Pub Date : 2021-09-15DOI: 10.1080/17415977.2021.1974855
H. Fu, Hongyu Qi, Ran Hua
ABSTRACT We study the full-waveform inversion (FWI) problem for the recovery of velocity model/image in acoustic media. FWI is formulated as a typical nonlinear optimization problem, many regularization techniques are used to guide the optimization process because the FWI problem is strongly ill-posed. Recently, sparsity regularization has attracted considerable attention in the field of inverse problems. In addition, the nonlocal similarity is also an inherent property of many subsurface images themselves. In this paper, we present a novel computational framework for FWI based on joint local sparsity and nonlocal self-similarity. First, principal component analysis (PCA)-based dictionary learns from noisy approximation images (the estimated results from certain local optimization method) and the learned dictionary is used to guide similar patch grouping. Second, the sparse representation and the nonlocal similarity are introduced as the regularization term. At last, the relative total variation (RTV) algorithm is used to further eliminate the residual artefacts in the reconstructed model more thoroughly. In our inversion strategy, the external optimization knowledge, and the intrinsic local sparsity and nonlocal self-similarity prior of model are used jointly for FWI. Computational results demonstrate the proposed method is obviously superior to existing inversion methods both qualitatively and quantitatively, including total variation FWI method in model-derivative domain and sparsity promoting FWI method in the curvelet domain.
{"title":"Combining adaptive dictionary learning with nonlocal similarity for full-waveform inversion","authors":"H. Fu, Hongyu Qi, Ran Hua","doi":"10.1080/17415977.2021.1974855","DOIUrl":"https://doi.org/10.1080/17415977.2021.1974855","url":null,"abstract":"ABSTRACT We study the full-waveform inversion (FWI) problem for the recovery of velocity model/image in acoustic media. FWI is formulated as a typical nonlinear optimization problem, many regularization techniques are used to guide the optimization process because the FWI problem is strongly ill-posed. Recently, sparsity regularization has attracted considerable attention in the field of inverse problems. In addition, the nonlocal similarity is also an inherent property of many subsurface images themselves. In this paper, we present a novel computational framework for FWI based on joint local sparsity and nonlocal self-similarity. First, principal component analysis (PCA)-based dictionary learns from noisy approximation images (the estimated results from certain local optimization method) and the learned dictionary is used to guide similar patch grouping. Second, the sparse representation and the nonlocal similarity are introduced as the regularization term. At last, the relative total variation (RTV) algorithm is used to further eliminate the residual artefacts in the reconstructed model more thoroughly. In our inversion strategy, the external optimization knowledge, and the intrinsic local sparsity and nonlocal self-similarity prior of model are used jointly for FWI. Computational results demonstrate the proposed method is obviously superior to existing inversion methods both qualitatively and quantitatively, including total variation FWI method in model-derivative domain and sparsity promoting FWI method in the curvelet domain.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3148 - 3166"},"PeriodicalIF":1.3,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43700052","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 : 2021-09-15DOI: 10.1080/17415977.2021.1975700
Jia Liu, Ting-jun Zhang, G. Clow, Elchin E. Jafarov
We present a numerical Tikhonov regularization method that can be used to reconstruct past ground surface temperature (GST) records from borehole temperatures. The present ground temperature preserves past climatic signals according to the heat diffusion process in permafrost-affected soils. To track past surface temperature, we employ an inverse method based on a physical connection between GST and measured borehole temperatures. We validate this method by applying it to two synthetic surface temperature cases. Since measured borehole data include uncertainty, we add random noise to our synthetic input borehole data to simulate the process of noise suppression. GST recovered with corresponding uncertainty shows a close match with synthetic surface temperature for both cases. We show that this method can successfully suppress the noise disturbance and achieve smoother solutions.The ability of borehole temperature data to resolve past climatic events is investigated using the Tikhonov method. We investigated past GST of Wudaoliang on Qinghai-Tibet plateau and the inversion result shows the increasing trend of 1.8 (±1.6) in the past 308 years. This GST trend fits the air temperature observation trend but has small value deviation caused by local topography and surface energy budgets of the ground surface.
