基于时空解耦的分布随机动态载荷识别与稀疏表征

Obtaining accurate information of distributed random dynamic loads provides effective input for dynamic problems such as vibration control, vibration isolation design, and health monitoring and fault diagnosis. It is an important basis for ensuring the safety and reliability of related complex structural design, optimization, verification and evaluation. In this proposal, the theory and method of identification and sparse characterization of distributed random dynamic loads are studied in time domain, taking into account the difficulties of spatio-temporal coupling, large amount of nested calculation, ill-posed problem, and lack of sample data. Firstly, a spatio-temporal decoupling modeling method of distributed dynamic loads based on proper orthogonal decomposition is developed to separate the identification of time history and spatial distribution of the load. Secondly, considering the non-uniqueness of the distributed dynamic load identification, the load time history identification method based on blind source separation and the sparse representation method based on orthogonal matching pursuit are studied to achieve the equivalent optimal identification of the distributed dynamic load. Thirdly, the interval process characterization of distributed random dynamic loads is studied, and the identification method of statistical characteristics of distributed random dynamic loads based on K-L expansion is developed. Finally, the system integration and application verification of the relevant models and algorithms are carried out. The completion of this proposal will provide a new approach for simplifying the loading conditions of distributed random dynamic loads in engineering, and improve the accuracy and engineering practicability of numerical simulation.

获取准确的分布随机动态载荷信息，为振动控制、减振隔振设计、健康监测与故障诊断等动力学问题提供有效的输入，是保障相关复杂结构设计、优化、校核和评估安全可靠的重要基础。本项目针对分布随机动态载荷时空耦合、嵌套求解计算量大、不适定、样本数据缺乏等难点，在时域内研究其识别与稀疏表征的理论和方法。首先，发展基于本征正交分解的分布动态载荷时空解耦建模方法，实现载荷时间历程和空间分布识别的分离；其次，考虑分布动态载荷识别解的非唯一性，研究基于盲源分离的载荷时间历程识别方法和基于正交匹配追踪的载荷空间分布稀疏表征方法，实现分布动态载荷的等效最优识别；再次，研究分布随机动态载荷的区间过程表征，发展基于K-L展开的分布随机动态载荷统计特性识别方法；最后对相关模型和算法进行系统集成与应用验证。本项目的完成有望为简化工程中分布随机动态载荷的加载条件提供一条新的研究思路，将有效提高数值模拟的准确性和工程实用性。

分布随机动态载荷在工程实际中普遍存在但却难以通过测量获取。其作为振动控制、减振隔振设计、可靠性设计、动力学优化与评估、健康监测与故障诊断等诸多动力学问题的激励条件，是相关结构高可靠性设计、优化、校核和评估的重要基础。为此，本项目围绕载荷表征、载荷时空识别和载荷统计特性反演等关键问题展开研究，提出了一套集载荷本征正交建模、不适定性改善、模态载荷重构、时间历程盲源分离、空间分布稀疏表征以及随机特性区间描述和K-L展开为一体的分布随机动态载荷识别与稀疏表征理论和方法。在载荷数学建模方面，提出了适用于时空独立分布动态载荷和时空耦合分布动态载荷的本征正交解耦模型，通过空间分布函数和时间历程函数描述了载荷的空间和时间特点，并分析了载荷与结构响应的内在映射关系，实现了识别问题的转化；在确定性分布动态载荷识别方面，发展了基于模态载荷重构和盲源分离的载荷时间历程识别方法，针对载荷空间分布函数识别存在多解的情况，提出了载荷等效稀疏表征方法；在载荷的统计特性识别方面，提出了区间过程建模方法，降低了对样本量的依赖，发展了基于K-L级数展开和谱分解的载荷协方差矩阵、半径函数及相关系数函数识别方法；在系统集成及工程应用方面，初步模块化封装了分布动态载荷识别的相关程序，并将相关研究成果应用于某航空发动机叶片的气动载荷识别中。基于该方法，准确获取了分布随机动态载荷的表征模型，合理度量了载荷空间参量和时间参量对结构响应的贡献，有效识别了分布动态载荷时间历程和空间分布的形式、稳定反求了分布随机动态载荷的统计特性，为复杂结构的可靠性设计与评估提供了重要的理论支撑。