Pub Date : 2024-11-26DOI: 10.1016/j.apnum.2024.11.014
Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han
In this paper, we present a frozen iteratively regularized approach for solving ill-posed problems and conduct a thorough analysis of its performance. This method involves incorporating Nesterov's acceleration strategy into the Levenberg-Marquardt-Kaczmarz method and maintaining a constant Fréchet derivative of at an initial approximation solution throughout the iterative process, which called the frozen strategy. Moreover, convex functions are employed as penalty terms to capture the distinctive features of solutions. We establish convergence and regularization analysis by leveraging some classical assumptions and properties of convex functions. These theoretical findings are further supported by a number of numerical studies, which demonstrate the efficacy of our approach. Additionally, to verify the impact of initial values on the accuracy of reconstruction, the data-driven strategy is adopted in the third numerical example for comparison.
在本文中，我们提出了一种用于求解问题的冻结迭代正则化方法，并对其性能进行了深入分析。该方法将涅斯捷罗夫加速策略融入 Levenberg-Marquardt-Kaczmarz 方法中，并在整个迭代过程中保持 Fi 在初始近似解 x0 处的弗雷谢特导数不变，这就是所谓的冻结策略。此外，还采用凸函数作为惩罚项，以捕捉解的显著特征。我们利用凸函数的一些经典假设和特性，建立了收敛性和正则化分析。这些理论结论得到了大量数值研究的进一步支持，证明了我们方法的有效性。此外，为了验证初始值对重建精度的影响，我们在第三个数值示例中采用了数据驱动策略进行比较。
{"title":"A frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems","authors":"Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han","doi":"10.1016/j.apnum.2024.11.014","DOIUrl":"10.1016/j.apnum.2024.11.014","url":null,"abstract":"<div><div>In this paper, we present a frozen iteratively regularized approach for solving ill-posed problems and conduct a thorough analysis of its performance. This method involves incorporating Nesterov's acceleration strategy into the Levenberg-Marquardt-Kaczmarz method and maintaining a constant Fréchet derivative of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> at an initial approximation solution <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> throughout the iterative process, which called the frozen strategy. Moreover, convex functions are employed as penalty terms to capture the distinctive features of solutions. We establish convergence and regularization analysis by leveraging some classical assumptions and properties of convex functions. These theoretical findings are further supported by a number of numerical studies, which demonstrate the efficacy of our approach. Additionally, to verify the impact of initial values on the accuracy of reconstruction, the data-driven strategy is adopted in the third numerical example for comparison.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 187-207"},"PeriodicalIF":2.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.apnum.2024.11.010
Shaoshuai Chu , Alexander Kurganov , Igor Menshov
We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the recently proposed LDCU numerical fluxes computed using the point values reconstructed with the help of adaptively selected nonlinear limiters. To this end, we use a smoothness indicator to detect “rough” parts of the computed solution, where the piecewise linear reconstruction is performed using an overcompressive limiter, which leads to extremely sharp resolution of shock and contact waves. In the “smooth” areas, we use a more dissipative limiter to prevent appearance of artificial kinks and staircase-like structures there. In order to avoid oscillations, we perform the reconstruction in the local characteristic variables obtained using the local characteristic decomposition. We use a smoothness indicator from Löhner (1987) [34] and apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate that the new adaptive LDCU schemes outperform the original ones.
{"title":"New adaptive low-dissipation central-upwind schemes","authors":"Shaoshuai Chu , Alexander Kurganov , Igor Menshov","doi":"10.1016/j.apnum.2024.11.010","DOIUrl":"10.1016/j.apnum.2024.11.010","url":null,"abstract":"<div><div>We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the recently proposed LDCU numerical fluxes computed using the point values reconstructed with the help of adaptively selected nonlinear limiters. To this end, we use a smoothness indicator to detect “rough” parts of the computed solution, where the piecewise linear reconstruction is performed using an overcompressive limiter, which leads to extremely sharp resolution of shock and contact waves. In the “smooth” areas, we use a more dissipative limiter to prevent appearance of artificial kinks and staircase-like structures there. In order to avoid oscillations, we perform the reconstruction in the local characteristic variables obtained using the local characteristic decomposition. We use a smoothness indicator from Löhner (1987) <span><span>[34]</span></span> and apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate that the new adaptive LDCU schemes outperform the original ones.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 155-170"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.apnum.2024.11.013
Lei Lin , Junliang Lv , Tian Niu
This paper is concerned with scattering of electromagnetic waves by an orthotropic infinite cylinder. Such a scattering problem is modeled by a orthotropic media scattering problem. By constructing the Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the orthotropic media problem is reformulated as a bounded boundary value problem. An a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate contains the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element algorithm is proposed for solving the orthotropic media problem. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method.
