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This study advances dynamic force reconstruction in the time domain through the precise integration method (PIM), particularly effective for matrix exponential numerical solutions. Traditional PIM approaches, typically reliant on linear or step function assumptions within integration time steps, face limitations in handling large integration time step loads. Addressing this, our research introduces an innovative method employing velocity and displacement sensors in simple and complex structures, significantly enhancing load fitting accuracy, especially for nonlinear loads. We propose a refined version of PIM: the Chebyshev polynomial integration method (CPIM) and the adaptive precise integration method (APIM) based on wavelets. These methods are designed to fit force functions of varying orders across different time steps, thereby bolstering signal reconstruction robustness. The efficacy of these approaches is validated given adequate measurement response data. Furthermore, recognizing the growing emphasis on uncertainty in engineering, our work incorporates the collocation method for uncertainty quantification in load identification. To counteract the erratic results from polynomial fitting, particle swarm optimization (PSO) thresholding is employed to eliminate high-frequency noise, thus enhancing the Signal-to-Noise Ratio and minimizing signal distortion. Notably, we demonstrate that the Shannon wavelet surpasses the Chebyshev polynomial in fitting ability due to its tighter branch, rendering APIM more suitable for engineering applications compared to CPIM. APIM adeptly minimizes errors related to acquisition frequency by adaptively adjusting the number of discretization points and wavelet convergence levels to fulfill convergence criteria and matrix norm requisites. This paper proposes a multi-source uncertainty-oriented dynamic Force Reconstruction Framework, integrating adaptive fitting precise integration with PSO. Our numerical examples illustrate that APIM, as discussed herein, offers broader applications and is more time efficient than CPIM. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalized model of a viscoelastic beam, which takes into account the influence of axial forces and incorporates a fractional constitutive relationship. In addition, we propose a novel numerical calculation method for analyzing fractional-order viscoelastic beams. This method takes the transverse displacement and bending moment of the beam as state variables, transforms the beam model into a discrete state space equation through the application of the central difference method, and utilizes an improved precise integration algorithm to solve the equation. To evaluate the performance of the method, the responses of the beam under two types of excitations, namely uniformly distributed transverse load and the motion of the support at both ends, are calculated under fixed hinge conditions. The results demonstrate that the present method has excellent accuracy and convergence, and also reveal some nonlinear phenomena of the system. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Precision exogenous gene knock-in is an attractive field for transgenic Gallus gallus (chicken) generation. In this article, we constructed multiple Precise Integration into Target Chromosome (PITCh) plasmid systems mediated by microhomology-mediated end-joining (MMEJ) for large-fragment integration in DF-1 cells and further assess the possibility of GAPDH (glyceraldehyde-3-phosphate dehydrogenase) as a genomic safe harbor for chickens. We designed three targeted sgRNAs for the all-in-one plasmid at the 3′UTR of GAPDH near the stop codon. The donor-plasmid-carrying microhomology arms correspond to sgRNA and EGFP fragments in the forward and reverse directions. MMEJ-mediated EGFP insertion can be efficiently expressed in DF-1 cells. Moreover, the differences between the forward and reverse fragments indicated that promoter interference does affect the transfection efficiency of plasmids and cell proliferation. The comparison of the 20 bp and 40 bp microhomology arms declared that the short one has higher knock-in efficiency. Even though all three different transgene insertion sites in GAPDH could be used to integrate the foreign gene, we noticed that the G2-20R-EGFP cell reduced the expression of GAPDH, and the G3-20R-EGFP cell exhibited significant growth retardation. Taken together, G1, located at the 3′UTR of GAPDH on the outer side of the last base of the terminator, can be a candidate genomic safe harbor (GSH) loci for the chicken genome. In addition, deleted-in-azoospermia-like (DAZL) and actin beta (ACTB) site-specific gene knock-in indicated that MMEJ has broad applicability and high-precision knock-in efficiency for genetically engineered chickens. [ABSTRACT FROM AUTHOR]

As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method. [ABSTRACT FROM AUTHOR]

