Pseudo-excitation Method Research Articles

Crack Identification of Cantilever Plates Based on a Kriging Surrogate Model

This work presents an effective method to identify the tip locations of an internal crack in cantilever plates based on a Kriging surrogate model. Samples of varying crack parameters (tip locations) and their corresponding root mean square (RMS) of random responses are used to construct the initial Kriging surrogate model. Moreover, the pseudo excitation method (PEM) is employed to speed up the spectral analysis. For identifying crack parameters based on the constructed Kriging model, a robust stochastic particle swarm optimization (SPSO) algorithm is adopted for enhancing the global searching ability. To improve the accuracy of the surrogate model without using extensive samples, a small number of samples are first used. Then an optimal point-adding process is carried out to reduce computational cost. Numerical studies of a cantilever plate with an internal crack are performed. The effectiveness and efficiency of this method are demonstrated by the identified results. The effect of initial sampling size on the precision of the identified results is also investigated.

Non-stationary seismic response analysis of base-isolated buildings with many hysteretic devices

Based on reduction of the number of the equivalent linearization differential equations, an efficient approximation method is presented for the computation of the stochastic non-stationary response of base-isolated buildings represented by large Finite Element models. The analysis combines the pseudo excitation method and the equivalent linearization method. In the stochastic analysis, it is supposed that the superstructure of the isolated system remains elastic even when subjected to a major earthquake ground motion, and so the modal superposition method is used to reduce the number of degrees of freedom of the system. Meanwhile the static correction procedure is employed to consider the contributions of the higher modes of the structure, with minimal increase in computation effort. The proposed method can deal with different types of isolators, and obtain the performance of each isolator during the earthquake. However the number of the equivalent linearization differential equations is reduced greatly by assuming that isolators of the same type have equal hysteretic components in the same direction. This improves the computation efficiency and accuracy. Finally, the stochastic response of a simple base-isolated frame structure is obtained by both the Monte Carlo method and the pseudo excitation method presented, in order to verify the accuracy of the latter even for large finite element structures with many hysteretic devices.

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle–track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli–Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.

Stochastic seismic analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional multiple excitations

This paper presents a comprehensive theoretical analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional spatial seismic motions using the pseudo-excitation method. Formulations for modelling tridirectional spatial ground motions at varying site conditions are first derived. A site response analysis is presented for the tridirectional motions based on deterministic wave propagation theory, assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the multiple layered site with an assumed incident angle. Integration between the structural health monitoring (SHM) technique and the structural seismic analysis is proposed and conducted for the finite element (FE) model calibration of the CFST arch bridge through the model updating approach. Using the calibrated FE model, stochastic seismic analysis of the CFST arch bridge is conducted in a comprehensive and systematic way, by considering the dimensionality, incoherence effect, wave-path effect of ground motions, and local site effects with different and irregular site conditions. Critical conclusions are drawn and can be applied in the actual seismic design of the half-through CFST arch bridges under tridirectional multiple excitations.

Analytical sensitivity and Hessian matrix analysis of PSD functions for random seismic responses

This paper describes three analytical methods to calculate sensitivity and Hessian matrix of structural Power Spectral Density (PSD) functions for random seismic responses. The methods are derived based on Complete Quadratic Combination method (CQC), Square Root of the Sum of Squares method (SRSS) and Pseudo-Excitation Method (PEM) by direct differentiation. A planar frame and a building are demonstrated. The results indicate the first and second derivatives of PSD functions, achieved by CQC-based method, PEM-based method, are exactly same. The first and second derivatives achieved by SRSS-based method are almost the same as that obtained by other two methods. PEM-based method is the most efficient method. SRSS-based method is much more efficient than CQC-based method.

상이한 지반조건을 갖는 아치구조물의 지진응답 분석

Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response of spatial structure for seismic design of spatial structure. An arch structure is used as an example structure because it has primary characteristics of spatial structures. Multiple support excitation may be subjected to supports of a spatial structure because ground condition of spatial structures is different. In this study, the response analysis of the arch structure under multiple support excitation and simple support excitation is studied. By means of the pseudo excitation method, the seismic response is analyzed for long span spatial structure. It shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. It is known that the seismic response of spatial structure under multiple support excitation and simple support excitation are the different in some case. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation because the spatial structure supports may be different.

In-plane dynamic response analysis of curved pipe conveying fluid subjected to random excitation

A new approach was presented to analyze the dynamic response of the Timoshenko curved pipe conveying fluid under random excitation. The in-plane motion equations of Timoshenko curved pipe conveying fluid were deduced via Hamilton's principle for the open system, in which the fluid–structure interaction and the effect of shear deformation were taken into account. The exact shape functions describing radial and axial displacements as well as cross-section rotations were found in algebraic-trigonometric form. Based on these shape functions, using virtual work principle, the finite element model of in-plane vibration for Timoshenko curved pipe conveying fluid was established. The pseudo excitation method in conjunction with the complex mode superposition method was performed to solve these equations. In the example, the critical velocities and the natural frequencies of a semi-circular pipe conveying fluid with different boundary condition were discussed. By the proposed method, the displacement and velocity of the curved pipe were derived, and their power spectrum densities and spectral moments were also yielded. Then, the influences of fluid velocities on the natural frequencies and the standard deviation of dynamic response were studied.