{"title":"An adaptive DtN-FEM for the scattering problem from orthotropic media","authors":"Lei Lin , Junliang Lv , Tian Niu","doi":"10.1016/j.apnum.2024.11.013","DOIUrl":"10.1016/j.apnum.2024.11.013","url":null,"abstract":"<div><div>This paper is concerned with scattering of electromagnetic waves by an orthotropic infinite cylinder. Such a scattering problem is modeled by a orthotropic media scattering problem. By constructing the Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the orthotropic media problem is reformulated as a bounded boundary value problem. An a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate contains the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element algorithm is proposed for solving the orthotropic media problem. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 140-154"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.apnum.2024.11.012
Georgios D. Kolezas, George Fikioris, John A. Roumeliotis
The method of auxiliary sources (MAS), also known as the method of fundamental solutions (MFS), is a well-known computational method for the solution of boundary-value problems. The final solution (“MAS solution”) is obtained once we have found the amplitudes of N auxiliary “MAS sources.” Past studies have shown that it is possible for the MAS solution to converge to the true solution even when the N auxiliary sources diverge and oscillate. Here, we extend the past studies by demonstrating this possibility within the context of Laplace's equation with Neumann boundary conditions. The correct solution can thus be obtained from sources that, when N is large, must be considered unphysical. We carefully explain the underlying reasons for the unphysical results, distinguish from other difficulties that might concurrently arise, and point to significant differences with time-dependent problems studied in the past.
辅助源法（MAS），又称基本解法（MFS），是一种著名的边界值问题求解计算方法。当我们找到 N 个辅助 "MAS 源 "的振幅后，就得到了最终解（"MAS 解"）。过去的研究表明，即使 N 个辅助源发散和振荡，MAS 解也有可能收敛到真解。在这里，我们扩展了过去的研究，在具有新曼边界条件的拉普拉斯方程中证明了这种可能性。因此，可以从 N 较大时必须被视为非物理的源中获得正确的解。我们仔细解释了非物理结果的根本原因，区分了可能同时出现的其他困难，并指出了与过去研究的时间相关问题的显著区别。
{"title":"Convergence, divergence, and inherent oscillations in MAS solutions of 2D Laplace-Neumann problems","authors":"Georgios D. Kolezas, George Fikioris, John A. Roumeliotis","doi":"10.1016/j.apnum.2024.11.012","DOIUrl":"10.1016/j.apnum.2024.11.012","url":null,"abstract":"<div><div>The method of auxiliary sources (MAS), also known as the method of fundamental solutions (MFS), is a well-known computational method for the solution of boundary-value problems. The final solution (“MAS solution”) is obtained once we have found the amplitudes of <em>N</em> auxiliary “MAS sources.” Past studies have shown that it is possible for the MAS solution to converge to the true solution even when the <em>N</em> auxiliary sources diverge and oscillate. Here, we extend the past studies by demonstrating this possibility within the context of Laplace's equation with Neumann boundary conditions. The correct solution can thus be obtained from sources that, when <em>N</em> is large, must be considered unphysical. We carefully explain the underlying reasons for the unphysical results, distinguish from other difficulties that might concurrently arise, and point to significant differences with time-dependent problems studied in the past.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 171-186"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.apnum.2024.11.011
Jorge Aguayo , Rodolfo Araya
This article presents an a priori error estimation for a finite element discretization applied to an optimal control problem governed by a mixed formulation for linear elasticity equations, where weak symmetry is imposed for the stress tensor. The optimal control is given by a discontinuity jump in displacements, representing the coseismic slip along a fault plane. Inferring the fault slip during an earthquake is crucial for understanding earthquake dynamics and improving seismic risk mitigation strategies, making this optimal control problem scientifically significant. We establish an a priori error estimate using appropriate finite element spaces for control and states. Our theoretical convergence rates were validated through numerical experiments.
