Date of Award

August 2019

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Anoop K Dhingra

Committee Members

Ronald Perez, Ilya Avdeev, Devendra Misra, Wilkistar Otieno


D-optimal design, finite element, frequency response function, load identification, optimal sensor placement, Transmissibility


A knowledge of loads acting on a structure is important for analysis and design. There are many applications in which it is difficult to measure directly the dynamic loads acting on a component. In such situations, it may be possible to estimate the imposed loads through a measurement of the system output response. Load identification through output response measurement is an inverse problem that is not only ill-conditioned, but in general leads to multiple solutions. Therefore, additional information, such as number and locations of the imposed loads must be provided ahead of time in order to allow for a unique solution. This dissertation focuses on cases where such information is not readily accessible and presents a method for identification of loads applied to a structure using the concept of response transmissibility. The solution approach is divided into two phases that involve finding the number and location of forces first followed by a reconstruction of the load vector. To achieve the first phase, a complete description of the structure in terms of degrees of freedom needs to be specified and a numerical model, usually a finite element model is built. In order to determine the number of forces and their locations, the proposed algorithm combines the dynamic responses measured experimentally along with the transmissibility matrices obtained from the numerical model. Once the number of loads and their locations are known, a regeneration of the load vector is achieved during the second phase by combining the measured dynamic responses with the transmissibility matrix from the numerical model.

In this dissertation, identification of loads through measurement of structural response at a finite number of optimally selected locations is also investigated. Optimum sensor locations are identified using the D-optimal design algorithm. Two different types of measurements are considered, acceleration measurements using accelerometers and the strain measurements using strain gages.

A series of simulated results on multi-degree of freedom (MDOF) discrete and continuous systems are presented to illustrate the load identification technique based on response transmissibility. One of the factors that affects the accuracy of load reconstruction is the number of vibration modes included in the analysis, which can be a large number. Improvements using model order reduction, not only help reconstruct the input forces accurately, but it also reduces the computational burden significantly.

The developed algorithms are implemented using the finite element tool ANSYS in conjunction with MATLAB software. Numerical sensitivity analysis is also implemented to examine the effect of presence of uncertainties (noise) in experimental data. The results obtained confirm that the techniques presented are robust even in the presence of simulated noise; it is seen that the applied loads are recovered accurately.