Domain Decomposition Research Articles

An integrated frequency domain decomposition and deep neural network approach for short-term PV power forecast

An integrated frequency domain decomposition and deep neural network approach for short-term PV power forecast

A unified Jacobi-Ritz-spectral BEM for vibro-acoustic behavior of spherical shell

In order to solve the vibration and acoustic characteristics of spherical shell in light fluid environment, based on Jacobi-Ritz-spectral BEM, a unified analysis formula for acoustic vibration of spherical shell under arbitrary boundary conditions is established. Based on the First-order shear deformation theory (FSDT) and domain decomposition method (DDM), the theoretical model of spherical shell structure is established. The improved Jacobi polynomial is innovatively used to construct the displacement tolerance function of the spherical shell. Based on the spectral Kirchhoff-Helmholtz integral formula, the theoretical model of the acoustic fluid outside the spherical shell is established. The special form of Jacobi polynomial Chebyshev polynomial is used to describe the excitation sound pressure on the spherical shell segment, so as to ensure that the generalized coordinates of the structure can be perfectly matched with the acoustic boundary element nodes. In addition, the integration along the meridian of the shell is used to control the movement of the fluid, which simplifies the surface integration. The CHIEF method is used to solve the problem of non-unique solution of acoustic variables of rotary structure. Compared with the published literature, numerical simulation results and experimental results, the proposed method has higher calculation accuracy. In addition, based on this method, the influence of boundary conditions, geometric dimensions and other factors on the acoustic and vibration characteristics of spherical shells is discussed, which accumulates data for analyzing the acoustic and vibration behavior of spherical shells.

Efficient matrix algebra encoding for urban solar irradiation simulation: fine-grid ground-level estimation with vector data

Conducting a detailed assessment of solar irradiation at the pedestrian scale on all ground surfaces of a city can assist in identifying cooler routes for pedestrian navigation or preparing the city for potential overheating issues by pinpointing overexposed areas. This article proposes an effective method for conducting such an assessment within a GIS with metric resolution across territories exceeding 100 km². It is based on standard datasets and implements an efficient strategy that relies on separation of variables, domain decomposition, and dimensionality reduction. This strategy involves creating a synthetic representation of the facades of the surrounding buildings (spatial dimension) which accelerates the calculation of shadows based on the sun’s position (temporal dimension). To demonstrate the effectiveness of this method, we applied it to a French city, generating fourteen maps illustrating the solar irradiation of the area for different months of the year or for two given dates with specific weather conditions. The proposed strategy, along with the synthetic representation of building facades, opens up a wide range of possibilities. In addition to synthesizing machine learning labeled datasets, we can also consider calculating solar irradiation with time steps of a few minutes to update weather conditions throughout a journey.

A refined output-only modal identification technique for structural health monitoring of civil infrastructures

The increasing installation of structural health monitoring systems has raised the need for efficient and rapid data interpretation algorithms. Operational modal analysis is currently one of the most used techniques for extracting modal properties, and some attempts have been made to automate this procedure. However, automated techniques often require manual calibration of hyperparameters and show inconsistencies across different case studies. This paper proposes a refined version of the automated frequency domain decomposition (AFDD) using the modal assurance criterion (MAC) to obtain natural frequencies and mode shapes. Sensitivity analyses were conducted on the ambient vibration response of the Yonghe cable-stayed bridge in China, accounting for influential factors including noise levels, acceleration record length, sensor layouts. A novel approach is then introduced to interpret the results of the sensitivity analyses. The approach consists in plotting the result of each analysis in a stabilization diagram and then using a Gaussian mixture model that clusters the poles into core and outliers. This allows to identify regions where the MAC thresholds are optimal. By comparing the results of all the sensitivity analyses it was possible to define a single optimal MAC threshold, avoiding the need for fixing a value based on the user’s experience. Three substantially different case studies were analyzed to extensively test the methodology: the Yonghe cable-stayed bridge, the PolyU footbridge in Hong Kong, and Moletta Tower in the Circus Maximus archeological site in Italy. The analysis compared the proposed AFDD algorithm to the traditional frequency domain decomposition and covariance-driven stochastic subspace identification. Specifically, the efficiency in identifying close frequencies, weakly excited modes, spurious peaks, and complex modes was evaluated for each method, which highlighted the robustness of the proposed optimized AFDD. The analysis showcases peculiar characteristics and drawbacks of each method when trying to identify complex vibrational modes of the specific case studies. It was found that the proposed AFDD procedure performs better than traditional methods despite it may misidentify complex modes due to the constraints of a narrower modal domain and similar geometries.

