Pub Date : 2021-08-03DOI: 10.1080/17415977.2020.1832090
Shuyong Duan, Bo Yang, F. Wang, Guirong Liu
Appropriate regularization parameter specification is the linchpin for solving ill-posed inverse problems when regularization method is applied. This paper presents a novel technique to determine cut off singular values in the truncated singular value decomposition (TSVD) methods. Simple formulae are presented to calculate the index number of the singular value, beyond which all the smaller singular values and the corresponding vectors are truncated. The determination method of optimal truncation threshold is firstly theoretically inferred. Two-dimensional inverse problems processing Radon transform are then exemplified. Formulae to solve the problem with insufficient image resolution and projection angle number are derived by the currently proposed method. The results show that accuracy of the current method is similar to that of TSVD but with much superior efficiency. On the other hand, insufficiency in input data affects the output accuracy of the inverse solution, a least square method can be engaged to establish formulae calculating the truncation threshold. For an insufficient set of input data, the percentage difference between inversely reconstructed signal and TSVD reconstructed signal is about 3%. The current formulae offer reliable and more efficient approach to calculate the truncation threshold when TSVD is applied to solve inverse problems with known system characteristics.
{"title":"Determination of singular value truncation threshold for regularization in ill-posed problems","authors":"Shuyong Duan, Bo Yang, F. Wang, Guirong Liu","doi":"10.1080/17415977.2020.1832090","DOIUrl":"https://doi.org/10.1080/17415977.2020.1832090","url":null,"abstract":"Appropriate regularization parameter specification is the linchpin for solving ill-posed inverse problems when regularization method is applied. This paper presents a novel technique to determine cut off singular values in the truncated singular value decomposition (TSVD) methods. Simple formulae are presented to calculate the index number of the singular value, beyond which all the smaller singular values and the corresponding vectors are truncated. The determination method of optimal truncation threshold is firstly theoretically inferred. Two-dimensional inverse problems processing Radon transform are then exemplified. Formulae to solve the problem with insufficient image resolution and projection angle number are derived by the currently proposed method. The results show that accuracy of the current method is similar to that of TSVD but with much superior efficiency. On the other hand, insufficiency in input data affects the output accuracy of the inverse solution, a least square method can be engaged to establish formulae calculating the truncation threshold. For an insufficient set of input data, the percentage difference between inversely reconstructed signal and TSVD reconstructed signal is about 3%. The current formulae offer reliable and more efficient approach to calculate the truncation threshold when TSVD is applied to solve inverse problems with known system characteristics.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1127 - 1157"},"PeriodicalIF":1.3,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1832090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44701718","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 : 2021-07-30DOI: 10.1080/17415977.2021.1956207
M. Colaço
Professor Carlos Jose Santos Alves was born in Caldas da Rainha, Portugal, in 1966. He graduated in Mathematics at the University of Lisbon, Portugal, in 1988 and obtained his Ph.D. in Applied Math...
{"title":"Carlos José Santos Alves (1966–†2021)","authors":"M. Colaço","doi":"10.1080/17415977.2021.1956207","DOIUrl":"https://doi.org/10.1080/17415977.2021.1956207","url":null,"abstract":"Professor Carlos Jose Santos Alves was born in Caldas da Rainha, Portugal, in 1966. He graduated in Mathematics at the University of Lisbon, Portugal, in 1988 and obtained his Ph.D. in Applied Math...","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1956207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41969014","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 : 2021-07-29DOI: 10.1080/17415977.2021.1955875
Iman Tabatabaei Ardekani, J. Kaipio, D. Castello
This paper considers a statistical method for damage identification of simply-supported elastic beams from static data. The problem is cast as an inverse problem and analyzed in Bayesian inversion ...
{"title":"Bayesian damage identification of simply supported beams from elastostatic data","authors":"Iman Tabatabaei Ardekani, J. Kaipio, D. Castello","doi":"10.1080/17415977.2021.1955875","DOIUrl":"https://doi.org/10.1080/17415977.2021.1955875","url":null,"abstract":"This paper considers a statistical method for damage identification of simply-supported elastic beams from static data. The problem is cast as an inverse problem and analyzed in Bayesian inversion ...","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1955875","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41569966","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 : 2021-07-22DOI: 10.1080/17415977.2021.1954178
J. Shokri, S. Pishbin
This paper presents a study of the performance of the Tau method using Chebyshev basis functions for solving fourth-order differential equation with boundary conditions. Existence and uniqueness of the solution of this equation are investigated transforming it into the Volterra–Fredholm integral equation. We use the operational Tau matrix representation with Chebyshev basis functions for constructing the algebraic equivalent representation of the problem.This representation is an special semi lower triangular system whose solution gives the components of the vector solution. Applying Gronwall’s and the generalized Hardy’s inequality, convergence analysis and error estimation of the Tau method are discussed. The error analysis indicates that the numerical errors decay exponentially when the source function are sufficiently smooth. Illustrative examples are given to represent the efficiency and the accuracy of the proposed method. Also, some comparisons are made with existing results such that the results obtained by Tau method are more accurate than the proposed methods in this case.
