Prediction of failure in bending of an aluminium sheet alloy

This work is dedicated to numerical prediction of the bending of thin aluminium alloy sheets, with a focus on the material parameter identification and the prediction of rupture with or without pre-strains in tension prior to bending. The experimental database consists of i) mechanical tests at room temperature, such as tension and simple shear, performed at several orientations to the rolling direction and biaxial tension ii) air bending tests of rectangular samples after (or not) pre-straining in tension. The mechanical model is composed of the Yld2004-18p anisotropic yield criterion (Barlat et al. [3]) associated with a mixed hardening rule. The material parameters (altogether 21) are optimized with an inverse approach, in order to minimize the gap between experimental data and model predictions. Then, the Hosford-Coulomb rupture criterion is used in an uncoupled way, and the parameters are determined from tensile tests, both uniaxial and biaxial, with data up to rupture. In a second step, numerical simulations of the bending tests are performed, either on material in its original state or after pre-straining in tension, with pre-strain magnitudes increasing from 0.19 up to 0.3. The comparisons are performed on different outputs: load evolution, strain field and prediction of the rupture. A very good correlation is obtained over all the tests, in the identification step as well as in the validation one. Moreover, the fracture criterion proves to be successful whatever the amount of pre-strain may be. A convincing representation of the mechanical behavior at room temperature for an aluminium alloy is thus obtained.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Carbon fluxes and pelagic ecosystem dynamics near two western Antarctic Peninsula Adélie penguin colonies: an inverse model approach

An inverse food-web model for the western Antarctic Peninsula (WAP) pelagic food web was constrained with data from Palmer Long Term Ecological Research (PAL-LTER) project annual austral summer sampling cruises. Model solutions were generated for 2 regions with Adelie penguin Pygoscelis adeliae colonies presenting different population trends (a northern and a southern colony) for a 12 yr period (1995-2006). Counter to the standard paradigm, comparisons of carbon flow through bacteria, microzooplankton, and krill showed that the diatom-krill-top predator food chain is not the dominant pathway for organic carbon exchanges. The food web is more complex, including significant contributions by microzooplankton and the microbial loop. Using both inverse model results and network indices, it appears that in the northern WAP the food web is dominated by the microbial food web, with a temporal trend toward its increasing importance. The dominant pathway for the southern WAP food web varies from year to year, with no detectable temporal trend toward dominance of microzooplankton versus krill. In addition, sensitivity analyses indicated that the northern colony of Adelie penguins, whose population size has been declining over the past 35 yr, appears to have sufficient krill during summer to sustain its basic metabolic needs and rear chicks, suggesting the importance of other processes in regulating the Adelie population decline.

Modelling regular and estimable inverse demand systems : a distance function approach

To be useful for policy simulation in the current climate of rapid structural change, inverse demand systems must remain regular over substanstial variations in quantities. The distance function is a convenient vehicle for generating such systems. It also allows convenient imposition of prior ideas about the structure of preferences required for realistic policy work. While the distance function directly yields Hicksian inverse demand functions via the Shepard-Hanoch lemma, they are usually explicit in the unobservable level of utility (u), but lack a closed-form representation in terms of the observable variables. Note however that the unobservability of u need not hinder estimation. A simple one-dimensional numerical inversion allows the estimation of the distance function via the parameters of the implied Marshallian inverse demand functions. This paper develops the formal theory for using distance functions in this context, and reports on initial trials on the operational feasibility of the method.

