Model Construction and Physical Parameter Identification from Spectral Data

Yitshak M. Ram，路易斯安那州立大学，提案号：9978786光谱数据的模型构建和物理参数识别。研究了基于谱数据的模型重构逆问题，提出了振动系统低阶模型的构造方法。系统的物理参数由导出的模型确定。解决这一问题的主要困难在于振动结构是分布参数系统，而描述分析模型是有限维的。连续系统的谱与相关的有限维模型的谱不一致。为了克服光谱数据不一致带来的困难，将具有连续变量的分布参数系统近似为具有有限个物理参数的连续系统。因此，引入了一个新的具有超越矩阵元素的非线性特征值问题。从波传播的角度出发，用迭代梯度法和牛顿法求解了反问题。利用模态试验数据确定了非均匀振动杆的密度函数和刚度函数，并通过室内实验验证了结果。从光谱数据中识别系统物理参数的基本问题在许多科学和工程领域具有理论重要性和实际应用，例如动态系统控制，声纳和雷达探测。所引入的新的超越逆问题有可能弥合分布参数系统的无限谱和它们的离散代表模型的有限谱之间的差距。因此，表征该特征值问题的性质具有重要的理论和实际意义。

Yitshak M. Ram, Louisiana State University,Proposal Number: 9978786Model Construction and Physical Parameter Identification from Spectral DataProposal Abstract. The inverse problem of reconstructing a model based on spectral data is investigated, and methods for constructing low order models for vibrating systems are developed. The physical parameters of the systems are determined by the derived model. The main difficulty in addressing this problem is that vibrating structures are distributed parameter systems, whereas the descriptive analytical models are finite dimensional. The spectrum of a continuous system is inconsistent with that of the associated finite dimensional model. In order to overcome the difficulty associated with the inconsistency of the spectral data, the distributed parameter system with continuous variables is approximated by a continuous system with a finite number of physical parameters. As a result a new non-linear eigenvalue problem, with transcendental matrix elements, is introduced. The inverse problem is approached by iterative gradient and Newton's methods, and from a wave propagation standpoint. The results are validated by laboratory experiments where the density and rigidity functions of non-uniform vibrating rods are determined by using data from modal tests. The fundamental problem of identifying the physical parameters of a system from spectral data has theoretical importance and practical applications in many areas of science and engineering, e.g. dynamic system control, and sonar and radar detection. The new transcendental inverse problem introduced has the potential of bridging the gap between the infinite spectrum of distributed parameter systems and the finite spectrum of their discrete representative models. Characterization of the properties of this eigenvalue problem is thus of great theoretical and practical importance.