Complex system simulation resolving method based on mixed gradient search

Abstract

The invention discloses a complex system simulation resolving method based on hybrid gradient search, which aims at high-performance simulation resolving requirements of a system model under an explicit mechanism and implicit model hybrid modeling strategy, and provides a complex system simulation resolving method based on hybrid gradient search under a mechanism description specification based on data and mechanism mixing. The method comprises the following three main steps: a solution path automatic optimization step based on constraint qualitative information, a differential item automatic conversion step based on a robust Euler method, and a grey box system solution step based on mixed gradient search, and adaptively establishes a solution path of a system-level mechanism model. And a high-precision grey box calculation guarantee is provided for a simulation task of a hybrid modeling strategy.

Description

Technical Field

[0001] The invention relates to a complex system simulation and solution method, in particular to a complex system simulation and solution method based on hybrid gradient search. Background Art

[0002] With the current large-scale and continuous operation of equipment in the fields of aviation, aerospace, nuclear power, etc., the high-quality operation capability of equipment is becoming more and more important, and digital twins based on mechanism models have provided a highly interpretable and reliable strategy for monitoring the operation status of equipment. However, due to the increasing coupling of boundary conditions of different mechanism units within the equipment, the high-fidelity model that digital twins rely on has become more and more difficult to build.

[0003] Specifically, there are two main strategies for the mechanism modeling process of complex equipment at present, namely, the simplified modeling method based on explicit mechanism and the proxy modeling method based on implicit model. The simplified modeling method based on explicit mechanism is represented by bond graph, which aims to normalize the representation structure of multi-domain mechanisms through basic laws such as energy conservation, and further integrate the explicit / implicit constraints of each mechanism unit with the help of multi-domain common variables such as generalized energy to construct a simplified mechanism model at the equipment system level. The proxy monitoring method based on implicit model is represented by Kriging interpolation modeling method, which aims to collect sufficient data through unit experiments or equivalent simulations, and construct a numerical model based on polynomial isomodal interpolation.

[0004] However, although the simplified model based on explicit mechanism can effectively realize the system-level collation modeling of multi-domain signals and mechanisms, it is difficult to achieve high-precision characterization of strong nonlinear units at the local detail level, especially for complex mechanisms such as motor torque and output efficiency, battery charge state and open circuit voltage, it is difficult to directly construct an explicit mechanism description method. Although the proxy model based on implicit model can meet the high-fidelity characterization requirements of local mechanisms, the data-driven modeling method is still difficult to directly meet the modeling requirements of complex equipment for system-level equipment digital twins due to the scarcity of actual equipment operation data and the limited sensor layout. How to combine the strategic advantages of explicit multi-domain modeling and implicit high-precision modeling to build a universal simulation and solution framework for data and mechanism hybrid modeling is a key task to break through the current bottleneck of complex equipment digital twin applications. Furthermore, the hybrid strategy also makes it impossible for the modeling method to require complex mechanism constraints to be converted into a recursive relationship from input to output, which further limits the universal implementation of the hybrid modeling strategy on different complex equipment. Therefore, compared with the technical problems at the modeling level, how to build an autonomous solution mechanism for the hybrid model and improve the degree of autonomy of the hybrid modeling strategy at the simulation level, thereby eliminating the strict characterization requirements of the modeling process, is the real core of breaking through the high-quality digital twin technology of complex equipment.

[0005] Based on the engineering requirements of the above-mentioned data and mechanism hybrid simulation and solution, the present invention proposes a complex system simulation and solution method based on a hybrid gradient search strategy, which aims to standardize the information entry 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 the simulation tasks of the hybrid modeling strategy. Summary of the invention

[0006] In order to solve the problem of difficulty in simulating and solving system models under a hybrid modeling strategy of explicit mechanism and implicit model, the present invention proposes a simulation and solving method for complex equipment based on a hybrid gradient search strategy. By improving the autonomous solving capability at the simulation level and reducing the constraint characterization requirements at the modeling level, a more general mechanism model guarantee is provided for the digital twin tasks of complex equipment based on a data-mechanism hybrid modeling strategy.