Leakage Detection And Localization Method Based On A Hybrid Inverse/Direct Modelling Approach Suitable For Handling Multiple-Leak Scenarios

When an accurate hydraulic network model is available, direct modeling techniques are very straightforward and reliable for on-line leakage detection and localization applied to large class of water distribution networks. In general, this type of techniques based on analytical models can be seen as an application of the well-known fault detection and isolation theory for complex industrial systems. Nonetheless, the assumption of single leak scenarios is usually made considering a certain leak size pattern which may not hold in real applications. Upgrading a leak detection and localization method based on a direct modeling approach to handle multiple-leak scenarios can be, on one hand, quite straightforward but, on the other hand, highly computational demanding for large class of water distribution networks given the huge number of potential water loss hotspots. This paper presents a leakage detection and localization method suitable for multiple-leak scenarios and large class of water distribution networks. This method can be seen as an upgrade of the above mentioned method based on a direct modeling approach in which a global search method based on genetic algorithms has been integrated in order to estimate those network water loss hotspots and the size of the leaks. This is an inverse / direct modeling method which tries to take benefit from both approaches: on one hand, the exploration capability of genetic algorithms to estimate network water loss hotspots and the size of the leaks and on the other hand, the straightforwardness and reliability offered by the availability of an accurate hydraulic model to assess those close network areas around the estimated hotspots. The application of the resulting method in a DMA of the Barcelona water distribution network is provided and discussed. The obtained results show that leakage detection and localization under multiple-leak scenarios may be performed efficiently following an easy procedure.

Inverse scattering approach for massive Thirring models with integrable type-II defects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Prediction of Cranio-Maxilofacial Surgical Planning using an Inverse Soft Tissue Modelling Approach

In cranio-maxillofacial surgery, the determination of a proper surgical plan is an important step to attain a desired aesthetic facial profile and a complete denture closure. In the present paper, we propose an efficient modeling approach to predict the surgical planning on the basis of the desired facial appearance and optimal occlusion. To evaluate the proposed planning approach, the predicted osteotomy plan of six clinical cases that underwent CMF surgery were compared to the real clinical plan. Thereafter, simulated soft-tissue outcomes were compared using the predicted and real clinical plan. This preliminary retrospective comparison of both osteotomy planning and facial outlook shows a good agreement and thereby demonstrates the potential application of the proposed approach in cranio-maxillofacial surgical planning prediction.

A guided heuristic approach to the MEG inverse problem.

There is general agreement within the scientific community in considering Biology as the science with more potential to develop in the XXI century. This is due to several reasons, but probably the most important one is the state of development of the rest of experimental and technological sciences. In this context, there are a very rich variety of mathematical tools, physical techniques and computer resources that permit to do biological experiments that were unbelievable only a few years ago. Biology is nowadays taking advantage of all these newly developed technologies, which are been applied to life sciences opening new research fields and helping to give new insights in many biological problems. Consequently, biologists have improved a lot their knowledge in many key areas as human function and human diseases. However there is one human organ that is still barely understood compared with the rest: The human brain. The understanding of the human brain is one of the main challenges of the XXI century. In this regard, it is considered a strategic research field for the European Union and the USA. Thus, there is a big interest in applying new experimental techniques for the study of brain function. Magnetoencephalography (MEG) is one of these novel techniques that are currently applied for mapping the brain activity1. This technique has important advantages compared to the metabolic-based brain imagining techniques like Functional Magneto Resonance Imaging2 (fMRI). The main advantage is that MEG has a higher time resolution than fMRI. Another benefit of MEG is that it is a patient friendly clinical technique. The measure is performed with a wireless set up and the patient is not exposed to any radiation. Although MEG is widely applied in clinical studies, there are still open issues regarding data analysis. The present work deals with the solution of the inverse problem in MEG, which is the most controversial and uncertain part of the analysis process3. This question is addressed using several variations of a new solving algorithm based in a heuristic method. The performance of those methods is analyzed by applying them to several test cases with known solutions and comparing those solutions with the ones provided by our methods.

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Inverse forecasting:a new approach for predictive modelling

In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecasting have become increasingly important in various fields of research such as data mining, economics, business, engineering, medicine, politics, and many others. Despite the large uses of linear programming in forecasting models there is no a single application of inverse optimization reported in the forecasting literature when the time series data is available. Thus the goal of this paper is to introduce inverse optimization into forecasting field, and to provide a streamlined approach to time series analysis and forecasting using inverse linear programming. An application has been used to demonstrate the use of inverse forecasting developed in this study. © 2007 Elsevier Ltd. All rights reserved.