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A dual-explicit model-based integration algorithm with higher-order accuracy for structural dynamics

APPLIED MATHEMATICAL MODELLING 2022年 110卷 513-541页

作者： Fu, Bo Zhang, Fu-Tai Changan Univ Sch Civil Engn Xian 710061 Peoples R China

Several model-based or structure-dependent integration algorithms with explicit displacement formulation and unconditional stability are recently developed. According to the difference equations, these algorithms can be divided into dual-explicit and semi-explicit, where the first category algorithms are explicit for both displacement and velocity, while the second category are only explicit for displacement. The well-known Chen-Ricles (CR) and Chang algorithms are two representatives of dual-explicit and semi-explicit model-based algorithms, respectively. The model-based integration algorithms are promising with excellent computing efficiency, but most of them are second-order accurate. In this paper, a new dual-explicit (NDE) algorithm with higher-order accuracy is developed. The integration parameters of the NDE algorithm are obtained by using the pole mapping and second-order Pade approximation. Numerous important numerical characteristics including the consistency and local truncation error, stability, numerical dispersion and energy dissipation and overshoot are systematically analyzed for the new algorithm. It is found that the NDE algorithm is fourth-order accurate for free vibration without damping. As for forced vibration with/without damping and free vibration with damping, the NDE algorithm is no longer fourth-order accurate, but it is still more accurate than the CR and Chang algorithms. In addition, the period error of the algorithm is extremely small. Three representative numerical examples are finally provided to demonstrate the high accuracy of the NDE algorithm. Several classical and latest model-based integration algorithms and three fourth-order accurate algorithms are also adopted for comparisons. It has been proved that the NDE algorithm has much better performance than other selected model-based algorithms. (C) 2022 Elsevier Inc. All rights reserved.

关键词： integration algorithm Explicit Model-based Accuracy Period elongation Structural dynamics

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Strapdown inertial navigation integration algorithm design Part 2: Velocity and position algorithms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1998年第2期21卷 208-221页

作者： Savage, PG Strapdown Associates Inc Maple Plain MN 55359 USA

This series of two papers (Parts 1 and 2) provides a rigorous comprehensive approach to the design of the principal software algorithms utilized in modern-day strapdown inertial navigation systems: integration of angular rate into attitude, acceleration transformation/integration into velocity, and integration of velocity into position. The algorithms are structured utilizing the two-speed updating approach originally developed for attitude updating;an analytically exact equation is used a moderate speed to update the integration parameter (attitude, velocity, or po sition) with input provided from sr high-speed algorithm measuring rectified dynamic motion within the parameter update time interval [coming far attitude updating, sculling for velocity updating, and scrolling (writer's terminology) for high-resolution position updating]. The algorithm design approach accounts for angular rate/specific force acceleration inputs from the strapdown system inertial sensors, as well as rotation of the navigation frame used for attitude referencing and velocity integration. The Pare 1 paper (Savage, P. G., "Strapdown Inertial Navigation integration algorithm Design Part 1: Attitude algorithms," Journal of Guidance Control, and Dynamics, Vol. 21, No, 1, 1998, pip 19-28) defined the overall design requirement for the strapdown inertial navigation integration function and developed the attitude updating algorithms. This paper, Part 2, deals with design of the acceleration transformation/velocity integration and position integration algorithms. Although Parts I and 2 often cover basic concepts, the material presented is intended for use by the practitioner who is already familiar with inertial navigation fundamentals.

关键词： Strapdown Inertial Navigation System integration algorithm Inertial Sensor Strapdown System Earth Accelerometer Synthetic Aperture Radar Resonance Frequencies Software Architecture Taylor Series

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Analysis of implicit HHT-a integration algorithm for real-time hybrid simulation

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2012年第5期41卷 1021-1041页

作者： Chen, Cheng Ricles, James M. San Francisco State Univ Sch Engn San Francisco CA 94132 USA Lehigh Univ ATLSS Res Ctr Dept Civil & Environm Engn Bethlehem PA 18015 USA

Real-time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate-dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real-time hybrid simulation. The implicit HHT a-algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real-time hybrid simulation. Consequently, the HHT a-algorithm has been implemented for real-time hybrid simulation using a fixed number of substep iterations. The resulting HHT a-algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT a-algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT a-algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time-step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT a-algorithm with a fixed number of substep iterations. Both numerical and real-time hybrid simulations are conducted to ve

关键词： real-time hybrid simulation stability accuracy discrete transfer function integration algorithm

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A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method

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INTERNATIONAL JOURNAL OF PLASTICITY 2008年第2期24卷 267-288页

作者： Li, H. W. Yang, H. Sun, Z. C. Northwestern Polytech Univ Coll Mat Sci & Engn Xian 710072 Peoples R China

