The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.
This paper reports the results of a ground penetrating radar (GPR) survey of the ground-floor of Academia Gallery (Florence, Italy) where the Michelangelo’s David is exhibited to the public. The equipment used was a step-frequency GPR operating in the 100 MHz-1 GHz band, named ORFEUS. The survey covered an area of 13 m × 7.3 m, and the scans were performed along two orthogonal directions. Acquisitions in the same direction were separated by 0.25 m from each other. The GPR was able to confirm the underground structure, as it can be deducted by planimetry and historical documentation. In particular, the radar clearly detected the air-conditioning ducts under the floor and an approximately circular foundation below the basement of the statue.
Abstract
In this paper, we will consider an optimal shape problem of heat insulation introduced by [D. Bucur, G. Buttazzo and C. Nitsch, Two optimization problems in thermal insulation, Notices Amer. Math. Soc.
64 (2017), 8, 830–835].
We will establish the existence of optimal shapes in the class of 𝑀-uniform domains.
We will also show that balls are stable solutions of the optimal heat insulation problem.
Updated Kriging-Assisted Shape Optimization of a Gravity Dam
