Numerical Experiments Research Articles

Pure quasi-P-wave modeling and imaging using an approximated space-domain pseudo-differential operator in vertical transverse isotropy media

Incorporating anisotropy in seismic modeling and imaging is important to produce the correct locations of subsurface reflectors. Traditional wave equations for quasi-P-wave in transverse isotropic media either suffer from S-wave artifacts or require complicated and expensive computation strategies. To mitigate this issue, we develop a novel pure quasi-P-wave equation with an approximated space-domain pseudo-differential operator in the vertical transverse isotropic (VTI) medium. For the pure quasi-P-wave equation, we first simplify it to an elliptical anisotropy equation with an additional pseudo-differential correction term. Then, we directly approximate the pseudo-differential term with a space-domain convolution operator that is calculated by solving a nonlinear inverse problem. Phase-velocity analysis and numerical modeling show that the new space-domain pseudo-differential operator has good accuracy in describing wave propagation in the VTI medium. In addition, it is more suitable for parallel computation with domain-decomposition than the Fourier transform, which is necessary for solving traditional pseudo-differential operators. Finally, we apply our quasi-P-wave propagator to reverse time migration to correct the anisotropic effects in seismic imaging. Numerical experiments for the benchmark models and a land survey demonstrate the feasibility and adaptability of our method.

A meshless stochastic method for Poisson-Nernst-Planck equations.

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson-Nernst-Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift-diffusion process with time- and space-varying drift. We leverage Green's functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method's convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Formation of Symmetric Gradient Microstructure in Carbon Steel Bars

In recent years, severe plastic deformation has attracted the most attention as a way to improve the mechanical properties of steel bars. Obtaining ultrafine grains and nanostructures in such bars leads to a strong increase in strength properties but strongly reduces their plastic properties. This study shows that the formation of a gradient microstructure allows simultaneous improvement in the strength and plastic properties of carbon steel bars, taking into account the symmetry of the microstructure distribution from the center of machining. A new combined technology is proposed to obtain such a microstructure. This technology consists of drawing bars from medium carbon steel on a radial-displacement rolling mill and carrying out subsequent drawing. Steel bars with a diameter of 30 mm were strained in three passes to a diameter of 16 mm at room temperature. The results show that the average value of microhardness in the center, neutral, and surface areas for the three straining cycles were 1890 MPa, 2335 MPa, and 2920 MPa, respectively. This symmetrical distribution of microhardness confirms the gradient microstructure. Strength characteristics also increased almost twofold: the yield strength increased from 330 to 735 MPa, and the ultimate strength increased from 600 MPa to 1025 MPa. Relative elongation decreased from 18 to 14 MPa, and relative reduction decreased from 40 to 31%, but remained at a fairly good level for AISI 1045 steel. The validity of all results was confirmed through numerous experiments using a set of traditional and modern research methods, which included optical, scanning, and transmission microscopy. EBSD analysis allowed precise positioning of the field of vision for studying microstructural changes across the entire bar cross-section. All of these methods used together, including tensile testing of the mechanical properties and the fractographic method, allow us to assess changes in microhardness and the reproduction of results.

Dynamic analysis of a class of fractional‐order dry friction oscillators

This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin.

Time history seismic response prediction of multiple homogeneous building structures using only one deep learning‐based Structure Temporal Fusion Network

AbstractStructural response prediction under earthquakes is crucial for evaluating the structural performance and subsequent functional restoration. Deep learning provides the potential to rapidly obtain the responses by skipping the time‐consuming nonlinear finite element analysis. However, a single deep learning network may only predict the time history responses of one specific structure, resulting in redundancy and resource waste when building multiple networks for modeling different structures. Thus, this study proposes a Structure Temporal Fusion Network (STFN) that can predict responses of various homogeneous structures using a single network. The key concept is that the seismic waves and the structural characteristics, such as story numbers, are fused together to predict diverse time history responses. Two numeric experiments are conducted, including predicting responses of ideal single‐degree‐of‐freedom (SDOF) structures and regular multistory reinforced concrete frames. Furthermore, a series of ablation analyses are carried out to validate the network architecture. The results indicate that STFN can predict nonlinear time history responses of different structures with mean square errors in the magnitude of and for two experiments, respectively. The solutions also highlight the importance of fusing static characteristics for the modeling of various structures with only one network. The STFN presents a promising solution for time history response prediction across multiple structures in regions.