[0007] The complex equipment simulation solution method is mainly aimed at medium and large equipment with complex internal mechanisms and high twin accuracy requirements. Specifically, the complex equipment simulation solution method based on the hybrid gradient search strategy is mainly based on the mechanism characterization specification of the mixture of data and mechanism, including the automatic optimization step of the solution path based on the constrained qualitative information, the automatic transformation step of the differential term based on the robust Euler method, and the gray box system solution step based on the hybrid gradient search.

[0008] The characteristics of the present invention are:

[0009] (1) The complex equipment simulation solution method is oriented to the task characteristics of the hybrid modeling strategy at the simulation level, and can achieve high-performance solution of internal simulation signals based on positive gray box constraint relationships, 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 to 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 and solution method 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 digital twin difficulties caused by the complexity of the equipment structure at the simulation level. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 Simulating and solving complex system processes based on hybrid gradient search

[0013] Figure 2Automatically optimize the process for solving paths based on qualitative information of constraints

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

[0015] Figure 4 Gray box system solution process based on hybrid gradient search DETAILED DESCRIPTION

[0016] A complex system simulation solution method based on hybrid gradient search provided by the present invention is described in detail below with reference to the accompanying drawings.

[0017] The present invention provides a complex system simulation and solution method based on hybrid gradient search. The complex system simulation and solution method based on hybrid gradient search is aimed at the high-fidelity system-level digital twin requirements of complex equipment. On the basis of the data-mechanism hybrid modeling strategy, it aims to realize a universal simulation and solution mechanism under real-time excitation for multi-signal gray box systems characterized by data-mechanism hybrids, and break through the existing application bottleneck of digital twins of complex equipment at the simulation level.

[0018] The complex system simulation solution method based on hybrid gradient search is mainly based on the mechanism characterization specification of data and mechanism mixing, including the solution path automatic optimization step based on constraint qualitative information, the differential term automatic transformation step based on robust Euler method, and the gray box system solution step based on hybrid gradient search. Figure 1 As shown, the mechanism characterization specification based on the mixture of data and mechanism is responsible for clarifying the mechanism information required at the simulation level, thereby effectively separating the two specific tasks of unit modeling of local mechanism and system solution of overall mechanism. On the basis of the mechanism characterization specification, the automatic optimization step of the solution path automatically analyzes the two aspects of simulation signal and constraint relationship based on constraint qualitative information calculation, and clarifies the coupling relationship between each signal and each constraint in the solution process; the automatic transformation step of differential terms 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 level; the gray box system solution step is based on the hybrid gradient search method to realize 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 mixture of data and mechanism

[0020] The mechanism characterization specification based on the mixture of data and mechanism mainly defines three basic specification contents, namely the basic type of functional unit, the internal variable definition specification and the constraint characterization specification, so as to normalize the mechanism characterization process of multi-functional units of complex equipment based on ontology constraints and meet the basic model information required for subsequent simulation solution steps.

[0021] The basic types of functional units mainly include source units, transfer elements, dissipation elements, and detection elements. The source unit mainly corresponds to external excitations of the system such as voltage sources and current sources. Considering that in the simulation field represented by thermodynamics, there may be certain complex constraints on the excitation side itself (for example, the steam generator water supply unit needs to supplement the pressure and energy flow information based on the water supply material flow and temperature on the input side according to the saturation assumption), the external excitation and the relevant parameters defining the complex constraint excitation on the input side are all used as configurable parameters, and the excitation received in the actual system model is used as the parameter to be solved, so as to meet the general definition requirements of the excitation side. The transfer element and dissipation element correspond to energy transfer 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 input and output sides of the element at the corresponding energy type are used as the parameters to be solved for defining the interaction between product elements. The remaining parameters such as density, specific enthalpy, etc. that participate in the dynamic solution during the solution process are used as parameters to be solved inside the product, and the parameters such as impedance and capacitive reactance that describe the inherent performance of the functional unit are used as configurable parameters. The detection element corresponds to a measurement unit of a local signal value such as a current measurement point and a voltage measurement point. Considering the complex measurement processes such as unit changes and equivalent measurements inside the measurement unit, it needs to be accurately characterized.

