建模作业-1

Course Work 1

The course of the Mathematical Modeling has already been taken about four weeks. Through the course we had learnt a lot of knowledge about the Model in Mathematical method--especially in the domain of conception design, the definitions of “System”, ”experiment”, ”model”, ”simulation”, etc.

“System” is characterized by the fact that we can specify how it interacts with its environment. That means System has a clearly boundary by which we could separate it from its environments. And the System also could be defined as a list of pieces of data and/or variables; it has its own organization about all of the data and variables. The last characteristic is that System must contain input and output department for the reason it must interact with its environments, and the interactions performed as the data input into and/or output from the System.

“Experiment” is another concept, whose description should be that: “An experiment is the process of extracting data from a system by exerting it through its inputs”. Also it has its own characteristics, like its controllable and observable. Although the major disadvantage of experiment could be that its own data and/or variables were hardly accessible.

“Model”, the description as below: “A model for a system and an experiment is anything to which experiment can be applied in order to answer questions about system”! This sentence clearly separated “model” from “system”. In this partition, we learnt that model always relate to system and experiment, and any model is valid for the “null experiment” applied to any system. On the other hand, no model of a system is valid for all possible experiments except the system itself or an identical copy there of.

The concept of “Simulation” is that the fact which all “inputs” and “outputs” are accessible. So everybody could execute the simulation applicable to the real system. The simulation is an experiment performed on a model. Furthermore, a mathematical simulation is a coded description of an experiment with a reference to the model to which this experiment is to be applied.

After all of the conception study, as we had acknowledged exactly characteristics about all the departments mentioned above, we studied modeling importance, simulation importance, simulation dangerous, and so on. So we could make much better use of the simulation, model, etc. In order to using model successfully, known the type of mathematical models may be useful. The type should be separated as follow: 1. Discrete-Time Model; 2. Continuous-Time Model; 3. Qualitative Model; 4. Discrete-Event Model. But this separation about mathematical modeling is just one of the kinds of the separation. It should be taken special analysis in the very situation.

After that, we learnt professional knowledge about model, like: how to build models, how to research models, how to test and/or use models. It take me into the model world, I knew the methods whatever I want to do with models. The steps are: BuildingàStudying (if not compatible go back to building) àTesting (if not compatible go back to building) àUse. The building model step includes details: 1. System analysis, make basic assumptions and/or edit an operation flow diagram; 2.Choose mathematical equations, data preparation; 3.Solving equations, analytically and/or numerically. The Studying Models step contains details: 1.Dimensionless form; 2.Asymptotic behavior; 3.Sensitivity analysis; 4.Modelling model output. The last step Testing models include parts like: 1.Prediction of previously unused data; 2.estimation model parameters; 3.comparing two models for the same system.

After model building, studying, testing, we could use the models for solve some problems. At the using step, there are something should be concentrated. They are the predictions with estimates of precision and the decision support.

After the basic theory study, Prof. Zhou explained two useful modeling examples.

First example is the emergent modeling for structural design. That modeling is a kind of optimization method of computational modeling processes. It raised a kind of non-conventional method, not the top-down sequences steps, because of the hard real time interactive with the models conventional offered. In that opinion, as the computer technology improved, the user’s needs are more and more difficult to be satisfied. Users need time efficient dynamic review of the designed progress. The conventional method consumed so many times, and the results are difficult for clients to visualize. So the alternation must be taken. They posed a virtual reality modeling which is supported by the VRML (a kind of modeling language). Consequently, the author altered the model’s behaviors and inducted the structures principle, in order to create structure model in VRML. It says the essences of structures are: 1.multiple components; 2.simple rules for individual components: Newton’s laws of motion; 3.local interaction between the components. The essay contains many kinds of examples of the new model, include the analysis, studying, testing, and using. As the examples show, that this new model can better satisfy the needs of engineers and clients are clear.

The second example is empirical modeling. This kind of models just focus on the state of the system, that means the model could be not very concisely, and just care about the changes of the system state. It is much more satisfied a large domain, like: the economic and/or market. Of course, this models are just models, they should be studying and testing before it can be used.

Summary

It is just the beginning of the modeling study; we have just learnt the basic concepts of the mathematical modeling. I think we should touch some issue, some useful example in our field. So far as we learnt mathematic, we have never built a model before. But I think the experience, the analysis are very important. We should improve our skill on these fields.

Answer for the questions

1. The model is adapted special system and experiment. Its proper is answer questions about system which we can or can not experiment on it. The model built for prediction, gaming and understanding is belonged to its characteristics.

2. The range of model could be typed as Discrete-Time Model, Continuous-Time Model, Qualitative Model, and Discrete-Event Model.

3. There are 3 types: the direct problem, the identification problem, the control problem.

4. The real experiment data should be input, at the model processing, if needed, it is important to control the model progress real time, so the control command should be input into the model system.

5. The approximate results of many simulation models’ results, includes the control variables, results, and etc.

6. The model solve their errors were determined by whom the model served in the reality. Consider the real world is explicitly, implicitly, and otherwise.