| Abstract: | Two separate theoretical models are developed to predict the number of heat applications necessary to repair specified bends in damaged steel plates. One model is an application of the theory of reliability; this idealization is subsequently further simplified for practical engineering applications. The second is an application of the theory of stochastic processes: envisioning the record of plastic rotations obtained from the actual heat-straightening of a subject plate as a finite portion of a member of the infinite ensemble of possible records for the repair, and assuming this process to be stationary and ergodic in the heat-number domain, the theory of discrete spectral analysis is used to construct the power spectral density function of the process, and simulate artificial records. Then, simple statistical analysis allows the prediction with any desired degree of confidence. These independent probability-based estimates successfully verify each other. As expected, the required number of repair heats for each test in the ensuing experimental program, under carefully controlled laboratory conditions, was consistently smaller than the corresponding theoretical prediction. |