Overlapping domain decomposition methods for finite volume discretizations

Two-level additive overlapping domain decomposition methods are applied to solve the linear system arising from the cell-centered finite volume discretization methods (FVMs) for the elliptic problems. The conjugate gradient (CG) methods are used to accelerate the convergence. To analyze the preconditioned CG algorithm, a discrete L2 norm, an H1 norm, and an H1 semi-norm are introduced to connect the matrices resulting from the FVMs and related bilinear forms. It has been proved that, with a small overlap, the condition number of the preconditioned systems does not depend on the number of the subdomains. The result is similar to that for the conforming finite element. Numerical experiments confirm the theory.

Non-iterative two-grid parallel scheme based upon overlapping domain decomposition for the Stokes problem

Non-iterative two-grid parallel scheme based upon overlapping domain decomposition for the Stokes problem

Gas-Kinetic Unified Algorithm for Aerodynamics Covering Various Flow Regimes by Computable Modeling of Boltzmann Equation

The gas-kinetic unified algorithm (GKUA), to solve the modeling of the Boltzmann equation, has been developed to study the aerothermodynamics problems with the effects of wall activation energy covering various flow regimes. The unified velocity distribution function equation could be accordingly presented on the basis of the Boltzmann-Shakhov model. To remove the dependence of the distribution function on velocity space, the conservational discrete velocity ordinate method has been developed for hypervelocity flows. The gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by the operator splitting technique. The discrete velocity numerical integration method with the Gauss-type weight function has been developed to evaluate the macroscopic flow variables. Specially, to model the real physical process between gas molecules and the surface, the Maxwell-type gas-surface interaction model has been presented by the MD (molecular dynamic) simulation to obtain the energy adaptability coefficient. The multi-processing domain decomposition strategy and parallel implementation of high parallel efficiency and expansibility designed for the gas-kinetic numerical method is presented with good load balance and data communication efficiency. To validate the accuracy and feasibility of the present algorithm, the supersonic flows past two-dimensional circular cylinder are simulated covering various flow regimes. The results are in good agreement with the related theoretical, DSMC (Direct Simulation Monte Carlo), N-S (Navier-Stokes), and experimental data. The hypersonic reentry flows with the effects of wall activation energy around the Tianzhou-5 cargo spacecraft are simulated by the present GKUA and the massive parallel strategy. It has been confirmed that the present algorithm from the gas-kinetic point of view probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes during the re-entry and disintegration of the large-scale spacecraft.

An Experimental Study on the Effect of GFRP and CFRP Strengthening on the Static and Dynamic Behavior of R/C Beams Under Progressive Damage

This paper aims to investigate the effect of glass fiber-reinforced polymer (GFRP) and carbon fiber-reinforced polymer (CFRP) strengthening materials on the static and dynamic behavior of reinforced concrete (R/C) beams subjected to progressive damage. Four identical beams, each strengthened with either GFRP or CFRP, are tested under a cyclic quasi-static loading pattern. Impact hammer tests are performed for undamaged states and various damage levels of the beams. The dynamic test data are analyzed using the Enhanced Frequency Domain Decomposition (EFDD) method to estimate the dynamic characteristics of the beams. In this context, the first three vibration modes in both vertical and horizontal directions are considered. Strengthening is applied to both pre-damaged and undamaged beams, enabling a comparison of their performance before and after the strengthening procedure. Beams strengthened with CFRP exhibit a higher load-bearing capacity and stiffness but also fail at lower displacement levels compared to those strengthened with GFRP, which demonstrate more ductile behavior. Furthermore, the modal frequency ratios indicate that the first vibration mode is more sensitive to damage than the second and third modes. This study highlights the effectiveness of both strengthening materials in enhancing the structural performance of both undamaged and damaged beams.

Differential Evolution-based Time Domain Decomposition Method for Multi-impact Vibration Signals of Reciprocating Machinery

Abstract To solve the problem of extracting the impact component from the complex time-domain vibration signal of reciprocating machinery vibration signals, a differential evolution-based time domain decomposition method is proposed to achieve adaptive extraction of impact components. The method establishes new decomposition window containing three adjustment parameters to adapt to multiple forms of impact components. Furthermore, with the optimization objectives of minimizing reconstruction loss, amplitude moment loss, and similarity loss, a decomposition parameter optimization algorithm based on differential evolution is established to achieve the optimization process of decomposition parameters. The results of processing simulated and actual vibration signals of diesel engines show that the new method can adaptively and accurately identify the impact component and impact time center in the vibration component, with a signal reconstruction loss of less than 2.5% and a decomposition time of only 54.1s.

