Search results

Estimating parameters of constrained optimization models in a consistent way requires a different set of methods than what is available in a typical econometric toolkit. We identify three complications likely to arise in this context, and suggest solutions to those complications: (i) the bi-level programming character, (ii) ill-posedness, and (iii) derivation of estimator properties. The solutions suggested involve a combination of numerical techniques and utilization of out-of-sample information through Bayesian techniques. The proposed framework is also suitable for typical empirical problems arising in trade analysis such as the estimation of trade equilibrium models and data balancing exercises.

The purpose of this paper is to develop an algorithm, using PCA‐based neural network, to retrieve the vertical rainfall structure in a precipitating atmosphere. The algorithm is powered by a rigorous solution to the plane parallel radiative transfer equation for the atmosphere with thermodynamically consistent vertical profiles of humidity, temperature and cloud structures, together with “measured” vertical profiles of the rain structure derived from a radar.

The raining atmosphere is considered to be a plane parallel, radiatively participating medium. The atmospheric thermodynamic profiles such as pressure, temperature and relative humidity along with wind speed at sea surface and cloud parameters corresponding to Nargis, a category 4 tropical cyclone that made its landfall on May 2, 2008 at the Republic of Myanmar, are obtained by solving the flux form of Euler's equations in three‐dimensional form. The state‐of‐the‐art community software Weather Research and Forecasting has been used for solving the set of equations. The three‐dimensional rain profiles for the same cyclone at the same instant of time are obtained from National Aeronautics and Space Administration's space borne Tropical Rainfall Measuring Mission's precipitation radar over collocated pixels. An in‐house Micro‐Tropiques code is used to perform radiative transfer simulations for frequencies corresponding to a typical space borne radiometer, and hence to generate the database which is later used for training the neural network. The back propagation‐based neural network is optimized with reduced number of parameters using principal component analysis (PCA).

The results show that neural network is capable of retrieving the vertical rainfall structure with a correlation coefficient of over 0.99. Further, reducing the ill‐posedness in retrieving 56 parameters from just nine measurements using PCA has improved the root mean square error in the retrievals at reduced computational time.

The paper shows that combining numerically generated atmospheric profiles together with radar measurements to serve as input to a radiative transfer model brings in the much‐required synergy between numerical weather prediction, radar measurements and radiative transfer. This strategy can be gainfully used in satellite meteorology. Using principal components to reduce the ill‐posedness, thereby increasing the robustness in retrieving vertical rain structure, has been attempted for the first time. A well‐trained network can be used as one possible option for an operational algorithm for the proposed Indian climate research satellite Megha‐Tropiques, due to be launched in early 2011.

A dual integral formulation for a cracked bar under torsion is derived, and a dual boundary element method is implemented. It is shown that as the thickness of the crack becomes thinner, the ill‐posedness for the linear algebraic matrix becomes more serious if the conventional BEM is used. Numerical experiments for solution instability due to ill‐posedness are shown. To deal with this difficulty, the hypersingular equation of the dual boundary integral formulation is employed to obtain an independent constraint equation for the boundary unknowns. For the sake of computational efficiency, the area integral for the torsion rigidity is transformed into two boundary integrals by using Green’s second identity and divergence theorem. Finally, the torsion rigidities for cracks with different lengths and orientations are solved by using the dual BEM, and the results compare well with the analytical solutions and FEM results.

A novel numerical technique is presented with which the temperature profile within a selected transverse plane of an object can be reconstructed provided the boundary data around the transverse plane are known. Numerical simulations of the proposed computed tomography technique are performed to verify its feasibility and accuracy using several heat conduction examples whose exact solutions can be found in literature. Restrictions of and mathematical difficulties encountered in the proposed technique are presented.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker.

Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W² in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W¹ in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W¹. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values.

With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W² and using edge elements in space W¹. When solving the inverse problem in space W¹, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred.

The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

This study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.

