Pub Date : 2020-12-28DOI: 10.1080/17415977.2020.1865344
D. S. Faria, L. T. Stutz, D. Castello
The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters on the modal properties of the system. Inverse analyses are performed under the Bayesian framework and samples of the posterior density function are obtained by means of the Delayed Rejection Adaptive Metropolis (DRAM). The inverse analyses consider a nonlocal viscoelastic beam model with one internal variable and they address three aspects, namely: the impact of a misspecification of the beam diameter, the impact of modelling the beam diameter as an unknown but uninteresting model parameter and the model calibration when synthetic experimental data comes from a model containing two internal variables. The model parameters were chosen such that the system resembles a Single-Walled Carbon Nanotube (SWCNT).
{"title":"Nonlocal viscoelastic Euler-Bernoulli beam model: a Bayesian approach for parameter estimation using the delayed rejection adaptive metropolis algorithm","authors":"D. S. Faria, L. T. Stutz, D. Castello","doi":"10.1080/17415977.2020.1865344","DOIUrl":"https://doi.org/10.1080/17415977.2020.1865344","url":null,"abstract":"The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters on the modal properties of the system. Inverse analyses are performed under the Bayesian framework and samples of the posterior density function are obtained by means of the Delayed Rejection Adaptive Metropolis (DRAM). The inverse analyses consider a nonlocal viscoelastic beam model with one internal variable and they address three aspects, namely: the impact of a misspecification of the beam diameter, the impact of modelling the beam diameter as an unknown but uninteresting model parameter and the model calibration when synthetic experimental data comes from a model containing two internal variables. The model parameters were chosen such that the system resembles a Single-Walled Carbon Nanotube (SWCNT).","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1672 - 1701"},"PeriodicalIF":1.3,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1865344","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49558047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-22DOI: 10.1080/17415977.2020.1864348
B. Sixou
In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied in detail. The variance of the KL functional for Poisson noise is also investigated. The method is applied to the spectral CT inverse problem. Better reconstruction results are obtained with the bilevel method of choice than with a scalar regularization parameter.
{"title":"Adaptative regularization parameter for Poisson noise with a bilevel approach: application to spectral computerized tomography","authors":"B. Sixou","doi":"10.1080/17415977.2020.1864348","DOIUrl":"https://doi.org/10.1080/17415977.2020.1864348","url":null,"abstract":"In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied in detail. The variance of the KL functional for Poisson noise is also investigated. The method is applied to the spectral CT inverse problem. Better reconstruction results are obtained with the bilevel method of choice than with a scalar regularization parameter.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1519 - 1536"},"PeriodicalIF":1.3,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1864348","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48919803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-10DOI: 10.1080/17415977.2020.1849180
M. Dehghan, Nasim Shafieeabyaneh, Mostafa Abbaszadeh
This article is devoted to applying a local meshless method for specifying an unknown control parameter in one- and multi-dimensional inverse problems which are considered with a temperature overspecification condition at a specific point or an energy overspecification condition over the computational domain. Finding the unknowns in inverse problems is a challenge because these problems are modeled as non-classical parabolic problems and also have a significant role in describing physical phenomena of the real world. In this study, a combination of the meshless method of radial basis functions and finite difference method (called radial basis function-finite difference method) is used to solve inverse problems because this method has two important features. First it does not require any mesh generation. Consequently, it can be exerted to handle the high-dimensional inverse problems. Secondly, since this method is local, at each time step, a system with a sparse coefficient matrix is solved. Hence, the computational time and cost will be much low. Various numerical examples are examined, and also the accuracy and computational time required are presented. The numerical results indicate that the mentioned procedure is appropriate for the identification of the unknown parameter of inverse problems.
