Stochastic approximation algorithm for industrial process optimisation

Abstract

Stochastic approximation algorithms are alternative linear search methods for optimising control systems where the functional relationship between the response variable and the controllable factors in a process and its analytical model remain unknown. These algorithms have no criteria for selecting succession measurements ensuring convergence, meaning that, when implemented in practice, they may diverge with consequent waste of resources. The objective of this research was to determine industrial processes’ optimum operating conditions by using a modified stochastic approximation algorithm, where its succession measurements were validated by obtaining response variable values for each iteration through simulation. The algorithm is presented in nine stages; its first six describe which are process independent and dependent variables, the type of experimental design selected, the experiments assigned and developed and the second order models obtained. The last three stages describe how the algorithm was developed, and the optimal values of the independent variables obtained. The algorithm was validated in 3 industrial processes which it was shown to be efficient for determining independent variables’ optimum operating conditions (temperature and time): the first three iterations were obtained at 66°C in 3 hours 42 minutes for process 1, unlike processes 2 and 3 where the first iteration was obtained at 66°C in 6 hours 06 minutes and 80°C in 5 hours 06 minutes, respectively.

Keywords

• stochastic approximation algorithm
• dependent variable
• independent variable
• iterative process
• simulation