Stability lobe diagrams (SLDs) can be employed to determine the stability behavior of a milling process. Hence, SLD recognition is an important issue for an effective stable machining monitoring system. Various methods have been developed for prediction of milling stability. However, the main shortcoming of such methods is that they cannot accurately and efficiently predict milling stability. This study proposes a novel precise integration-based updated numerical integration method (PI-UNIM) that can be both accurate and efficient in milling stability prediction. The fifth-order Hermite interpolation polynomial for numerical integration formula derivation is addressed in this work. Transition matrix is obtained with the precise integration algorithm. The numerical results obtained using extensive simulation indicate that the proposed method can effectively recognize SLDs for not only low immersion milling situation but also high immersion milling situation. Empirical comparisons show that the proposed method performs better than existing methods in terms of computation accuracy and computation efficiency. A demonstrative example is provided to illustrate the usage of the proposed method. [ABSTRACT FROM AUTHOR]

Precision exogenous gene knock-in is an attractive field for transgenic Gallus gallus (chicken) generation. In this article, we constructed multiple Precise Integration into Target Chromosome (PITCh) plasmid systems mediated by microhomology-mediated end-joining (MMEJ) for large-fragment integration in DF-1 cells and further assess the possibility of GAPDH (glyceraldehyde-3-phosphate dehydrogenase) as a genomic safe harbor for chickens. We designed three targeted sgRNAs for the all-in-one plasmid at the 3′UTR of GAPDH near the stop codon. The donor-plasmid-carrying microhomology arms correspond to sgRNA and EGFP fragments in the forward and reverse directions. MMEJ-mediated EGFP insertion can be efficiently expressed in DF-1 cells. Moreover, the differences between the forward and reverse fragments indicated that promoter interference does affect the transfection efficiency of plasmids and cell proliferation. The comparison of the 20 bp and 40 bp microhomology arms declared that the short one has higher knock-in efficiency. Even though all three different transgene insertion sites in GAPDH could be used to integrate the foreign gene, we noticed that the G2-20R-EGFP cell reduced the expression of GAPDH, and the G3-20R-EGFP cell exhibited significant growth retardation. Taken together, G1, located at the 3′UTR of GAPDH on the outer side of the last base of the terminator, can be a candidate genomic safe harbor (GSH) loci for the chicken genome. In addition, deleted-in-azoospermia-like (DAZL) and actin beta (ACTB) site-specific gene knock-in indicated that MMEJ has broad applicability and high-precision knock-in efficiency for genetically engineered chickens.

In this article, a precise integral method (PIM) for the load identification of continuous structures based on the polynomial nonlinear hypothesis is presented. Essentially, load identification can be regarded as solving a dynamic equation in an inverse process. PIM is famous for its high precision in positive engineering problems. It has been already used in load reconstruction, but most cases are with discrete structures. In each time step, the dynamic responses of the measured points are used to identify the load without establishing a recursive chain, so PIM is not sensitive to the initial value and has no accumulated error. Legendrepolynomials (LPIM) is a computational scheme. The dynamic load is assumed to be a polynomial fitting nonlinear function in each integral time step with LPIM. Just with the first modal, LPIM can reliably identify the concentrated load. In addition, as uncertainty is getting more and more attention in engineer, it is also needed to be considered in load identification. In linear systems, interval vertex is a reliable method to obtain the load bounds in the virtue of multisource uncertainties. The results of identified load are too lumpy because of the polynomial fitting. To improve the precision, Savitsky–Golay (S–G) filters which fit the curves by polynomials in a frame length is introduced to smooth down the load in high fidelity. Eight numerical examples are investigated to demonstrated the efficiency and precision of the developed method. [ABSTRACT FROM AUTHOR]

As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method.