{"title":"A priori error estimates for a coseismic slip optimal control problem","authors":"Jorge Aguayo , Rodolfo Araya","doi":"10.1016/j.apnum.2024.11.011","DOIUrl":"10.1016/j.apnum.2024.11.011","url":null,"abstract":"<div><div>This article presents an a priori error estimation for a finite element discretization applied to an optimal control problem governed by a mixed formulation for linear elasticity equations, where weak symmetry is imposed for the stress tensor. The optimal control is given by a discontinuity jump in displacements, representing the coseismic slip along a fault plane. Inferring the fault slip during an earthquake is crucial for understanding earthquake dynamics and improving seismic risk mitigation strategies, making this optimal control problem scientifically significant. We establish an a priori error estimate using appropriate finite element spaces for control and states. Our theoretical convergence rates were validated through numerical experiments.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 84-99"},"PeriodicalIF":2.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.apnum.2024.11.008
Patrick Bammer, Lothar Banz, Andreas Schröder
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading to a three field formulation. The finite element discretization is conforming in the displacement field and the plastic strain but potentially non-conforming in the Lagrange multiplier as its Frobenius norm is only constrained in a certain set of Gauss quadrature points. A discrete inf-sup condition with constant 1 and the well posedness of the discrete mixed problem are shown. Moreover, convergence and guaranteed convergence rates are proved with respect to the mesh size and the polynomial degree, which are optimal for the lowest order case. Numerical experiments underline the theoretical results.
{"title":"Mixed finite elements of higher-order in elastoplasticity","authors":"Patrick Bammer, Lothar Banz, Andreas Schröder","doi":"10.1016/j.apnum.2024.11.008","DOIUrl":"10.1016/j.apnum.2024.11.008","url":null,"abstract":"<div><div>In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading to a three field formulation. The finite element discretization is conforming in the displacement field and the plastic strain but potentially non-conforming in the Lagrange multiplier as its Frobenius norm is only constrained in a certain set of Gauss quadrature points. A discrete inf-sup condition with constant 1 and the well posedness of the discrete mixed problem are shown. Moreover, convergence and guaranteed convergence rates are proved with respect to the mesh size and the polynomial degree, which are optimal for the lowest order case. Numerical experiments underline the theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 38-54"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.apnum.2024.11.009
Jia Li , Wei Guan , Shengzhu Shi , Boying Wu
In this paper, we study the local discontinuous Galerkin (LDG) method for one-dimensional nonlinear convection-diffusion equation. In the LDG scheme, local Lax-Friedrichs numerical flux is adopted for the convection term, and a modified central flux is proposed and applied to the nonlinear diffusion coefficient. The modified central flux overcomes the shortcomings of the traditional flux, and it is beneficial in proving the stability of the LDG scheme. By virtue of the Gauss-Radau projections and the local linearization technique, the optimal error estimates are also obtained. Numerical experiments are presented to confirm the validity of the theoretical results.
{"title":"A local discontinuous Galerkin methods with local Lax-Friedrichs flux and modified central flux for one dimensional nonlinear convection-diffusion equation","authors":"Jia Li , Wei Guan , Shengzhu Shi , Boying Wu","doi":"10.1016/j.apnum.2024.11.009","DOIUrl":"10.1016/j.apnum.2024.11.009","url":null,"abstract":"<div><div>In this paper, we study the local discontinuous Galerkin (LDG) method for one-dimensional nonlinear convection-diffusion equation. In the LDG scheme, local Lax-Friedrichs numerical flux is adopted for the convection term, and a modified central flux is proposed and applied to the nonlinear diffusion coefficient. The modified central flux overcomes the shortcomings of the traditional flux, and it is beneficial in proving the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stability of the LDG scheme. By virtue of the Gauss-Radau projections and the local linearization technique, the optimal error estimates are also obtained. Numerical experiments are presented to confirm the validity of the theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 124-139"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.apnum.2024.11.007
Guodong Ma , Wei Zhang , Jinbao Jian, Zefeng Huang, Jingyi Mo
The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems.