An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation

Abstract In this work, we propose and analyze an extension of the approximate component mode synthesis (ACMS) method to the two-dimensional heterogeneous Helmholtz equation. The ACMS method has originally been introduced by Hetmaniuk and Lehoucq as a multiscale method to solve elliptic partial differential equations. The ACMS method uses a domain decomposition to separate the numerical approximation by splitting the variational problem into two independent parts: local Helmholtz problems and a global interface problem. While the former are naturally local and decoupled such that they can be easily solved in parallel, the latter requires the construction of suitable local basis functions relying on local eigenmodes and suitable extensions. We carry out a full error analysis of this approach focusing on the case where the domain decomposition is kept fixed, but the number of eigenfunctions is increased. The theoretical results in this work are supported by numerical experiments verifying algebraic convergence for the method. In certain, practically relevant cases, even super-algebraic convergence for the local Helmholtz problems can be achieved without oversampling.

Overlapping Domain Decomposition Methods Based on Tensor Format for Solving High-Dimensional Partial Differential Equations

Overlapping Domain Decomposition Methods Based on Tensor Format for Solving High-Dimensional Partial Differential Equations

Bridge monitoring using mobile sensing data with traditional system identification techniques

AbstractMobile sensing has emerged as an economically viable alternative to spatially dense stationary sensor networks, leveraging crowdsourced data from today's widespread population of smartphones. Recently, field experiments have demonstrated that using asynchronous crowdsourced mobile sensing data, bridge modal frequencies, and absolute mode shapes (the absolute value of mode shapes, i.e., mode shapes without phase information) can be estimated. However, time‐synchronized data and improved system identification techniques are necessary to estimate frequencies, full mode shapes, and damping ratios within the same context. This paper presents a framework that uses only two time‐synchronous mobile sensors to estimate a spatially dense frequency response matrix. Subsequently, this matrix can be integrated into existing system identification methods and structural health monitoring platforms, including the natural excitation technique eigensystem realization algorithm and frequency domain decomposition. The methodology was tested numerically and using a lab‐scale experiment for long‐span bridges. In the lab‐scale experiment, synchronized smartphones atop carts traverse a model bridge. The resulting cross‐spectrum was analyzed with two system identification methods, and the efficacy of the proposed framework was demonstrated, yielding high accuracy (modal assurance criterion values above 0.94) for the first six modes, including both vertical and torsional. This novel framework combines the monitoring scalability of mobile sensing with user familiarity with traditional system identification techniques.

Dynamic Behaviors of Composite-Laminated Concentrically Stiffened Rectangular Plates by Substructure Modal Synthesis

Existing numerical analysis methods often incur high computational costs when directly solving multi-degree-of-freedom systems due to computer capacity limitations. To address this issue, this paper took the composite laminated concentrically stiffened rectangular plate as the research object. The modal synthesis method was employed to reduce the degrees of freedom of the model, enabling the solution of complex dynamic characteristics. In the research process, the domain decomposition theory was used to divide the research object into plate and rib substructures. Based on the spectral Chebyshev method, the substructure dynamic model of the composite laminated rectangular plate was constructed. Subsequently, the function expressions of the complex load excitation on each substructure were derived, and the fixed modal synthesis method was introduced to construct the spectral Chebyshev reduced model of the substructures. According to the artificial spring theory equivalent, the interface force, and the whole reduction model of the composite laminated concentrically stiffened rectangular plate were obtained by assembling the substructure models. The time–domain and frequency–domain dynamic behaviors of composite laminated concentrically stiffened rectangular plates are yielded by solving the whole reduced model. The novelty of this work lies in combining the spectral Chebyshev method with the modal synthesis method. The established reduced model no longer depended on mesh quality and required fewer matrix dimensions and computation time compared to the whole model, while still achieving sufficiently accurate results. Additionally, based on the reduced model, an effective parametric study scheme was proposed to analyze the impact of dimensions and material properties of rib substructures on the dynamic behaviors of the composite laminated concentrically stiffened rectangular plate. These findings can be used to guide the optimal design of laminated concentrically stiffened rectangular plates in engineering practice.

Microwave Digital Twin Prototype for Shoulder Injury Detection.

One of the most common shoulder injuries is the rotator cuff tear (RCT). The risk of RCTs increases with age, with a prevalence of 9.7% in those under 20 years old and up to 62% in individuals aged 80 years and older. In this article, we present first a microwave digital twin prototype (MDTP) for RCT detection, based on machine learning (ML) and advanced numerical modeling of the system. We generate a generalizable dataset of scattering parameters through flexible numerical modeling in order to bypass real-world data collection challenges. This involves solving the linear system as a result of finite element discretization of the forward problem with use of the domain decomposition method to accelerate the computations. We use a support vector machine (SVM) to differentiate between injured and healthy shoulder models. This approach is more efficient in terms of required memory resources and computing time compared with traditional imaging methods.

