive characterization requirements of traditional simulation methods for the coupling mechanism between multiple signals.

[0010] (2) The complex equipment simulation solution method is oriented towards the task characteristics of the hybrid modeling strategy at the simulation level. Through the differential system solution method based on the robust Euler method, the automatic transformation of the time-dependent system to the quasi-static system is realized, thereby meeting the twin requirements of the actual complex equipment for the time-dependent mechanism.

[0011] (3) The complex equipment simulation solution method described above is oriented towards the task characteristics of the hybrid modeling strategy at the simulation level. Through the automatic optimization technology of the solution path, it improves the adaptive solution capability for the multi-coupling constraint relationship of complex equipment, thereby solving the difficulties of digital twins caused by the complexity of equipment structure at the simulation level. Attached Figure Description

[0012] Figure 1 Simulation solution process for complex systems based on hybrid gradient search

[0013] Figure 2Automatic optimization process for solution paths based on constraint qualitative information

[0014] Figure 3 Automatic transformation process for differential terms based on robust Euler method

[0015] Figure 4 Solution process for gray box system based on hybrid gradient search Detailed Implementation

[0016] The following description, in conjunction with the accompanying drawings, details a method for simulating and solving complex systems based on hybrid gradient search provided by the present invention.

[0017] This invention provides a simulation solution method for complex systems based on hybrid gradient search. This method addresses the high-fidelity system-level digital twin requirements of complex equipment. Based on a data-mechanism hybrid modeling strategy, it aims to achieve a generalized simulation solution mechanism under real-time excitation for multi-signal gray-box systems characterized by a data-mechanism hybrid approach, thus overcoming existing application bottlenecks in the simulation layer of complex equipment digital twins.

[0018] The complex system simulation solution method based on hybrid gradient search is mainly based on a mechanism characterization specification that combines data and mechanism. It includes an automatic optimization step for the solution path based on constraint qualitative information, an automatic transformation step for differential terms based on robust Euler's method, and a gray-box system solution step based on hybrid gradient search. For example... Figure 1 As shown, the mechanism characterization specification based on data and mechanism hybridization is responsible for clarifying the mechanism information required at the simulation level, thereby effectively separating the two specific tasks of unit modeling of local mechanisms and system solution of the overall mechanism. Based on the mechanism characterization specification, the automatic solution path optimization step automatically analyzes the simulation signals and constraint relationships based on constraint qualitative information calculation, clarifying the coupling relationship between each signal and constraint in the solution process; the automatic differential term transformation step transforms the time-dependent system of complex equipment into a quasi-static system based on the robust Euler method, while ensuring the solution stability of the simulation task at the time domain; the gray-box system solution step, based on the hybrid gradient search method, realizes the generalized and efficient solution function of complex nonlinear equations in quasi-static form, thereby realizing the gray-box system simulation task of complex equipment after hybrid strategy modeling.

[0019] 1. Mechanism characterization specification based on a combination of data and mechanism

[0020] The mechanism characterization specification based on data and mechanism hybridization mainly defines three basic specifications: basic types of functional units, internal variable definition specifications, and constraint characterization specifications. This standardizes the mechanism characterization process of complex equipment multi-functional units based on ontological constraints, thus satisfying the basic model information required for subsequent simulation and calculation steps.

[0021] The basic types of functional units mainly include four types: source units, transmission elements, dissipation elements, and detection elements. The source units primarily correspond to external excitations such as voltage sources and current sources. However, considering that in simulation fields such as thermodynamics, the excitation side itself may have certain complex constraints (e.g., a steam generator feedwater unit, based on the saturation assumption, needs to supplement pressure and energy flow information on the input side based on feedwater mass flow rate and temperature), the relevant parameters of external excitations and the excitations defining complex constraints on the input side are all treated as configurable parameters, while the excitations received within the actual system model are treated as parameters to be solved, thus meeting the general definition requirements of the excitation side. The transmission elements and dissipation elements correspond to energy transmission or conversion units such as converters and motors, and energy dissipation or storage units such as resistors and capacitors, respectively. The potential and flow of the corresponding energy type on the input and output sides of the elements are used as parameters to be solved for the interaction between product elements. Other parameters, such as density and specific enthalpy, which participate in the dynamic solution process, are treated as parameters to be solved within the product. Parameters describing the inherent performance of the functional unit, such as impedance and capacitive reactance, are treated as configurable parameters. The aforementioned detection element corresponds to the measurement unit for local signal values ​​such as current measurement points and voltage measurement points. Considering the complex measurement processes such as unit changes and equivalent measurements within the measurement unit, it is necessary to accurately characterize it.

