Establish the mathematical model of the system
Simulation is a model-based activity, which uses model simulation instead of real system for experiments and research. Therefore, first of all, it is necessary to quantitatively describe the problem to be simulated, that is, to establish the mathematical model of the system.
Models are colorful imitations of the real world, so the models are also varied;
According to whether the model contains random factors, it can be divided into random model and deterministic model.
According to whether the model is time-varying, it can be divided into dynamic model and static model.
According to whether the model parameters change continuously in space, it can be divided into distributed parameter model and lumped parameter model.
According to whether the model parameters change continuously with time, it can be divided into continuous system model and discrete system model.
According to the mathematical description of the model, it can be divided into ordinary differential equation, partial differential equation, difference equation, discrete event model and so on.
For the above different types of models, we will not discuss them in depth here, but only discuss several * * * problems in establishing the mathematical model of the system.
1) The modeling process is an information processing process. In other words, information is the "raw material" for building a model. According to the different types of "raw materials" used in modeling, modeling methods can be divided into two categories:
One is deductive modeling, that is, modeling with prior technical information. The process is: from some premises, assumptions, principles and rules, through mathematical logic deduction, establish a model. Therefore, this is a process from general to special, that is, a special description of the simulated object is derived according to the general technical principles.
The other is inductive modeling, that is, using the experimental data information of real system to model. The process is: get the data by testing the real system, which contains information that can reflect the essence of the real system, and then get the description of the regularity of the real system through data processing, such as the well-known least square regression model. This is a process from special to general.
However, in practical application, the above two methods are often combined to establish a model, that is, mixed method modeling.
No matter which modeling method is adopted, the key lies in the understanding of the real system. If we don't fully understand the real system correctly, then the model will not accurately imitate the essence of the real system.
2) The credibility of the model. Since the model is an imitation of the real system, there is a problem of imitation, that is, the similarity and accuracy of the model.
The credibility of the model depends on whether the information "raw materials" (prior knowledge and experimental data) used in modeling are correct and complete, and also depends on whether the modeling methods (deduction and induction) used are reasonable and rigorous. In addition, for many simulation software, it is necessary to transform the mathematical model into a simulation model that the simulation algorithm can handle. Therefore, there is also the problem of model conversion accuracy. Any mistake in modeling will affect the credibility of the model.
Therefore, after the model is established, it is an essential and important step to test the credibility of the model. The method to test the reliability of the model is usually: firstly, experts who are familiar with the simulation system analyze and evaluate the model, then statistically analyze the data used in modeling, and finally try the model and compare the preliminary simulation results with the estimated results.
analog computation
Simulation calculation is a process of numerical experiment and solution to the established simulation model, and different models have different solutions. For example, continuous systems are usually described by ordinary differential equations, transfer functions and even partial differential equations. Because it is almost impossible to get analytical solutions of these equations, numerical solutions are always used. For example, various numerical integration methods are mainly used for ordinary differential equations, and finite difference method, characteristic method, Monte Carlo method or finite element method are used for partial differential equations.
For another example, for discrete event systems, probability models are usually used, and the simulation process is actually a numerical experiment process, and these parameters must conform to certain probability distribution laws. Different types of discrete event systems (such as stochastic service system, stochastic inventory system and stochastic network planning) have different simulation methods. ).
With the increasing complexity of simulation objects and the urgent need for real-time simulation, it has always been an important task to study new simulation algorithms, especially various parallel simulation algorithms.
Simulation result analysis
In order to draw correct and effective conclusions through simulation, it is necessary to analyze the simulation results scientifically. Early simulation software output simulation results in the form of a large number of data, so it is necessary to sort out the simulation results data and make various statistical analysis in order to draw scientific conclusions. Visualization technology is widely used in modern simulation software, which vividly shows the various states of the simulation object through graphics, charts and even animations, making the output information of the simulation more abundant and detailed, which is more conducive to scientific analysis of the simulation results.