The estimation of the disturbance input acting on a vehicle from its given responses is an inverse problem. To overcome some of the issues related to ill-posed inverse problems, this work proposes a method of reconstructing the road roughness based on the Kalman filter method. A half-car model that considers both the vehicle and equipment is established, and the joint input-state estimation method is used to identify the road profile. The capabilities of this methodology in the presence of noise are numerically demonstrated. Moreover, to reduce the influence of the driving speed on the estimation results, a method of choosing the calculation frequency is proposed. A road vibration test is conducted to benchmark the proposed method. [ABSTRACT FROM AUTHOR]

The third-order and fourth-order semi-discretization methods (3rd SDM and 4th SDM) are presented to predict milling stability based on precise integration. Firstly, the milling system is mathematically represented by a delay differential equation (DDE) and re-expressed in the state space. After dividing the tooth passing period into free and forced vibration time intervals, the forced vibration time interval is equally discretized into many small-time intervals. Then, the DDE is integrated on any small-time interval and solved in the framework of the semi-discretization algorithm. Subsequently, the 3rd SDM and 4th SDM are derived for predicting the stability limits in milling. In the 3rd SDM and 4th SDM, the third-order and fourth-order interpolation polynomials are used to approximate the delayed term, respectively. The periodic-coefficient matrix is approximated by linear interpolation polynomial. The convergence rates of the one degree of freedom (one-DOF) milling system and the milling system with multiple modes are conducted. The results indicate the convergence rates of the 3rd SDM and 4th SDM are higher than those of the benchmark methods. Besides, no matter for large or low radial immersion conditions, the stability lobe diagrams (SLDs) obtained by the proposed 3rd SDM and 4thSDM are closer to the reference than those obtained by the benchmark methods. The computational efficiency of the 3rd SDM and 4th SDM is also evaluated. Compared with the benchmark methods, the presented 3rd SDM and 4th SDM are superior in computational efficiency. Generally, the main advantage of the proposed methods is the improvement of computational efficiency. The proposed 3rd SDM and 4th SDM can use a smaller discrete number for achieving the desired accuracy to reduce the size of the state transition matrix and improve the computational efficiency. • This work proposes two high-order semi-discretization methods to predict the milling stability based on precise integration. • The convergence rate of the 3rd SDM is higher than that of the other methods, and that of the 4th SDM is also desirable. • The stability lobe diagrams obtained by the proposed SDMs are closer to the reference than those of the benchmark methods. • Compared with the benchmark methods, the presented 3rd SDM and 4th SDM are superior in computational efficiency. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Global navigation satellite system (GNSS) positioning depends on the correct integer ambiguity resolution (AR). If the double difference equation for solving the float solution remains ill-conditioned, often happening due to the environment complexity and the equipment mobility, the correct AR is difficult to achieve. Concerning the ill-conditioned problem, methods of modifying the equation coefficient matrix are widely applied, whose effects are heavily dependent on modifying parameters. Besides, the direct-inversion of the ill-conditioned coefficient matrix can lead to a reduction in the accuracy and stability of the float solution. To solve the problem of ill-conditioned matrix inversion and further improve the accuracy, the present study for the first time proves the positive definite symmetry of the coefficient matrix in AR model and employs precise integration method to the indirect inverse of coefficient matrix. AR model for the GNSS positioning and the general resolving strategies introduction are briefly introduced. An indirect-inversion algorithm via precise integration for ill-conditioned coefficient matrix is proposed. According to the simulations and comparisons, the proposed strategy has higher precision and stability on float solution, and less dependence on modifying parameters. [ABSTRACT FROM AUTHOR]

Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis. However, the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation. A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced. The dynamic equilibrium equation is decomposed into two parts, namely displacement excitation and velocity excitation, and precise integration and mode superposition methods are combined to solve the equation. Ritz vectors are then used to calculate the static response of the truncated modes of the structure, and a method for determining the number of participating modes is obtained. Using multi-degree-of-freedom systems as two computational examples, the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed. It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation. [ABSTRACT FROM AUTHOR]