[0022] The aforementioned internal variable definition specifications mainly include three types: external unsolved parameters, internal unsolved parameters, and configurable intrinsic parameters. When characterizing functional units, all external and internal unsolved parameters involved in the unit must be registered, i.e., the parameter names of all unsolved parameters must be filled in a list format, thus providing readable internal identifiers for the unsolved parameters in subsequent constraint characterization steps. Configurable intrinsic parameters mainly include two forms: functional and numerical. Functional configurable parameters are primarily responsible for introducing externally constructed local proxy models (such as the temperature-saturation pressure model of a steam chamber, or the torque-output efficiency model of a motor), while numerical models are primarily responsible for instantiating the performance conditions (such as impedance, capacitive reactance, etc.) related to the product itself within the explicit mechanism model for specific product-specific instantiation, thereby achieving the initial integration of the hybrid strategy mechanism in the simulation phase based on the connectivity relationships of the external unsolved parameters.

[0023] The constraint characterization specification primarily breaks down unit mechanisms into multi-dimensional constraint characterization, encompassing both qualitative constraint relationships and quantitative constraint mechanisms. The qualitative constraint relationship characterization mainly defines the participation relationships of the parameters to be solved in each constraint dimension. Specifically, it registers a list of parameters to be solved for each constraint dimension, and the entered parameters must use the parameter names agreed upon during the internal variable definition declaration phase. If the constraint relationship definition of a dimension depends on the parameters to be solved, then the list of parameters to be solved for that constraint dimension is entered; otherwise, irrelevant parameters are not entered. The quantitative constraint mechanism characterization mainly provides quantitative expressions for the participation relationships of the list of parameters to be solved in each constraint dimension. These expressions only involve explicit computational logic between the parameters to be solved and configurable intrinsic parameters. This uses explicit mechanisms as a framework and embeds implicit proxy models within configurable functions in functional form, ensuring that the model input from the simulation solution side meets the data-mechanism hybrid modeling requirements at the functional unit level.

[0024] 2. Automatic Optimization Steps for Solution Path Based on Constraint Qualitative Information

[0025] The automatic optimization step of the solution path based on constraint qualitative information mainly analyzes the dependency relationship between each parameter to be solved and each constraint dimension in the solution process by registering a list of parameters to be solved for each constraint dimension. This determines the search priority of constraint dimensions and parameters to be solved in the subsequent gray box solution process, and automatically optimizes the parameters to be solved and constraint dimensions entered manually in arbitrary order into a better solution path that meets the needs of the solution process.

[0026] The automatic optimization steps for the solution path based on constraint qualitative information are as follows: Figure 2 As shown, it mainly includes two steps: initial construction of the parameter-constraint dimension relationship matrix to be solved and generation of solution priority.

[0027] ① Initial construction steps of the relationship matrix between parameters to be solved and constraint dimensions

[0028] The initial construction of the parameter-constraint dimension relationship matrix is ​​directly defined through the list of parameters to be solved registered for each constraint dimension. Specifically, this step first names, expands, and sorts the parameters to be solved according to their connection relationships. The naming expansion defines the name of the external parameter to be solved as "[e(potential) / f(flow)][_diff(if it belongs to the differential term)]_[connection output side unit number]_[connection output side interface number]_[connection input side unit number]_[connection input side interface number]_ext", and the internal parameter as "[parameter internal name][_diff(if it belongs to the differential term)]_[unit number]_inn". The parameters are sorted in the order of differential terms of the parameters to be differentiated, original terms of the parameters to be differentiated, and non-differentiable parameters, ensuring that the order of differential terms and original terms of the parameters to be differentiated is consistent in their respective subsequences, thereby constructing the global identifiers and numbers of the variables to be solved in the system. Then, based on the obtained global indices of the variables to be solved, a parameter-constraint dimension relationship matrix is ​​constructed, i.e.:

