Abstract

Recently the data fusion between a camera and a depth sensor of LiDAR type, has become an issue of major concern in industry and engineering. The quality of the delivered 3D models depends greatly on a proper calibration between sensors. This paper presents a sensitivity analysis in a camera-lidar calibration model. The variability of each parameter was calculated individually by the Sobol method, based on ANOVA technique, and the FAST method, which is based on Fourier analysis. Multiple sets of parameters were simulated using Monte Carlo and Latin Hypercube methods for the purpose of comparing the results of the sensitivity analysis. We defined which parameters are the most sensitive and prone to introduce error into our reconstruction platform. Statistics for the total and global sensibility analysis for each sensor and for each parameter are presented. Furthermore, results on the sensitivity ratio on camera-LiDAR calibration, computational cost, time simulation, discrepancy and homogeneity in the simulated data are presented.

Abstract

A general methodology to optimize the weight of power transmission structures is presented in this article. This methodology is based on the simulated annealing algorithm defined by Kirkpatrick in the early ‘80s. This algorithm consists of a stochastic approach that allows to explore and analyze solutions that do not improve the objective function in order to develop a better exploration of the design region and to obtain the global optimum. The proposed algorithm allows to consider the discrete behavior of the sectional variables for each element and the continuous behavior of the general geometry variables. Thus, an optimization methodology that can deal with a mixed optimization problem and includes both continuum and discrete design variables is developed. In addition, it does not require to study all the possible design combinations defined by discrete design variables. The algorithm proposed usually requires to develop a large number of simulations (structural analysis in this case) in practical applications. Thus, the authors have developed first order Taylor expansions and the first order sensitivity analysis involved in order to reduce the CPU time required. Exterior penalty functions have been also included to deal with the design constraints. Thus, the general methodology proposed allows to optimize real power transmission structures in acceptable CPU time.

Abstract

The Urban Seismic Risk index (USRi) published in a previous article (Carreño et al., Nat Hazards 40:137–172, 2007) is a composite indicator that measures risk from an integrated perspective and guides decision-making for identifying the main interdisciplinary
factors of vulnerability to be reduced or intervened. The first step of the method is the evaluation of the potential physical damage (hard approach) as a result of the convolution of the seismic hazard with the physical vulnerability of buildings and infrastructure.
Subsequently, a set of social context conditions that aggravate the physical effects is also considered (soft approach). According to this procedure, the physical risk index is evaluated for each unit of analysis from existing loss scenarios, whereas the total risk index is obtained by multiplying the former index by an impact factor using an aggravating coefficient, based on variables associated with the socio-economic conditions of each unit of analysis. The USRi has been developed using the underlying holistic and multi-hazard approach of the Urban Risk Index framework proposed for the evaluation of disaster risk in different megacities worldwide. This article presents the sensitivity analysis of the index to different parameters such as input data, weights and transformation functions used for the scaling or normalization of variables. This analysis has been performed using the Monte Carlo simulation to validate the robustness of this composite indicator, understanding as robustness how the cities maintain the ranking as well as predefined risk
level ranges, when compared with the deterministic results of risk. Results are shown for different cities of the world.

Abstract

This work analyzes the influence of the discretization error associated with the finite element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of an algorithm for the mesh generation by projection of the discretization error, which reduces the computational cost associated with the adaptive FE analysis of each geometrical configuration and (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process.

Abstract

Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural analysis of an important number of different designs, this making the computational cost of the analysis of each design a critical issue. For this reason, each design must be analyzed at a minimum computational cost but ensuring a minimum quality of the results.

It is well known that the cheapest mesh for producing a solution with a fixed quality at minimum cost is an adapted one. Nevertheless, traditional adapted meshes are obtained from adaptive remeshing strategies, where each design has to be analyzed more than once, thereby also causing a high computational cost.

This work presents a new strategy that allows generating an adapted mesh for each design without the necessity of performing a full adaptive remeshing procedure for each of them. It is based on the use of sensitivity analysis of all magnitudes related with adaptive remeshing (location of nodes, error estimation, etc.) with respect to the design variables. This sensitivity analysis is performed only once using a geometry of reference and it is used to project the results of the corresponding analysis to all other designs to be analyzed. The projected information allows generating an appropriate adapted mesh for each new design in one shot, greatly reducing the computational cost compared with standard strategies.

Abstract

Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture.

Abstract

This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by structural shape optimization algorithms over the behaviour of the algorithm. If the FE analyses are not accurate enough, the final solution will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper also proposes the use of the algorithm described in [1] in order to reduce the computational cost associated to the adaptive FE analysis of each geometrical configuration when evolutive optimization algorithms are used.

Abstract

The Finite Element Method (FEM) has become the most popular numerical method for solving a wide variety of complex engineering problems. However, from the programming point of view, when a FEM program has a lot of computational capabilities it is very difficult to maintain and enlarge the program codes. Recently the object-oriented programming paradigm has become a powerful method for overcoming such difficulties. This paper contains the description of an open environment for the FEM, written in C++, with explanations about how the sensitivity analysis and the non-linear material behaviour (damage models) have been taken into accoun

Abstract

This paper presents a formulation for the obtainment of the sensitivity analysis of a point wise error estimator with respect to the nodal coordinates using the adjoint state method. The proposed point wise error estimator is based on the SPR method.

The numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh. The capability of the presented sensitivity analysis for the detection of pollution error has also been tested.

A new adaptive remeshing strategy based on the sensitivity analysis of the point wise error estimation has been developed and tested. This strategy produces very cheap meshes for the accurate evaluation of stresses at specific points.