{"title":"Study of fourth-order boundary value problem based on Volterra–Fredholm equation: numerical treatment","authors":"J. Shokri, S. Pishbin","doi":"10.1080/17415977.2021.1954178","DOIUrl":"https://doi.org/10.1080/17415977.2021.1954178","url":null,"abstract":"This paper presents a study of the performance of the Tau method using Chebyshev basis functions for solving fourth-order differential equation with boundary conditions. Existence and uniqueness of the solution of this equation are investigated transforming it into the Volterra–Fredholm integral equation. We use the operational Tau matrix representation with Chebyshev basis functions for constructing the algebraic equivalent representation of the problem.This representation is an special semi lower triangular system whose solution gives the components of the vector solution. Applying Gronwall’s and the generalized Hardy’s inequality, convergence analysis and error estimation of the Tau method are discussed. The error analysis indicates that the numerical errors decay exponentially when the source function are sufficiently smooth. Illustrative examples are given to represent the efficiency and the accuracy of the proposed method. Also, some comparisons are made with existing results such that the results obtained by Tau method are more accurate than the proposed methods in this case.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2862 - 2876"},"PeriodicalIF":1.3,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1954178","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42908384","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 : 2021-07-20DOI: 10.1080/17415977.2021.1954921
Ge Zhang, Liqun Tang, Zejia Liu, Licheng Zhou, Yiping Liu, Zhenyu Jiang, Jingsong Chen, S. Sun
Principal component analysis (PCA) methods have been widely applied to damage identification in the long-term structural health monitoring (SHM) of infrastructure. Usually, the first few eigenvector components derived by PCA methods are treated as damage-sensitive features. In this paper, the effective method of double-window PCA (DWPCA) and novel features are proposed for better damage identification performance. In the proposed method, spatial and temporal windows are introduced to the traditional PCA method. The spatial windows are applied to group damage-sensitive sensors and exclude those sensors insensitive to damage, while the temporal window is applied to better discriminate eigenvectors between the damaged and healthy states. In addition, the length and directional angle of the eigenvector variation between the healthy and damaged states are used as the damage-sensitive features, instead of the components of the eigenvector variation used in previous studies. Numerical simulations based on a large-scale bridge reveal that the proposed features are successful in identifying the damage located far from sensors due to the use of both spatial and temporal windows as well as the length of the eigenvector variation. In addition, compared to the previous PCA and moving PCA methods, the novel features have higher sensitivity and resolution in damage identification.
{"title":"Enhanced features in principal component analysis with spatial and temporal windows for damage identification","authors":"Ge Zhang, Liqun Tang, Zejia Liu, Licheng Zhou, Yiping Liu, Zhenyu Jiang, Jingsong Chen, S. Sun","doi":"10.1080/17415977.2021.1954921","DOIUrl":"https://doi.org/10.1080/17415977.2021.1954921","url":null,"abstract":"Principal component analysis (PCA) methods have been widely applied to damage identification in the long-term structural health monitoring (SHM) of infrastructure. Usually, the first few eigenvector components derived by PCA methods are treated as damage-sensitive features. In this paper, the effective method of double-window PCA (DWPCA) and novel features are proposed for better damage identification performance. In the proposed method, spatial and temporal windows are introduced to the traditional PCA method. The spatial windows are applied to group damage-sensitive sensors and exclude those sensors insensitive to damage, while the temporal window is applied to better discriminate eigenvectors between the damaged and healthy states. In addition, the length and directional angle of the eigenvector variation between the healthy and damaged states are used as the damage-sensitive features, instead of the components of the eigenvector variation used in previous studies. Numerical simulations based on a large-scale bridge reveal that the proposed features are successful in identifying the damage located far from sensors due to the use of both spatial and temporal windows as well as the length of the eigenvector variation. In addition, compared to the previous PCA and moving PCA methods, the novel features have higher sensitivity and resolution in damage identification.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2877 - 2894"},"PeriodicalIF":1.3,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1954921","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42114907","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 : 2021-07-17DOI: 10.1080/17415977.2021.1952409
Gyan Ranjan, R. Tiwari, H. Nemade
On-site estimation of multiple fault parameters has been performed in a rotor integrated with active-magnetic bearing (AMB) with a cracked shaft supported on flexible conventional bearings. In addition to external viscous damping (at flexible bearings), internal damping (at transverse crack) is considered to show its influence on the dynamics of the cracked system. The instability generated in the rotor system due to the effect of internal damping at high speed are reduced with the control action of the AMB. A Multiple Harmonic Influence Coefficient Method (MHICM) has been proposed that requires the full spectrum amplitude and phases of the rotor responses and excitation forces to obtain the fault parameters of the rotor. The additive crack stiffness, residual unbalances, and internal damping can be estimated in the operating condition with less information on the rotor system. The intensity of the fault parameters is required to be monitored periodically to identify the safe operating speed of the system. As the AMB is an integral part of the rotor system, the multi-harmonic excitation can be initiated without changing the physical condition of the system. To check the robustness of the algorithm, different percentages of random noise are added to the rotor responses.