Automatic High-Resolution Operational Modal Identification of Thin-Walled Structures Supported by High-Frequency Optical Dynamic Measurements.

High-frequency optical dynamic measurement can realize multiple measurement points covering the whole surface of the thin-walled structure, which is very useful for obtaining high-resolution spatial information for damage localization. However, the noise and low calculation efficiency seriously hinder its application to real-time, online structural health monitoring. To this end, this paper proposes a novel high-resolution frequency domain decomposition (HRFDD) modal identification method, combining an optical system with an accelerometer for measuring high-accuracy vibration response and introducing a clustering algorithm for automated identification to improve efficiency. The experiments on the cantilever aluminum plate were carried out to evaluate the effectiveness of the proposed approach. Natural frequency and damping ratios were obtained by the least-squares complex frequency domain (LSCF) method to process the acceleration responses; the high-resolution mode shapes were acquired by the singular value decomposition (SVD) processing of global displacement data collected by high-speed cameras. Finally, the complete set of the first nine order modal parameters for the plate within the frequency range of 0 to 500 Hz has been determined, which is closely consistent with the results obtained from both experimental modal analysis and finite element analysis; the modal parameters could be automatically picked up by the DBSCAN algorithm. It provides an effective method for applying optical dynamic technology to real-time, online structural health monitoring, especially for obtaining high-resolution mode shapes.

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Domain decomposition with local time discretization for the nonlinear Stokes–Biot system

This work presents a domain decomposition method for the fluid-poroelastic structure interaction (FPSI) system, which utilizes local time integration for subproblems. To derive the domain decomposition scheme, we introduce a Lagrange multiplier and define time-dependent Steklov–Poincaré-type operators based on the interface conditions. These operators are employed to transform the coupled system into an evolutionary nonlinear interface problem, which is then solved using an iterative algorithm. This approach provides the flexibility to use different time discretization schemes and step sizes in subdomains, making it an efficient method for simulating multiphysics systems. We present numerical tests for both non-physical and physical problems to demonstrate the accuracy and efficiency of this method.

Spatially mixed implicit–explicit schemes in hydro-mechanically coupled soil dynamics

Mixed implicit–explicit (IMEX) schemes combine elements of both implicit and explicit time integration methods. This allows to efficiently handle boundary value problems with severe differences in stiffness, such as often encountered in soil dynamics. A spatially mixed IMEX scheme, in which different parts of the computational domain may be treated implicitly or explicitly depending on their behaviour, is discussed in this work. Domain decomposition by means of a mortar contact discretisation is used for this purpose and multiple systems of equations are solved. The merits of the scheme in solving problems of soil dynamics are demonstrated, for which the governing equations are extended to hydro-mechanical coupling.

Dynamic Modeling and Vibration Characteristic Analysis of Fiber Woven Composite Shaft–Disk Rotor with Weight-Reducing Holes

In order to achieve the goal of a lightweight shaft–disk rotor, this paper applies the fiber woven composite material to the disk structure, and at the same time considers the design of the weight-reducing holes on the porous disk. It introduces the domain decomposition and coordinate mapping technology for this, and then establishes the dynamics model of the fiber woven composite material shaft–disk rotor. The model is based on the differential quadrature finite element method, which is suitable for fiber woven composite rotors with arbitrary complex hole patterns. The validity of the model is verified by comparing the results with the literature, finite element simulation, and experiments, and the mechanism of the influence of the material parameters and pore parameters on the vibration characteristics of the system is investigated, which provides the data support and theoretical basis for the analysis of the dynamics of the fiber woven composite rotor.

A distributionally robust optimization approach of multi-park integrated energy systems considering shared energy storage and Uncertainty of Demand Response

To enhance the economic efficiency and renewable energy integration capacity of multi-park integrated energy systems (MPIES) and address the issue of insufficient consideration of demand response uncertainty in existing studies, this paper proposes a distributionally robust optimization approach for multi-park integrated energy systems, considering shared energy storage and the uncertainty of demand response. First, models of the shared energy system and demand response are established. Based on these models, a deterministic optimization scheduling model for MPIES is developed, aiming to minimize system costs while considering constraints such as grid power balance. To address uncertainty in demand response, this paper employs Interval Type-2 Fuzzy Theory to construct uncertainty sets and considers system reliability constraints. The original optimization problem is then transformed into an equivalent robust counterpart model, and the optimal distributionally robust solution is obtained through parameter domain decomposition methods. Finally, the proposed method is validated using the IEEE 33-bus system. The results show that considering shared energy storage and demand response individually can reduce total system costs by 4.86 % and 26.46 %, respectively. After accounting for the uncertainty in demand response, the total system cost increases only slightly by 4.36 %, but this improves the system's robustness.