Characteristic value decomposition: A unifying paradigm for data-driven modal analysis

Data-driven modal analysis is an indispensable means to understand the dynamic behavior of engineered structures and natural systems. It effectively captures active dynamic behavior and embeds them in a set of identified linear modal subspaces, unveiling complex dynamic behavior via the superposition of simpler hierarchical spatiotemporal dynamics. Despite the existence of many methods, there is no unified perspective connecting these modal analysis techniques. This paper proposes a new modal decomposition method, the characteristic value decomposition (CVD), that provides a unifying paradigm for data-driven modal analysis. CVD identifies identical spatial modes and temporal coordinates from two measurement data matrices. The modal parameters are identified through an eigendecomposition to a quotient of auto-covariance and cross-covariance matrices of the two data matrices. This paper shows that several data-driven modal analysis methods, namely, the state-variable decomposition, the dynamic mode decomposition, the Ibrahim time domain method, and the eigensystem realization algorithm, are special cases of CVD when the two data matrices are appropriately selected. Moreover, the CVD identifies the modal parameters with higher accuracy and is robust to added noise compared to established methods, as demonstrated using numerical experiments. It is also shown that the CVD flexibly utilizes data from multiple experiments and undersampled data sets to unveil system dynamics.

Exploring the influence of concave-convex surface modifications on piezoelectric wind energy harvesting: A numerical analysis

Wireless health monitoring sensors are significant for the safety of sea-crossing bridges, and their operation is dependent on a durable and reliable power source. Piezoelectric wind energy harvesters (PWEHs) can be effectively utilized in windy marine environments and provide a sustainable power supply for these sensors. This paper examines the influence of concave-convex surface modifications of a circular cylinder on the performance of the PWEH through numerical research to improve the output and operational bandwidth of traditional harvesters using cylindrical bluff bodies. An electromechanical model, coupled with computational fluid dynamics on low-Reynolds-number flows, was developed and different concave-convex configurations were proposed to explore the impact by numerical experiments. The results show that the configuration with two protrusions plus one groove is the optimal design. This configuration exhibits a much higher output with a maximum voltage of 19.5 V, representing a 464% increase compared to the cylindrical bluff body's 4.2 V, and a broader bandwidth with no upper limit across the wind speed range. This study provides insight into effective and ineffective efforts to enhance energy harvesting through concave-convex surface modifications and is advantageous to the advancement of self-powered marine sensing systems, particularly in the health monitoring of sea-crossing bridges.

Study on ultra-precision diamond cutting of polymers: Factors affecting dimensional accuracy and material removal mechanism

Polymers with surface microstructure have promising prospects for applications in the domains of aerospace, integrated circuits, and optical engineering. Ultra-precision cutting has unique advantages in the preparation of microstructure with high precision and complex shape. However, the inherent characteristics of polymers such as high elasticity, strong toughness, and poor thermal conductivity bring ultra-precision cutting a great challenge. In this study, the rectangular groove microstructures on polymers were fabricated by ultra-precision diamond cutting, and the influence of matrix material, feedrate and cutting depth on cutting performance and dimensional accuracy was quantitatively evaluated. The results indicate that the polyimide (PI) exhibits a good machinability compared with polyetheretherketone (PEEK) and polytetrafluoroethylene (PTFE). In addition, the feedrate have a negligible influence on the morphologies and dimensional accuracy of groove structure, while the groove width decreases and the ridge width increases as the cutting depth increases from 10 μm to 100 μm. The groove structure has the best dimensional accuracy when the cutting depth is 10 μm. Furthermore, the material removal mechanism of PI was discussed detailedly based on the results of numerical simulation and experiment.

Output feedback distributed economic model predictive control for parallel system in process networks

Abstract This paper proposes a distributed economic model predictive control algorithm for parallel systems which uses only output feedback. Such parallel systems are a fundamental system architecture frequently encountered in process networks where, in many cases, the state of the plant is not measurable. Economic performance is a key consideration in the operation of such industrial plants and it is of interest to develop theoretically rigorous approaches to tackle what is a practically very relevant scenario. The competitive couplings and competitive constraints inherent in parallel systems are explicitly addressed in the proposed controller design framework. Three measures are considered for optimization of such parallel systems including an economic stage cost function, energy efficiency and tracking accuracy. An economic cost function is optimized by the resulting distributed controller which can realize global control performance while also reducing the computational time for large-scale parallel systems. Stability of the system is formally proved using the principles of dissipativity. Finally, the effectiveness of the proposed theoretical approach is verified by both numerical simulation and experimentation to demonstrate practical relevance.

