## Theses and Dissertations

August 2015

Thesis

#### Degree Name

Master of Science

Engineering

Anoop Dhingra

#### Committee Members

Tim Hunter, Ilya Avdeev

#### Keywords

Distributed Load, Inverse Method, Load Recovery

#### Abstract

Inverse load recovery is a well-researched topic which involves determining an unknown force acting on a structure from the induced strain. The methodology used to determine an unknown loading imposed on a structure begins with a finite element model of the structure. Unit loads are applied at each known load location and the strain data is collected from the model. The strain data collected from the structure during operation or from simulation is compared to the strain produced from the unit loads. The result is an estimate of the imposed load.

In order to obtain the best results possible for the load estimates, the placement of strain gauges are optimized. This research expands on the load recovery topic by exploring the recovery of distributed loads acting on a structure using optimal gauge placement. The objective is to recover an unknown distributed load by utilizing unit basis loading functions comprised of the following distributed load profiles: uniform, ramp up, ramp down, half sine, and exponential functions. Through D-optimal design, the most sensitive locations and orientations for strain gauges for each basis function are found and stored into a correlation matrix. Using the left pseudo inverse of this matrix and multiplying by the strains from an unknown distributed load, a vector representing the relative weight of each basis function required to create the unknown load is obtained. It was found that a distributed load can be accurately recovered using basis functions when the imposed load is a linear combination of the basis functions. If the imposed load does not meet this condition then the load estimation will not be accurate, even though the strains estimated accurately match the strains induced.

As an alternate approach to estimate an imposed load, a full-field analysis method is implemented. This method discretizes a distributed load into point loads which each can then be successfully recovered. This approach is not constrained to any distributed profiles but demands a higher number of gauges to be used.

In both methods (basis functions and full-field) it is seen that the accuracy of estimated loads is directly correlated to the number of gauges used. Increasing the number of gauges will yield a more accurate result. When a 5% signal error is introduced into the problem, both methods struggle to recover the imposed load but are able to recover the strains within 5% of their imposed strains. The error seen in the load recovery is due to the unstable nature of the inverse problem. To counter the instability Tikhonov regularization is utilized.

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