Chatter stability prediction is of great practical importance for stable machining because regenerative chatter in the milling process will result in poor surface quality and low machining efficiency. Full-discretization method and its variants have been demonstrated to be effective for the prediction of milling stability. However, the main shortcoming of such methods is that they can predict milling stability but involve inverse matrix calculation, which would lead to increases in computational complexity and reductions in numerical stability. In addition, there may not necessarily exist good inverse matrix for these methods. This study proposes a precise integration-based third-order full-discretization method that can be both accurate and efficient in milling stability prediction without the need of any inverse matrix calculation. The performance evaluation performed by the simulation demonstrates that the proposed method outperforms the conventional methods with respect to stability prediction accuracy and speed. Extensive simulation is also carried out to investigate the effects of interpolation order for the simplified state term on the performance of the proposed method. Three demonstrative examples are employed to demonstrate how the proposed method can function effectively in the prediction of milling chatter stability. Although a chatter stability prediction tool for the milling process is the particular application presented here, the proposed method can be applied to other machining processes, such as turning, boring, and drilling. [ABSTRACT FROM AUTHOR]

Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-cylindrical shell into consideration, the field transfer matrix of the coupled shell is constructed. According to the boundary conditions at the ends of the coupled shell, the natural frequencies of the coupled shell are solved by the precise integration method. An approach for studying the free vibration characteristics of isotropic coupled conical-cylindrical shells is obtained. Comparison of the natural frequencies obtained using the present method with those from literature confirms the validity of the proposed approach. The effects of the boundary conditions, the shell thickness and the semivertex conical angle on vibration characteristics are presented.

Vibration of a high-speed elevator is one of the major factors contributing to a safe, stable and comfortable ride. Vibration control and systematic optimization rely on the establishment of an accurate and reliable model. An energy-based vibration model (EVM) is proposed in this paper to describe the multi-directional coupling properties of high-speed elevators. After analyzing the structural and kinematic characteristics, a combination of the kinematic energy, elastic potential energy and virtual works is implemented to describe the vibrational characteristics. The Gaussian precise integration method is implemented to obtain accurate solutions because of the infinite degrees of freedom and the time-varying parameters. An example study is conducted using the KLK2 high-speed elevator. EVM is established to obtain the Max(Pk)/Pk and A95 indices of the X, Y, Z axis vibrational acceleration through simulations. A comparison is proposed between the proposed EVM method, conventional methods based on differential-equation vibration model (DVM) and real prototype experimental data. Results show that the proposed EVM method could achieve more accurate results than the conventional DVM method. Deviations of these indicators are less than 5%, which suggest the efficiency, precision and reliability of the proposed EVM.

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties. [ABSTRACT FROM AUTHOR]

Trimmed B-spline surfaces are common in the geometric computer aided design (CAD) community due to their capability to represent complex shapes that can not be modeled with ease using tensor product B-spline and NURBs surfaces. However, in many cases, handling trimmed-surfaces is far more complex than tensor-product (non-trimmed) surfaces. Many algorithms that operate on tensor-product surfaces, such as algorithms toward rendering, analysis and manufacturing, need to be specially adapted to consider the trimming domains. Frequently, these special adaptations result in lack of accuracy and elevated complexity. In this paper, we present an algorithm for converting general trimmed surfaces into a set of tensor-product (typically B-spline) surfaces. We focus on two algorithms to divide the parametric space of the trimmed surface into four-sided quadrilaterals with freeform curved boundaries, which is the first step of the algorithm. Then, the quadrilaterals are parameterized as planar parametric patches, only to be lifted to the Euclidean space using a surface-surface composition, resulting in tensor product surfaces that precisely tile the input trimmed surface in Euclidean space. The algorithm is robust and precise. We show that we can handle complex, industrial level, objects, with numerous high orders and rational surfaces and trimming curves. Finally, the algorithm provides user control on some properties of the generated tensor-product surfaces. [ABSTRACT FROM AUTHOR]

Based on the precise Runge-Kutta method, in view of the characteristics of the non-homogeneous terms of the state space equations and the particular distribution of the loads, a new improved precise Runge-Kutta method was presented for solving the structural dynamic equations. Through partitioning of the related state space matrices, the improved method not only inherited the advantage of high precision of the precise Runge-Kutta method, but also greatly promoted the computational efficiency, making it suitable for solving large-scale structural dynamic problems and conducting long-time simulations. The results of numerical examples show the correctness and validity of the proposed simplified method. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new modal precise integration method is proposed. [•] It is applied to vertical acceleration of pedestrian loaded bridges. [•] A closed-form approach for simply-supported bridges is determined. [•] The method is compared to Newmark-Beta method for the same problem. [•] It is shown to be computationally efficient and accurate for the problem. [Copyright &y& Elsevier]

