Bayesian Optimization of Process Parameters of a Sensor-Based Sorting System using Gaussian Processes as Surrogate Models

TL;DR

This work tackles the challenge of optimizing sensor-based sorting (SBS) process parameters under material- and measurement-driven uncertainty, while balancing dual quality objectives for accept and reject streams. It adopts Bayesian optimization with Gaussian process regression surrogates to model the relationship between three controllable parameters $(T_R, T_E, S_E)$ and sorting accuracy metrics derived from confusion matrices, incorporating measurement variance through a variance-weighted kernel. A weighted multi-objective BO uses two GP surrogates (one per output stream) and a combined expected improvement to select successive parameter settings, enabling inline adjustments as material properties change. The method, demonstrated on a lab-scale SBS with 250 candidate configurations, converges in a few steps and identifies a practical optimum $(T_R^*, T_E^*, S_E^*) \approx (15.27, 1.29, 6.30)$, with guidance to extend the bounding box to improve hit probability and robustness. This approach reduces experimental burden and supports adaptive operation in real-time sorting scenarios.

Abstract

Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process parameters must be set depending on the properties of the material stream, the dimensioning of the system, and the required sorting accuracy. However, continuous verification and re-adjustment are necessary due to changing requirements and material stream compositions. In this paper, we introduce an approach for optimizing, recurrently monitoring and adjusting the process parameters of a sensor-based sorting system. Based on Bayesian Optimization, Gaussian process regression models are used as surrogate models to achieve specific requirements for system behavior with the uncertainties contained therein. This method minimizes the number of necessary experiments while simultaneously considering two possible optimization targets based on the requirements for both material output streams. In addition, uncertainties are considered during determining sorting accuracies in the model calculation. We evaluated the method with three example process parameters.

Figures (5)

• Figure 1: Overview of process parameter exploration of a sensor-based sorting (SBS) system using Bayesian optimization (BO). Starting from an initial set of parameters, the resulting accept and reject material streams are analyzed and new parameters for subsequent sorting experiments are proposed using Gaussian process regression (GPR) models.
• Figure 2: Box plot of the normalized TP (top) and TN (bottom), with an acquisition interval of 10 seconds during the sorting process as a function of the reaction lines parameter with constant other process parameter values (expanded time and space are set to zero).
• Figure 3: Sequence of the Bayesian optimization (BO) approach of the process parameters of a sensor-based sorting system using two separate Gaussian process regression (GPR) models for the accepted and rejected material streams and a combined expected improvement (EI).
• Figure 4: Results of the Gaussian process regression (GPR) models for predicting the normalized and scaled TP value based on the reaction lines parameter for different weightings of the variance in the calculation of the GPR models. (1): $\lambda = 0.1$, (2): $\lambda = 0.01$ and (3): $\lambda = 0$.
• Figure 5: Evolution of the Gaussian process regression (GPR) model for the normalized TP value. The mean of the predicted TP values is plotted against two of the three process parameters for each case. 1st row: GPR model after the initial sorting experiments; 2nd row: GPR model with all TP values from the dataset.