{"title":"A local meshless procedure to determine the unknown control parameter in the multi-dimensional inverse problems","authors":"M. Dehghan, Nasim Shafieeabyaneh, Mostafa Abbaszadeh","doi":"10.1080/17415977.2020.1849180","DOIUrl":"https://doi.org/10.1080/17415977.2020.1849180","url":null,"abstract":"This article is devoted to applying a local meshless method for specifying an unknown control parameter in one- and multi-dimensional inverse problems which are considered with a temperature overspecification condition at a specific point or an energy overspecification condition over the computational domain. Finding the unknowns in inverse problems is a challenge because these problems are modeled as non-classical parabolic problems and also have a significant role in describing physical phenomena of the real world. In this study, a combination of the meshless method of radial basis functions and finite difference method (called radial basis function-finite difference method) is used to solve inverse problems because this method has two important features. First it does not require any mesh generation. Consequently, it can be exerted to handle the high-dimensional inverse problems. Secondly, since this method is local, at each time step, a system with a sparse coefficient matrix is solved. Hence, the computational time and cost will be much low. Various numerical examples are examined, and also the accuracy and computational time required are presented. The numerical results indicate that the mentioned procedure is appropriate for the identification of the unknown parameter of inverse problems.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1369 - 1400"},"PeriodicalIF":1.3,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1849180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47060215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-10DOI: 10.1080/17415977.2020.1858077
A. Timonov
The total variation minimization is proposed for use in recovering the mass density of a fluid medium from back-scattered acoustic waves by the dynamical version of the boundary control method. This may be of particular interest to underwater acoustic imaging or ultrasound tomography. In particular, an analogue of the regularized mean curvature flow equation is proposed and developed to obtain numerical solution of the system of linear equations with the ill-conditioned Gram matrix. To demonstrate the computational effectiveness of the proposed numerical technique, we conduct a series of numerical experiments with the inverse problem for a 1 + 1 dimensional acoustic wave equation.
{"title":"Regularization of the boundary control method for numerical solutions of the inverse problem for an acoustic wave equation","authors":"A. Timonov","doi":"10.1080/17415977.2020.1858077","DOIUrl":"https://doi.org/10.1080/17415977.2020.1858077","url":null,"abstract":"The total variation minimization is proposed for use in recovering the mass density of a fluid medium from back-scattered acoustic waves by the dynamical version of the boundary control method. This may be of particular interest to underwater acoustic imaging or ultrasound tomography. In particular, an analogue of the regularized mean curvature flow equation is proposed and developed to obtain numerical solution of the system of linear equations with the ill-conditioned Gram matrix. To demonstrate the computational effectiveness of the proposed numerical technique, we conduct a series of numerical experiments with the inverse problem for a 1 + 1 dimensional acoustic wave equation.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1477 - 1496"},"PeriodicalIF":1.3,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1858077","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45393313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-10DOI: 10.1080/17415977.2020.1856102
Kai Yang, Jinbo Liu, T. Zhu, Hui Wang, Xinxin Zhu
ABSTRACT Fuzzy inference method is applied to formulate an algorithm capable of estimating material elastic constants (ECs) of a specimen by solving an inverse problem with a group of measured resonance frequencies obtained via Resonant Ultrasound Spectroscopy (RUS). The algorithm is validated with RUS data from a specimen of polycrystalline aluminium alloy. Then the algorithm is found to be sensitive to the initial ECs by processing RUS data from a specimen of fine-grain polycrystalline Ti–6Al–4V, the same as the Levenberg–Marquardt (L–M) method popularly used in solving inverse problems. To overcome such a drawback, a hybrid method of Particle Swarm Optimization (PSO) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is proposed. And it is used to generate several groups of initial ECs for the fuzzy inference method. There is a trade-off between computational time and accurately estimated ECs, since the hybrid method needs more time to directly find out accurate ECs.
