Inverse Estimation Problem Research Articles

An inverse problem of temperature estimation for the combination of the linear and nonlinear resistances

The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich). The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.

Dynamic Experiment Design Regularization Approach to Adaptive Imaging with Array Radar/SAR Sensor Systems

We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the “model-free” variational analysis (VA)-based image enhancement approach and the “model-based” descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations.

ICONE19-43403 Inversion Method of Source Term in Nuclear Accident based on Gaussian Puff Model

The inverse problem of source terms information estimation in nuclear accident is important for emergency response. In this study a review of data assimilation applied on atmospheric dispersion is given. For the atmospheric dispersion model is nonlinear and with model errors, ensemble Kalman filter is adopted for data assimilation. The dispersion consequences is described by Gaussian puff model, and the source term emission rate and release height is estimated real-time. To determine the best first guess parameters' value and errors, more than 10 twin experiments have been carried on. The results show that the ensemble Kalman filter can be applied successfully to estimate the source term information when there are one or two unknown parameters, the estimated accuracy is related to first guess value, and is impacted by the standard deviation of perturbation. To reduce the estimation error, first guess value setting to the half to two times of true value is recommended.

A Generalized Cross Validation Method for the Inverse Problem of 3-D Maxwell's Equation

The inverse problem of estimation of the electrical conductivity in the Maxwell’s equation is considered, which is reformulated as a nonlinear equation. The Generalized Cross Validation is used to estimate the global regularization parameter and the damped Gauss-Newton is applied to impose local regularization. The damped Gauss-Newton method requires no calculation of the Hessian matrix which is expensive for traditional Newton method. GCV method decreases the computational expense and overcomes the influence of nonlinearity and ill-posedness. The results of numerical simulation testify that this method is efficient.

ANN based estimation of heat generation from multiple protruding heat sources on a vertical plate under conjugate mixed convection

Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of heat generation in multiple two dimensional protruding heat sources on a vertical plate, a geometry frequently encountered in the cooling of electronic equipment, is carried out from the information available on the temperature distribution on the substrate on which these sources are mounted. A non-iterative method is applied utilizing Artificial Neural Networks (ANN) and covariance analysis to estimate the heat generation in the protruding heat sources on a vertical plate. The forward model involving laminar, two dimensional, steady, incompressible fluid flow and mixed convection heat transfer is numerically solved with FLUENT 6.3 for known values of heat generation in the protruding sources and the temperature distribution thus obtained on the PCB substrate is utilized to train the ANN for the inverse model. Parametric studies are conducted on the forward model to investigate the effect of Richardson number, Reynolds number, the chip and substrate conductivities on the heat dissipation to the fluid flowing over the heat sources. The trained networks are finally used to estimate the heat generation from the sources for a given temperature distribution on the substrate wall generated, for known values of the heat generation rates, which serve as the “measured” temperature distribution. Use is made of covariance analysis in order to identify the important temperature locations sufficient to carry out the inverse analysis. Finally, a systematic investigation on the effect of noise in the temperature “measurements” on the estimates also has been carried out.

An approach to parameters estimation of a chromatography model using a clustering genetic algorithm based inverse model

Genetic algorithms are tools for searching in complex spaces and they have been used successfully in the system identification solution that is an inverse problem. Chromatography models are represented by systems of partial differential equations with non-linear parameters which are, in general, difficult to estimate many times. In this work a genetic algorithm is used to solve the inverse problem of parameters estimation in a model of protein adsorption by batch chromatography process. Each population individual represents a supposed condition to the direct solution of the partial differential equation system, so the computation of the fitness can be time consuming if the population is large. To avoid this difficulty, the implemented genetic algorithm divides the population into clusters, whose representatives are evaluated, while the fitness of the remaining individuals is calculated in function of their distances from the representatives. Simulation and practical studies illustrate the computational time saving of the proposed genetic algorithm and show that it is an effective solution method for this type of application.

A Principal Component Analysis and neural network based non-iterative method for inverse conjugate natural convection

Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of boundary heat flux for a given temperature distribution on the walls of a two dimensional square cavity with a finite wall thickness is considered. A non-iterative method is applied utilizing Artificial Neural Network (ANN) and Principal Component Analysis (PCA) to estimate the parameters that define the boundary heat flux. The forward model is numerically solved with Fluent 6.3 for known values of a linearly varying boundary heat flux and the temperature distribution thus obtained is utilized to train the ANN for the inverse model. A parametric study is carried out to determine the effect of the thermal conductivity of the top and bottom walls on the flow and temperature distribution in the cavity. PCA analysis is carried out to reduce the dimensions of the input data set for the inverse model. These reduced dimensions are used to train the network and due to low dimensionality of the input, the effort required to train the network is considerably less. The trained networks are finally used to estimate boundary heat flux for any desired temperature distribution on the top and bottom walls. Additionally, covariance analysis is carried out in order to estimate the required number of temperatures during an experiment, on the top and bottom walls for the prediction of heat flux with a reasonable accuracy. The inverse model with covariance analysis is compared with the inverse model with PCA and both the methods are found to be equally potent.

