Solving and Analyzing Nonlinear Multibody Dynamic Engineering Systems with a Piecewise Linearization Approach

使用分段线性化方法求解和分析非线性多体动态工程系统

• 批准号: RGPIN-2020-06926
• 负责人: Dai, Liming
• 金额: $ 2.33万
• 依托单位: University of Regina
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=718027
• 关键词: Solving; Analyzing; Nonlinear; Multibody; Dynamic

Almost all dynamic systems used in engineering fields are multibody dynamic (MBD) systems, such as those in robotics, aircrafts, artificial limbs, etc. Solving for such systems can be challenging as the systems are typically multidimensional and can be nonlinear and complex with a high degree of coupling between variables. In practice, therefore, one may have to rely on numerical or approximate approaches for solving the systems as analytical solutions of the MBD systems is difficult to achieve, if not impossible. Moreover, in solving such systems with existing methods, linearization and simplifications are usually unavoidable, which negatively affect the accuracy and reliability and may even lead to erroneous solutions. An innovative methodology with higher degree of accuracy and reliability is therefore desired for solving and analyzing MBD systems in general. Significant research progresses have been achieved by the applicant and his research team in developing new analytical and numerical methods for solving nonlinear complex dynamic systems. Highly accurate and reliable results have been obtained with less computational time, when compared against other numerical methods such as the most popular Runge-Kutta method. The methods and techniques developed by the applicant provide a solid foundation and tools for advancing the proposed research program. The aim of the proposed research program is to develop a piecewise linearization approach suitable for accurately and reliably solving and analyzing nonlinear MBD systems which are difficult to solve with desired accuracy and reliability using existing methods. To achieve the aim, the P-T method previously developed by the applicant and other methods will be modified and extended. The proposed research will combine the modified P-T method, Taylor expansion, Laplacian transformation, and residue theorem to theoretically and numerically solve for MBD systems. Analytical solutions for linear MBD systems are expected to be achieved and continuous semi-analytical solutions, along with numerical solutions, are expected to be derived for nonlinear MBD systems. An engineering application oriented algorithm for solving nonlinear MBD systems is also expected to be developed using the aforementioned piecewise linearization approach. The approach to be developed, along with the computational algorithm and their orientation towards industrial applications, will significantly advance current approaches for solving, analyzing and optimizing linear and nonlinear MBD systems. The results of the proposed research program will therefore tangibly improve the design as well as operation and control quality of MBD systems. This is particularly significant for complex, precise, highspeed and AI controlled equipment and machines that are in increasing demand in industry.

工程领域中使用的几乎所有动态系统都是多体动态 (MBD) 系统，例如机器人、飞机、假肢等中的系统。解决此类系统可能具有挑战性，因为这些系统通常是多维的，并且可能是非线性且复杂的变量之间耦合程度高。因此，在实践中，人们可能不得不依靠数值或近似方法来求解系统，因为 MBD 系统的解析解即使不是不可能，也很难实现。此外，在用现有方法求解此类系统时，通常不可避免地进行线性化和简化，这会对精度和可靠性产生负面影响，甚至可能导致错误的解决方案。因此，通常需要一种具有更高准确度和可靠性的创新方法来求解和分析 MBD 系统。 申请人及其研究团队在开发求解非线性复杂动态系统的新分析和数值方法方面取得了重大研究进展。与其他数值方法（例如最流行的龙格库塔方法）相比，可以用更少的计算时间获得高度准确和可靠的结果。申请人开发的方法和技术为推进拟议的研究计划提供了坚实的基础和工具。 所提出的研究计划的目的是开发一种分段线性化方法，适用于准确可靠地求解和分析非线性 MBD 系统，而使用现有方法很难以所需的精度和可靠性求解这些系统。为了实现这一目标，申请人先前开发的P-T方法和其他方法将被修改和扩展。本研究将结合改进的 P-T 方法、泰勒展开、拉普拉斯变换和留数定理，对 MBD 系统进行理论和数值求解。预计将获得线性 MBD 系统的解析解，并且预计将导出非线性 MBD 系统的连续半解析解以及数值解。预计还可以使用上述分段线性化方法开发一种面向工程应用的算法来求解非线性 MBD 系统。 待开发的方法以及计算算法及其面向工业应用的方向，将显着推进当前求解、分析和优化线性和非线性 MBD 系统的方法。因此，拟议研究计划的结果将切实改善 MBD 系统的设计以及操作和控制质量。这对于工业中需求不断增长的复杂、精确、高速和人工智能控制的设备和机器来说尤其重要。