Seismic Response of Spatial Structure Subjected to Multi-Support Earthquake Load

장경간의 대공간구조물은 지진하중에 의하여 일반구조물과는 다른 응답특성이 나타나고 있으므로 대공간구조물에 대한 내진설계를 위해서는 대공간구조물의 동적특성 및 지진응답특성에 대한 정확한 분석이 필요하다. 본 논문에서는 예제 구조물로 대공간구조물의 동적특성을 기본적으로 내재하고 있는 장견간의 아치구조물로 선정하여 다중지점 지진하중이 가진되는 대공간구조물의 진동응답 특성을 분석하였다. 다중지점 지진하중은 대공간구조물의 지점 지반조건이 다른 경우 그리고 시간지연을 갖는 지진하중이 가진되는 경우로 하여 수치해석을 수행하였다. 다중지점 지진하중 적용한 경우의 지진응답이 단일 지진하중 적용에 의한 지진응답과 비교하여 경우에 따라서 상이한 지진응답을 나타내고 있다. 따라서 대공간구조물의 경우에 정확한 지진응답 분석 및 적절한 내진설계를 위해서는 다중지점 지진하중을 적용하여 지진응답을 분석하는 것 바람직하다. Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response for seismic design of spatial structure. Keel arch structure is used as an example structure because it has primary characteristics of spatial structures. In case of spatial structures with different ground condition and time lag, multiple support excitation may be subjected to supports of a keel arch structure. In this study, the response of the keel arch structure under multiple support excitation and with time lag are analyzed by means of the pseudo excitation method. Pseudo excitation method shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. It is known that the seismic responses of spatial structure under multiple support excitation are different from those of spatial structure under simple excitation. And the seismic response of spatial structure with time lag are different from those of spatial structure without time lag. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation and time lag because the spatial structure supports may be different and very long span. It is shown that the seismic response of spatial structure under multiple support seismic excitation are different from those of spatial structure under unique excitation.

Application of an efficient stochastic calculation method on the seismic analysis of an isolated structure

An isolated structure often possesses distinct non-proportional damping characteristics. However, traditional seismic calculation theory and methods are derived based on the assumption that damping is proportional. Based on this drawback, a new, more efficient stochastic calculation method, an improvement on the pseudo-excitation method, is introduced. This method is then applied to the seismic analysis of an isolated structure. By comparing it with the forced decoupling, matrix inversion and iteration methods, it is shown that the presented method can produce accurate results while increasing the efficiency of the stochastic analysis. Moreover, the calculation process of the seismic response of an isolated structure is convergent. Based on the results of the example presented in this paper, the given method is applicable to the seismic analysis of an isolated structure and can be utilized in practice.

A general symplectic method for the response analysis of infinitely periodic structures subjected to random excitations

A general symplectic method for the random response analysis of infinitely periodic structures subjected to stationary/non-stationary random excitations is developed using symplectic mathematics in conjunction with variable separation and the pseudo-excitation method (PEM). Starting from the equation of motion for a single loaded substructure, symplectic analysis is firstly used to eliminate the dependent degrees of the freedom through condensation. A Fourier expansion of the condensed equation of motion is then applied to separate the variables of time and wave number, thus enabling the necessary recurrence scheme to be developed. The random response is finally determined by implementing PEM. The proposed method is justified by comparison with results available in the literature and is then applied to a more complicated time-dependent coupled system.

Dynamical Reliability of Four-high Rolling Mill under Stochastic Strip Characteristics Excitation

It has great significance to research the dynamical reliability probability of rolling mill rolls system for improving its stochastic dynamical reliability and products quality rolled. The fifth-octave vertical vibration stochastic dynamical model of rolls system was established, and the pseudo-excitation method was used to obtain the power spectral density and the variance variation characteristics with the rolling speed and time under stationary rolling force stochastic excitation, and the stochastic dynamical reliability of rolls system was analyzed by using the first-passage failure criterion. The results show that rolls system reliability has strong relationship with stochastic excitation intensity and thickness tolerance of rolled strip and damping of the roll gap, among them, the stochastic excitation intensity and thickness tolerance of rolled strip have greater influence on the dynamical reliability of rolls system than other parameters, and rolls system stochastic dynamical reliability can be improved by mainly controlling the rolled plate/strip accuracy and roll gap damping, thus improving the quality of rolled strip in rolling operation.

