Dynamic optimization and real-time correction system for simulation models of complex systems

Abstract

The present invention relates to the technical field of simulation models, and specifically discloses a dynamic optimization and real-time correction system for simulation models of complex systems, comprising: a logic framework generation module constructing a simulation model logic framework of a complex system based on all core constituent variables, causal relationship diagrams, and feedback loops of the complex system; a simulation model construction module injecting multi-source heterogeneous data of the complex system into the simulation model logic framework to generate a system dynamics simulation model of the complex system; a sensitivity analysis module identifying all sensitive variables of the system dynamics simulation model; a model optimization and correction module analyzing the stable convergence performance of the logic closed loop of the system dynamics simulation model based on all sensitive variables and the system dynamics simulation model, and optimizing and correcting the system dynamics simulation model based on the stable convergence performance of the logic closed loop to obtain a stable system dynamics simulation model; providing a more reliable basis for the analysis, prediction, and decision-making of complex systems.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation models, and in particular to a dynamic optimization and real-time correction system for simulation models oriented to complex systems. Background Art

[0002] In today's era of rapid technological advancement, complex systems are ubiquitous in various fields, such as aerospace, transportation, energy management, and ecological environments. These complex systems are composed of numerous interconnected and interacting components, and their behavior and characteristics are often highly nonlinear and uncertain. Simulation models have become indispensable tools for gaining a deeper understanding of the operating mechanisms of complex systems, predicting their future development trends, and developing effective decision-making strategies. Simulation models can be constructed to abstract and simplify complex systems and simulate their behavior under varying conditions. However, due to the inherent complexity and dynamic nature of complex systems, as well as the ever-changing external environment, traditional simulation models often fail to accurately reflect the system's true state. Therefore, dynamic optimization and real-time correction systems for simulation models of complex systems are of vital importance.

[0003] However, existing simulation modeling technologies for complex systems struggle to fully construct a complete and accurate simulation model logical framework. Due to the imperfections of this logical framework, the accuracy and reliability of the model are significantly compromised when injecting multi-source heterogeneous data to generate a system dynamics simulation model. The generated simulation model lacks effective sensitivity analysis tools, making it impossible to fully identify sensitive variables within the model, resulting in a lack of understanding of the model's key factors. Without in-depth analysis of the stable convergence performance of the model's logical closed loop based on sensitive variables, targeted optimization and correction of the model is impossible. This makes it difficult for the simulation model to adapt to the dynamic changes of complex systems and accurately simulate system behavior, severely impacting research and decision support capabilities for complex systems.

[0004] Therefore, the present invention proposes a dynamic optimization and real-time correction system for simulation models of complex systems. Summary of the Invention

[0005] The present invention provides a dynamic optimization and real-time correction system for simulation models of complex systems. The system can construct an accurate simulation model logic framework based on the structure and operating characteristics of the complex system, and inject multi-source heterogeneous data into it to generate a system dynamics simulation model. By performing sensitivity analysis on the model, key sensitive variables are identified, and then the logical closed-loop stable convergence performance of the model is analyzed and optimized based on these variables, so that the simulation model can more accurately simulate the behavior of the complex system, improve the accuracy of the prediction and the reliability of the decision-making. With the continuous development of technologies such as big data and artificial intelligence, the dynamic optimization and real-time correction system for simulation models of complex systems will be more widely used in various fields, promoting the scientific and intelligent development of complex system research and management.

[0006] The present invention provides a complex system-oriented simulation model dynamic optimization and real-time correction system, comprising:

[0007] The logical framework generation module is used to parse out all the core components of the complex system, the causal relationship diagram, and the feedback loop, and build the simulation model logical framework of the complex system based on all the core components of the complex system, the causal relationship diagram, and the feedback loop;

[0008] The simulation model building module is used to inject multi-source heterogeneous data of complex systems into the simulation model logic framework to generate a system dynamics simulation model of the complex system;

[0009] Sensitivity analysis module, used to perform local sensitivity analysis and global sensitivity analysis on the system dynamics simulation model and identify all sensitive variables of the system dynamics simulation model;

[0010] The model optimization and correction module is used to analyze the stable convergence performance of the logic closed loop of the system dynamics simulation model based on all sensitive variables and the system dynamics simulation model, and optimize and correct the system dynamics simulation model based on the stable convergence performance of the logic closed loop to obtain a stable system dynamics simulation model.

[0011] Optionally, all core constituent variables include system state variables, speed variables, and auxiliary variables.

[0012] Optionally, it also includes:

[0013] The verification input module is used to input multiple sets of initial conditions and historical parameters of the complex system into the simulation model logic framework of the complex system, and solve the simulation through numerical integration to obtain the model output under the corresponding initial conditions and historical parameters;

[0014] The verification output module is used to compare the model output under each set of initial conditions and historical parameters with the corresponding historical output to obtain the verification accuracy of the simulation model logic framework;

[0015] The verification judgment module is used to rebuild a new simulation model logic framework of the complex system when the verification accuracy of the simulation model logic framework is less than the preset accuracy threshold, and stop rebuilding the simulation model logic framework until the verification accuracy of the latest simulation model logic framework is not less than the preset accuracy threshold.

[0016] Optionally, the multi-source heterogeneous data of the complex system includes system state variables acquired in real time through IoT devices deployed in the complex system.

[0017] Optionally, a sensitivity analysis module includes:

[0018] The elasticity coefficient analysis submodule is used to analyze the rate of change of all system output variables when only a single core component variable produces a small fluctuation based on the system dynamics simulation model, and calculate the elasticity coefficient of each core component variable when a small fluctuation occurs based on the rate of change of all system output variables when only each core component variable produces a small fluctuation;

[0019] The Sobol variance decomposition submodule is used to determine the variance proportion explained by each core component variable individually and the total effect index including all interactions with the corresponding core component variables based on the Sobol variance decomposition method;

[0020] The local sensitivity analysis submodule is used to analyze the local sensitivity value of each core component variable based on the proportion of variance explained by each core component variable and the elasticity coefficient when small fluctuations occur;

[0021] A global sensitivity analysis submodule is used to analyze the global sensitivity value of each core component variable based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables;

[0022] The sensitivity variable screening submodule is used to screen out all sensitive variables of the system dynamics simulation model from all core constituent variables based on the local sensitivity value and global sensitivity value of each core constituent variable.

[0023] Optionally, the local sensitivity analysis submodule includes:

[0024] A normalization processing unit is used to normalize the variance proportions explained by all core component variables individually and the elasticity coefficients when small fluctuations occur, and obtain the normalized variance proportions and normalized elasticity coefficients of each core component variable;

[0025] The weighted operation unit is used to perform weighted operation on the normalized variance ratio and normalized elasticity coefficient of each core component variable to obtain the local sensitivity value of each core component variable.

