Two New Mixture Models Related to the Inverse Gaussian Distribution

This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other well-known distributions.     

DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.     

Numerical solution of an inverse problem for a two-dimensional mathematical model of sorption dynamics

We consider a two-dimensional mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion. The inverse problem of determining the sorption isotherm from an experimental dynamic output curve is investigated for this model and stable solution methods are proposed for the inverse and the direct problem. The efficiency of the solution methods is explored in computer experiments.     

MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

In this paper,we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon(MOS) capactior,First,the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problems is presented .Some matrix analysis tools are applied to explore the parameters‘ sensitivities,And thired,the parameters are extracted using Levenberg-Marquardt optimization method.The essential difficulty arises from the effect of multi-scale physical differeence of the parameters.We explore the relationship between the parameters‘ sensitivitites and the sequencs for optimization,which can seriously affect the final inverse modeling results.An optimal sequence can efficiently overcome the multip-scale problem of these parameters,Numerical experiments show the efficiency of the proposed methods.     

An inverse non-Fourier heat conduction problem approach for estimating the boundary condition in electronic device

This study is intended to provide an inverse method for estimating the unknown boundary condition T(0,y,t) in a non-Fourier heat conduction electronic device. In this study, finite-difference methods are employed to discretize the problem domain, and then a linear inverse model is constructed to identify the unknown boundary condition. The present approach is to rearrange the matrix forms of the differential governing equations and to estimate the unknown conditions. Then, the linear least-squares method is adopted to obtain the solution.The results show that one measuring point is sufficient to estimate the unknown boundary condition T(0,y,t) without measurement errors. When considering the measurement errors, the magnitudes of the discrepancies in the boundary condition T(0,y,t) are directly proportional to the size of measurement errors. Due to the complicated reflection and interaction of the thermal waves, this phenomenon reflects the fact that the inverse non-Fourier heat conduction problem is different from the inverse Fourier heat conduction problem.In contrast to the traditional approach, the advantage of applying this method in inverse analysis is that no prior information is needed on the functional form of the unknown quantities. In addition, no initial guess is required and the calculation can be done in only one iteration.     

Numerical solution method for the inverse problem of the modified fitzhugh–nagumo model

The article considers a modified FitzHugh–Nagumo model that may be applied to model processes associated with myocardial infarct analysis. The inverse problem for this model involves finding the coefficient of a system of partial differential equations dependent on the spatial variables and the solution from supplementary observations of the solution on the boundary. This inverse problem may be interpreted as determining the shape and the location of the region of the heart damaged by myocardial infarct. A numerical method is proposed for the solution of the inverse problem and some computer experiments illustrating its implementation are reported.     

A stochastic model for the direct and inverse problem of adhesive materials

This work deals with the generation of artificial data based on experimental data for adhesive materials and the application of this data to the inverse and the direct problem. In reality there are only a very limited number of experimental data available. Therefore, the prediction of material behaviour is difficult and a statistical analysis with a stochastic proved thesis is nearly impossible. In order to increase the number of tests a method of stochastic simulation based on time series analysis is applied. With artificial data an arbitrary number of data is available and the process of the parameter identification can be statistically analysed. Additionally, one example is shown, which adapts the analysed material parameter to the direct problem. The stochastic finite element method is used to take into account the distribution and deviation of the fracture strain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and analysis of the latent period of osteosarcomas induced by incorporated Pu: The role of immune responses

This paper considers the utility of a stochastic model of carcinogenesis, proposed earlier by Yakovlev and Polig, in quantitative analysis of the incidence of radiation-induced osteosarcomas in beagels injected with various amounts of ²³⁹Pu. The original version of the model failed to provide a good fit to our experimental data. The model has been generalized by incorporating a simple mechanism of lesion elimination, which is likely to be mediated by the immune system. Two versions of the model were developed: the first version ( Model 1 ) assumed malignant cells to be a target for the immune attack, while in Model 2 initiated cells were assumed to be such a target. Model 2 was rejected by the likelihood ratio test, thereby indicating that the competing model provides a more plausible explanation of the experimental data. Since in experiments with incorporated radionuclides the dose rate varies with time, dose-rate effects cannot be observed directly, and one must rely on mathematical models. The results of our numerical experiments show that, depending on the time of observation, both the direct and the inverse dose-rate effects may manifest themselves even at a fixed total dose level.     

The inverse estimation of kinetic parameters of composite materials without using DSC data

Determining the kinetic parameters of a chemical model of the curing process in polymer composites plays an important role in the design of proper cure conditions. The employment of data obtained from the differential scanning calorimetry (DSC) is the main method to estimate the parameters. In this paper, the kinetic parameters are estimated utilizing an inverse heat transfer algorithm and the temperature obtained from a one-dimensional model of cure process without resorting to DSC. The six constants of the Kamal and Sourour model are estimated simultaneously for a composite material by using the Levenberg-Marquardt algorithm. The results of this study agree well with those obtained by experimental methods. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 547–558, July–August, 2008.     