A novel application of neural networks for instant iron-ore grade estimation

The inverse problem of magnetic petrophysics is to determine magnetic contents of rocks/ores provided with their susceptibility readings already known. This has not been studied yet due to its unknown applications. This paper proposes a novel application of solving this inverse problem for instant estimation of iron-ore grade in mining. This application is based on numerical simulation using neural networks assisted with 2D interpolation for determining the magnetite and hematite contents through known magnetic susceptibility data. This study shows that a four-layer multilayer perceptron (MLP) trained properly is able to accurately simulate the magnetic contents of iron-ores, which can lead to instant estimation of iron-ore grade in situ in iron-ore mining.

Unifying Experiment Design and Convex Regularization Techniques for Enhanced Imaging With Uncertain Remote Sensing Data—Part I: Theory

This paper considers the problem of high-resolution remote sensing (RS) of the environment formalized in the terms of a nonlinear ill-posed inverse problem of estimation of the power spatial spectrum pattern (SSP) of the wavefield scattered from an extended remotely sensed scene via processing the discrete measurements of a finite number of independent realizations of the observed degraded data signals [single realization of the trajectory signal in the case of synthetic aperture radar (SAR)]. We address a new descriptive experiment design regularization (DEDR) approach to treat the SSP reconstruction problem in the uncertain RS environment that unifies the paradigms of maximum likelihood nonparametric spectral estimation, descriptive experiment design, and worst case statistical performance optimization-based regularization. Pursuing such an approach, we establish a family of the DEDR-related SSP estimators that encompass a manifold of algorithms ranging from the traditional matched filter to the modified robust adaptive spatial filtering and minimum variance beamforming methods. The theoretical study is resumed with the development of a fixed-point iterative DEDR technique that incorporates the regularizing projections onto convex solution sets into the SSP reconstruction procedures to enforce the robustness and convergence. For the imaging SAR application, the proposed DEDR approach is aimed at performing, in a single optimized processing, adaptive SAR focusing, speckle reduction and RS scene image enhancement, and accounts for the possible presence of uncertain trajectory deviations.

Groundwater contaminant boundary input flux estimation in a two-dimensional aquifer

The present study considers the estimation of groundwater input contaminant flux and its transient distribution in a hypothetical two-dimensional aquifer. The paper proposes Kalman filter with recursive least square algorithm (RLSA) technique for the inverse estimation problem. Numerical simulation results reveal that the proposed estimator has outstanding estimation performance both for smooth and abruptly varying input flux. The study further takes into account the dependence of the RLSA technique on the process noise. Selected input scenarios are examined to count for the effect of measurement sensor arrangement and RLSA shows more improved results when sensors number is increased and they are placed closer to the supposed input location.

Inverse heat transfer problem of thermal contact conductance estimation in periodically contacting surfaces

The problems involving periodic contacting surfaces have different practical applications. An inverse heat conduction problem for estimating the periodic Thermal Contact Conductance (TCC) between one-dimensional, constant property contacting solids has been investigated with conjugate gradient method (CGM) of function estimation. This method converges very rapidly and is not so sensitive to the measurement errors. The advantage of the present method is that no a priori information is needed on the variation of the unknown quantities, since the solution automatically determines the functional form over the specified domain. A simple, straight forward technique is utilized to solve the direct, sensitivity and adjoint problems, in order to overcome the difficulties associated with numerical methods. Two general classes of results, the results obtained by applying inexact simulated measured data and the results obtained by using data taken from an actual experiment are presented. In addition, extrapolation method is applied to obtain actual results. Generally, the present method effectively improves the exact TCC when exact and inexact simulated measurements input to the analysis. Furthermore, the results obtained with CGM and the extrapolation results are in agreement and the little deviations can be negligible.

A Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems

This paper investigates a nonlinear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. A Bayesian inference approach is presented for the solution of this problem. The prior modeling is achieved via the Markov random field (MRF). The use of a hierarchical Bayesian method for automatic selection of the regularization parameter in the function estimation inverse problem is discussed. The Markov chain Monte Carlo (MCMC) algorithm is used to explore the posterior state space. Numerical results indicate that MRF provides an effective prior regularization, and the Bayesian inference approach can provide accurate estimates as well as uncertainty quantification to the solution of the inverse problem.

Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative

This paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test is not subject to the ill-posed inverse problem of nonparametric instrumental variable estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n − 1 / 2 , where n is the sample size. Monte Carlo simulations illustrate the finite-sample performance of the test.