[0026] Optionally, a global sensitivity analysis submodule includes:

[0027] An interaction coefficient obtaining unit is used to construct an equation group based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables, and to solve the interaction coefficients between all core component variables based on the equation group;

[0028] Relationship network building unit, used to build a full variable relationship network based on the interaction coefficients between all core component variables;

[0029] A link matrix building unit is used to analyze all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network, and to build a relationship link matrix for each core component variable based on all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network;

[0030] A global link weight analysis unit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the relationship link matrix of each core component variable;

[0031] The global sensitivity value determination unit is used to take the ratio of the global link weight of each core component variable in the full variable relationship network and the core coefficient of the corresponding core component variable in the full variable relationship network as the global sensitivity value of the corresponding core component variable.

[0032] Optionally, the global link weight analysis unit includes:

[0033] The path propagation influence analysis subunit is used to determine the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable based on the relationship link matrix of each core component variable; based on the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable, calculate the path propagation influence of the corresponding core component variable;

[0034] The eigenvector influence analysis subunit is used to take the ratio of the maximum eigenvalue to all eigenvalues ​​obtained after eigendecomposition of the relationship link matrix of each core component variable as the eigenvector influence of the corresponding core component variable;

[0035] A comprehensive influence value analysis subunit is used to calculate the comprehensive influence value of each core component variable based on the path propagation influence and eigenvector influence of each core component variable;

[0036] The global link weight analysis subunit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the comprehensive influence value of all core component variables.

[0037] Optionally, the model optimization and correction module includes:

[0038] A logic closed loop identification submodule is used to identify all positive feedback loops and negative feedback loops of the system dynamics simulation model as logic closed loops of the system dynamics simulation model;

[0039] The state matrix construction submodule is used to linearize the complex system into state space equations based on the system dynamics simulation model and the corresponding logic closed loop, and solve the state matrix;

[0040] The model optimization and correction submodule is used to determine that the stable convergence performance of the logical closed loop of the system dynamics simulation model does not meet the requirements when the real part of the eigenvalue of all the eigenvalues ​​of the state matrix is ​​greater than 0, and to optimize and correct the system dynamics simulation model based on all sensitive variables to obtain a stable system dynamics simulation model.

[0041] Optionally, the model optimization and correction submodule includes:

[0042] Gradient analysis unit, used to analyze the gradient of the real part of all eigenvalues ​​in the state matrix with respect to a single sensitive variable;

[0043] The optimization and correction unit is used to increase the single sensitive variable with a positive gradient based on the preset change gradient table, and at the same time, reduce the single sensitive variable with a negative gradient based on the preset change gradient table, until the real parts of all eigenvalues ​​in the latest state matrix are less than 0, then stop optimizing and correcting the system dynamics simulation model to obtain a stable system dynamics simulation model.

[0044] The beneficial effects of the present invention compared to the prior art are as follows: by analyzing the core constituent variables, causal relationship diagrams and feedback loops of complex systems to construct a simulation model logic framework, the system structure is clearly sorted out, an orderly basis is provided for subsequent modeling, and it is ensured that the model can accurately reflect the internal logic of the complex system. Multi-source heterogeneous data are injected into the logical framework to generate a system dynamics simulation model, so that the model can integrate multiple data types and simulate the operating state of complex systems more comprehensively and realistically. Local and global sensitivity analysis is performed on the simulation model to identify sensitive variables, clarify the key factors that have a greater impact on the model results, and provide a precise direction for model optimization. Based on the stable convergence performance of the sensitive variables and model analysis logic closed loop, the model is optimized and corrected accordingly to improve the stability and reliability of the model, and a stable system dynamics simulation model is obtained, thereby providing a more reliable basis for the analysis, prediction and decision-making of complex systems, helping relevant personnel to better understand and manage complex systems.

[0045] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in this application document.

[0046] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0048] Figure 1 Schematic diagram of a dynamic optimization and real-time correction system for a simulation model of a complex system in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0050] like Figure 1 As shown, the present invention provides an implementation of a dynamic optimization and real-time correction system for a simulation model of a complex system, including:

[0051] The logical framework generation module is used to parse out all the core components of the complex system, the causal relationship diagram, and the feedback loop, and build the simulation model logical framework of the complex system based on all the core components of the complex system, the causal relationship diagram, and the feedback loop;

[0052] The simulation model building module is used to inject multi-source heterogeneous data of complex systems into the simulation model logic framework to generate a system dynamics simulation model of the complex system;

[0053] Sensitivity analysis module, used to perform local sensitivity analysis and global sensitivity analysis on the system dynamics simulation model and identify all sensitive variables of the system dynamics simulation model;

[0054] The model optimization and correction module is used to analyze the stable convergence performance of the logic closed loop of the system dynamics simulation model based on all sensitive variables and the system dynamics simulation model, and optimize and correct the system dynamics simulation model based on the stable convergence performance of the logic closed loop to obtain a stable system dynamics simulation model.

[0055] In this embodiment, complex systems refer to systems that are widely found in various fields such as aerospace, transportation, energy management, and ecological environment. They are composed of many interconnected and interacting parts, and their behaviors and characteristics are highly nonlinear and uncertain. For example, large water-cooled cooling systems.

[0056] In this embodiment, all core constituent variables of the complex system include state variables, speed variables, and auxiliary variables. State variables are used to describe the state of the system at a certain moment. For example, in the simulation of a large water-cooled cooling system, the water temperature in the water-cooled cooling device is a state variable. Speed ​​variables reflect the rate of change of state variables over time. For example, the growth rate of the water temperature in the water-cooled cooling device is a speed variable. Auxiliary variables are variables introduced to help describe the relationship between variables in the system. For example, in a complex system describing economic growth, in order to more clearly illustrate the relationship between investment and output, an auxiliary variable may be introduced to represent investment efficiency, which helps explain the interaction between state variables and speed variables.

[0057] In this embodiment, a causal relationship diagram for complex systems is a graphical tool for displaying the causal relationships between variables in a complex system. For example, in the power system, variables such as power generation, transmission loss, and electricity demand have causal relationships. An increase in electricity demand (the cause) may lead to an increase in power generation (the result), while also potentially increasing transmission loss (another result). A causal relationship diagram clearly displays these variables and the causal relationships between them using lines and arrows.

[0058] In this embodiment, a feedback loop in a complex system refers to a cyclical structure within the system in which changes in one variable affect the system through a series of cause-and-effect relationships. Feedback loops can be categorized as positive or negative. For example, in a population growth model, an increase in population leads to increased resource consumption and competition for living space, which in turn affects the birth and death rates. This can form a negative feedback loop, regulating the population growth rate to a certain extent. In a scientific and technological innovation system, the emergence of a new technology may attract more investment in R&D, which in turn promotes the emergence of more new technologies. This can form a positive feedback loop, accelerating the process of technological innovation.