Severe numerical instability in the integration of rate dependent crystal plasticity (RDCP) model is one of the main problems for implementing RDCP into finite element method (FEM), especially for simulating dynamic/transient forming process containing complicated contact conditions under large step length, large strain and high strain rate. In order to overcome the problem, an implicit model is deduced with the primary unknowns of shear strain increments of slip systems under the corotational coordinate system in the paper. The homotopy auto-changing continuation method combined with the Newton-Raphson (N-R) iteration is adopted. The subroutine VUMAT is developed for implementing RDCP model in ABAQUS/Explicit. Simulation results show that the algorithm is stable and accurate in 3D FE simulations on both dynamic simple loading and complicated loading process containing nonlinear contacts under the conditions of the maximal step length of 3.5 x 10(-6) s, the maximal strain of 1.05, the maximal loading speed of 120 mm s(-1), and the minimal material rate sensitivity coefficient of 0.01. The predictions of the model on crystal behaviors of anisotropy, rate sensitivity and elasticity, as well as ear profiles in deep cup drawing are in agreement with experiments. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： crystal plasticity homotopy continuation method integration algorithm explicit FEM

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Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2009年第1期38卷 23-44页

作者： Chen, Cheng Ricles, James M. Marullo, Thomas M. Mercan, Oya Lehigh Univ Dept Civil & Environm Engn ATLSS Engn Res Ctr Bethlehem PA 18015 USA

Real-time hybrid testing combines experimental testing and numerical simulation, and provides a viable alternative for the dynamic testing of Structural Systems. An integration algorithm is used in real-time hybrid testing to compute the structural response based on feedback restoring forces from experimental and analytical substructures. Explicit integration algorithms are usually preferred over implicit algorithms as they do not require iteration and are therefore computationally efficient. The time step size for explicit integration algorithms, which are typically conditionally stable, can be extremely small in order to avoid numerical stability when the number of degree-of-freedom of the structure becomes large. This paper presents the implementation and application of a newly developed unconditionally stable explicit integration algorithm for real-time hybrid testing. The development of the integration algorithm is briefly reviewed. An extrapolation procedure is introduced in the implementation of the algorithm for real-time testing to ensure the Continuous movement of the servo-hydraulic actuator. The stability of the implemented integration algorithm is investigated Using control theory. Real-time hybrid test results of single-degree-of-freedom and multi-degree-of-freedom structures with a passive elastomeric damper subjected to earthquake ground motion are presented. The explicit integration algorithm is shown to enable the exceptional real-time hybrid test results to be achieved. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： integration algorithm real-time hybrid testing stability explicit discrete transfer function

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Development of an explicit time integration algorithm based on optimal integration parameter updating

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2023年第15期52卷 5117-5140页

作者： Fu, Zhao-Yang Li, Hong-Nan Li, Chao Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian Peoples R China Shenyang Jianzhu Univ Sch Civil Engn Shenyang Peoples R China Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian 116023 Peoples R China

integration algorithm is an important mean to solve the discrete time equations of structural dynamics in earthquake engineering. In this paper, a new model-based explicit integration algorithm, featured by optimization-based integration parameter updating, is developed for a more accurate and efficient solution of structural dynamic problems. The new integration algorithm is designed to yield minimum error and controllable numerical dispersion under the premise of stability by defining objective functions and constraints. Numerical properties of the new integration algorithm are investigated in details using the amplification matrix method for a linear elastic single degree-of-freedom system. Meanwhile, representative numerical examples and complex structure examples are analyzed and compared with other representative algorithms. As a result, the proposed algorithm yields comparable numerical characteristics with other methods, but exhibits pronounced superiority in controllable algorithmic dissipation, higher precision, and better efficiency. Therefore, the new integration algorithm possesses extensive application prospect in solving complicated linear and nonlinear structural dynamic problems.

关键词： dynamic analysis explicit method integration algorithm numerical analysis stability

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An integration algorithm for Stator Flux Estimation of a Direct-Torque-Controlled Electrical Excitation Flux-Switching Generator

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2012年第2期27卷 411-420页

作者： Wang, Yu Deng, Zhiquan Nanjing Univ Aeronaut & Astronaut Dept Elect Engn Nanjing 210016 Peoples R China

This paper presents an integration algorithm for stator flux estimation of direct torque control (DTC). This algorithm only contains a fifth-order low-pass filter (LPF), a high-pass (HP) filter, and a simple logical calculation part, where the fifth-order LPF and the HP filter can effectively filter out HF harmonics and the dc drift in the back EMF, respectively. The alpha- and beta-axis back EMFs passing through the two filters will obtain beta-axis stator flux linkage and opposite polarity a-axis stator flux linkage, respectively, and then by the logical calculation part can finally achieve alpha- and beta-axis stator flux linkages. At any synchronous angular frequency, the amplitude-and phase-frequency characteristics of this algorithm are same as those of the pure integrator, and meanwhile its dc gain is zero. The proposed algorithm with high estimation accuracy behaves well in both steady state and dynamic performance when used in a DTC-based electrical excitation flux-switching generator dc power system, which is verified by experimental results.