Two Degree-Of-Freedom Online Compensation of a Piezoelectric Micro-Positioning Unit

Due to their almost unlimited resolution and fast dynamics, piezoelectric actuators are a common choice for mechatronic systems targeting positioning tasks with high demands on precision. However, these piezoelectric actuators inherently suffer from nonlinear characteristics (mainly hysteresis and creep effects) which need to be addressed by appropriate control strategies. The operator-based modified Prandtl-Ishlinksii (mPI) approach does not only model hysteresis effects with asymmetries and creep effects but also provides an analytical solution for its inverse model. Online feedforward compensation of the aforementioned nonlinear effects can be realized by using the inverse model and additional weight adaptation. In this paper, online compensation via the mPI model is applied to a commercial micro-positioning unit driven by piezoelectric actuators with more than one degree of freedom (DOF). For validation of the proposed approach, two coupled trajectories in the X-Y plane are utilized. Subsequent tracking error analysis validates the efficacy of the stated approach. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample

In this paper, two sample Bayesian prediction intervals for order statistics (OS) are obtained. This prediction is based on a certain class of the inverse exponential-type distributions using a right censored sample. A general class of prior density functions is used and the predictive cumulative function is obtained in the two samples case. The class of the inverse exponential-type distributions includes several important distributions such the inverse Weibull distribution, the inverse Burr distribution, the loglogistic distribution, the inverse Pareto distribution and the inverse paralogistic distribution. Special cases of the inverse Weibull model such as the inverse exponential model and the inverse Rayleigh model are considered.     

A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography

Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.     

Acoustical Performance of Concreted Wood Fiber Materials

In this paper, an inverse acoustical characterization for determination of porosity, flow resistivity, tortuosity and other parameters of a concreted wood material was proposed. Sound absorption measurements for a concreted wood fiber material were made in an impedance tube. Four acoustical models from literature were briefly described. Each model was fitted to the experimental data in order to compute their unknown parameters. Using a least-square method, the experimental data (sound absorption coefficient) was used to optimize the acoustical models by best-fitting the unknown parameters. The results of this paper show that the presented technique leads to reliable estimates of the physical parameters of the material. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Objective Bayesian analysis for the accelerated degradation model based on the inverse Gaussian process

The inverse Gaussian process is an attractive stochastic process to model monotone degradation paths in degradation analysis. In this paper, we propose an objective Bayesian method to analyze the accelerated degradation model based on the inverse Gaussian process. Noninformative priors including the Jeffreys prior and reference priors are derived, and the propriety of the posteriors under each prior is validated. A simulation study is carried out to investigate the performance of the approach compared with the maximum likelihood method and the Bootstrap method. Numerical results show that the proposed method has better performance in terms of the mean squared error and the frequentist coverage probability. The reference prior ${\pi }_{R_2}$ is recommended to use in practice. Finally, the Bayesian approach is applied to a real data.     

The cosparse analysis model and algorithms

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial.In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments, and provide a detailed study of the model associated with the 2D finite difference analysis operator, a close cousin of the TV norm.     

三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

The application of parameter sensitivity analysis methods to inverse simulation models

Knowledge of the sensitivity of inverse solutions to variation of parameters of a model can be very useful in making engineering design decisions. This article describes how parameter sensitivity analysis can be carried out for inverse simulations generated through approximate transfer function inversion methods and also through the use of feedback principles. Emphasis is placed on the use of sensitivity models and the article includes examples and a case study involving a model of an underwater vehicle. It is shown that the use of sensitivity models can provide physical understanding of inverse simulation solutions that is not directly available using parameter sensitivity analysis methods that involve parameter perturbations and response differencing.     

Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the inverse of certain patterned sums of matrices with Kronecker product structures

In this article, we derive explicit expressions for the entries of the inverse of a patterned matrix that is a sum of Kronecker products. This matrix keeps the Kronecker structure under matrix inversion, and it is used, for example, in statistics, in particular in the linear mixed model analysis. The obtained results present new and extended existing algorithms for the inversion of the considered patterned matrices. We also obtain a closed-form inverse in terms of block matrices.     

Characterization of short fiber reinforced polymers

This contribution presents ideas, how composite materials can be characterized with respect to experimental testing. The material properties of the investigated short glass fiber reinforced polymer are obtained by providing results from the experiment in order to seperate different material effects, such as elasticity, plasticity, damage, viscoelasticity, compressibility and anisotropy. Therefore, at first, linear uniaxial tensile tests with cyclic loadings have been realized. The application of the material in this work is the machining by a three-dimensional forming process. Hence, multiaxial loadings have to be additionally taken into account matching these conditions. In order to provide more information, biaxial tensile tests have to be realized using a testing device supplying the additional necessary experimental data [1, 2]. A final aim of this work is to develope a verification experiment representing the three-dimensional forming process as realistically as possible, e. g. a Nakajima test [4]. For this case, a three-dimensional optical analysis in order to get the necessary measurement data, is indispensable to realize an inverse method [3] by comparing the information of the complete deformation field as well as the force data of the experiment using a given material model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)