Finding Optimal Jetting Waveform Parameters with Bayesian Optimization

Abstract: Jet printing is a method in surface mount technology (SMT) in which small volumes of solder paste or other electronic materials are applied to printed circuit boards (PCBs). The solder paste is shot onto the boards by a piston powered by a piezoelectric stack. The characteristics of jetted results can be controlled by a number of factors, one of which is the waveform of the piezo actuation voltage signal. While in theory any waveform is possible, in practice, the signal is defined by seven parameters for the specific technology studied here. The optimization problem of finding the optimal parameter combination cannot be solved by standard derivative based methods, as the objective is a black-box function which can only be sampled though noisy and time-consuming evaluations. The current method for optimizing the parameters is an expert guided grid search of the two most important parameters, while the remaining five are kept constant at default values. Bayesian optimization is a heuristic model based search method for efficient optimization of possibly noisy functions with unavailable derivatives. An implementation of the Bayesian optimization algorithm was adapted for the optimization of the waveform parameters, and used to optimize various combinations of the parameters. Results from different trials produced similar values for the two known parameters, with differences within the uncertainty caused by noise. For the remaining five parameters results were more ambiguous. However, a closer examination of the model hyperparameters showed that these five parameters had almost no impact on the objective function. Thus, the best found parameter values were affected more by random noise than the objective. It is concluded that Bayesian optimization might be a suitable and effective method for waveform parameter optimization, and some directions for further development are suggested based on the results of this project.