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The problem of performing automated dynamic system simulation and how to solve this problem using AI techniques will be considered. Next, we’re going to consider some of the key ideas involved in the mathematical model simulation process. Then, as a software program, we can explore how these concepts can be applied.

a. Simulation of mathematical engineering models

If we consider a particular mathematical model, the problem of performing an effective simulation for a specific engineering system can be better understood. Let us consider the model below: X′ = σ(Y-X) Y′ = rX - Y - XZ (1.1)

Figure 1.2 Two state Markov model.

(1.1)

where X, Y, Z, σ, r, b ∈ R, and σ, r and b are three parameters, which are usually taken to be optimistic, regardless of their physical origins. For different values of r in 0 < r < ∞, equations are also studied. Few researchers has studied this mathematical model to some degree, but there are still several questions to be answered regarding this model with regard to its very complicated dynamics for some ranges of parameter values [4].

For example, if we consider simulating eq. (1.1), the problem is choosing the appropriate parameter values for σ, r, b, so that the model’s interesting dynamic behaviour can be extracted. As we need to consider a three-dimensional search space σ r b and there are several possible dynamic behaviours for this model, the problem is not a simple one. In this case, the model is composed of three simultaneous differential equations, the behaviors can range from simple periodic orbits to very complicated chaotic attractors. Once the parameter values are selected then the problem becomes a numerical one, since then we need to iterate an appropriate map to approximate the solutions numerically.

b. Method for automated simulation using AI

Then determining the “best” set of parameter values BP for the mathematical model is the issue of performing automatic simulation for a specific engineering system. Here is where the technique of AI is really beneficial. In AI, the main concept is that we can use those techniques to simulate human experts in a specific application domain. In this case, we then use heuristics and statistical estimates derived from experts in this field to limit the computer program’s search space. You may define the algorithm for selecting the “best” set of parameter values as follows [9].

 Step 1: Read the mathematical model M.

 Step 2: Analyze the model M to “understand” its complexity.

 Step 3: Generate a set of permissible AP parameters using the model’s initial “understanding.” This collection is generated by heuristics (expressed in the knowledge base as rules) and by solving some mathematical relationships that will later be described.

 Step 4: Perform a selection of the “best” set of parameter values BP. This set is generated using heuristics (expressed as rules in the knowledge base).

 Step 5: Execute the simulations by numerically solving the mathematical model equations. The various forms of complex behaviours are described at this stage.

A computer algorithm that can be called an intelligent device for simulating dynamical engineering systems is the result of this implementation [5].