{"title":"Application of Tikhonov regularization to reconstruct past climate record from borehole temperature","authors":"Jia Liu, Ting-jun Zhang, G. Clow, Elchin E. Jafarov","doi":"10.1080/17415977.2021.1975700","DOIUrl":"https://doi.org/10.1080/17415977.2021.1975700","url":null,"abstract":"We present a numerical Tikhonov regularization method that can be used to reconstruct past ground surface temperature (GST) records from borehole temperatures. The present ground temperature preserves past climatic signals according to the heat diffusion process in permafrost-affected soils. To track past surface temperature, we employ an inverse method based on a physical connection between GST and measured borehole temperatures. We validate this method by applying it to two synthetic surface temperature cases. Since measured borehole data include uncertainty, we add random noise to our synthetic input borehole data to simulate the process of noise suppression. GST recovered with corresponding uncertainty shows a close match with synthetic surface temperature for both cases. We show that this method can successfully suppress the noise disturbance and achieve smoother solutions.The ability of borehole temperature data to resolve past climatic events is investigated using the Tikhonov method. We investigated past GST of Wudaoliang on Qinghai-Tibet plateau and the inversion result shows the increasing trend of 1.8 (±1.6) in the past 308 years. This GST trend fits the air temperature observation trend but has small value deviation caused by local topography and surface energy budgets of the ground surface.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3167 - 3189"},"PeriodicalIF":1.3,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44684140","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 : 2021-09-11DOI: 10.1080/17415977.2021.1972997
A. Carasso
Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed, forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized, marched backward in time, and provide useful reconstructions in an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier–Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. Eventually, this leads to a distortion away from the true solution. This is the stabilization penalty. In many interesting cases, that penalty is sufficiently small to allow for useful results. Effective smoothing operators based on , with real p>2, can be efficiently synthesized using FFT algorithms. Similar stabilizing techniques were successfully applied in several other ill-posed evolution equations. The analysis of numerical stability is restricted to a related linear problem. However, as is found in leapfrog computations of well-posed meteorological and oceanic wave propagation problems, such linear stability is necessary but not sufficient in the presence of nonlinearities. Here, likewise, additional Robert–Asselin–Williams (RAW) time-domain filtering must be used to prevent characteristic leapfrog nonlinear instability unrelated to ill-posedness. Several 2D Navier–Stokes backward reconstruction examples are included, based on the stream function-vorticity formulation, and focusing on pixel images of recognizable objects. Such images, associated with non-smooth underlying intensity data, are used to create severely distorted data at time T>0. Successful backward recovery is shown to be possible at parameter values significantly exceeding expectations.
{"title":"Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)2 stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations","authors":"A. Carasso","doi":"10.1080/17415977.2021.1972997","DOIUrl":"https://doi.org/10.1080/17415977.2021.1972997","url":null,"abstract":"Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed, forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized, marched backward in time, and provide useful reconstructions in an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier–Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. Eventually, this leads to a distortion away from the true solution. This is the stabilization penalty. In many interesting cases, that penalty is sufficiently small to allow for useful results. Effective smoothing operators based on , with real p>2, can be efficiently synthesized using FFT algorithms. Similar stabilizing techniques were successfully applied in several other ill-posed evolution equations. The analysis of numerical stability is restricted to a related linear problem. However, as is found in leapfrog computations of well-posed meteorological and oceanic wave propagation problems, such linear stability is necessary but not sufficient in the presence of nonlinearities. Here, likewise, additional Robert–Asselin–Williams (RAW) time-domain filtering must be used to prevent characteristic leapfrog nonlinear instability unrelated to ill-posedness. Several 2D Navier–Stokes backward reconstruction examples are included, based on the stream function-vorticity formulation, and focusing on pixel images of recognizable objects. Such images, associated with non-smooth underlying intensity data, are used to create severely distorted data at time T>0. Successful backward recovery is shown to be possible at parameter values significantly exceeding expectations.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3062 - 3085"},"PeriodicalIF":1.3,"publicationDate":"2021-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41626244","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 : 2021-09-07DOI: 10.1080/17415977.2021.1973455
Sufia Khatoon, J. Phirani, Supreet Singh Bahga
The forecast for oil production from an oil reservoir is made with the aid of reservoir simulations. The model parameters in reservoir simulations are uncertain whose values are estimated by matching the simulation predictions with production history. Bayesian inference (BI) provides a convenient way of estimating parameters of a mathematical model, starting from a probable distribution of parameter values and knowing the production history. BI techniques for history matching require Markov chain Monte Carlo (MCMC) sampling methods, which involve large number of reservoir simulations. This limits the application of BI for history matching in petroleum reservoir engineering, where each reservoir simulation can be computationally expensive. To overcome this limitation, we use polynomial chaos expansions (PCEs), which represent the uncertainty in production forecasts due to the uncertainty in model parameters, to construct proxy models for model predictions. As an application of the method, we present history matching in simulations based on the black-oil model to estimate model parameters such as porosity, permeability, and exponents of the relative permeability curves. Solutions to these history matching problems show that the PCE-based method enables accurate estimation of model parameters with two orders of magnitude less number of reservoir simulations compared with MCMC method.
