Collaborative Research: Methodology for Computer Experiments with Special Application to Orthopedic Research

在生物力学工程问题的推动下，这个合作研究项目开发并实现了统计工具，用于设计和分析计算机实验，这些实验在假体设计中具有特殊的应用。这些工具用于在骨盆骨适配的3D模型有限元模型中创建抗骨盆骨溶解的王牌表状杯设计。第二个特定的生物力学任务是验证/校准来自机械膝关节模拟器研究的膝关节部件中聚乙烯磨损的计算机代码。更广泛地说，这项工作提供了一套实现的工具，允许对广泛的产品应用进行具有成本效益的快速工程开发。它帮助合并统计和工程设计界，迫使前者处理完全明确的设计问题，而后者以严格的随机和统计方法解决这些问题。这种方法在其他大型计算机模型的分析中也可能被证明是有用的，例如环境科学中使用的气候、暴露和污染模型。在统计学方面，探索性设计是为计算机实验开发的，它允许更好地估计极端结果，这对于评估使用给定假体设计时给定患者群体中危险的高应力应变情况的频率非常重要。这一目标可以被认为是给定假体设计的健壮性评估工具。其次，序贯设计是为约束优化问题设计的，这在假肢设计中非常重要，因为在假肢设计中经常出现多个相互竞争的结果。在分析方面，预测器被开发出来，给出了对预测表面的最优的更准确的评估；这些预测器被用来产生约束优化问题的更快的(从需要较少的时间要求的计算机代码评估的意义上)解决方案。最后，为同时使用定性和定量输入的计算机代码开发了预测方法。这个项目开发和实现了统计工具，用于设计和分析计算机实验，这些实验在假体设计中有特殊的应用。计算机实验在产品的广泛应用的快速工程开发中具有成本效益。该项目开发了在当前假体设计应用之外有用的统计和数学工具。

Motivated by problems of biomechanical engineering, this collaborative research project develops and implements statistical tools for the design and analysis of computer experiments that have particular application to prosthesis design. These tools are used to create ace tabular cups designs that are resistant to pelvic osteolysis in a 3D model finite-element model for bone adaptation in the pelvis. A second specific biomechanical task is to validate/calibrate the computer codes for polyethylene wear in knee components from mechanical knee simulator studies. More generally, this work provides a suite of implemented tools that allow cost-effective and rapid engineering development of a wide range of product applications. It helps merge the statistical and engineering design communities by forcing the former to address fully articulated design problems and the latter to anchor the solution of these problems in rigorous stochastic and statistical methodology. The methodology may also prove useful in the analysis of other large computer models such as the climate, exposure, and pollution models used in environmental science. On the statistical front, exploratory designs are developed for computer experiments that allow better estimation of extreme outcomes, important for assessing the frequency of dangerous high stress-strain situations in a given patient population when a given prosthesis-design is used. This objective can be thought of as a robustness assessment tool for the given prosthesis design. Second, sequential designs are devised for constrained optimization problems, which are important in prosthesis design where multiple, competing outcomes occur frequently. On the analysis front, predictors are developed that give more accurate assessment of optima of predicted surfaces; these are used to produce faster (in the sense of requiring fewer evaluation of time-demanding computer code) solutions of constrained optimization problems. Finally, prediction methodology is developed for computer codes that use both qualitative and quantitative inputs. This project develops and implement statistical tools for the design and analysis of computer experiments that have particular application to prosthesis design. Computer experiments are cost-effective in rapid engineering development of a wide range of product applications. The project develops both statistical and mathematical tools that are useful outside of the current application of prosthesis design.