[0022] The internal variable definition specification mainly includes three types: external parameters to be solved, internal parameters to be solved and configurable inherent parameters. When characterizing a functional unit, the external parameters to be solved and the internal parameters to be solved involved in the unit must be registered, that is, the parameter names of all parameters to be solved are filled in the form of a list, so as to provide the unit's internal readable identification of the parameters to be solved for the subsequent constraint characterization steps. The configurable inherent parameters mainly include two forms: function and numerical value. The configurable parameters in the form of function are mainly responsible for introducing the externally constructed local proxy model (such as the temperature-saturation pressure model of the steam chamber, the torque-output efficiency model of the motor), while the numerical model is mainly responsible for the performance status related to the product itself (such as impedance, capacitance, etc.) in the explicit mechanism model. The instantiation description is oriented to the specific product, thereby realizing the initialization integration of the hybrid strategy mechanism in the simulation stage based on the connectivity relationship of the external parameters to be solved.

[0023] The constraint characterization specification mainly splits the unit mechanism into multiple dimensions for constraint characterization, including qualitative constraint relationships and quantitative constraint mechanisms. The qualitative constraint relationship characterization is mainly responsible for defining the participation relationship of the parameters to be solved in each constraint dimension, that is, registering the list of parameters to be solved for each constraint dimension, and the filled parameters to be solved must use the parameter names agreed upon in the internal variable definition declaration stage. If the constraint relationship definition of the dimension depends on the parameters to be solved, fill in the list of parameters to be solved of the constraint dimension; otherwise, do not fill in the irrelevant parameters to be solved. The quantitative constraint mechanism characterization is mainly responsible for providing a quantitative expression of the participation relationship of the list of parameters to be solved in each constraint dimension, and the expression only involves the explicit operation logic between the parameters to be solved and the configurable inherent parameters, so as to use the explicit mechanism as the framework and embed the implicit proxy model in the configurable function in the form of function, so that the model form input by the simulation solution side meets the data-mechanism hybrid modeling requirements for the functional unit level.

[0024] 2. Automatic optimization steps of 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 between each parameter to be solved and each constraint dimension during the solution process through the list of parameters to be solved registered by constraint dimension by constraint dimension, thereby determining the search priority of the constraint dimension and the parameters to be solved in the subsequent gray box solution process, and automatically optimizes the parameters to be solved and the constraint dimensions entered in any order manually into a better solution path that meets the needs of the solution process.

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

[0028] The initial construction of the parameter-constraint dimension relationship matrix to be solved is directly defined by the list of parameters to be solved registered by each constraint dimension. Specifically, this step first expands and sorts the parameters to be solved according to the connection relationship. 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 serial number]_[connection output side interface serial number]_[connection input side unit serial number]_[connection input side interface serial number]_ext", and the internal parameter is defined as "[parameter internal name][_diff(if it belongs to the differential term)]_[unit serial number]_inn", and sorts them in the order of the differential terms of the parameters to be solved that need to be differentiated, the original terms of the parameters to be solved that need to be differentiated, and the non-differential parameters to be solved, ensuring that the arrangement order of the differential terms of the parameters to be solved that need to be differentiated and the original terms of the parameters to be solved that need to be differentiated are consistent in their respective subsequences, thereby constructing the system-wide variable identification and serial number to be solved. Then, the parameter-constraint dimension relationship matrix to be solved is constructed according to the obtained sequence number of the global variables to be solved, that is:

[0029]

[0030] ②Solution priority generation steps

[0031] The solution priority generation step is based on the parameter-constraint dimension relationship matrix to be solved. 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 completing the initialization of the priority part of the constraint dimension and the parameter to be solved, the solution priority generation step further generates and updates the priority area based on the parameter-constraint dimension relationship matrix to be solved, that is: first, according to the corresponding row of the current constraint dimension priority in the parameter-constraint dimension relationship matrix to be solved, the difference set of the variables that are not 0 in each row and the parameters with the priority of the parameter to be solved is loaded into the priority of the parameter to be solved as the next priority parameter to be solved; then, based on the parameters with the priority of the parameter to be solved, the constraint dimension that is not 0 in each column is found, and the difference set between it and the priority constraint dimension that has been entered is used as the constraint dimension of the next priority, and at the same time, all the matrix units where the parameters with the priority of the parameter to be solved in the corresponding row of the current constraint dimension are set to 0; finally, check whether the parameters and constraints to be solved have all completed the iteration, and exit the iteration process if the check passes. Through the above-mentioned solving priority generation step, the constraint dimensions and the parameters to be solved input by the user have realized the filtering of the relationship matrix between the parameters to be solved and the constraint dimensions and the determination of their respective priorities.