关键词： Direct torque control (DTC) electrical excitation flux-switching (EEFS) generator integration algorithm stator flux estimation

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Numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2007年第10期69卷 1997-2035页

作者： Helm, D. Univ Kassel Dept Mech Engn Inst Mech D-34109 Kassel Germany

The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as well as the one-way and two-way shape memory effects are utilized. These material properties are caused by martensitic phase transitions between austenite and martensite. In the present contribution, a recently proposed constitutive theory is numerically treated in the context of the finite element method. This constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys. For the numerical integration of the evolution equations, the backward Euler method is applied. In spite of the complexity of the constitutive theory, it is shown that an improved integration procedure can be formulated, which merely involves the solution of three non-linear equations for three scalar-valued unknown variables. Numerical examples show the capability of the proposed model and the improved integration algorithm. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： shape memory alloys martensitic phase transitions integration algorithm thermomechanical constitutive theory computational mechanics

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Combining multi-layer integration algorithm with background prior and label propagation for saliency detection

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2017年第Oct.期48卷 110-121页

作者： Xia, Chenxing Zhang, Hanling Gao, Xiuju Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Hunan Peoples R China Nanjing Univ Informat Sci & Technol Jiangsu Engn Ctr Network Monitoring Nanjing 210044 Jiangsu Peoples R China

In this paper, we propose a novel approach to automatically detect salient regions in an image. Firstly, some corner superpixels serve as the background labels and the saliency of other superpixels are determined by ranking their similarities to the background labels based on ranking algorithm. Subsequently, we further employ an objectness measure to pick out and propagate foreground labels. Furthermore, an integration algorithm is devised to fuse both background-based saliency map and foreground-based saliency map, meanwhile an original energy function is acted as refinement before integration. Finally, results from multiscale saliency maps are integrated to further improve the detection performance. Our experimental results on five benchmark datasets demonstrate the effectiveness of the proposed method. Our method produces more accurate saliency maps with better precision-recall curve, higher F-measure and lower mean absolute error than other 13 state-of-the-arts approaches on ASD, SED, ECSSD, iCoSeg and PASCAL-S datasets. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Corner Objectness Energy function integration algorithm Multi-layer

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Multimodel ensemble estimation of Landsat-like global terrestrial latent heat flux using a generalized deep CNN-LSTM integration algorithm

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AGRICULTURAL AND FOREST METEOROLOGY 2024年 349卷

作者： Guo, Xiaozheng Yao, Yunjun Tang, Qingxin Liang, Shunlin Shao, Changliang Fisher, Joshua B. Chen, Jiquan Jia, Kun Zhang, Xiaotong Shang, Ke Yang, Junming Yu, Ruiyang Xie, Zijing Liu, Lu Ning, Jing Zhang, Lilin Beijing Normal Univ Fac Geog Sci State Key Lab Remote Sensing Sci Beijing 100875 Peoples R China Liaocheng Univ Sch Geog & Environm Liaocheng 252000 Peoples R China Univ Hong Kong Dept Geog Sci Hongkong 999077 Peoples R China Chinese Acad Agr Sci Inst Agr Resources & Reg Planning State Key Lab Efficient Utilizat Arid & Semiarid A Natl Hulunber Grassland Ecosyst Observat & Res Stn Beijing 100081 Peoples R China Chapman Univ Schmid Coll Sci & Technol Univ Dr Orange CA 92866 USA Michigan State Univ Dept Geog Environm & Spatial Sci E Lansing MI 48823 USA Space Engn Univ Sch Space Informat Beijing 101416 Peoples R China Univ Twente Fac Geoinformat & Earth Observat ITC NL-7500 AE Enschede Netherlands

Accurate estimates of high-spatial-resolution global terrestrial latent heat flux (LE) from Landsat data are crucial for many basic and applied research. Yet current Landsat-derived LE products were developed using single algorithm with large uncertainties and discrepancies. Here we proposed a convolutional neural network-long short-term memory (CNN-LSTM)-based integrated LE (CNN-LSTM-ILE) framework that integrates five Landsatderived physical LE algorithms, topography-related variables (elevation, slope and aspect) and eddy covariance (EC) observations to estimate 30-m global terrestrial LE. CNN-LSTM-ILE not only conserves good performance of LE estimation from pure deep learning (DL) algorithm, but partially inherits physical mechanism of the individual physical algorithms for improving the generalization of the integration algorithms for extreme cases. CNN-LSTM is an algorithm that combines two deep learning structures (CNN and LSTM) to effectively utilize the spatial and temporal information contained in the forcing inputs. The data were collected from 190 globally distributed EC observations from 2000 to 2015 and were provided by FLUXNET. The cross-validation results indicated that the CNN-LSTM integration algorithm improved the LE estimates by reducing the root mean square error (RMSE) of 5-8 W/m2 and increasing Kling-Gupta efficiency (KGE) of 0.05-0.16 when compared with the individual LE algorithms and the results of three other machine learning integration algorithms (multiple linear regression, MLR;random forest, RF;and deep neural networks, DNN). The CNN-LSTM integration algorithm had highest KGE (0.81) and R2 (0.66) compared to ground-measured and was applied to generate the Landsat-like regional and global terrestrial LE. An innovation of our strategy is that the CNN-LSTM-ILE model integrates pixel proximity effects and daily LE variations to enhance the accuracy of 16-day LE estimations. This approach can produce a more reliable Landsat-like global ter

关键词： Latent heat flux integration algorithm CNN-LSTM Landsat High -spatial -resolution products

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