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Chapter 12
Logarithm Transformation of the Output Response Data for Optimization

## Excerpt

When engineers optimize a system, they focus on improving its functional input-output relationship. The functional input-output relationship is commonly defined as the basic function of a system. In the electric motor case study, engineers studied how coil wire diameter and the number of coils affected the basic function of an electric motor, which is the relationship between input electric power and output response (e.g., maximum rotational speed). Let the two control factors be A and B. Assume that the wire diameter has two levels, 0.3 and 0.4 mm, and the number of coils has two levels, 200 and 300 turns. Thus, the levels of the control factors are summarized in Table 12.1.

Engineers change the levels of control factors to improve the functional robustness of the input-output energy transformation of a system under noise conditions. Engineers vary the input energy to different levels and measure the changes in output (energy-related) responses. However, for measurement convenience, engineers calibrate other easily controlled factors to change the amount of input energy and measure the corresponding output responses. Take the electric motor for example. The input is electric power and the output responses are RPM (rotations per minute) and torque. Change the wire diameter and number of coils to assess the functional relationship between input and output responses. Measure the two output responses and the corresponding input electric power to find the input-output relationship. Let the parameter that directly affects the input energy be a signal factor (M). One typical signal factor for an electric motor is the multiplication of input electric current and input voltage.

• 12.1 Functional Input-Output Relationship and Control Factor Levels
• 12.2 Ideal Function of Input-Output Energy Transformation
• 12.3 A Metric of Functional Robustness for Design Optimization
• 12.4 Functional Relationship Between Input Energy and Output Response
• 12.5 Functional Relationship of a System
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