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System Models and Modeling Techniques (1)

#系統工程學#課程筆記#Systems Engineering112
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This text provides an overview of models and modeling. Models are idealized abstractions or simplified representations of real systems, depicting key characteristics for research purposes. System models serve as substitutes for real systems, describing their components, interactions, and causal relationships. Modeling is the method of describing a system's structure and behavior by selecting relevant factors and expressing them in a certain way, such as mathematically or graphically. The text also discusses the nature, role, and classification of models, as well as general principles and steps for model construction. It outlines basic modeling methods, including analytical, experimental, integrated, heuristic, and dialectical approaches. Additionally, it covers the simplification of models through reducing variables, changing variable properties, merging variables, altering functional relationships, and modifying constraints.

Overview of Models and Modeling#

Definition of Models and Modeling#

A model is an idealized abstraction or concise representation of a real system, depicting certain key features of the real system, in order to facilitate the study and development of the system.

Characteristics of models: Models are abstractions or imitations of a part of the real world; they consist of factors relevant to analyzing problems; they indicate the relationships between these factors.

A system model is a substitute for a real system, used to describe an abstraction of the real world. The model reflects the main components of the system, the interactions between individual parts, and the causal effects and relationships under operating conditions.

Modeling is the process of describing the composition and behavior of a system, selecting appropriate factors from the physical system, and expressing the system's entities in a certain way (such as mathematical or graphical methods).

Essence, Function, and Status of Modeling#

The essence of modeling lies in the use of a certain aspect of similarity between the model and the prototype, using the model to replace the prototype in the research process, and obtaining some information about the prototype through the study of the model.

The function of modeling can be divided into three points:

  • The model itself is an expression of people's research results on a certain degree of subject system. This expression is concise and formal.

  • Models provide a basis for logical reasoning and computation independent of specific content, which promotes the discovery of scientific laws, theories, and principles.

  • Models can be used for "thought" experiments.

The status of modeling: The nature of the model determines the limitations of its function. The model cannot replace the study of objective system content. Only when it is used in conjunction with the objective system can the function of the model be fully realized.

Classification of Models#

Diagram of Model Classification

General Principles of Model Construction#

  1. Consider the collectiveness of the system - block diagram.

  2. Consider the relevance of information.

  3. Consider the accuracy of information.

  4. Consider the hierarchy of the system.

Basic Steps of Modeling#

  1. Clearly define the purpose and requirements of modeling.

  2. Provide a general language description of the system.

  3. Understand the main factors (variables) in the system and their relationships (structural relationships, functional relationships).

  4. Determine the structure of the model.

  5. Estimate the parameters of the model.

  6. Conduct experimental research.

  7. Make necessary modifications.

Basic Methods of Modeling#

  1. Analytical method: Analyze and dissect the problem, study the details of the internal structure, form, and functional relationships of the object system. Use logical reasoning methods to derive system models from axioms and laws. For example, $ Mx'' + Bx' + kx = F(t) $.

  2. Experimental method: Use observations and analysis of experimental results to induce system models, with mathematical and physical modeling methods being typical representatives. The experimental method can be divided into three categories: simulation, statistical data analysis (such as linear regression), and experimental analysis.

  3. Synthetic method: Emphasize the value of experimental data while recognizing the value of theory. Unify experimental data and theoretical deductions. Experimental data and theory are inseparable. Without experiments, theories cannot be established, and without theoretical deductions, useful data cannot be obtained. Deductive methods are usually used to derive models from known theorems, and experimental methods are used to supplement certain unknowns. Inductive methods are then used to clarify relationships based on experimental data and establish models.

  4. Expert method: Mainly refers to the Delphi method. Through heuristic discussions among experts, the understanding of the system is gradually improved and models are constructed. This method is commonly used in social system planning and decision-making.

  5. Dialectical method: Its basic viewpoint is that a system is a unity of opposites, composed of two contradictory aspects. The transformation and unity of the two contradictory aspects are the real situation. Phenomena are not essence, and forms are not content. Therefore, two opposing analytical models must be constructed. The same data can be explained by two models. This method can prevent one-sidedness and produces better results than one-sided results.

Simplification of Models#

  1. Reduce variables.

  2. Change the nature of variables.

  3. Merge variables (aggregation).

  4. Change the functional relationship.

  5. Change the constraint conditions.

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The original link is https://nishikori.tech/posts/systems-engineering-note/System-Model-and-Modeling-Technology-1

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