{"title":"Accelerated Bayesian inference-based history matching of petroleum reservoirs using polynomial chaos expansions","authors":"Sufia Khatoon, J. Phirani, Supreet Singh Bahga","doi":"10.1080/17415977.2021.1973455","DOIUrl":"https://doi.org/10.1080/17415977.2021.1973455","url":null,"abstract":"The forecast for oil production from an oil reservoir is made with the aid of reservoir simulations. The model parameters in reservoir simulations are uncertain whose values are estimated by matching the simulation predictions with production history. Bayesian inference (BI) provides a convenient way of estimating parameters of a mathematical model, starting from a probable distribution of parameter values and knowing the production history. BI techniques for history matching require Markov chain Monte Carlo (MCMC) sampling methods, which involve large number of reservoir simulations. This limits the application of BI for history matching in petroleum reservoir engineering, where each reservoir simulation can be computationally expensive. To overcome this limitation, we use polynomial chaos expansions (PCEs), which represent the uncertainty in production forecasts due to the uncertainty in model parameters, to construct proxy models for model predictions. As an application of the method, we present history matching in simulations based on the black-oil model to estimate model parameters such as porosity, permeability, and exponents of the relative permeability curves. Solutions to these history matching problems show that the PCE-based method enables accurate estimation of model parameters with two orders of magnitude less number of reservoir simulations compared with MCMC method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3086 - 3116"},"PeriodicalIF":1.3,"publicationDate":"2021-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47429471","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 : 2021-09-02DOI: 10.1080/17415977.2021.1967344
Shuyong Duan, Li Wang, Fang Wang, Xu Han, Guirong Liu
Joint stiffnesses of robot arms play a critical role in the control of the posture and movement of the arm tip. This work develops a systematic approach for inverse real-time quantitative identification of the stiffnesses of joints for robotic arms using the TubeNet proposed by Liu. To start with, a finite element (FE) model for a six-axis tandem robot arm is established. Experiments are then conducted to measure the first few lowest natural frequencies of the robot arm to be compared with numerical results for the validation of the FE model. Using the validated FEM model, sensitivity analyses of the joint stiffnesses to the natural frequencies are carried out to ensure sufficient sensitivity for inverse analyses and a neural network data set is established. The selection of appropriate TubeNet layers and activation functions is exposited. Subsequently, the direct-weights-inversion (DWI) formulae for the TubeNet is adopted to inversely compute the joint stiffnesses explicitly in real time. The predicated joint stiffness using the currently proposed DWI formulae of the TubeNet is accurate with the maximum root-mean-square of test errors less than 0.0020 N·m/rad.