[0029]

[0030] ② Steps for generating solution priorities

[0031] The solution priority generation step is based on the parameter-constraint dimension relationship matrix. Specifically, the solution priority generation step first uses the constraint dimension where the source element is located as the starting highest priority constraint dimension. After initializing the priority parts of the constraint dimensions and the parameters to be solved, the solution priority generation step further performs priority region generation and update based on the parameter-constraint dimension relationship matrix. That is: first, according to the current constraint dimension priority in the corresponding row of the parameter-constraint dimension relationship matrix, the difference between the non-zero variables in each row and the input parameter priority parameters is used as the next priority parameter to be solved and loaded into the priority of the parameter to be solved; then, based on the parameters with input parameters priority, the non-zero constraint dimensions in each column are found, and the difference between them and the input priority constraint dimensions is used as the next priority constraint dimension. At the same time, all matrix cells containing parameters with input parameters priority in the current constraint dimension's corresponding row are set to 0; finally, it is checked whether all parameters and constraints have been iterated. If the check passes, the iteration process is exited. Through the aforementioned priority generation step, the constraint dimensions and parameters to be solved entered by the user have already achieved the filtering of the parameter-constraint dimension relationship matrix and the determination of their respective priorities.

[0032] 3. Steps for Automatic Transformation of Differential Terms Based on Robust Euler Method

[0033] The automatic conversion step of differential terms based on the robust Euler method mainly improves the traditional Euler method through double exponential linear interpolation. On the one hand, the simulation process can effectively improve the trend smoothness of the simulation time sequence under constraints, thereby effectively avoiding the simulation failure risk introduced by excitation disturbance and solution error. On the other hand, the simulation process can improve the trend prediction of the approximate position of the simulation result through the double exponential linear interpolation method, thereby reducing the time cost of subsequent gray box system solution steps through a better initial position.

[0034] The automatic transformation steps of differential terms based on robust Euler method are as follows: Figure 3 As shown, the main steps include initial position estimation in the simulation step, quasi-static constraint construction, and subsequent signal trend update. The subsequent gray box system solution steps based on hybrid gradient search will be performed between the quasi-static constraint construction and the subsequent signal trend update.

[0035] ① Simulation step: Initial position estimation step

[0036] The initial position estimation step of the simulation step is mainly achieved through the prediction function of the double exponential linear smoothing method, that is:

[0037]

[0038] In the formula: y - represents the value of the non-differential unsolved parameter obtained in the previous simulation step, and x and y represent the values ​​of the differential unsolved parameter and the non-differential unsolved parameter in this simulation step. This represents the differential value of the parameter to be solved that needs to be differentiated in this simulation step. and This represents the prior differential value of the parameter to be solved, which was estimated by updating the biexponential linear interpolation in the previous simulation step.

[0039] ② Quasi-static constraint construction steps

[0040] The quasi-static constraint construction step is mainly responsible for transforming time-dependent system information into quasi-static solution paths and problems. The quasi-static transformation step of the solution path information is mainly responsible for integrating the solution path information of the differential term and its corresponding differential term, i.e.:

[0041]

[0042] Where: n d With n nd D represents the number of parameters to be solved by differentiation and the number of parameters to be solved by non-differentiation. s The quasi-static unsolved parameters (differentiated and non-differentiated unsolved parameters) - constraint dimension relationship matrix after transformation; varOrd s The solution path represents the quasi-static parameters to be solved.

[0043] The quasi-static transformation step of the problem-solving process is mainly responsible for defining the parameters to be differentiated based on the differential of the parameters to be solved, thereby escaping the uncertainties introduced by the differential constraints during the system solution process. Specifically, the quasi-static transformation step of the problem-solving process is implemented based on the robust Euler method, that is:

[0044]

[0045] In the formula: α represents the differential value of the parameter to be solved in the previous simulation step; α represents the differential smoothing coefficient to achieve robustness of Euler method solution; f represents the quantitative constraint mechanism of each constraint dimension.