[0032] 3. Automatic transformation steps of differential terms based on robust Euler method

[0033] The automatic transformation 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 series under constraints, thereby effectively avoiding the simulation failure risk introduced by the excitation side 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 the subsequent gray box system solution step through a better initial position.

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

[0035] ①Simulation step initial position estimation step

[0036] The simulation step initial position estimation step is mainly realized by the prediction function of the double exponential linear smoothing method, namely:

[0037]

[0038] Where: y - represents the value of the non-differential parameter to be solved obtained in the previous simulation step, x and y represent the values ​​of the differential parameter to be solved and the non-differential parameter to be solved in this simulation step, It represents the differential value of the parameter to be solved in this simulation step. and It represents the prior differential value of the parameter to be solved estimated by double exponential linear interpolation update in the previous simulation step.

[0039] ② Quasi-static constraint construction steps

[0040] The quasi-static constraint construction step is mainly responsible for converting the time-dependent system information into a quasi-static solution path and problem. The quasi-static transformation step of the solution path information is mainly responsible for integrating the solution path information of the required differential term and the corresponding differential term, that is:

[0041]

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

[0043] The quasi-static transformation step of the problem solving is mainly responsible for defining the parameters to be differentiated based on the differentiation of the parameters to be differentiated, thereby getting rid of the uncertain operations introduced by the differential constraints in the system solving process. Specifically, the quasi-static transformation step of the problem solving is implemented based on the robust Euler method, that is:

[0044]

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

[0046] ③Signal trend subsequent update steps

[0047] The subsequent update step of the signal trend is mainly responsible for updating the a priori trend value required for the transfer between simulation steps, which is achieved through the update step of double exponential parameter linear interpolation, namely:

[0048]

[0049] Where: and Represents the prior trend value after the current simulation step is updated; and Represents the updated posterior smoothed value of the current simulation step; and Represents the updated prior trend value of the previous simulation step; and Represents the updated a posteriori smoothing value of the previous simulation step; β is the numerical smoothing coefficient to achieve the robustness of the Euler method solution.

[0050] 4. Gray box system solution steps based on hybrid gradient search

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

[0052] ① Unadapted constrained gradient search step

[0053] The unadapted constraint gradient search step first searches for constraint dimensions that exceed the simulation accuracy requirement based on the current quasi-static parameter value to be solved, and then obtains the parameters to be solved involved in realizing the partial dimensional constraints through the parameter to be solved-constraint dimension relationship matrix. The selected parameters to be solved are realized by the Gaussian-fastest gradient descent method, that is:

[0054]

[0055] Where: pinv represents pseudo-inverse operation; represents the Jacobian matrix operation; f C Represents the mechanism constraint definition under the selected local constraint dimensions and local parameters to be solved; represents the approximate exact line search operation. The Jacobian matrix operation is implemented by the difference method, that is:

[0056]

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

[0058] The approximate exact line search operation is iterated by a heuristic binary search method. The approximate exact line search operation first determines the initial optimal search step length by a two-sided backtracking method and defines the initial search range, namely:

[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] Where: θ bt With s bt represents the initial step and expansion coefficient of the two-sided backtracking method; h represents the line search problem to be optimized; θ 0 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 through a heuristic dichotomy, namely:

[0063]

[0064] Where: θ cRepresents the estimated optimal position in the current iteration. If the estimated optimal position is less than the function value of the start and end positions, the start and end positions are updated to the position where the smaller value of the start and end positions is located and the estimated optimal position; if the estimated optimal position function is between the function values ​​of the start and end positions, the line search range is updated with the smaller value of the start and end positions updated as the center and the general distance of the smaller value of the start and end positions updated to the estimated optimal position as the radius; if the estimated optimal position is greater than the function value of the start and end positions, the two new line search ranges are searched with "updated to the start and end positions" as the center and the general distance of the start and end positions updated to the estimated optimal position as the radius, and the function minimum position of the search result is taken as the search result. The number of search branches of this type is controlled by the branch upper limit to avoid excessive waste of computing resources. Once the function value is less than the expected search accuracy or the search range is less than the minimum search range, the iterative search ends, and the minimum value of the function in the search process is the approximate and accurate search result output in the end.