[0059] In this embodiment, the logical framework for a simulation model of a complex system is constructed based on all of the complex system's core constituent variables, causal relationship diagrams, and feedback loops. This involves building a conceptual framework based on the core constituent variables, the causal relationships between variables displayed in the causal relationship diagram, and the structural characteristics of the feedback loops. This framework serves to guide the construction of the simulation model. For example, when constructing a simulation model for regional economic development, core constituent variables such as gross regional product (state variable), industry growth rate (speed variable), and policy support intensity (auxiliary variable) are used as nodes. A causal relationship diagram is drawn based on the input-output causal relationships between industries. The feedback loops formed by self-reinforcement (positive feedback) and regulatory mechanisms (negative feedback) in economic growth are also considered, thereby constructing a logical framework for the simulation model that reflects the inherent logical relationships of the regional economic system.

[0060] In this embodiment, multi-source heterogeneous data from a complex system is injected into the simulation model logic framework to generate a system dynamics simulation model for the complex system. This involves populating the model with data from different channels, in different formats, and with different characteristics, such as system state variables acquired in real time through IoT devices deployed in the complex system, and other multi-source heterogeneous data, such as historical statistical data and sensor data, according to the structure and relationships specified by the simulation model logic framework, to form a system dynamics simulation model capable of simulating the dynamic behavior of the complex system. For example, when constructing a system dynamics simulation model for urban traffic, real-time traffic flow data (one type of multi-source heterogeneous data) acquired by road sensors is injected into the model based on the relationships between traffic flow and variables such as traffic congestion and driving speed, as defined in the previously constructed simulation model logic framework. This generates a system dynamics simulation model capable of dynamically simulating the operation of urban traffic.

[0061] In this embodiment, the stable convergence performance of the logic closed loop of the system dynamics simulation model refers to whether the logic closed loop composed of the positive feedback loop and the negative feedback loop in the model can tend to a stable state during operation, and whether it can quickly recover to a stable state after being subjected to external interference. For example, in a system dynamics simulation model that simulates ecological balance, there are feedback loops such as changes in the number of species. If the logic closed loop of this model has good stable convergence performance, then when the number of a certain species fluctuates due to external factors (such as climate change), the model will gradually restore the number of the species and the entire ecosystem to a relatively stable state through the regulation of the feedback loop, and there will be no situation where the number of species increases indefinitely or decreases sharply, leading to the collapse of the ecosystem.

[0062] In this embodiment, the stable system dynamics simulation model is a model that has been optimized and corrected to ensure that the stable convergence performance of its logic closed loop meets the requirements. In other words, when simulating a complex system, the model can operate stably and respond reasonably and stably to changes in various internal and external factors without abnormal fluctuations or divergence. For example, when optimizing and correcting the system dynamics simulation model of the power system, by adjusting sensitive variables such as power generation power and power demand in the model, as well as analyzing and improving the logic closed loop, the model can stably simulate the operating state of the power system and accurately predict changes in power supply and demand when facing different power peaks, power generation equipment failures, etc. Such a model is a stable system dynamics simulation model, which can provide a reliable basis for decisions such as planning and scheduling of the power system.

[0063] In order to clearly define the core variable categories involved in the construction of complex system simulation models, it is further proposed that all core constituent variables include system state variables, speed variables, and auxiliary variables.

[0064] In this embodiment, system state variables are used to describe the state of a complex system at a specific moment in time. They quantify certain aspects of the system's properties. For example, for a city's water supply system, the water storage capacity in each area of ​​the city is a system state variable. These variables can intuitively display the water reserve status of different areas at a specific point in time.

[0065] In this embodiment, the velocity variable reflects how quickly the system state variable changes over time. Continuing with the example of a city water supply system, the change in water storage volume in each region per unit time (e.g., daily) is the velocity variable. It describes the dynamic trend of the system state and helps predict the system's future state.

[0066] In this embodiment, auxiliary variables are variables introduced to more clearly describe the relationship between variables in a complex system. They do not directly represent the state or rate of change of the system, but they play an auxiliary role in understanding and building system models. In the urban water supply system, it is assumed that there is a "water efficiency coefficient" as an auxiliary variable, which can be used to measure the water efficiency of different regions or different types of users. Through this auxiliary variable, the relationship between water storage volume (system state variable) and water demand changes (related to the speed variable) can be established more accurately. For example, in areas with a higher water efficiency coefficient, the water storage volume decreases relatively slowly under the same water demand, which helps to more accurately simulate and analyze the operating mechanism of the water supply system in the model.

[0067] In order to verify the accuracy of the constructed simulation model logic framework and ensure that it can effectively reflect the complex system, it is further proposed to include:

[0068] The verification input module is used to input multiple sets of initial conditions and historical parameters of the complex system into the simulation model logic framework of the complex system, and solve the simulation through numerical integration to obtain the model output under the corresponding initial conditions and historical parameters;

[0069] The verification output module is used to compare the model output under each set of initial conditions and historical parameters with the corresponding historical output to obtain the verification accuracy of the simulation model logic framework;

[0070] The verification judgment module is used to rebuild a new simulation model logic framework of the complex system when the verification accuracy of the simulation model logic framework is less than the preset accuracy threshold, and stop rebuilding the simulation model logic framework until the verification accuracy of the latest simulation model logic framework is not less than the preset accuracy threshold.

[0071] In this embodiment, multiple sets of initial conditions and historical parameters of the complex system are used to verify the logical framework of the simulation model. The initial conditions describe the state of the complex system at the beginning of the simulation. For example, when simulating an urban traffic system, the initial conditions may include the number of vehicles on each road at the start time and the initial speed limits of different road sections. Historical parameters are data collected from the past operation of the complex system, such as traffic volume and traffic accident rates at different time periods over a period of time. Multiple sets of such data can more comprehensively verify the performance of the simulation model under different circumstances.

[0072] In this embodiment, multiple sets of initial conditions and historical parameters of the complex system are input into the simulation model logic framework of the complex system, and the simulation is solved by numerical integration to obtain the model output under the corresponding initial conditions and historical parameters. This means that the prepared multiple sets of initial conditions and historical parameters are input into the constructed simulation model logic framework in sequence. Since the model of a complex system often involves a dynamic process that changes over time, numerical integration methods (such as the Euler method and the Runge-Kutta method) solve these dynamic equations to simulate the evolution of the system over time. For example, when simulating a complex system of a chemical reaction process, the concentration changes of each substance at different time points can be calculated through numerical integration based on historical parameters such as the initial reactant concentration (initial conditions) and the reaction rate. These concentration change values ​​are the model output under the corresponding initial conditions and historical parameters.

[0073] In this embodiment, the model output under corresponding initial conditions and historical parameters refers to the result obtained by numerically integrating the simulation model after inputting specific initial conditions and historical parameters. Taking the economic growth model as an example, if the initial conditions are set as GDP and population size in a particular year of a region, and the historical parameters include investment growth rates and consumption propensity of the past few years, the GDP forecasts and per capita income changes for the next several years calculated by the model are the model outputs under these initial conditions and historical parameters. These outputs reflect the model's simulation and prediction of the complex system under the given conditions.