[0046] ③ Subsequent update steps for signal trends

[0047] The subsequent signal trend update step is mainly responsible for updating the prior trend value required for inter-step transfer in the simulation. This is achieved through a double exponential parameter linear interpolation update step, namely:

[0048]

[0049] In the formula: and This represents the prior trend value updated in the current simulation step; and Represents the posterior smoothed value after the current simulation step update; and This represents the prior trend value updated in the previous simulation step; and β represents the posterior smoothing value updated in the previous simulation step; β is the numerical smoothing coefficient that enables robustness of the Euler method solution.

[0050] 4. Solution steps for gray-box systems based on hybrid gradient search

[0051] The solution steps for the gray box system based on hybrid gradient search are as follows: Figure 4 As shown, it is mainly responsible for iteratively searching for the optimal quasi-static solution parameter values ​​(differentiated and non-differentiated solution parameters) of the current simulation step based on the initial position of the quasi-static constraint system and prior prediction. The iterative sub-steps of the gray box system solution include two steps: gradient search without adaptive constraints and gradient search for each constraint. When the gradient search without experimental constraints cannot reduce the overall residual, it is transformed into two steps of gradient search for each constraint; otherwise, it directly enters the next iteration.

[0052] ① Unfitted constraint gradient search steps

[0053] The aforementioned unfitted constraint gradient search step first searches for constraint dimensions that exceed the simulation accuracy requirements based on the current quasi-static values ​​of the parameters to be solved. Then, it obtains the parameters to be solved for achieving these dimensional constraints through the parameter-constraint dimension relationship matrix. The selected parameters to be solved are obtained using the Gaussian-steepest gradient descent method, i.e.:

[0054]

[0055] In the formula: pinv represents the pseudo-inverse operation; f represents the operation of finding the Jacobian matrix; C This represents the definition of mechanistic constraints under the selected local constraint dimensions and local parameters to be solved; This represents an approximate exact line search operation. The Jacobian matrix calculation is implemented using the finite difference method, i.e.:

[0056]

[0057] In the formula: ε represents the approximate step size used in the differential operation of the difference method fitting.

[0058] The approximate exact line search operation is performed iteratively using a heuristic binary search method. The approximate exact line search operation first determines the initial optimal search step size and defines the initial search range using a two-sided backtracking method, i.e.:

[0059]

[0060] θ s =min(θ) 0 / s bt ,s bt θ 0 );θ e =max(θ) 0 / s bt ,s bt θ 0 )

[0061] In the formula: θ bt With s bt θ represents the initial steps and expansion coefficient of the two-sided backtracking method; h represents the line search problem to be optimized; θ 0 This represents the initial optimal step size.

[0062] Then, under the control of the maximum number of iterations, the minimum search range, and the expected search accuracy, an iterative search is performed using a heuristic binary search method, namely:

[0063]

[0064] In the formula: θ cThis represents the estimated optimal position in the current iteration. If the estimated optimal position is less than the function value of the initial and final positions, the initial and final positions are updated to the position of the smaller value of the initial and final positions plus the estimated optimal position. If the estimated optimal position lies between the function values ​​of the initial and final positions, the line search range is updated with the smaller value of the updated initial and final positions as the center and the general distance between the smaller value of the updated initial and final positions and the estimated optimal position as the radius. If the estimated optimal position is greater than the function value of the initial and final positions, a search is performed on two new line search ranges, each centered on the updated initial and final positions and with the general distance between the updated initial and final positions and the estimated optimal position as the radius. The minimum function value of the search results is taken as the search result. The number of search branches for this type is controlled by the branch limit to avoid excessive waste of computational resources. Once the function value is less than the expected search precision or the search range is less than the minimum search range, the iterative search ends, and the minimum function value during the search process is used as the final output approximate accurate search result.

[0065] If the search result of the unconstrained gradient search step is due to the current optimal solution, then the subsequent steps in the current iteration step are not executed, the optimal solution is directly updated, and the current search result is used as the result of the next iteration; otherwise, the subsequent steps in the current iteration step are executed.