[0065] If the search result of the unadapted constrained gradient search step is the current optimal solution, the subsequent steps in the current iteration step will not be executed, the optimal solution will be updated directly, and the current search result will be used as the next iteration result; otherwise, the subsequent steps in the current iteration step will be executed.

[0066] ② Constrained gradient search step

[0067] The constraint-by-constraint gradient search step is executed when the function value of the unadapted constraint gradient search step does not decrease, 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 unadapted constraint dimension one by one in the order of constraint dimension priority from high to low, that is:

[0068]

[0069] When the above-mentioned constraint-by-constraint gradient search step completes the search of each unadapted constraint dimension, the unadapted dimension after the search will be further verified, and the a priori calibration will be completed through the unadapted constraint gradient search step. If the search result is better than the current result, the optimal solution is updated, and the current search result is used as the next iteration result; otherwise, the optimal solution is not updated, and the better solution of the two solutions of the unadapted constraint gradient search step and the constraint-by-constraint gradient search step is selected as the next iteration result.

Claims

1. A complex system simulation solution method based on hybrid gradient search, characterized by: The complex system simulation and solution method based on hybrid gradient search is aimed at the high-performance simulation and solution requirements of system models under the hybrid modeling strategy of explicit mechanism and implicit model. It reduces the constraint characterization requirements at the modeling level by improving the solution autonomy at the simulation level, and utilizes the multi-threshold information contained in the parameter fault detection method. It is mainly based on the mechanism characterization specification of the mixture of data and mechanism, including the automatic optimization step of the solution path based on the qualitative information of the constraint, the automatic transformation step of the differential term based on the robust Euler method, and the gray box system solution step based on hybrid gradient search.

2. According to claim 1, the complex system simulation solution method based on hybrid gradient search is characterized by: The complex system simulation and solution method is based on a hybrid mechanism characterization specification of data and mechanism, which includes three basic specification contents: basic types of functional units, internal variable definition specifications, and constraint characterization specifications. It particularly defines three types of internal variable definition specifications: external parameters to be solved, internal parameters to be solved, and configurable inherent parameters, as well as two content constraint characterization specifications: qualitative constraint relationships and quantitative constraint mechanisms, so that the model form input on the simulation and solution side meets the data-mechanism hybrid modeling requirements for modeling at the functional unit level.

3. According to claim 1, the complex system simulation solution method based on hybrid gradient search is characterized by: The complex system simulation solution method comprises a mechanism characterization specification step based on a mixture of data and mechanism. This step mainly includes two main steps: initial construction of the relationship matrix between the parameters to be solved and the constraint dimension, and generation of the solution priority. The step is responsible for analyzing the dependency relationship between each parameter to be solved and each constraint dimension during the solution process through the list of parameters to be solved registered by each constraint dimension, thereby determining the search priority of the constraint dimension and the parameters to be solved in the subsequent gray box solution process, and automatically optimizing the parameters to be solved and the constraint dimensions entered in any order manually into a better solution path that meets the needs of the solution process.

4. According to claim 1, the complex system simulation solution method based on hybrid gradient search is characterized by: The complex system simulation and solution method includes an automatic conversion step of differential terms based on the robust Euler method, which mainly includes three main steps: initial position estimation of simulation steps, construction of quasi-static constraints, and subsequent update of signal trends. The traditional Euler method is improved by double exponential linear interpolation, thereby effectively improving the trend smoothness of the simulation timing, avoiding the risk of simulation failure introduced by excitation-side disturbances and solution errors, and reducing the time cost of subsequent gray-box system solution steps through a better initial position.

5. According to claim 1, the complex system simulation solution method based on hybrid gradient search is characterized by: The complex system simulation and solution method includes a gray box system solution step based on hybrid gradient search, which mainly includes two steps: gradient search without adapted constraints and gradient search by constraints. It is responsible for iteratively searching for the optimal quasi-static parameter value to be solved for the current simulation step based on the quasi-static constraint system and the initial position predicted a priori.

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