[0074] In this embodiment, the corresponding historical output is real data generated during the past actual operation of the complex system. Continuing with the economic growth model as an example, the actual GDP value and actual change in per capita income for the relevant time period corresponding to the previously set initial conditions and historical parameters are the corresponding historical outputs. This historical data is objective and is used to compare with the model output to assess the model's accuracy.

[0075] In this embodiment, the model output under each set of initial conditions and historical parameters is compared with the corresponding historical output to obtain the verification accuracy of the simulation model's logical framework. Specifically, a specific algorithm is used to measure the degree of proximity between the model output and the historical output. For example, metrics such as the mean absolute error or root mean square error (RMSE) between the GDP forecast output by the model and the actual historical GDP value can be calculated. These error metrics can be transformed to obtain verification accuracy. If the verification accuracy is high, it indicates that the model output is close to the actual historical situation and that the model logical framework has a high degree of accuracy in simulating complex systems. Conversely, if the verification accuracy is low, it indicates that the model may have deviations and requires further improvement.

[0076] In this embodiment, the preset accuracy threshold is a pre-set criterion used to determine whether the simulation model's logical framework meets requirements. This threshold is determined based on the characteristics of the specific complex system and the expected model accuracy. For example, in some aerospace orbit simulation systems with high accuracy requirements, the preset accuracy threshold may be set very strictly, such as 0.95, and the error between the model output and historical data must be kept within a very small range. In contrast, in some macroeconomic trend simulation scenarios, the preset accuracy threshold may be relatively relaxed. When the model's verification accuracy reaches or exceeds the preset accuracy threshold (for example, 0.9), the model's logical framework meets the requirements; otherwise, the model needs to be adjusted.

[0077] In this embodiment, reconstructing a new simulation model logical framework for a complex system means that when the verification accuracy of the simulation model logical framework is less than a preset accuracy threshold, the original model logical framework needs to be redesigned and rebuilt. This may involve re-analyzing the core constituent variables, causal relationship diagrams, and feedback loops of the complex system to check whether important factors have been omitted or the relationship between variables is not accurately described. For example, when reconstructing the logical framework of the simulation model of an urban traffic system, it may be found that the impact of the new traffic policy on vehicle speed and flow has been ignored before, so relevant variables and causal relationships are added to the new logical framework, and the model is rebuilt in the hope of improving the verification accuracy of the model so that it can more accurately simulate and predict the operation of the urban traffic system.

[0078] In order to clarify the specific sources of multi-source heterogeneous data of complex systems and provide real-time and effective data support for the construction of simulation models, it is further proposed that the multi-source heterogeneous data of complex systems include system state variables obtained in real time through IoT devices deployed in complex systems.

[0079] In this embodiment, the system state variables acquired in real time through IoT devices deployed in complex systems refer to the deployment of various sensors and monitoring equipment at key locations or nodes in complex system scenarios such as aerospace, transportation, and energy management, leveraging IoT technology to collect and transmit relevant variable data reflecting the system's current state in real time. For example, in a complex smart grid system, IoT devices can be deployed at power plants, substations, transmission lines, and various power terminals. IoT devices at power plants can acquire real-time system state variables such as generator output power and operating temperature; devices on transmission lines can monitor line current, voltage, temperature, and fault conditions; and devices at power terminals can collect variables such as real-time power consumption and power usage time. These system state variables acquired in real time through IoT devices provide critical, real-time data support for building and optimizing simulation models for complex systems.

[0080] In order to comprehensively and accurately identify the sensitive variables of the system dynamics simulation model by combining multiple analysis methods, a sensitivity analysis module is further proposed, including:

[0081] The elasticity coefficient analysis submodule is used to analyze the rate of change of all system output variables when only a single core component variable produces a small fluctuation based on the system dynamics simulation model, and calculate the elasticity coefficient of each core component variable when a small fluctuation occurs based on the rate of change of all system output variables when only each core component variable produces a small fluctuation;

[0082] The Sobol variance decomposition submodule is used to determine the variance proportion explained by each core component variable individually and the total effect index including all interactions with the corresponding core component variables based on the Sobol variance decomposition method;

[0083] The local sensitivity analysis submodule is used to analyze the local sensitivity value of each core component variable based on the proportion of variance explained by each core component variable and the elasticity coefficient when small fluctuations occur;

[0084] A global sensitivity analysis submodule is used to analyze the global sensitivity value of each core component variable based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables;

[0085] The sensitivity variable screening submodule is used to screen out all sensitive variables of the system dynamics simulation model from all core constituent variables based on the local sensitivity value and global sensitivity value of each core constituent variable.

[0086] In this embodiment, causing a small fluctuation in all core component variables refers to making a relatively small change in only one core component variable (such as a state variable, speed variable, or auxiliary variable) in a system dynamics simulation model. For example, in a system dynamics model simulating enterprise production and sales, one of the core component variables is the production speed of the product (the speed variable). This production speed is subjected to a small fluctuation, such as a 1% increase or decrease, while all other core component variables remain unchanged. This allows the impact of this variable change on the entire system to be observed.

[0087] In this embodiment, the system dynamics simulation model is used to analyze the rate of change of all system output variables when only a single core component variable experiences a small fluctuation. Specifically, the model calculates and analyzes the degree of change in all system output variables (such as a company's sales and profits) when a single core component variable experiences a small fluctuation. For example, when product production speed increases by 1%, the company's sales increase by what percentage, and how profits change, are observed. The ratio of the magnitude of the change in these output variables, such as sales and profits, to the magnitude of the small fluctuation in production speed is the rate of change. By analyzing these rates of change, it is possible to understand how small changes in a single core component variable affect the system's ultimate output.

[0088] In this embodiment, the elasticity coefficient of each core component variable when it produces a small fluctuation is calculated based on the rate of change of all system output variables when only each core component variable produces a small fluctuation. The elasticity coefficient is an indicator that measures the sensitivity of one variable to the change of another variable. In this scenario, taking production speed and sales as an example, the elasticity coefficient is equal to the rate of change of sales divided by the rate of change of production speed. If a 1% increase in production speed leads to a 2% increase in sales, then the elasticity coefficient of production speed to sales is 2 (2% ÷ 1%). Each core component variable can calculate a corresponding elasticity coefficient for different system output variables, and these elasticity coefficients reflect the sensitivity of the correlation between the core component variable and the system output variable.

[0089] In this embodiment, the Sobol variance decomposition method is used to determine the proportion of variance explained by each core component variable individually (i.e., the first-order sensitivity index: a measure of the direct impact of a single variable on the output) and the total effect index (a measure of the total impact of a variable and its interactions with other variables) that includes all interactions with the corresponding core component variable. The Sobol variance decomposition method is a method used for global sensitivity analysis. In a complex system, each core component variable contributes to the total variance of the system output. The proportion of variance explained by each core component variable indicates the extent to which changes in a single core component variable contribute to the variance of the system output. For example, in an ecosystem model, the abundance of species A is a core component variable. The proportion of variance explained by this core component variable alone can indicate the extent to which changes in the abundance of species A can explain the variance of a specific indicator of the entire ecosystem (such as a biodiversity index). The total effect index considers the impact of the interactions between this core component variable and all other core component variables on the variance of the system output. This includes not only the impact of the variable itself but also the impact of its interactions with other variables.