[0066] ② Constraint-by-constraint gradient search steps

[0067] The constraint-by-constraint gradient search step is executed when the function value of the unfitted constraint gradient search step has not decreased, and is responsible for further expanding the search range through multiple iterations. Specifically, the constraint-by-constraint gradient search step will first perform a line search operation on the unfitted constraint dimensions in descending order of constraint priority, that is:

[0068]

[0069] After the constrained gradient search step completes the search for each unfitted constraint dimension, the unfitted dimensions are further verified through the unfitted constraint gradient search step for verification calibration. If the search result is better than the current result, the optimal solution is updated, and the current search result is used as the result of the next iteration; otherwise, the optimal solution is not updated, and the better solution between the unfitted constraint gradient search step and the constrained gradient search step is selected as the result of the next iteration.

Claims

1. A method for solving complex system simulation based on hybrid gradient search, characterized in that: The complex system simulation solving method based on the hybrid gradient search faces the high-performance simulation solving demand of the system model under the mixed modeling strategy of explicit mechanism and implicit model, improves the solving autonomy of the simulation level of complex equipment, reduces the constraint description demand of the modeling level, utilizes the multi-threshold information contained in the parameter fault detection method, and is based on the mechanism description specification mixed with data and mechanism, and includes the automatic optimization step of the solving path based on the constraint qualitative information, the automatic transformation step of the differential item based on the robust Euler method, and the gray-box system solving step based on the hybrid gradient search; The mechanism description specification mixed with data and mechanism of the complex system simulation solving method includes three basic specification contents of the basic type of functional unit, internal variable definition specification, and constraint description specification. The basic type of functional unit includes four types of source unit, transmission element, dissipation element, and detection element. The source unit corresponds to the external excitation of the voltage source and the current source, and the related parameters of the external excitation and the definition of the input side complex constraint excitation are regarded as configurable parameters, and the actual system model received excitation is regarded as a to-be-solved parameter. The automatic optimization step of the solving path based on the constraint qualitative information of the complex system simulation solving method includes two steps of initial construction of the to-be-solved parameter-constraint dimension relationship matrix and generation of the solving priority, is responsible for analyzing the dependency relationship between each to-be-solved parameter and each constraint dimension in the solving process through the to-be-solved parameter list registered by each constraint dimension, and determining the search priority of the constraint dimension and the to-be-solved parameter in the subsequent gray-box solving process, so as to automatically optimize the to-be-solved parameter and the constraint dimension manually inputted in an arbitrary order into a more optimal solving path suitable for the solving process; The automatic transformation step of the differential item based on the robust Euler method of the complex system simulation solving method includes three steps of initial position estimation of the simulation step, construction of the quasi-static constraint, and subsequent update of the signal trend, improves the traditional Euler method through double exponential linear interpolation, thereby effectively improving the trend smoothness of the simulation time sequence, avoiding the simulation failure risk introduced by the excitation side disturbance and the solving error, and reducing the time cost of the subsequent gray-box system solving step through a more optimal initial position. The grey-box system solving step based on the mixed gradient search of the complex system simulation solving method comprises an unconstrained gradient search step and a constraint-by-constraint gradient search step, is responsible for searching for a constraint dimension exceeding a simulation precision requirement based on a current quasi-static to-be-solved parameter value through the unconstrained gradient search step, obtaining a to-be-solved parameter involved in achieving the constraint dimension through a to-be-solved parameter-constraint dimension relationship matrix, and further executing the constraint-by-constraint gradient search step in a case where a function value of the unconstrained gradient search step does not decrease, and is responsible for performing a line search operation on the unconstrained constraint dimension in a constraint dimension priority from high to low order, and further verifying the searched unconstrained dimension after the constraint-by-constraint gradient search step completes the search of each unconstrained constraint dimension, and completing a posterior calibration through the unconstrained gradient search step; if the search result is better than a current result, then updating the optimal solution, taking the current search result as a next iteration result; otherwise, not updating the optimal solution, and selecting a better solution of the two solutions of the unconstrained gradient search step and the constraint-by-constraint gradient search step as the next iteration result.

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