{"title":"Fault identification in cracked rotor-AMB system using magnetic excitations based on multi harmonic influence coefficient method","authors":"Gyan Ranjan, R. Tiwari, H. Nemade","doi":"10.1080/17415977.2021.1952409","DOIUrl":"https://doi.org/10.1080/17415977.2021.1952409","url":null,"abstract":"On-site estimation of multiple fault parameters has been performed in a rotor integrated with active-magnetic bearing (AMB) with a cracked shaft supported on flexible conventional bearings. In addition to external viscous damping (at flexible bearings), internal damping (at transverse crack) is considered to show its influence on the dynamics of the cracked system. The instability generated in the rotor system due to the effect of internal damping at high speed are reduced with the control action of the AMB. A Multiple Harmonic Influence Coefficient Method (MHICM) has been proposed that requires the full spectrum amplitude and phases of the rotor responses and excitation forces to obtain the fault parameters of the rotor. The additive crack stiffness, residual unbalances, and internal damping can be estimated in the operating condition with less information on the rotor system. The intensity of the fault parameters is required to be monitored periodically to identify the safe operating speed of the system. As the AMB is an integral part of the rotor system, the multi-harmonic excitation can be initiated without changing the physical condition of the system. To check the robustness of the algorithm, different percentages of random noise are added to the rotor responses.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2831 - 2861"},"PeriodicalIF":1.3,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1952409","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46414781","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 : 2021-07-08DOI: 10.1080/17415977.2021.1949591
Chein-Shan Liu, Jiang-Ren Chang
In the paper, we solve two Stefan problems. The first problem recovers an unknown moving boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second problem finds a time-dependent heat flux on the left-end, such that a desired moving boundary can be achieved. Then, we solve an inverse Cauchy-Stefan problem, using the over-specified Cauchy boundary conditions on a given moving boundary to recover the solution. Resorting on a homogenization function method, we recast these problems into the ones having homogeneous boundary and initial conditions. Consequently, the approximate solution is obtained by solving a linear system obtained from the collocation method in a reduced domain. For the first Stefan problem the moving boundary can be determined accurately, after solving a nonlinear equation at each discretized time. For the second Stefan problem, we can obtain the required boundary heat flux without needing of iteration. Numerical examples, including non-smooth ones, confirm that the novel methods are simple and robust against large noise. Moreover, the Stefan and inverse Cauchy-Stefan problems are solved without initial conditions.
{"title":"A homogenization method to solve inverse Cauchy–Stefan problems for recovering non-smooth moving boundary, heat flux and initial value","authors":"Chein-Shan Liu, Jiang-Ren Chang","doi":"10.1080/17415977.2021.1949591","DOIUrl":"https://doi.org/10.1080/17415977.2021.1949591","url":null,"abstract":"In the paper, we solve two Stefan problems. The first problem recovers an unknown moving boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second problem finds a time-dependent heat flux on the left-end, such that a desired moving boundary can be achieved. Then, we solve an inverse Cauchy-Stefan problem, using the over-specified Cauchy boundary conditions on a given moving boundary to recover the solution. Resorting on a homogenization function method, we recast these problems into the ones having homogeneous boundary and initial conditions. Consequently, the approximate solution is obtained by solving a linear system obtained from the collocation method in a reduced domain. For the first Stefan problem the moving boundary can be determined accurately, after solving a nonlinear equation at each discretized time. For the second Stefan problem, we can obtain the required boundary heat flux without needing of iteration. Numerical examples, including non-smooth ones, confirm that the novel methods are simple and robust against large noise. Moreover, the Stefan and inverse Cauchy-Stefan problems are solved without initial conditions.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2772 - 2803"},"PeriodicalIF":1.3,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1949591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42904894","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 : 2021-07-07DOI: 10.1080/17415977.2021.1945050
M. Mint Brahim, A. Godin, M. Azaïez, E. Palomo Del Barrio
A new method for estimating the thermal properties of composite materials is proposed. It uses a previously developed thermal characterization method that is based on Karhunen–Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other kind of experimental device providing dense data in spatial coordinates. The novelty of this work lies in the introduction of two techniques based on two phase-wise defined test functions that extend the previously developed method to cases where the morphology of the composite material is not straightforward. Thanks to the orthogonal properties of KLD, only a few eigenelements are needed for an accurate estimation, which allows for a significant amplification of the signal/noise ratios. Furthermore, the proposed methods represent an attractive combination of parsimony and robustness to noise thanks to spatially uncorrelated noise being entirely reported on states. The effectiveness and accuracy of both techniques are proven with numerical tests.