[0090] In this embodiment, the local sensitivity value of each core component variable is a value obtained by comprehensively considering the proportion of variance explained by each core component variable individually and the elasticity coefficient when small fluctuations occur. It is used to measure the sensitivity of the core component variable to the system output within a local range (only considering the impact of the variable's own changes on the system output).

[0091] In this embodiment, the global sensitivity value of each core component variable measures the sensitivity of a core component variable to the system output, taking into account the interactions between all core component variables. It is derived based on the local sensitivity values ​​of all core component variables and the total effect index that includes all interactions with the corresponding core component variables. By constructing a system of equations to solve the interaction coefficients between the core component variables, and then building a full-variable relationship network and relationship link matrix, a series of steps are performed, taking into account factors such as the core component variable's position in the full-variable relationship network and its interactions with other variables, to ultimately determine its global sensitivity value. For example, although a core component variable may have a limited impact on the system output on its own (a moderate local sensitivity value), if it has strong interactions with multiple other key variables, its global sensitivity value may be high, indicating that it has a significant impact on the system output within the context of the entire system.

[0092] In this embodiment, based on the local sensitivity value and global sensitivity value of each core component variable, all sensitive variables of the system dynamics simulation model are screened out from all core component variables. By setting certain criteria (such as both the local sensitivity value and the global sensitivity value being above a certain threshold), variables that have a greater impact on system output, i.e., sensitive variables, can be identified from among the numerous core component variables. For example, in a system dynamics simulation model of enterprise operations, after calculating and comparing the local and global sensitivity values ​​of all core component variables, it is found that the local and global sensitivity values ​​of product price (one of the core component variables) are both very high (both greater than a preset sensitivity threshold), thus making product price a sensitive variable. These sensitive variables have a key impact on system behavior and output. Identifying them helps to optimize and analyze the system dynamics simulation model more targeted and understand the key drivers of complex systems.

[0093] In order to accurately calculate the local sensitivity value of each core component variable through normalization and weighted operations, a local sensitivity analysis submodule is further proposed, including:

[0094] A normalization processing unit is used to normalize the variance proportions explained by all core component variables individually and the elasticity coefficients when small fluctuations occur, and obtain the normalized variance proportions and normalized elasticity coefficients of each core component variable;

[0095] The weighted operation unit is used to perform weighted operation on the normalized variance ratio and normalized elasticity coefficient of each core component variable to obtain the local sensitivity value of each core component variable.

[0096] In this embodiment, the variance ratios and elasticity coefficients explained individually by all core constituent variables and when small fluctuations are generated are normalized separately to obtain the normalized variance ratios and normalized elasticity coefficients of each core constituent variable. This is because the value ranges of the variance ratios and elasticity coefficients of different core constituent variables may vary greatly, and directly comparing their contributions to local sensitivity is not very accurate. Through normalization, these values ​​can be mapped to a unified range, which is convenient for subsequent comprehensive analysis. Commonly used normalization methods such as minimum-maximum normalization are used. In this way, the normalized variance ratios and normalized elasticity coefficients of each core constituent variable under a unified scale can be obtained, which can more accurately measure their respective influences.

[0097] In this embodiment, a weighted calculation is performed on the normalized variance ratio and normalized elasticity coefficient of each core component variable to obtain a local sensitivity value for each core component variable. This comprehensively considers the contribution of the variance ratio and elasticity coefficient to the local sensitivity of the core component variable. Because the variance ratio reflects the degree to which changes in a single core component variable affect the variance of the system output, and the elasticity coefficient reflects the sensitivity of the system output variable to changes in small fluctuations of that variable, both describe the effect of the variable on the system output from different perspectives. Through averaging or weighting, for example, assuming a weight of 0.6 for the normalized variance ratio and a weight of 0.4 for the normalized elasticity coefficient, and for a core component variable with a normalized variance ratio of 0.7 and a normalized elasticity coefficient of 0.8, the local sensitivity value of this core component variable is 0.6 × 0.7 + 0.4 × 0.8 = 0.74. This local sensitivity value helps understand the relative importance of each core component variable to the system output, without considering complex interactions with other variables.

[0098] In order to deeply analyze the global sensitivity value of each core component variable through the steps of constructing equation groups, relationship networks and link matrices, a global sensitivity analysis submodule is further proposed, including:

[0099] An interaction coefficient obtaining unit is used to construct an equation group based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables, and to solve the interaction coefficients between all core component variables based on the equation group;

[0100] Relationship network building unit, used to build a full variable relationship network based on the interaction coefficients between all core component variables;

[0101] A link matrix building unit is used to analyze all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network, and to build a relationship link matrix for each core component variable based on all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network;

[0102] A global link weight analysis unit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the relationship link matrix of each core component variable;

[0103] The global sensitivity value determination unit is used to take the ratio of the global link weight of each core component variable in the full variable relationship network and the core coefficient of the corresponding core component variable in the full variable relationship network as the global sensitivity value of the corresponding core component variable.

[0104] In this embodiment, a system of equations is constructed based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables, and the interaction coefficients between all core component variables are solved based on the system of equations, for example:

[0105] The assumed core variables include: X1: generator excitation gain (control voltage); X2: load power factor (affecting reactive power demand); X3: reactive power compensation device capacity (improving voltage stability).

[0106] Outcome variable Y: distance to the critical point of voltage collapse of the power system (safety margin, unit: kV).

[0107] The local sensitivity values ​​(first-order effects) are:

[0108] Adjust X1 separately: For every 1 unit increase in excitation gain, the safety margin increases by S1=0.2kV.

[0109] Adjust X2 separately: For every 0.1 increase in power factor, the safety margin increases by S2=0.3kV.

[0110] Adjust X3 separately: For every 1Mvar increase in reactive capacity, the safety margin increases by S3=0.1kV.

[0111] The total effect index (including interaction) is:

[0112] When adjusting all variables simultaneously:

[0113] The total effect of X1 is ST1 = 0.6 kV (the actual increase is 0.6 kV, including the interaction with X2 and X3);

[0114] The total effect of X2, ST2 = 0.7 kV;

[0115] The total effect of X3 is ST3 = 0.4kV.

[0116] 3. Constructing the system of equations: Total effect = local effect + interaction effect

[0117] For variable X1: ST1=S1+S12+S13, substitute the data: 0.6=0.2+S12+S13 (1);

[0118] For variable X2: ST2=S2+S12+S23, substitute the data: 0.7=0.3+S12+S23 (2);

[0119] For variable X3: ST3=S3+S13+S23, substitute the data: 0.4=0.1+S13+S23 (3).

[0120] Then simplify by elimination, using equations (1)-(2):

[0121] 0.6-0.7=(0.2-0.3)+(S12-S12)+(S13-S23);

[0122] So: -0.1=-0.1+S13-S23⇒S13=S23(4).