{"title":"An inertial hybrid DFPM-based algorithm for constrained nonlinear equations with applications","authors":"Guodong Ma , Wei Zhang , Jinbao Jian, Zefeng Huang, Jingyi Mo","doi":"10.1016/j.apnum.2024.11.007","DOIUrl":"10.1016/j.apnum.2024.11.007","url":null,"abstract":"<div><div>The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 100-123"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.1016/j.apnum.2024.11.006
Abdulkarim Hassan Ibrahim , Suliman Al-Homidan
Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equations. The proposed method's global convergence is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudo-monotone). This is the first convergence result for a DFPM with double inertial step to solve nonlinear equations. Numerical experiments are conducted using well-known test problems to show the proposed method's effectiveness and robustness compared to two existing methods in the literature.
{"title":"A derivative-free projection method with double inertial effects for solving nonlinear equations","authors":"Abdulkarim Hassan Ibrahim , Suliman Al-Homidan","doi":"10.1016/j.apnum.2024.11.006","DOIUrl":"10.1016/j.apnum.2024.11.006","url":null,"abstract":"<div><div>Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equations. The proposed method's global convergence is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudo-monotone). This is the first convergence result for a DFPM with double inertial step to solve nonlinear equations. Numerical experiments are conducted using well-known test problems to show the proposed method's effectiveness and robustness compared to two existing methods in the literature.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 55-67"},"PeriodicalIF":2.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.1016/j.apnum.2024.11.004
Vittoria Bruni , Rosanna Campagna , Domenico Vitulano
Multicomponent signals play a key role in many application fields, such as biology, audio processing, seismology, air traffic control and security. They are well represented in the time-frequency plane where they are mainly characterized by special curves, called ridges, which carry information about the instantaneous frequency (IF) of each signal component. However, ridges identification usually is a difficult task for signals having interfering components and requires the automatic localization of time-frequency interference regions (IRs). This paper presents a study on the use of the frequency parameter of a hyperbolic-polynomial penalized spline (HP-spline) to predict the presence of interference regions. Since HP-splines are suitably designed for signal regression, it is proved that their frequency parameter can capture the change caused by the interaction between signal components in the time-frequency representation. In addition, the same parameter allows us to define a data-driven approach for IR localization, namely HP-spline Signal Interference Detection (HP-SID) method. Numerical experiments show that the proposed HP-SID can identify specific interference regions for different types of multicomponent signals by means of an efficient algorithm that does not require explicit data regression.
多分量信号在生物、音频处理、地震学、空中交通管制和安全等许多应用领域都发挥着重要作用。多分量信号在时频平面上有很好的表现，其主要特征是特殊曲线（称为脊），其中包含每个信号分量的瞬时频率（IF）信息。然而，对于具有干扰成分的信号来说，脊线识别通常是一项艰巨的任务，需要自动定位时频干扰区域（IR）。本文研究了如何利用双曲-多项式惩罚样条曲线（HP-样条曲线）的频率参数来预测干扰区域的存在。由于 HP 样条适合于信号回归，因此证明了其频率参数可以捕捉时频表示中信号成分之间相互作用所引起的变化。此外，同一参数还允许我们定义一种数据驱动的红外定位方法，即 HP 样条信号干扰检测（HP-SID）方法。数值实验表明，所提出的 HP-SID 可以通过无需明确数据回归的高效算法，识别不同类型多分量信号的特定干扰区域。
{"title":"Multicomponent signals interference detection exploiting HP-splines frequency parameter","authors":"Vittoria Bruni , Rosanna Campagna , Domenico Vitulano","doi":"10.1016/j.apnum.2024.11.004","DOIUrl":"10.1016/j.apnum.2024.11.004","url":null,"abstract":"<div><div>Multicomponent signals play a key role in many application fields, such as biology, audio processing, seismology, air traffic control and security. They are well represented in the time-frequency plane where they are mainly characterized by special curves, called ridges, which carry information about the instantaneous frequency (IF) of each signal component. However, ridges identification usually is a difficult task for signals having interfering components and requires the automatic localization of time-frequency interference regions (IRs). This paper presents a study on the use of the frequency parameter of a hyperbolic-polynomial penalized spline (HP-spline) to predict the presence of interference regions. Since HP-splines are suitably designed for signal regression, it is proved that their frequency parameter can capture the change caused by the interaction between signal components in the time-frequency representation. In addition, the same parameter allows us to define a data-driven approach for IR localization, namely HP-spline Signal Interference Detection (HP-SID) method. Numerical experiments show that the proposed HP-SID can identify specific interference regions for different types of multicomponent signals by means of an efficient algorithm that does not require explicit data regression.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 20-37"},"PeriodicalIF":2.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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