• Augmented Kalman filter based on sparse constraint theory is proposed. • Force estimation is transformed into constrained optimization based on the l 1 -norm. • Drift problem in the force estimation is solved in the proposed method. • Robustness and identification accuracy are improved by the sparse constraint. • New augmented state-space model is developed using the precise integration method. To ensure the accurate analysis and evaluation of structural integrity and vibration responses, a novel technique is required for load identification with minimal error. Accordingly, this paper presents an augmented Kalman filter (AKF) based on sparse constraint theory for solving state and input estimation problems. In the scheme developed in this study, the space-sparse characteristic of the force (as prior information) is introduced into the AKF via a pseudo- measurement equation. The unconstrained optimization of the AKF is transformed into constrained optimization based on the l 1 -norm. The proposed method solves the force drift problem in AKF more effectively than classical dummy measurements. Moreover, the stability of the system and its estimation accuracy are significantly increased. Additionally, a new augmented state-space model was established based on the augmented precise integration method, which can be applied more extensively than the zero-order hold model. To assess the performance of the proposed method, three cases were examined, namely, two numerical simulations and an experiment involving a three-story shear building. The results indicated that the proposed method outperforms the traditional dummy measurement method under a non-underdetermined and collocated sensor configuration. [ABSTRACT FROM AUTHOR]

Horizontal components of electric and magnetic field are continuous at interface of layered system. In order to match boundary conditions at the interface, the Maxwell equation in frequency domain is modified into the first-order ordinary differential equation, which only contains the horizontal components of electric and magnetic field. The reflection and transmission of electromagnetic waves in layered lossy medium are analyzed by precise integration method based on two-point boundary value problem. By this method, the problem of data overflow from multiplication of exponential matrix in calculating process is avoided. Compared with numerical results, precision and numerical stability of precise integration method are better than generalized propagation matrix method. [ABSTRACT FROM AUTHOR]

An approximate model of wind-induced responses of the cylindrical structure is proposed based on the beam-rigid element method, and the weak fluid-structure interaction analysis is executed by using the FLUENT code of computational fluid dynamics (CFD) technology combined with dynamic meshing method, and the precise integration method is employed to improve the computational efficiency. The top displacement and acceleration of a 3-D cylindrical structure under different wind speeds are compared based on the proposed beam-rigid element approximate model, rigid model and elastic model. The experimental results show that the increment of wind speed nonlinearly increases the amplitude of across-wind vibration. For the rigid model, the neglect of coupling between fluid and structure may lead to bigger errors. [ABSTRACT FROM AUTHOR]

Based on the state-space expression of the dynamic differential equation of the TMD-structure, a new method for the random earthquake response analysis of the TMD-structure is proposed using the pseudo-excitation method and the precise integration method. This method can both get over the complicacies of the complex mode method and the insufficient accuracy of the mode-superposition response spectrum method, which is a fast and accurate method in calculating the random seismic response of the TMD-structure system with stationary and non stationary excitations. Then, based on the first-passage failure theory, the comparision analysis is made between the structure with/w. o TMD control using the reliability index with the boundary of the maximum story drift angle. The dynamic reliability is taken as the index of performance to evaluate the control effectiveness. An 8-story shear-shaped steel frame structure has been employed herein as a numerical example, the results confirm that the proposed method has validity and efficiency. [ABSTRACT FROM AUTHOR]