[0123] Substituting S13=S23 into equation (3): 0.4=0.1+2S13⇒2S13=0.3 (5), we get S13=0.15;

[0124] Substitute into other equations in turn and gradually solve to obtain the final interaction coefficients: S12=0.25, S13=0.15, S23=0.15;

[0125] The engineering significance of the two-variable interaction (such as S12 = 0.25) is that when the excitation gain (X1) and the load power factor (X2) are increased at the same time, the synergistic effect of the two will increase the safety margin by an additional 0.25kV.

[0126] In this embodiment, a full-variable relationship network is constructed based on the interaction coefficients between all core component variables. The interaction coefficient reflects the degree and nature of the interaction between different core component variables. Taking a simulation model of an economic system as an example, the core component variables may include interest rates, inflation rates, employment rates, etc. Changes in interest rates may have an impact on inflation rates and employment rates, and the quantitative manifestation of these impacts is the interaction coefficient. The full-variable relationship network uses these core component variables as nodes and the interaction coefficients between them as edges to construct a network structure that shows the relationship between all core component variables in the system. In this network, each node (core component variable) is connected to other nodes through edges (interaction coefficients), clearly showing how the variables influence each other, helping to grasp the complex relationships between variables in a complex system from a holistic perspective.

[0127] In this embodiment, all direct link paths and interaction coefficients within each direct link path for each core component variable in the full-variable relationship network are analyzed. In the full-variable relationship network, a direct link path refers to the direct connection from a core component variable to an edge node of the full-variable relationship network. For example, in the full-variable relationship network of the economic system described above, there may be a direct link path from the "interest rate" node to the edge node "inflation rate." The interaction coefficient along this path indicates the degree to which the interest rate directly affects the inflation rate. For each core component variable, the direct connections between it and all other core component variables are identified, as well as the interaction coefficients corresponding to these connections.

[0128] In this embodiment, a relational link matrix is ​​constructed for each core component variable based on all direct link paths and all interaction coefficients in each direct link path in the full variable relational network. The relational link matrix is ​​a two-dimensional matrix, where each column element contains all interaction coefficients on a direct link path from far to near.

[0129] In this embodiment, the core coefficient of a core component variable in a full-variable relationship network (for example, the mean of the core component variable's degree centrality, betweenness centrality, and closeness centrality in the full-variable relationship network is used as the core coefficient) is an indicator used to measure the importance of a core component variable in the entire full-variable relationship network. The core coefficient may be determined based on a variety of factors, such as the number of connections (degree) between the core component variable and other variables, the extent to which it is on the critical path in the network, and the influence it has on other variables. In an ecosystem's full-variable relationship network, if a core component variable for species population is closely linked to numerous other species population variables and environmental factor variables, and its changes can trigger significant changes in a series of other variables, then its core coefficient is relatively high, indicating that it plays a key role in the dynamic changes of the entire ecosystem. The core coefficient is important in analyzing, such as calculating the global sensitivity value of core component variables, and can help better understand the position and role of each core component variable in the overall complex system.

[0130] In order to accurately calculate the global link weight of each core component variable in the full variable relationship network by analyzing the influence of the path propagation and the influence of the eigenvector, a global link weight analysis unit is further proposed, including:

[0131] The path propagation influence analysis subunit is used to determine the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable based on the relationship link matrix of each core component variable; based on the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable, calculate the path propagation influence of the corresponding core component variable;

[0132] The eigenvector influence analysis subunit is used to take the ratio of the maximum eigenvalue to all eigenvalues ​​obtained after eigendecomposition of the relationship link matrix of each core component variable as the eigenvector influence of the corresponding core component variable;

[0133] A comprehensive influence value analysis subunit is used to calculate the comprehensive influence value of each core component variable based on the path propagation influence and eigenvector influence of each core component variable;

[0134] The global link weight analysis subunit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the comprehensive influence value of all core component variables.

[0135] In this embodiment, the number of path steps between all core constituent variables that have an influence relationship with each core constituent variable and the corresponding core constituent variable and the interaction coefficient between the core constituent variables are determined based on the relationship link matrix of each core constituent variable. The relationship link matrix records the direct connection and interaction coefficient information between the core constituent variables. Taking a simple complex system model as an example, it is assumed that the core constituent variables are A, B, C, and D. It can be seen from the relationship link matrix that if there is a direct connection from A to B, its interaction coefficient is 0.5, which is a set of corresponding relationships. The number of path steps is 1 when there is a direct connection. If it is necessary to pass through B and C from A to D, that is, the path is ABCD, then the number of path steps between A and D is 3, and the interaction coefficients between A and B, B and C, and C and D can be found in the relationship link matrix respectively. This information is crucial for a comprehensive understanding of the influence path and degree between variables.

[0136] In this embodiment, the path propagation influence of the corresponding core component variable is calculated based on the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable. The number of path steps reflects the degree of indirect influence transmission, and the interaction coefficient reflects the intensity of the influence. Generally speaking, the more path steps there are, the more likely the influence will gradually weaken during the transmission process. For example, for core component variable A, variable B that has an influence relationship with it has a path step of 1 and an interaction coefficient of 0.8; variable C has a path step of 2, and the interaction coefficients are 0.6 for A and the intermediate variable, and 0.7 for the intermediate variable and C. When calculating path propagation influence, the attenuation effect of the number of path steps on the interaction coefficient may be taken into account. For example, if the path steps are weighted, assuming a weight of 1 for a path step of 1 and a weight of 0.8 for a path step of 2 (for example only), then the path propagation influence of A on B is 0.8 × 1 = 0.8, and the path propagation influence of A on C is 0.6 × 0.7 × 0.8 = 0.336. The path propagation influence of A is calculated by summing the path propagation influences corresponding to all variables that have an impact on A. This measures the comprehensive degree to which a core component variable affects other variables through different paths.

[0137] In this embodiment, the comprehensive influence value of each core component variable is calculated based on the path propagation influence and eigenvector influence of each core component variable. The eigenvector influence reflects the importance of the core component variable in the network from another perspective. It is obtained by performing eigendecomposition on the relationship link matrix and taking the ratio of the maximum eigenvalue to all eigenvalues. The path propagation influence focuses on the comprehensive consideration of the direct and indirect influence paths between variables, while the eigenvector influence considers the impact of the entire network structure on the importance of the variable. For example, the path propagation influence of the core component variable X is 0.6 and the eigenvector influence is 0.4. Assuming that these two influences are given the same weight of 0.5 (the actual weight can be adjusted according to the characteristics of the system), the comprehensive influence value of X is 0.6×0.5+0.4×0.5=0.5. The comprehensive influence value more comprehensively reflects the influence of the core component variable in the full variable relationship network, combining the specific influence paths between variables and the role of the overall network structure.

[0138] In this embodiment, the global link weight of each core component variable in the full variable relationship network is calculated based on the combined influence values ​​of all core component variables. The global link weight is used to determine the relative importance of each core component variable in the entire network. The combined influence values ​​of all core component variables are normalized so that their sum is 1, thus obtaining their respective global link weights.

