Types of Models:
Physical Models:
1. Physical models are tangible prototypes of actual products or processes.
2. Prototypes can use a 1 : 1 scale or any other feasible scale of choice. Such models provide a close-to-reality direct representation of the actual system and can be used to demonstrate the system’s structure, the role of each system element, and the actual functionality of the system of interest in a physical manner.
3. They help designers achieve a deeper understanding of system structure and details and to try out various configurations of design
Graphical Models:
1. Graphical models are abstractions of actual products or processes using graphical tools.
2. This type of modeling starts with paper and pencil sketches, progresses to engineering drawings, and ends with pictures and movies of the system of interest.
3. Common system graphical representations include a system layout, flow diagrams, block diagrams, network diagrams, process maps, and operations charts. Since graphical representations are static models, three-dimensional animations and clip videos are often used to illustrate the operation of a dynamic system or the assembly process of a product.
4. This adds to the difficulty of abstracting a complex system graphically, especially when the underlying product and process are still in the design phase. Such graphical tools often oversimplify the reality of the system in blocks and arrows and do not provide technical and functionality details of the process.
5. The absence of dynamic functionality in graphical representations makes it difficult to try out what-if scenarios and to explain how the system responds to various changes in model parameters and operating conditions.
Mathematical Models:
1. Mathematical modeling is the process of representing system behavior with formulas or mathematical equations. Such models are symbolic representations of systems functionality, decision (control) variables, response, and constraints.
2. They assist in formulating the system design problem in a form that is solvable using graphical and calculus-based methods.
3. Mathematical models use mathematical equations, probabilistic models, and statistical methods to represent the fundamental relationships among system components.
4. The equations can be derived in a number of ways. Many of them come from extensive scientific studies that have formulated a mathematical relationship and then tested it against real data.
5. Design formulas for stress–strain analyses and mathematical programming models such as linear and goal programming are examples of mathematical models.
6. Typically, a mathematical formula is a closed-form relationship between a dependent variable (Y) and one or more independent variables (X) in the form Y = f(X).
Computer Models:
1. Computer models are numerical, graphical, and logical representation of a system (a product or a process) that utilizes the capability of a computer in fast computations, large capacity, consistency, animation, and accuracy.
2. Computer simulation models, which represent the middleware of modeling, are virtual representations of real-world products and processes on the computer.
3. Computer simulations of products and processes are developed using different application programs and software tools. For example, a computer program can be used to perform finite element analysis to analyze stresses and strains for a certain product design.
