Uncertainty Analysis of Experimental Parameters for Reducing Warpage in Injection Molding

2026-01-08

AI Summary

This study addresses the challenge of warpage control in injection molding, which is significantly influenced by thermomechanical coupling effects and often exacerbated by the neglect of model parameter uncertainty in conventional optimization approaches. To overcome this limitation, a data-driven robust optimization framework is proposed, integrating polynomial regression surrogate models with Bayesian inference to jointly optimize key process parameters—mold temperature, injection speed, packing pressure, and packing time—while quantifying the posterior uncertainty of the optimal settings. Innovatively, a Monte Carlo simulation–based zero-level set boundary analysis method is introduced to visualize confidence regions associated with the transition between acceptable and defective warpage, thereby clearly delineating the robust processing window and failure boundaries within the parameter space.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Injection molding is a critical manufacturing process, but controlling warpage remains a major challenge due to complex thermomechanical interactions. Simulation-based optimization is widely used to address this, yet traditional methods often overlook the uncertainty in model parameters. In this paper, we propose a data-driven framework to minimize warpage and quantify the uncertainty of optimal process settings. We employ polynomial regression models as surrogates for the injection molding simulations of a box-shaped part. By adopting a Bayesian framework, we estimate the posterior distribution of the regression coefficients. This approach allows us to generate a distribution of optimal decisions rather than a single point estimate, providing a measure of solution robustness. Furthermore, we develop a Monte Carlo-based boundary analysis method. This method constructs confidence bands for the zero-level sets of the response surfaces, helping to visualize the regions where warpage transitions between convex and concave profiles. We apply this framework to optimize four key process parameters: mold temperature, injection speed, packing pressure, and packing time. The results show that our approach finds stable process settings and clearly marks the boundaries of defects in the parameter space.

Problem

• warpage
• injection molding
• uncertainty analysis
• process parameters
• robustness

Innovation

• Bayesian uncertainty quantification
• surrogate modeling
• Monte Carlo boundary analysis
• injection molding optimization
• warpage control