Robustness Improved Method for Deadbeat Predictive Current Control of PMLSM with Segmented Stators

Permanent magnet linear synchronous motors (PMLSMs) with stator segmented structures are widely used in the design of high-power propulsion systems. However, due to the inherent delay and segmented structure of the systems, there are parameter disturbances in the inductance and flux linkage of the motors. This makes the deadbeat predictive current control (DPCC) algorithm for a current loop less robust in the control system, leading to a decrease in control performance. Compensation methods such as compensation by observer and online estimation of parameters, are problematic to apply in practice due to the difficulty of parameter adjustment and the high complexity of the algorithm. In this paper, a robustness-improved incremental DPCC (RII-DPCC) method—which uses incremental DPCC (I-DPCC) to eliminate flux linkage parameters—is proposed. The stability of the current loop was evaluated through zero-pole analysis of the discrete transfer function. Current feedforward was introduced to improve the stability of I-DPCC. The inductance stability range of I-DPCC was increased from 0.8–1.25 times to 0–2 times the actual value, and the theoretical stability range was increased more than 4 times, effectively improving the robustness of the predictive model to flux linkage and inductance parameters. Finally, the effectiveness of the proposed method was verified through numerical simulation and experiment.

Continuous and synchronous calibration process of ovality and straightness for longitudinally submerged arc welding pipes with three rollers.

A new process of continuous and synchronous calibration process of ovality and straightness for LSAW (Longitudinally Submerged Arc Welding, LSAW) pipes with three rollers is proposed. Specifically, the process is introduced from three aspects: roller-shape, loading parameters and axial and circumferential deformation paths. The process is verified by numerical simulation and physical experiments. Further, the stress-strain in the Sections Ⅱ and Ⅳ is analyzed. The relationship between the process parameters and the residual ovality and residual straightness by experiments is discussed. The calibration scheme of LSAW pipes is put forward by using the control variable method. The results show that the shear stress is the principal stress direction in the Sections Ⅱ and Ⅳ. The residual ovality and residual straightness decrease with the increase of the radial reduction and times of reciprocating bending. The reciprocating bending process can eliminate the difference of the initial curvature, make the curvature of each section tend to be uniform. After calibration, the residual straightness is less than 0.2% and the residual ovality is less than 1%, demonstrating a good feasibility of this process.

Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable

In this work, we present the construction of two distinct finite element approaches to solve the porous medium equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous Galerkin method. In the second approach, we introduce additional potential and velocity variables to rewrite the PME into a system of equations, for which we construct a mixed finite element method. Both approaches are first-order accurate, mass conserving, and proved to be unconditionally energy stable for their respective energies. The mixed approach is shown to preserve positivity under a CFL condition, while a much stronger property of unconditional bound preservation is proved for the log-density approach. A novel feature of our schemes is that they can handle compactly supported initial data without the need for any perturbation techniques. Furthermore, the log-density method can handle unstructured grids in any number of dimensions, while the mixed method can handle unstructured grids in two dimensions. We present results from several numerical experiments to demonstrate these properties.

Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data

AbstractWe consider the Navier–Stokes–Fourier system governing the motion of a general compressible, heat conducting, Newtonian fluid driven by random initial/boundary data. Convergence of the stochastic collocation and Monte Carlo numerical methods is shown under the hypothesis that approximate solutions are bounded in probability. Abstract results are illustrated by numerical experiments for the Rayleigh–Bénard convection problem.

Fatigue assessment of bridges using interacting filtering approach with sub-structured predictor model based on current health

Fatigue estimation for critical structures necessitates comprehensive monitoring, which, in turn, requires dense instrumentation and models that heavily rely on computational resource models that heavily rely on computational resources. However, the fatigue vulnerability of different segments within the infrastructure can be considered to adopt a cost-effective substructure-based monitoring approach, minimizing the need for extensive instrumentation or complex models. However, estimating or instrumenting the substructure boundary adds to the complexity. In addition, conventional fatigue estimation approaches often assume constant structural health, disregarding the unknown current health status of aging structures. To overcome this limitation, a novel substructure-based fatigue life estimation approach is developed, incorporating an interacting ensemble-particle filter that considers the current health status while remaining robust against boundary forces. Numerical experiments validate the proposed approach on a simulated reinforced concrete box girder bridge, utilizing a 3D beam model that accounts for dynamic interaction with vehicles. A parametric analysis investigates the relationships between fatigue damage and factors such as surface roughness, vehicle speed, vehicle weight, and vehicle category, aiming to identify dominant stimuli. The results demonstrate an accurate estimation of health parameters and remaining useful life (RUL). Furthermore, a novel decomposed approach for RUL estimation is developed, enabling the mapping of traffic information to fatigue damage without requiring costly simulations. A case study highlights the practical applicability of the approach, focusing on a reinforced concrete box girder bridge in Himachal Pradesh, India.

