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，人工四肢等中的系统。解决此类系统的求解可能具有挑战性，因为该系统通常是多维的，并且可以是非线性和复杂的，并且具有高度耦合之间的偶数。因此，在实践中，可能必须依靠数值或近似方法来解决系统，因为MBD系统的分析解决方案很难实现，即使不是不可能。此外，在使用现有方法求解此类系统时，线性化和简化通常是不可避免的，这会对准确性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，对于解决和分析MBD系统的一种创新方法，具有更高程度的准确性和可靠性的创新方法。 申请人及其研究团队在开发新的分析和数值方法来解决非线性复杂动态系统方面取得了重大研究进展。与其他数值方法（例如最流行的runge-kutta方法）相比，在计算时间更少的情况下获得了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。 拟议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，这些方法很难使用现有方法以所需的准确性和可靠性来解决。为了实现目标，将修改和扩展申请人和其他方法开发的P-T方法。拟议的研究将结合修改的P-T方法，Taylor扩展，Laplacian转换以及残留理论，从理论和数值求解MBD系统。预计将实现线性MBD系统的分析解决方案，并预计将针对非线性MBD系统得出连续的半分析溶液以及数值解决方案。预计将使用上述分段线性化方法开发针对求解非线性MBD系统的工程应用算法。 将开发的方法以及计算算法及其对工业应用的取向，将大大推动当前的方法来解决，分析和优化线性和非线性MBD系统。因此，拟议的研究计划的结果将切实改善设计以及MBD系统的操作和控制质量。这对于复杂，精确，高速和AI受控的设备和机器尤其重要，这些设备和机器的需求不断增加。