### SysWatch Smart Operation

### Introduction

Our Response Surface generation methodology is a very powerful data modeling and visualization tool which allows to find high-dimensional non-linear response surfaces in the form whereby u is a vector representing some ambient conditions of a process, x is a vector representing the input- or control variables and y is the vector of output- or response variables. Let the dimensions of x, u and y be n, k and m respectively. Then f maps the (n+k)-dimensional real space onto the m-dimensional real space.

For instance look at a combustion engine emitting u-, x- and y-values at a high sampling rate. Assume these data are collected in a large file or database. This file is used to find the unknown function f by means of parametric or non-parametric regression techniques.

Using a certain graphical “trick” called pseudo projection it becomes possible to represent each component of f as a function of x – ignoring u for the moment – as a 3D structure, although x may have more than two dimensions. The trick consists in selecting two arbitrary components of x and fixing the remaining n-2 variables by setting them equal to the arithmetic mean of their respective input values.

Figure below illustrates this method using an arbitrary set of input data:

The user has two additional degrees of freedom to manipulate this 3D representation:

⦁ First, he/she may select arbitrarily two different input variables

⦁ In principle the n-2 non selected variables can be set on any value between their empirical minimum and their empirical maximum

In the monitoring scenario our efficient algorithm solves a combinatorial optimization problem on the computed response surface and provides optimal operating modes for the customer.