Application of a GEO + SA hybrid optimization algorithm to the solution of an inverse radiative transfer problem

In a former study (F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714), a new evolutionary optimization metaheuristic–the generalized extremal optimization (GEO) algorithm (F.L. de Sousa, F.M. Ramos, P.Paglione, and R.M. Girardi, A new stochastic algorithm for design optimization, AIAA J. 41 (2003), pp. 1808–1818)–was applied to the solution of an inverse problem of radiative properties estimation. A comparison with two other stochastic methods; simulated annealing (SA) and genetic algorithms (GA), was also performed, demonstrating GEO's competitiveness for that problem. In the present article, a recently developed hybrid version of GEO and SA (R.L. Galski, Development of improved, hybrid, parallel, and multiobjective versions of the generalized extremal optimization method and its application to the design of spatial systems, D.Sc. Thesis, Instituto Nacional de Pequisas Espaciais, Brazil, 2006, p. 279. INPE-14795-TDI/1238 (in Portuguese)) is applied to the same radiative transfer problem and the results obtained are compared with those from the previous study. The present approach was already foreseen (e.g. in F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714) as a technique that could significantly improve the performance of GEO for this problem. The idea is to make use of a scheduling for GEO's free parameter γ in a similar way to the cooling rate of SA. The main objective of this approach is to combine the good exploration properties of GEO during the early stages of the search with the good convergence properties of SA at the end of the search.

Parameter Estimation for Partial Differential Equations by Collage‐Based Numerical Approximation

The inverse problem of using measurements to estimate unknown parameters of a system often arises in engineering practice and scientific research. This paper proposes a Collage‐based parameter inversion framework for a class of partial differential equations. The Collage method is used to convert the parameter estimation inverse problem into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov‐Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.

Reservoir description using a binary level set model

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from time-lapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.

Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

In this paper, an incremental approach for the identification of a model for transport coefficients in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The identification of the transport model for this transport coefficient constitutes an ill-posed nonlinear inverse problem. We present a novel decomposition approach in which this inverse problem is split into a sequence of inverse subproblems. In the first identification step of this incremental approach a source is estimated by solving an affine-linear inverse problem by means of the conjugate gradient method. In the second identification step a nonlinear inverse problem has to be solved to reconstruct a transport coefficient. A Newton-type method using the conjugate gradient method in its inner iteration is used to solve this nonlinear inverse problem of coefficient estimation. Finally, in the third identification step a transport model structure is proposed and identified on the basis of the model-free transport coefficient reconstructed in the two previous steps. The ill-posedness of each inverse problem is examined by using artificially perturbed transient simulation data and appropriate regularization techniques. The identification methodology is illustrated for a three-dimensional convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.

Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem

The recently developed generalized extremal optimization (GEO) algorithm is applied for the solution of an inverse problem of radiative properties estimation. A comparison with two other stochastic methods, simulated annealing and genetic algorithms, is also performed, demonstrating that GEO is competitive. From the test case results we could also infer that a hybridization of GEO with gradient-based methods is very promising.

Aquifer parameter and zone structure estimation using kernel-based fuzzy c-means clustering and genetic algorithm

Summary In this study, we propose an inverse solution algorithm through which both the aquifer parameters and the zone structure of these parameters can be determined based on a given set of observations on piezometric heads. In the zone structure identification problem, kernel-based fuzzy c-means (KFCM) clustering method is used. The association of the zone structure with the transmissivity distribution is accomplished through a coupled simulation–optimization model. In the optimization model, genetic algorithm (GA) is used due to its efficiency in finding global or near global optimum solutions. Since the solution is based on the GA procedures, the optimization process starts with a randomly generated initial solution. Thus, there is no need to define an initial estimate of the solution. This is an advantage when compared to other studies reported in the literature. Further, the objective function used in the optimization model does not include a reference to field transmissivity data, which is another advantage of the proposed methodology. Numerical examples are provided to demonstrate the performance of the proposed algorithm. In the first example, transmissivity values and zone structures are determined for a known number of zones in the solution domain. In the second example, optimum number of zones as well as the transmissivity values and the zone structures are determined iteratively. A sensitivity analysis is also performed to test the performance of the proposed solution algorithm based on the number of observation data necessary to solve the problem accurately. Numerical results indicate that the proposed algorithm is effective and efficient and may be used in the inverse parameter estimation problems when both parameter values and zone structure are unknown.

Inverse Problem for Estimation of Loads and Support Constraints from Structural Response Data

An important source of uncertainty in finite element models used for static and fatigue analysis is due to inaccuracy In estimating both the magnitude and distribution of loads. Furthermore, it is often assumed in the models that the structure is rigidly supported even though there may be significant compliance at the support. It is often difficult to accurately estimate the compliance as well as the actual distribution of the load. Recent improvements in experimental techniques enable full-field strain measurement with relative ease for structural components. A method for using these measurements to compute the applied load and distribution, as well as compliances at the supported boundaries, is presented in this paper. Accurately determining the loads and boundary conditions can significantly improve the ability to predict fatigue life and the likely location of failure for structures.