[0139] In order to determine the stable convergence performance of the logic closed loop of the system dynamics simulation model by identifying the logic closed loop and building the state matrix, and to optimize and correct the model accordingly, a model optimization and correction module is further proposed, including:

[0140] A logic closed loop identification submodule is used to identify all positive feedback loops and negative feedback loops of the system dynamics simulation model as logic closed loops of the system dynamics simulation model;

[0141] The state matrix construction submodule is used to linearize the complex system into state space equations based on the system dynamics simulation model and the corresponding logic closed loop, and solve the state matrix;

[0142] The model optimization and correction submodule is used to determine that the stable convergence performance of the logical closed loop of the system dynamics simulation model does not meet the requirements when the real part of the eigenvalue of all the eigenvalues ​​of the state matrix is ​​greater than 0, and to optimize and correct the system dynamics simulation model based on all sensitive variables to obtain a stable system dynamics simulation model.

[0143] In this embodiment, all positive feedback loops and negative feedback loops of the system dynamics simulation model are identified and analyzed. In the system dynamics simulation model, the feedback loop is a key structure that reflects the cyclic influence relationship between the variables within the system. The positive feedback loop will enhance the system behavior in the direction of the original change. For example, in a business growth model, if the increase in product sales leads to more funds invested in marketing, and marketing further promotes the increase in product sales, this will form a positive feedback loop, which will drive the continuous growth of sales. The negative feedback loop will regulate the changes in the system and make the system stable. For example, in an ecosystem, when the number of a certain organism increases, its food resources will decrease, thereby limiting the continued growth of the number of the organism. This is a negative feedback loop.

[0144] In this embodiment, a complex system is linearized into state-space equations based on a system dynamics simulation model and a corresponding closed-loop logic loop, and a state matrix is ​​solved. The system dynamics simulation model describes the dynamic relationships between variables in a complex system, while the closed-loop logic loop clarifies the internal loop mechanism of the system. Linearization is a method for simplifying the analysis of complex systems, as actual complex systems are often nonlinear and difficult to process. By performing a linear approximation around a certain operating point, the complex system is converted into a state-space equation. This equation is generally expressed as y = Ax + Bu, where x is the state variable vector, u is the input variable vector, and y is the output variable vector. A is the state matrix to be solved, which reflects the dynamic relationships between the system's state variables. For example, in a simple circuit system dynamics model, combined with its closed-loop logic loop, the relationships between variables such as current and voltage are linearized to construct state-space equations, which are then solved using mathematical methods to obtain the state matrix. The state matrix is ​​crucial for analyzing system characteristics such as stability, controllability, and observability, providing a key basis for further optimizing and revising the system dynamics simulation model.

[0145] In order to accurately optimize and correct the system dynamics simulation model based on the gradient of the real part of the state matrix eigenvalue to sensitive variables according to the preset change gradient table, a model optimization and correction submodule is further proposed, including:

[0146] Gradient analysis unit, used to analyze the gradient of the real part of all eigenvalues ​​in the state matrix with respect to a single sensitive variable;

[0147] The optimization and correction unit is used to increase the single sensitive variable with a positive gradient based on the preset change gradient table, and at the same time, reduce the single sensitive variable with a negative gradient based on the preset change gradient table, until the real parts of all eigenvalues ​​in the latest state matrix are less than 0, then stop optimizing and correcting the system dynamics simulation model to obtain a stable system dynamics simulation model.

[0148] In this embodiment, the gradient of the real part of all eigenvalues ​​in the state matrix with respect to a single sensitive variable is analyzed in order to understand how a small change in the sensitive variable affects the real part of the eigenvalue of the state matrix. Mathematically, the gradient represents the rate of change of a function at a certain point. For the real part of the eigenvalue of the state matrix, it is a function of the sensitive variable. For example, assuming that the real part of a certain eigenvalue of the state matrix Re(λ) depends on the sensitive variable x, we can obtain Re(λ) / x, this value is the gradient. A positive gradient means that as the sensitive variable x increases, the real part of the eigenvalue also increases; a negative gradient means that as the sensitive variable x increases, the real part of the eigenvalue decreases. Analyzing these gradients can help identify the sensitive variables that have the greatest impact on the stability of the state matrix, providing guidance for subsequent optimization models.

[0149] In this embodiment, the preset change gradient table is a table set in advance, which specifies how different sensitive variables should change under different gradient conditions. This table is formulated based on prior knowledge, experience, and a large amount of experimental data of complex systems. For example, the table may stipulate that for a certain type of sensitive variable, when the gradient is between 0.1-0.3, the amplitude of each adjustment is 0.05; when the gradient is between 0.3-0.5, the amplitude of each adjustment is 0.1, etc. The preset change gradient table provides clear rules for the adjustment of sensitive variables, making the model optimization process more controllable and systematic, and avoiding the problem of model instability or non-convergence that may be caused by blind adjustment.

[0150] In this embodiment, increasing a single sensitive variable with a positive corresponding gradient based on a preset change gradient table is a key step in the model optimization and correction process. When the analysis shows that the gradient of a sensitive variable to the real part of the state matrix eigenvalue is positive, the amplitude of increasing the sensitive variable is determined according to the preset change gradient table. For example, if the gradient of a sensitive variable is 0.2, it is known from the preset change gradient table that the variable should be increased by 0.05. The purpose of this is to change the eigenvalue of the state matrix by adjusting the sensitive variable, thereby improving the stable convergence performance of the logic closed loop of the system dynamics simulation model. Because in the system stability analysis, the size of the real part of the eigenvalue of the state matrix is ​​closely related to the stability of the system, by reasonably increasing the sensitive variable with a positive gradient, it is possible to reduce the real part of the eigenvalue, thereby improving the stability of the system.

[0151] In this embodiment, a single sensitive variable with a negative corresponding gradient is reduced based on a preset change gradient table, also for the purpose of optimizing the stability of the model. When the gradient of the sensitive variable to the real part of the state matrix eigenvalue is negative, the value of the variable is reduced according to the preset change gradient table. For example, if the gradient of a sensitive variable is -0.3, it may need to be reduced by 0.1 according to the preset change gradient table. In this way, by utilizing the gradient relationship between the sensitive variable and the real part of the eigenvalue, the sensitive variable is adjusted in a targeted manner, so that the real part of the state matrix eigenvalue changes in a direction that is conducive to system stability, that is, it is adjusted in a direction less than 0, so as to achieve stable convergence of the logical closed loop of the system dynamics simulation model.