{"title":"A technique for inversely identifying joint stiffnesses of robot arms via two-way TubeNets","authors":"Shuyong Duan, Li Wang, Fang Wang, Xu Han, Guirong Liu","doi":"10.1080/17415977.2021.1967344","DOIUrl":"https://doi.org/10.1080/17415977.2021.1967344","url":null,"abstract":"Joint stiffnesses of robot arms play a critical role in the control of the posture and movement of the arm tip. This work develops a systematic approach for inverse real-time quantitative identification of the stiffnesses of joints for robotic arms using the TubeNet proposed by Liu. To start with, a finite element (FE) model for a six-axis tandem robot arm is established. Experiments are then conducted to measure the first few lowest natural frequencies of the robot arm to be compared with numerical results for the validation of the FE model. Using the validated FEM model, sensitivity analyses of the joint stiffnesses to the natural frequencies are carried out to ensure sufficient sensitivity for inverse analyses and a neural network data set is established. The selection of appropriate TubeNet layers and activation functions is exposited. Subsequently, the direct-weights-inversion (DWI) formulae for the TubeNet is adopted to inversely compute the joint stiffnesses explicitly in real time. The predicated joint stiffness using the currently proposed DWI formulae of the TubeNet is accurate with the maximum root-mean-square of test errors less than 0.0020 N·m/rad.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3041 - 3061"},"PeriodicalIF":1.3,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44418258","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 : 2021-08-26DOI: 10.1080/17415977.2021.1948543
Xiang Gao, Xiafei Li, Hong-juan Yang, J. Jiao, Cheng-hao Wang
The problem of target detection and localization in layered media can be solved by the mixed TR–RTM. The highlight of this paper is on multilayer media, where the target is harder to detect than in double-layered media, due to the interference of multiple interface reflection signals. The core idea of the TR–RTM mixed method, namely the RTM isochronism principle, is applied for the three cases. Typically, a target under a TR–RTM process can form a mountain-like acoustic field distribution. For the interface whose reflected signal is an interference, the acoustic field distribution is disordered and inhomogeneous, with a smaller amplitude. The TR–RTM greatly improves the signal-to-interference ratio, where the position of the summit is the just position of the target, thus, detecting and localizing the target.
{"title":"Target-detection and localization in multilayered media through mixed TR–RTM method","authors":"Xiang Gao, Xiafei Li, Hong-juan Yang, J. Jiao, Cheng-hao Wang","doi":"10.1080/17415977.2021.1948543","DOIUrl":"https://doi.org/10.1080/17415977.2021.1948543","url":null,"abstract":"The problem of target detection and localization in layered media can be solved by the mixed TR–RTM. The highlight of this paper is on multilayer media, where the target is harder to detect than in double-layered media, due to the interference of multiple interface reflection signals. The core idea of the TR–RTM mixed method, namely the RTM isochronism principle, is applied for the three cases. Typically, a target under a TR–RTM process can form a mountain-like acoustic field distribution. For the interface whose reflected signal is an interference, the acoustic field distribution is disordered and inhomogeneous, with a smaller amplitude. The TR–RTM greatly improves the signal-to-interference ratio, where the position of the summit is the just position of the target, thus, detecting and localizing the target.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1811 - 1820"},"PeriodicalIF":1.3,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49480297","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 : 2021-08-20DOI: 10.1080/17415977.2021.1966426
Qi Luo, Shijian Lin, Hongxia Wang
ABSTRACT Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements, which arises in various fields. In practical scenarios, partial measurements can be inevitably corrupted by outliers that can take arbitrary values. To handle this, we propose the median-SAF method which is the smoothed amplitude flow (SAF) method equipped with the median truncation strategy. We find that median-SAF has some inherent advantages in suppressing outliers. Theoretical analysis ensures that median-SAF converges linearly to the original signal via the gradient algorithm from an delicate initial estimate with high probability. Substantial numerical tests empirically illustrate that the proposed method is superior to other state-of-the-art methods in terms of the recovery rate and the performance on suppressing outliers.
{"title":"Robust phase retrieval via median-truncated smoothed amplitude flow","authors":"Qi Luo, Shijian Lin, Hongxia Wang","doi":"10.1080/17415977.2021.1966426","DOIUrl":"https://doi.org/10.1080/17415977.2021.1966426","url":null,"abstract":"ABSTRACT Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements, which arises in various fields. In practical scenarios, partial measurements can be inevitably corrupted by outliers that can take arbitrary values. To handle this, we propose the median-SAF method which is the smoothed amplitude flow (SAF) method equipped with the median truncation strategy. We find that median-SAF has some inherent advantages in suppressing outliers. Theoretical analysis ensures that median-SAF converges linearly to the original signal via the gradient algorithm from an delicate initial estimate with high probability. Substantial numerical tests empirically illustrate that the proposed method is superior to other state-of-the-art methods in terms of the recovery rate and the performance on suppressing outliers.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3024 - 3040"},"PeriodicalIF":1.3,"publicationDate":"2021-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43923485","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 : 2021-08-08DOI: 10.1080/17415977.2021.1960325
D. Dönmez, I. Akcali, E. Avşar, A. Aydın, H. Mutlu
Hexapod-type external fixators based on a general 6-6 Stewart platform structure are extensively used to manage orthopaedic disorders. While implementing these robotic devices, a practical visual aid is needed to quickly identify their uncontrollable states referred to as singularities. Thus, a visible correlation between the singularity of hexapod-type external fixators and their particular configurations has been explored geometrically in this work. A novel method called stereographic projection is utilized for that purpose. A mathematical procedure has been established to determine the characteristic values of the singular states. It is found that in case four- out of six-rod directions intersect each other at a common point, two different singular robot configurations result. Besides, if four joint angles at the top and bottom rings of the hexapod are equal, rings being parallel, then five-rod directions are intersected by two lines each passing through the end joints of the fifth rod.