{"title":"PSO-aided fuzzy inference of material elastic constants with resonant ultrasound spectroscopy","authors":"Kai Yang, Jinbo Liu, T. Zhu, Hui Wang, Xinxin Zhu","doi":"10.1080/17415977.2020.1856102","DOIUrl":"https://doi.org/10.1080/17415977.2020.1856102","url":null,"abstract":"ABSTRACT Fuzzy inference method is applied to formulate an algorithm capable of estimating material elastic constants (ECs) of a specimen by solving an inverse problem with a group of measured resonance frequencies obtained via Resonant Ultrasound Spectroscopy (RUS). The algorithm is validated with RUS data from a specimen of polycrystalline aluminium alloy. Then the algorithm is found to be sensitive to the initial ECs by processing RUS data from a specimen of fine-grain polycrystalline Ti–6Al–4V, the same as the Levenberg–Marquardt (L–M) method popularly used in solving inverse problems. To overcome such a drawback, a hybrid method of Particle Swarm Optimization (PSO) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is proposed. And it is used to generate several groups of initial ECs for the fuzzy inference method. There is a trade-off between computational time and accurately estimated ECs, since the hybrid method needs more time to directly find out accurate ECs.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1429 - 1444"},"PeriodicalIF":1.3,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1856102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46000500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-08DOI: 10.1080/17415977.2020.1849181
O. Furat, U. Frank, Matthias Weber, S. Wawra, W. Peukert, V. Schmidt
ABSTRACT The properties of complex particle systems typically depend on multivariate distributions of particle properties, like size and shape characteristics. Multidimensional particle property distributions can be a powerful tool to describe these systems. However, only few techniques exist which are able to simultaneously measure more than one property of individual particles in fast and efficient ways. It is shown how two-dimensional property spaces can be constructed by the combination of two univariate measurements to obtain bivariate particle size distributions. The proposed method is a general approach, which can be applied to a wide spectrum of particle systems and measurement devices. In this paper, the results of a case study are presented, which allow the estimation of bivariate distributions of length and diameter of nanorods, solely using univariate distributions of their particle mass and extinction-weighted sedimentation coefficient distributions. These quantities contain joint information about the particle lengths and diameters, which is used for the reconstruction. The method is validated in a simulation study in which the bivariate distribution to be reconstructed and the reconstruction parameters are varied. In addition, regularization techniques are introduced to reduce methodical errors. This approach can be transferred to other particle systems and measurement techniques, for which functional relationships between particle properties and measured quantities are well described.
{"title":"Estimation of bivariate probability distributions of nanoparticle characteristics, based on univariate measurements","authors":"O. Furat, U. Frank, Matthias Weber, S. Wawra, W. Peukert, V. Schmidt","doi":"10.1080/17415977.2020.1849181","DOIUrl":"https://doi.org/10.1080/17415977.2020.1849181","url":null,"abstract":"ABSTRACT The properties of complex particle systems typically depend on multivariate distributions of particle properties, like size and shape characteristics. Multidimensional particle property distributions can be a powerful tool to describe these systems. However, only few techniques exist which are able to simultaneously measure more than one property of individual particles in fast and efficient ways. It is shown how two-dimensional property spaces can be constructed by the combination of two univariate measurements to obtain bivariate particle size distributions. The proposed method is a general approach, which can be applied to a wide spectrum of particle systems and measurement devices. In this paper, the results of a case study are presented, which allow the estimation of bivariate distributions of length and diameter of nanorods, solely using univariate distributions of their particle mass and extinction-weighted sedimentation coefficient distributions. These quantities contain joint information about the particle lengths and diameters, which is used for the reconstruction. The method is validated in a simulation study in which the bivariate distribution to be reconstructed and the reconstruction parameters are varied. In addition, regularization techniques are introduced to reduce methodical errors. This approach can be transferred to other particle systems and measurement techniques, for which functional relationships between particle properties and measured quantities are well described.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1343 - 1368"},"PeriodicalIF":1.3,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1849181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48844932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-25DOI: 10.1080/17415977.2020.1849183
