Title:
REVERSE DESIGN OF EXPERIMENTS THEORY FOR CONTROLLING A WORK SYSTEM FOR IMPROVING GROUND MACHINES

Authors:
Thanh Duc Le, Viet Nam

Abstract:

The purpose of this paper is to provide a new mathematical approach to control the black-box parameters related to the reverse design of experiments (DoE). This approach can be applied to the improving ground machines. The aim is to help the machine improve workability, productivity and quality
The (DoE) finds relationships among parameters and is widely applied in science. For example, There are three experimental parameters described in the following table. Those parameters are humidity (W%), temperature (t⁰), material strength (s).

Table 1 Data of X1, X2, and Y

Based on the available data, by DoE theory, it is possible to build a regression equation as follows:
Y = 0,29X1– 0.0315X2
The reverse steps of DoE have not been used. In a programmable control system, the machines encounter problems when they don’t have sensors to identify the working object. Specifically, when the soil properties randomly change (e.g., soil viscosity and composition), the machine working parameters may not adapt to such changes. Mathematics has not been fully applied to this problem. Thus, the author proposes a temporary method: using known mathematical rules on the soil (similar to the regression equation)
 The computer can control the system. In nature and reality, many processes are considered black boxes because science cannot explain the explicit rules of the object. Every behavior examining the black box is almost illogical. If the black box is assumed to have a mathematical rule (regression equation), the operator uses an automated computer system to analyze and make a decision to control the machine. The decision may not be optimal, but it has a clear basis. Then, the workers know exactly what they want in the black box.
In previous example, from humidity (X1) and temperature (X2), the strength of the material (Y), the laws can be obtained. Conversely, from the known strength, by reversing DoE theory, it is possible to control the system of two parameters x1, x2 according to the regression equation. This is described in more detail in the following example.
This method has great application potential. In weather forecasting, if there are statistics on temperature, pressure, wind speed...etc. at different locations, DoE can be relied on to establish regression equations (i.e. weather laws are described mathematically). Based on this equation, reverse DoE can know the path of the storm. This mathematical equation can be a theoretical basis for forecasting because it is based on the axiom that “the natural world has laws”
The limitation of the paper is that the theory has not been tested in practice