The time-delay discrete-time equations are derived directly from the differential vibration equations for structures in state space, with discrete parameters obtained via the precise integration method. Then a state vector expansion method is used to transform these equations into ones which do not contain time-delay terms explicitly. Next, the order of this system is substantially reduced by using the balanced reduction method to form a dominant subsystem which is based on the eigenmodes of the state subspace with highest controllability. The controllers are then designed by the discrete time-delay optimal control theory, which contains the control terms not only of the current state but also of a few previous states, in order to reflect the effect of time delays. By using the proposed method, the order of the controller is very substantially reduced without causing any essential difference in the control effect. A numerical example for a shear-type building is presented and it shows the effectiveness of the proposed method even when time delays are quite large. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, precise integration is compounded with Runge–Kutta method and a new effective integration method is presented for solving nonlinear dynamical system. Arbitrary dynamical system can be expressed as nonhomogeneous linear differential equation problem. Precise integration is used to solve its corresponding homogeneous equation and Runge–Kutta methods can be used to calculate the nonhomogeneous, nonlinear items. The precise integration may have large time step and the time step of the Runge–Kutta methods can be adjusted to improve the computational precision. The handling technique in this paper not only avoids the matrix inversion but also improves the stability of the numerical method. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper covers propagation of non-stationary random waves in stratified materials. The layered solid considered is located above the bedrock, whose material properties are assumed to be much stiffer than the solid, and known power spectrum densities of the non-stationary random excitations are input at the bedrock. The governing differential equations are derived in the frequency and wavenumber domain and the response power spectrum densities of the ground are investigated. The solution method presented uses the pseudo-excitation method in combination with the precise integration method and the extended Wittrick–Williams algorithm. The examples have up to three layers. [Copyright &y& Elsevier]

In this paper the theory of the element-free precise integration method (EFPIM) is presented as well as its applications in seismic modelling and imaging. The key point of this method is the absence of elements, which makes nodes free from the elemental restraint. Due to the moving least-squares (MLS) fitting instead of interpolation, the EFPIM results in high accuracy for both the dependent variable and its gradient. The EFPIM improves the implicit element-free method (EFM) by cutting the computational cost significantly. At the same time, the accuracy of this method keeps as good as that of the implicit EFM. The scheme of EFPIM is shown for the full scalar wave equation. Numerical stability is examined for the scheme subsequently. Based on the theory, a simple example of vibrant film is discussed in details to indicate the effectivity of the EFPIM. Main factors affecting the accuracy of the method are illustrated. Furthermore, we show some synthetic examples to demonstrate good performance of the EFPIM in seismic modelling and imaging problems. Both post-stack and pre-stack cases are considered. Combined with appropriate absorbing boundary conditions, the EFPIM can generate sections with accurate traveltimes and amplitudes. Complex structures can be imaged clearly such as high-angle dip and embedded high-velocity anomalies. [ABSTRACT FROM AUTHOR]

In this paper, a new three-dimensional time-domain method for solving vector Maxwell's equations, called the precise-integration time-domain (PITD) algorithm, is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on the precise-integration technique. It is shown that this method is quite stable even when the CFL condition is not satisfied. Although the memory requirement of the PITD method is much larger than that of the finite-difference time-domain (FDTD) method, this new algorithm is very appealing since the time step used in the simulation is no longer restricted by stability. As a result, computation speed can be improved. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than the FDTD scheme. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the accuracy of the PITD is independent of the time-step size. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, the computation for the nonlinear dynamic system is discussed. Firstly the nonlinear dynamic system is converted into an augmented dynamic system in the Minkowski space, which results in the system of Lie type locally. Then Runge–Kutta Munthe-Kaas (RKMK) methods are used to the new augmented dynamic system and group-preserving integration scheme for the augmented dynamic system is constructed, in which the precise integration method is used to compute the exponential mapping. In the process of computation, the numerical schemes are formulated for nonlinear dynamic system directly. The advantages of the method presented in this paper lie in not only its group-preserving character but also in its simplicity. [Copyright &y& Elsevier]

Propagation of stationary random waves in viscoelastic stratified transverse isotropic materials is investigated. The solid was considered multi-layered and located above the bedrock, which was assumed to be much stiffer than the soil, and the power spectrum density of the stationary random excitation was given at the bedrock. The governing differential equations are derived in frequency and wave-number domains and only a set of ordinary differential equations (ODEs) must be solved. The precise integration algorithm of two-point boundary value problem was applied to solve the ODEs. Thereafter, the recently developed pseudo-excitation method for structural random vibration is extended to the solution of the stratified solid responses. [ABSTRACT FROM AUTHOR]