Hoang-Hung Vo, Triet Le Minh, Phong Luu Hong, Canh Vo Van
Fractional derivative is an important notion in the study of the contemporary mathematics not only because it is more mathematically general than the classical derivative but also it really has applications to understand many physical phenomena. In particular, fractional derivatives are related to long power-law particle jumps, which can be understood as transient anomalous sub-diffusion model (see Sabzikar F, Meerschaert M, Chen J. Tempered fractional calculus. J Comput Phys. 2015;293:14–28; Sokolov IM, Klafter J, Blumen A. Fractional kinetics. Phys Today. 2002;55:48–54; Sokolov IM, Klafter J. Anomalous diffusion spreads its wings. Phys World. 2005;18:19–22; Zhang Y, Meerschaert MM, Packman AI. Linking fluvial bed sediment transport across scales. Geophys Res Lett. 2012;39(20):20404. doi:10.1029/2012GL053476). Based on the models given in Scher H, Montroll EW. Anomalous transit-time dispersion in amorphous solids. Phys Rev B. 1975;12(6):2455–2477 and Zheng GH, Wei T. Spectral regularization method for solving a time-fractional inverse diffusion problem. Appl Math Comput. 2011;218:1972–1990, we study an inverse problem for the advection equation with a nonlinear reaction term in a two-dimensional semi-infinite domain for which we recover the initial distribution from the observation data provided at the final location x = 1. This problem is severely ill-posed in the sense of Hadamard. Thus, we propose a regularization method to construct an approximate solution for the problem. From that, convergence rate of the regularized solution is obtained under some a priori bound assumptions on the exact solution. Eventually, a numerical experiment is given to show the effectiveness of the proposed regularization methods.
分数阶导数是当代数学研究中的一个重要概念，不仅因为它比经典阶导数在数学上更具有普遍性，而且在理解许多物理现象方面也有实际应用。特别是，分数阶导数与长幂律粒子跳变有关，可以理解为瞬态异常亚扩散模型(见Sabzikar F, Meerschaert M, Chen J.回火分数阶微积分)。计算物理学报，2015;29 (3):14 - 28;刘建军，张建军，张建军，等。物理学报。2002;55:48-54;李建军，李建军，李建军，等。物理世界。2005;18:19-22;张勇，Meerschaert MM, Packman AI。连接河床沉积物跨尺度运输。地球物理学报，2012;39(20):20404。gl053476 doi: 10.1029/2012)。基于Scher H给出的模型，Montroll EW。非晶态固体中的异常跃迁时间色散。郑光华，魏涛。求解时间分数阶逆扩散问题的谱正则化方法。物理学报，1995;12(6):2455-2477。应用数学计算，2011;18:1972 - 1990，研究了二维半无限域中非线性平流方程的反问题，从最终位置x = 1处提供的观测数据恢复了平流方程的初始分布。这个问题在Hadamard意义上是严重病态的。因此，我们提出一种正则化方法来构造该问题的近似解。由此，在精确解的先验界假设下，得到了正则解的收敛速率。最后，通过数值实验验证了所提正则化方法的有效性。
{"title":"An inverse problem for a time-fractional advection equation associated with a nonlinear reaction term","authors":"Hoang-Hung Vo, Triet Le Minh, Phong Luu Hong, Canh Vo Van","doi":"10.1080/17415977.2020.1849183","DOIUrl":"https://doi.org/10.1080/17415977.2020.1849183","url":null,"abstract":"Fractional derivative is an important notion in the study of the contemporary mathematics not only because it is more mathematically general than the classical derivative but also it really has applications to understand many physical phenomena. In particular, fractional derivatives are related to long power-law particle jumps, which can be understood as transient anomalous sub-diffusion model (see Sabzikar F, Meerschaert M, Chen J. Tempered fractional calculus. J Comput Phys. 2015;293:14–28; Sokolov IM, Klafter J, Blumen A. Fractional kinetics. Phys Today. 2002;55:48–54; Sokolov IM, Klafter J. Anomalous diffusion spreads its wings. Phys World. 2005;18:19–22; Zhang Y, Meerschaert MM, Packman AI. Linking fluvial bed sediment transport across scales. Geophys Res Lett. 2012;39(20):20404. doi:10.1029/2012GL053476). Based on the models given in Scher H, Montroll EW. Anomalous transit-time dispersion in amorphous solids. Phys Rev B. 1975;12(6):2455–2477 and Zheng GH, Wei T. Spectral regularization method for solving a time-fractional inverse diffusion problem. Appl Math Comput. 2011;218:1972–1990, we study an inverse problem for the advection equation with a nonlinear reaction term in a two-dimensional semi-infinite domain for which we recover the initial distribution from the observation data provided at the final location x = 1. This problem is severely ill-posed in the sense of Hadamard. Thus, we propose a regularization method to construct an approximate solution for the problem. From that, convergence rate of the regularized solution is obtained under some a priori bound assumptions on the exact solution. Eventually, a numerical experiment is given to show the effectiveness of the proposed regularization methods.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"23 6","pages":"1178 - 1198"},"PeriodicalIF":1.3,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1849183","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41272475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-21DOI: 10.1080/17415977.2020.1850716
Lijun Zhao
ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.