Different models based on DNNs are designed and proposed for the resolution of inverse electromagnetic problems either as fast solvers for the direct problem or as straightforward inverse problem solvers, with reference to the TEAM 25 benchmark problem for the sake of exemplification.

Using DNNs as straightforward inverse problem solvers has relevant advantages in terms of promptness but requires a careful treatment of the underlying problem ill-posedness.

This work is one of the first attempts to exploit DNNs for inverse problem resolution in low-frequency electromagnetism. Results on the TEAM 25 test problem show the potential effectiveness of the approach but also highlight the need for a careful choice of the training data set.

The equivalent currents method has proven to be particularly effective in the identification of plasma boundary in Tokamak fusion devices. Anyway, the ill‐posedness of the mathematical model to be inverted calls for the adoption of suitable regularization techniques to be adopted, in particular to reduce the influence of the measurement errors. In this paper the equivalent currents method is illustrated, together with some details on its application to the plasma identification. In addition, two algorithms for the optimal choice of the representation basis are presented, together with a discussion about the obtained numerical results.

The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least‐squares partial differential equations constrained optimization problems exploiting a multiphysics finite elements package. The estimation of the diffusion coefficient in a Poisson‐type diffusion equation is used as an example.

The authors derive the adjoint formulation in a continuous setting allowing to attribute to the direct and adjoint states the role of different fields to be solved for. They are one‐way coupled through the mismatch between measured and direct states acting as a source term in the adjoint equation. Having solved for the direct and adjoint state, the sensitivity of the cost function with respect to the design variables can then be obtained by a suitable post‐processing procedure. This sensitivity can then be used to efficiently solve the least‐squares problem.

The authors derived the adjoint formulation in a continuous setting allowing the direct and adjoint states to be attributed the role of different fields to be solved. They are one‐way coupled through the mismatch between measured and direct states acting as a source term in the adjoint equation. It is found that, having solved for the direct and adjoint state, the sensitivity of the cost function with respect to the design variables can then be obtained by a suitable post‐processing procedure.

This paper implies that modern multiphysics finite elements packages provide a flexible and extendable software environment for the experimentation with different adjoint formulations. Such tools are therefore expected to become increasingly important in solving notoriously difficult partial differential equation (PDE)‐constrained least‐squares problems. The framework also provides the possibility of experimentation with different regularization techniques (total variation and multiscale techniques for instance) to handle the ill‐posedness of the problem.

In this paper the adjoint sensitivity computation is casted as a multiphysics problem allowing for a flexible and extendable implementation.

The purpose of this paper is to explore gas/liquid two-phase flow is widely existed in industrial fields, especially in chemical engineering. Electrical resistance tomography (ERT) is considered to be one of the most promising techniques to monitor the transient flow process because of its advantages such as fast respond speed and cross-section imaging. However, maintaining high resolution in space together with low cost is still challenging for two-phase flow imaging because of the ill-conditioning of ERT inverse problem.

In this paper, a sparse reconstruction (SR) method based on the learned dictionary has been proposed for ERT, to accurately monitor the transient flow process of gas/liquid two-phase flow in a pipeline. The high-level representation of the conductivity distributions for typical flow regimes can be extracted based on denoising the deep extreme learning machine (DDELM) model, which is used as prior information for dictionary learning.

The results from simulation and dynamic experiments indicate that the proposed algorithm efficiently improves the quality of reconstructed images as compared to some typical algorithms such as Landweber and SR-discrete fourier transformation/discrete cosine transformation. Furthermore, the SR-DDELM has also used to estimate the important parameters of the chemical process, a case in point is the volume flow rate. Therefore, the SR-DDELM is considered an ideal candidate for online monitor the gas/liquid two-phase flow.

This paper fulfills a novel approach to effectively monitor the gas/liquid two-phase flow in pipelines. One deep learning model and one adaptive dictionary are trained via the same prior conductivity, respectively. The model is used to extract high-level representation. The dictionary is used to represent the features of the flow process. SR and extraction of high-level representation are performed iteratively. The new method can obviously improve the monitoring accuracy and save calculation time.