[0152] In this embodiment, the real parts of all eigenvalues ​​in the newly obtained state matrix are less than 0, indicating that the system dynamics simulation model has achieved the requirement of stable convergence after adjusting the sensitive variables. In system stability theory, for a linearized system (described by a state matrix), when the real parts of all eigenvalues ​​of the state matrix are less than 0, the system is asymptotically stable. This means that regardless of the initial state of the system, over time, the system will tend to a stable equilibrium state and will not experience unrestricted growth or oscillation. For example, in a simulation model of a mechanical vibration system, only when the real parts of the eigenvalues ​​of the state matrix are less than 0 will the vibration gradually decay and eventually stop, and the system will reach a stable state. Therefore, making the real parts of all eigenvalues ​​in the newly obtained state matrix less than 0 is an important goal of optimizing and correcting the system dynamics simulation model to ensure that the model can accurately and reliably simulate the stable operating state of a complex system.

[0153] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalents, the present invention is intended to include these modifications and variations.

Claims

1. Dynamic optimization and real-time correction system for simulation models of complex systems, characterized by: include: The logical framework generation module is used to parse out all the core components of the complex system, the causal relationship diagram, and the feedback loop, and build the simulation model logical framework of the complex system based on all the core components of the complex system, the causal relationship diagram, and the feedback loop; The simulation model building module is used to inject multi-source heterogeneous data of complex systems into the simulation model logic framework to generate a system dynamics simulation model of the complex system; Sensitivity analysis module, used to perform local sensitivity analysis and global sensitivity analysis on the system dynamics simulation model and identify all sensitive variables of the system dynamics simulation model; A model optimization and correction module is used to analyze the stable convergence performance of the logic closed loop of the system dynamics simulation model based on all sensitive variables and the system dynamics simulation model, and to optimize and correct the system dynamics simulation model based on the stable convergence performance of the logic closed loop to obtain a stable system dynamics simulation model; Model optimization and correction module, including: A logic closed loop identification submodule is used to identify all positive feedback loops and negative feedback loops of the system dynamics simulation model as logic closed loops of the system dynamics simulation model; The state matrix construction submodule is used to linearize the complex system into state space equations based on the system dynamics simulation model and the corresponding logic closed loop, and solve the state matrix; The model optimization and correction submodule is used to determine that the stable convergence performance of the logical closed loop of the system dynamics simulation model does not meet the requirements when the real part of the eigenvalue of all the eigenvalues ​​of the state matrix is ​​greater than 0, and to optimize and correct the system dynamics simulation model based on all sensitive variables to obtain a stable system dynamics simulation model.

2. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 1, characterized in that: All core constituent variables include system state variables, speed variables, and auxiliary variables.

3. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 1, characterized in that: Also includes: The verification input module is used to input multiple sets of initial conditions and historical parameters of the complex system into the simulation model logic framework of the complex system, and solve the simulation through numerical integration to obtain the model output under the corresponding initial conditions and historical parameters; The verification output module is used to compare the model output under each set of initial conditions and historical parameters with the corresponding historical output to obtain the verification accuracy of the simulation model logic framework; The verification judgment module is used to rebuild a new simulation model logic framework of the complex system when the verification accuracy of the simulation model logic framework is less than the preset accuracy threshold, and stop rebuilding the simulation model logic framework until the verification accuracy of the latest simulation model logic framework is not less than the preset accuracy threshold.

4. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 1, characterized in that: The multi-source heterogeneous data of complex systems include system state variables obtained in real time through IoT devices deployed in the complex systems.

5. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 1, characterized in that: Sensitivity analysis module, including: The elasticity coefficient analysis submodule is used to analyze the rate of change of all system output variables when only a single core component variable produces a small fluctuation based on the system dynamics simulation model, and calculate the elasticity coefficient of each core component variable when a small fluctuation occurs based on the rate of change of all system output variables when only each core component variable produces a small fluctuation; The Sobol variance decomposition submodule is used to determine the variance proportion explained by each core component variable individually and the total effect index including all interactions with the corresponding core component variables based on the Sobol variance decomposition method; The local sensitivity analysis submodule is used to analyze the local sensitivity value of each core component variable based on the proportion of variance explained by each core component variable and the elasticity coefficient when small fluctuations occur; A global sensitivity analysis submodule is used to analyze the global sensitivity value of each core component variable based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables; The sensitivity variable screening submodule is used to screen out all sensitive variables of the system dynamics simulation model from all core constituent variables based on the local sensitivity value and global sensitivity value of each core constituent variable.

6. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 5, characterized in that: Local sensitivity analysis submodule, including: A normalization processing unit is used to normalize the variance proportions explained by all core component variables individually and the elasticity coefficients when small fluctuations occur, and obtain the normalized variance proportions and normalized elasticity coefficients of each core component variable; The weighted operation unit is used to perform weighted operation on the normalized variance ratio and normalized elasticity coefficient of each core component variable to obtain the local sensitivity value of each core component variable.

7. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 5, characterized in that: Global sensitivity analysis submodule, including: An interaction coefficient obtaining unit is used to construct an equation group based on the local sensitivity values ​​of all core component variables and the total effect index including all interactions with the corresponding core component variables, and to solve the interaction coefficients between all core component variables based on the equation group; Relationship network building unit, used to build a full variable relationship network based on the interaction coefficients between all core component variables; A link matrix building unit is used to analyze all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network, and to build a relationship link matrix for each core component variable based on all direct link paths and all interaction coefficients of each direct link path of each core component variable in the full variable relationship network; A global link weight analysis unit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the relationship link matrix of each core component variable; The global sensitivity value determination unit is used to take the ratio of the global link weight of each core component variable in the full variable relationship network and the core coefficient of the corresponding core component variable in the full variable relationship network as the global sensitivity value of the corresponding core component variable.

8. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 7, characterized in that: Global link weight analysis unit, including: The path propagation influence analysis subunit is used to determine the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable based on the relationship link matrix of each core component variable; based on the number of path steps between all core component variables that have an influence relationship with each core component variable and the corresponding core component variable, as well as the interaction coefficient between the core component variables and the corresponding core component variable, calculate the path propagation influence of the corresponding core component variable; The eigenvector influence analysis subunit is used to take the ratio of the maximum eigenvalue to all eigenvalues ​​obtained after eigendecomposition of the relationship link matrix of each core component variable as the eigenvector influence of the corresponding core component variable; A comprehensive influence value analysis subunit is used to calculate the comprehensive influence value of each core component variable based on the path propagation influence and eigenvector influence of each core component variable; The global link weight analysis subunit is used to calculate the global link weight of each core component variable in the full variable relationship network based on the comprehensive influence value of all core component variables.

9. The complex system-oriented simulation model dynamic optimization and real-time correction system according to claim 1, characterized in that: Model optimization and correction submodule, including: Gradient analysis unit, used to analyze the gradient of the real part of all eigenvalues ​​in the state matrix with respect to a single sensitive variable; The optimization and correction unit is used to increase the single sensitive variable with a positive gradient based on the preset change gradient table, and at the same time, reduce the single sensitive variable with a negative gradient based on the preset change gradient table, until the real parts of all eigenvalues ​​in the latest state matrix are less than 0, then stop optimizing and correcting the system dynamics simulation model to obtain a stable system dynamics simulation model.

Images