{"title":"Submatrix constrained left and right inverse eigenvalue problem for centrosymmetric matrices","authors":"Lijun Zhao","doi":"10.1080/17415977.2020.1850716","DOIUrl":"https://doi.org/10.1080/17415977.2020.1850716","url":null,"abstract":"ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"11 1","pages":"1412 - 1428"},"PeriodicalIF":1.3,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1850716","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59998019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-20DOI: 10.1080/17415977.2020.1849182
Xiangcheng Zheng, Hong Wang
ABSTRACT We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be performed and ensures that with these observations the uniqueness of the identification is theoretically guaranteed.
{"title":"Uniquely identifying the variable order of time-fractional partial differential equations on general multi-dimensional domains","authors":"Xiangcheng Zheng, Hong Wang","doi":"10.1080/17415977.2020.1849182","DOIUrl":"https://doi.org/10.1080/17415977.2020.1849182","url":null,"abstract":"ABSTRACT We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be performed and ensures that with these observations the uniqueness of the identification is theoretically guaranteed.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1401 - 1411"},"PeriodicalIF":1.3,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1849182","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47670552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-20DOI: 10.1080/17415977.2020.1845669
Ulrika Lagerblad, H. Wentzel, A. Kulachenko
ABSTRACT This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration measurements. Two numerical examples are examined in order to study the influence of model errors and measurement noise on the estimate quality. From simulations of a simply supported beam, it is shown that estimates from the smoother are superior to those of a conventional Kalman filter, both when the level of model error and measurement noise are increased. By studying simulations of a truck component, the improvement due to smoothing over a conventional Kalman filter is shown to be even greater when the model error is present in both the eigenfrequencies and the mode shapes. In addition, a sensitivity analysis of a tuning methodology with the assumption of constant noise covariance matrices is performed. The result indicates that the proposed tuning methodology results in stable estimates with a good trade-off between estimator adaptability and noise sensitivity. The presented approach of tuning and evaluating the estimates is therefore suggested as a guideline for using the fixed-lag smoother when solving input and state estimation problems in vibrating structures.
{"title":"Study of a fixed-lag Kalman smoother for input and state estimation in vibrating structures","authors":"Ulrika Lagerblad, H. Wentzel, A. Kulachenko","doi":"10.1080/17415977.2020.1845669","DOIUrl":"https://doi.org/10.1080/17415977.2020.1845669","url":null,"abstract":"ABSTRACT This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration measurements. Two numerical examples are examined in order to study the influence of model errors and measurement noise on the estimate quality. From simulations of a simply supported beam, it is shown that estimates from the smoother are superior to those of a conventional Kalman filter, both when the level of model error and measurement noise are increased. By studying simulations of a truck component, the improvement due to smoothing over a conventional Kalman filter is shown to be even greater when the model error is present in both the eigenfrequencies and the mode shapes. In addition, a sensitivity analysis of a tuning methodology with the assumption of constant noise covariance matrices is performed. The result indicates that the proposed tuning methodology results in stable estimates with a good trade-off between estimator adaptability and noise sensitivity. The presented approach of tuning and evaluating the estimates is therefore suggested as a guideline for using the fixed-lag smoother when solving input and state estimation problems in vibrating structures.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1260 - 1281"},"PeriodicalIF":1.3,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1845669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42176944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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