# Determining input variable ranges in Industry 4.0: A heuristic for estimating the domain of a real-valued function or trained regression model given an output range

## TL;DR

This paper introduces a heuristic method to identify input variable ranges that produce desired output ranges in complex industrial processes, using synthetic data and decision trees, applicable to high-dimensional and non-numeric data.

## Contribution

It presents a novel non-stochastic heuristic for estimating input subspaces for any regression model or function, extending beyond traditional control methods.

## Key findings

- Successfully applied to a lamination factory case study
- Effective in high-dimensional, sparse, and categorical input spaces
- Provides a flexible approach for output range targeting in complex systems

## Abstract

Industrial process control systems try to keep an output variable within a given tolerance around a target value. PID control systems have been widely used in industry to control input variables in order to reach this goal. However, this kind of Transfer Function based approach cannot be extended to complex processes where input data might be non-numeric, high dimensional, sparse, etc. In such cases, there is still a need for determining the subspace of input data that produces an output within a given range. This paper presents a non-stochastic heuristic to determine input values for a mathematical function or trained regression model given an output range. The proposed method creates a synthetic training data set of input combinations with a class label that indicates whether the output is within the given target range or not. Then, a decision tree classifier is used to determine the subspace of input data of interest. This method is more general than a traditional controller as the target range for the output does not have to be centered around a reference value and it can be applied given a regression model of the output variable, which may have categorical variables as inputs and may be high dimensional, sparse... The proposed heuristic is validated with a proof of concept on a real use case where the quality of a lamination factory is established to identify the suitable subspace of production variable values.