Impulse influence matrix function is introduced based on that the de-centralized control analysis is analogous to the sub-structural analysis in structural mechanics. The static sub-structural analysis is analogous to the usual de-centralized control, whereas the dynamic sub-structural analysis corresponds to the de-centralized control theory. The reciprocal symmetry for the impulse influence matrix function is proved, and is solved by the precise integration method for time invariant system, giving the results up to computer precision. Based on the impulse influence functions of subsystems, the combination of subsystems can lead to a set of integral equations and be solved numerically. Numerical example demonstrates the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In the present paper, based on the precise integration method established in linear dynamic system, an improved precise integration method is presented for nonlinear dynamic system. Firstly, the nonlinear dynamic system is converted into an augmented Lie type dynamic system. Then the precise integration method is improved for solving the above augmented equation and preserving its group structure in the meantime. Finally, two numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. [Copyright &y& Elsevier]

To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the matrices, a computational method using state transition matrix of differential equation was presented. Numerical examples are provided to show the effectiveness of the present approach. [ABSTRACT FROM AUTHOR]

The variational approach is further applied to the measurement feedback H∞ control problems. Based on the induced norm description of the system Γ, the variational functionals Jc and Jp of state feedback H∞ control for the future time interval (t, tf], and of H∞ filter for the past time interval [0, t), respectively, are combined together to generate the variational functional of the measurement feedback for the whole time interval [0, tf]. The connection condition at the present time t is that the estimated state vector $$\bar x$$ (t) must be continuously extended to be the initial condition of the future state vector estimation. Another connection condition for the dual vector λ(t) can be naturally derived from the variational principle. The equations thus derived show that the third condition for the optimal parameter γ is again a bound of the smallest Rayleigh quotient. Therefore, the precise integration method developed formerly to determine the optimal parameter γ of H∞ control and of H∞ filter respectively can be further applied to the determination of the optimal parameter. [ABSTRACT FROM AUTHOR]

By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG control problem decomposes, or separates, into an optimal state-feedback control problem and an optimal state estimation problem. That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time-variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

• A crack-tip element for of 3D stationary dynamic cracks is constructed with a new near-field basis. • The adopted time-domain precise integration scheme is essentially an explicit scheme and unconditionally stable. • The time dependent fracture parameters can be solved directly without any post-processing. • The crack-tip element can be implemented into most of FE-packages directly. A crack-tip element to accurately capture dynamic response of three-dimensional (3D) cracks is proposed in the present contribution. Unlike other extended finite element methods (XFEM) which use branch functions from the analytical solution of two-dimensional cracks as the crack-tip enrichment, we construct a 3D crack-tip solution (in the form of eigen expansion) for the problem investigated. On that basis, the finite element formulation is derived strictly. It is interesting to find that the proposed crack-tip element works perfectly with an explicit precise integration method and thus gives high accuracy and efficiency. Thanks to the advantages of the precise integration method, the present method is essentially an explicit scheme and is unconditionally stable. The advantages of the combined crack-tip element and precise integration method provide a new insight of modelling 3D dynamic crack which is normally considered to be a complicated and costly task. [ABSTRACT FROM AUTHOR]

• The precise integration scheme is applied to solving the nonlinear phase field model for dynamic fracture. • The critical stable time interval is increased. • It is found that the time interval using the precise integration cannot be too long for phase field models. In this contribution, the phase field model for dynamic brittle fracture is investigated with an emphasis on the time discretization scheme. The precise integration scheme, which is known unconditionally stable for ordinary dynamics, is employed for the phase field model. The governing equation for the phase field model is thus formulated and discussed. Ways in the precise integration scheme for homogenizing the discretized equations for different loading scenarios are introduced. Numerical examples are provided to demonstrate the proposed method. The results show the proposed scheme allows a larger time interval then the widely used finite difference method for the phase field model. [ABSTRACT FROM AUTHOR]