{"title":"Thermal characterization of complex shape composite materials using Karhunen–Loève decomposition techniques","authors":"M. Mint Brahim, A. Godin, M. Azaïez, E. Palomo Del Barrio","doi":"10.1080/17415977.2021.1945050","DOIUrl":"https://doi.org/10.1080/17415977.2021.1945050","url":null,"abstract":"A new method for estimating the thermal properties of composite materials is proposed. It uses a previously developed thermal characterization method that is based on Karhunen–Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other kind of experimental device providing dense data in spatial coordinates. The novelty of this work lies in the introduction of two techniques based on two phase-wise defined test functions that extend the previously developed method to cases where the morphology of the composite material is not straightforward. Thanks to the orthogonal properties of KLD, only a few eigenelements are needed for an accurate estimation, which allows for a significant amplification of the signal/noise ratios. Furthermore, the proposed methods represent an attractive combination of parsimony and robustness to noise thanks to spatially uncorrelated noise being entirely reported on states. The effectiveness and accuracy of both techniques are proven with numerical tests.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2676 - 2695"},"PeriodicalIF":1.3,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1945050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49565826","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 : 2021-07-03DOI: 10.1080/17415977.2020.1815724
S. Jiang, Yujiang Wu
In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.
{"title":"Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method","authors":"S. Jiang, Yujiang Wu","doi":"10.1080/17415977.2020.1815724","DOIUrl":"https://doi.org/10.1080/17415977.2020.1815724","url":null,"abstract":"In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"990 - 1011"},"PeriodicalIF":1.3,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1815724","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48120363","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 : 2021-07-02DOI: 10.1080/17415977.2021.1948025
Mikhail Rem Romanovski
The approach is developed to specify a reconstruction of complicated functions using samples of limited size with invariant properties regarding the desired parameters. The idea is based on solutions to inverse problems, which should identify various representations of unknown parameters of a mathematical model and do so in a series. The sequential solutions to inverse problems ensure the identifiability of desired parameters that belong to an invariant family. The locally sequential refinement restricts local spikes additionally to the general regularization under a scheme of separate matching with observations. A simulation with inverse problems is applied to refine the known features of population dynamics. The reconstruction shows that the parameters of the Verhulst equation should be introduced as oscillatory functions. Based on the novel functional representation of the Verhulst equation parameters, the patterns of the COVID-19 spread and its progression in a given region are determined. The results emphasize the Verhulst equation’s character as a generalized and fruitful model for an object growth simulation.
{"title":"A locally sequential refinement of the growth dynamics identification","authors":"Mikhail Rem Romanovski","doi":"10.1080/17415977.2021.1948025","DOIUrl":"https://doi.org/10.1080/17415977.2021.1948025","url":null,"abstract":"The approach is developed to specify a reconstruction of complicated functions using samples of limited size with invariant properties regarding the desired parameters. The idea is based on solutions to inverse problems, which should identify various representations of unknown parameters of a mathematical model and do so in a series. The sequential solutions to inverse problems ensure the identifiability of desired parameters that belong to an invariant family. The locally sequential refinement restricts local spikes additionally to the general regularization under a scheme of separate matching with observations. A simulation with inverse problems is applied to refine the known features of population dynamics. The reconstruction shows that the parameters of the Verhulst equation should be introduced as oscillatory functions. Based on the novel functional representation of the Verhulst equation parameters, the patterns of the COVID-19 spread and its progression in a given region are determined. The results emphasize the Verhulst equation’s character as a generalized and fruitful model for an object growth simulation.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"2719 - 2756"},"PeriodicalIF":1.3,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1948025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46247385","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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