{"title":"Determination of particular singular configurations of Stewart platform type of fixator by the stereographic projection method","authors":"D. Dönmez, I. Akcali, E. Avşar, A. Aydın, H. Mutlu","doi":"10.1080/17415977.2021.1960325","DOIUrl":"https://doi.org/10.1080/17415977.2021.1960325","url":null,"abstract":"Hexapod-type external fixators based on a general 6-6 Stewart platform structure are extensively used to manage orthopaedic disorders. While implementing these robotic devices, a practical visual aid is needed to quickly identify their uncontrollable states referred to as singularities. Thus, a visible correlation between the singularity of hexapod-type external fixators and their particular configurations has been explored geometrically in this work. A novel method called stereographic projection is utilized for that purpose. A mathematical procedure has been established to determine the characteristic values of the singular states. It is found that in case four- out of six-rod directions intersect each other at a common point, two different singular robot configurations result. Besides, if four joint angles at the top and bottom rings of the hexapod are equal, rings being parallel, then five-rod directions are intersected by two lines each passing through the end joints of the fifth rod.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2925 - 2943"},"PeriodicalIF":1.3,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45070829","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 : 2021-08-06DOI: 10.1080/17415977.2021.1961767
D. Aydın, E. Yılmaz, N. Chamidah
This paper proposes a new smoothing technique based on rational function approximation using truncated total least squares (P−TTLS) and compares it with the widely used smoothing spline method, whi...
{"title":"Rational (Padé) approximation for estimating the components of the partially-linear regression model","authors":"D. Aydın, E. Yılmaz, N. Chamidah","doi":"10.1080/17415977.2021.1961767","DOIUrl":"https://doi.org/10.1080/17415977.2021.1961767","url":null,"abstract":"This paper proposes a new smoothing technique based on rational function approximation using truncated total least squares (P−TTLS) and compares it with the widely used smoothing spline method, whi...","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1961767","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42010878","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 : 2021-08-06DOI: 10.1080/17415977.2021.1960832
A. Charkaoui, A. El Badia, Nour Eddine Alaa
ABSTRACT This work proposes an identification method for reconstructing the characteristic source in the Helmholtz equation from boundary measurements. We formulate the inverse source problem into a shape optimization problem by introducing a least-squares cost function. Using the shape optimization techniques, we prove the existence of an optimal solution to the considered shape optimization problem and we calculate the gradient of the cost function with respect to the shape . By using the Level set method, we present an iterative algorithm to recover numerically the shape . We develop a new technique to initialize the level set algorithm, which permits capturing different hidden shapes. To examine the validity of the proposed method, we illustrate several numerical experiments with different hidden shapes. By adding a level of noise to the measured data, we evaluate the robustness of our reconstruction algorithm.
{"title":"An efficient and robust algorithm for source reconstruction in the Helmholtz equation","authors":"A. Charkaoui, A. El Badia, Nour Eddine Alaa","doi":"10.1080/17415977.2021.1960832","DOIUrl":"https://doi.org/10.1080/17415977.2021.1960832","url":null,"abstract":"ABSTRACT This work proposes an identification method for reconstructing the characteristic source in the Helmholtz equation from boundary measurements. We formulate the inverse source problem into a shape optimization problem by introducing a least-squares cost function. Using the shape optimization techniques, we prove the existence of an optimal solution to the considered shape optimization problem and we calculate the gradient of the cost function with respect to the shape . By using the Level set method, we present an iterative algorithm to recover numerically the shape . We develop a new technique to initialize the level set algorithm, which permits capturing different hidden shapes. To examine the validity of the proposed method, we illustrate several numerical experiments with different hidden shapes. By adding a level of noise to the measured data, we evaluate the robustness of our reconstruction algorithm.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2944 - 2970"},"PeriodicalIF":1.3,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1960832","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239136","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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