High accurate analysis by experiment and simulation using Bayesian inference for corrugated cardboard

Abstract

Corrugated cardboards are used in many fields. The design of corrugated cardboard, however, is based on experimentations. The subject of this paper is developing the technique for high accurate analysis of corrugated cardboards. The corrugated cardboard is complicated structures and its property is unknown. Therefore, it is difficult to analyze this structure. We did bending tests of corrugated cardboard and its homogenized analysis using finite elements. We estimated its property by comparing both results. The experimentations include a lot of variation because the sample varies widely. Therefore model verification and validation is necessary. We used Bayesian inference for this purpose. In Bayesian inference, a priori probability is important. We compared three a priori probabilities. The first one is a uniform distribution which means no a priori information. The second one is a normal distribution which indicates a priori information about ambiguous data of the property. The third one is a normal distribution of which mean is the exact property. It is not realistic to use the third one. Numerical results show a uniform distribution is useful for estimating the property. The variance of Bayesian inference using a uniform distribution is wide, but the mean value becomes exact value quickly. The numerical results show the validity of Bayesian inference.

Keywords

• corrugated cardboard
• fineite element analysis
• data assimilation
• bayesian inference
• equivalent analysis