A NEW CONVERGENCE ANALYSIS FOR MINIMUM NORM SOLUTION OF SPLIT SYSTEM OF NONSMOOTH MINIMIZATION PROBLEMS

This work presents a novel self-adaptive steepest-descent type algorithm for solving the split system of minimization problem (SSMP) related to convex nonsmooth functions. The algorithm includes a self-adaptive step size mechanism, which uses a step size that does not need prior information about the operator norm. Under certain weakened assumptions of parameters, a strong convergence theorem is established and proved for the algorithm. Specifically, the sequence generated by this new algorithm strongly converges towards the minimum norm element of the SSPM. To assess the implementation of our algorithm, a numerical example is provided. According to the numerical results, our algorithm showcases effectiveness and simplicity in its implementation. Furthermore, the primary numerical experiment results indicate that our proposed algorithm surpasses some existing results in the literature in terms of CPU time and iteration count. Our result represents an extension and enhancement of recent findings in this area.

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Super-localized orthogonal decomposition for convection-dominated diffusion problems

This paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coarse mesh, which defines a finite-dimensional coarse ansatz space with favorable approximation properties. For some relevant error measures, including the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-norm, the Galerkin projection onto this generalized finite element space even yields ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-independent error bounds, ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document} being the singular perturbation parameter. By constructing an approximate local basis, the approach becomes a novel multi-scale method in the spirit of the Super-Localized Orthogonal Decomposition (SLOD). The error caused by basis localization can be estimated in an a posteriori way. In contrast to existing multi-scale methods, numerical experiments indicate ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-robust convergence without pre-asymptotic effects even in the under-resolved regime of large mesh Péclet numbers.

Particle Swarm Optimization for a redundant repairable machining system with working vacations and impatience in a multi-phase random environment

With the increasing reliance on cloud computing as the foundational manufacturing systems with intricate dynamics, featuring multiple service areas, varying job arrival rates, diverse service requirements, and the interplay of failures and impatience, significant analytical challenges arise. Queueing networks offer a powerful stochastic modeling framework to capture such complex dynamics. This paper develops a novel, exhaustive queueing model for a finite-capacity redundant multi-server system operating in a multi-phase random environment. The proposed model uniquely integrates real-world factors, including server breakdowns and repairs, waiting servers, synchronous working vacations, and state dependent balking and reneging, into a single queueing model, representing a significant advancement in the field. Using the matrix-analytic method, we establish the steady-state solution and derive key performance metrics. Numerical experiments and sensitivity analyses elucidate the impact of system parameters on performance measures. Additionally, a cost model is formulated, enabling cost optimization analysis using direct search method and Particle Swarm Optimization (PSO) to identify efficient operating configurations.

Polynomial and Rational Measure Modifications of Orthogonal Polynomials via Infinite-Dimensional Banded Matrix Factorizations

AbstractWe describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via infinite-dimensional banded matrix factorizations and may be used to compute the modified Jacobi matrices all in linear complexity with respect to the truncation degree. A family of orthogonal polynomials with modified classical weights is constructed that support banded differentiation matrices, enabling sparse spectral methods with modified classical orthogonal polynomials. We present several applications and numerical experiments using an open source implementation which make direct use of these results.

Physics informed neural network based scheme and its error analysis for ψ-Caputo type fractional differential equations

This paper proposes a scientific machine learning approach based on Deep Physics Informed Neural Network (PINN) to solve ψ-Caputo-type differential equations. The trial solution is constructed based on the Theory of Functional Connection (TFC), and the loss function is built using the L1-based difference and quadrature rule. The learning is handled using the new hybrid average subtraction, standard deviation-based optimizer, and the nonlinear least squares approach. The training error is theoretically obtained, and the generalization error is derived in terms of training error. Numerical experiments are performed to validate the proposed approach. We also validate our scheme on the SIR model.