Non-stationary random vibration of a coupled vehicle–slab track system using a parallel algorithm based on the pseudo excitation method

A parallel algorithm based on the pseudo excitation method (PEM) is applied to investigate the non-stationary random response of a vertically coupled vehicle–slab track system subjected to random excitation induced by track irregularity. The vehicle is simplified as a multibody system with 10 degrees of freedom and the slab track is represented by a three layer Bernoulli–Euler beam model which includes the rail, slab and roadbed. Linear wheel–rail contact provides interaction between the vehicle and slab track models. The track irregularity is assumed to be a Gaussian random process with zero mean value and the non-stationary random response of the coupled vehicle–slab track system is solved using a combination of PEM and step-by-step integration. A parallel algorithm based on PEM is used to accelerate the computation and the effectiveness of the proposed method is verified by the Monte Carlo method. The basic random performance of the coupled vehicle–slab track system is analysed and the effects of the vehicle speed and slab track parameters on the random responses of the vehicle and slab track are investigated. The results indicate that the vehicle speed has a significant effect on the random response of the coupled vehicle–slab track system and that the rail pad parameters are the most important of the slab track parameters discussed.

Efficient and Accurate Method for Calculating the Stochastic Seismic Response of a Nonproportionally Damped Structure

AbstractIn the case of nonproportionally damped structures, the forced decoupling method is often adopted in approximate analysis. However, it generally cannot satisfy the precision requirements for practical engineering. Taking this into account, methods to calculate the stochastic seismic response of nonproportionally damped structures are systematically studied in this paper. Based on the pseudoexcitation method, an efficient and accurate iteration method with the advantages of high computational efficiency and iteration convergence is also proposed. This new method is preferred for practical engineering because of real expressions. Finally, a numerical example is carried out to verify the properties and advantages of the proposed method.

Stochastic Responses of Vehicle-Bridge Coupling System

In this paper,we want to obtain the research of virtual vehicle-birdge coupling system, a vehicle-bridge coupling model was established based on the multi-point Pseudo Excitation Method model, and then the simulation result was gained by ANSYS. First,a detailed multi-body dynamic model of the vehicle was established by using ADAMS/VIEW software package; secondly, a stochastic controller was designed for active suspension system and worked out by means of Matlab/Simulink, the proposed control algorithm was integrated with the multi-body dynamic vehicle model and the coupling system simulations could be performed repeatedly until a satisfactory controller was achieved, the system was compared with a conventional passive one. Simulation results showed that the proposed active suspension considerably improved both the ride and handling performance of the vehicle.

An iterative algorithm for analysis of coupled structural-acoustic systems subject to random excitations

This paper analyzes the random response of structural-acoustic coupled systems. Most existing works on coupled structural-acoustic analysis are limited to systems under deterministic excitations due to high computational cost required by a random response analysis. To reduce the computational burden involved in the coupled random analysis, an iterative procedure based on the Pseudo excitation method has been developed. It is found that this algorithm has an overwhelming advantage in computing efficiency over traditional methods, as demonstrated by some numerical examples given in this paper.

Grinding Load Identification of an Horomill Using Inverse Pseudo Excitation Method

A rigid-flexible coupling dynamic model is established for the grinding roller system of an Horomill. Two coordinates are chosen to describe the grinding roller motion, namely the linear displacement of the roller at the center of mass and its rotation around the centroid on the applied plane of the grinding forces. The grinding forces applied on the roller are simplified to be a force and a torque, acting respectively on the direction of two coordinates. The frequency response function (FRF) matrices, with the two grinding force components as input and the vibration acceleration responses of two measuring points on the roller as output, are obtained respectively by using multibody dynamics computational software. The auto-PSD and cross-PSD of the vibration response on two measuring points are known. An inverse pseudo excitation method (IPEM) is then used for solving the grinding dynamic load spectrum. The obtained load spectrum would be helpful for the Horomill dynamic design and the fatigue calculation.

The Random Response Analysis of Structure Subjected to Non-Stationary Seismic Excitation

The evolutionary power spectrum which can reflect the non-stationary characteristics of earthquake ground motion is estimated by the Hilbert-Huang Transform (HHT), and with reference to the experiential statistical method, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 121 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U S. The pseudo excitation method is adopted to acquire the solution for structure random response under specific non-stationary seismic excitation. The results demonstrate that the non-stationary contents included in seismic excitation will enlarge greatly the random response of structure in comparison with uniform modulation random excitation.

A Study on the Functional Reliability of Gravity Dam

The research objective is to design and construct a method for functional reliability analysis of concrete gravity dam. Firstly, the pseudo excitation method was utilized to analyze to calculate the probabilistic characteristics of concrete gravity dam excited by random seismic loading. Meanwhile, the response surface method based on weighted regression was associated to that method to analyze functional reliability of concrete gravity dam. Eventually, a test example was given to verify and analyze the convergence and stability of this method.

The Random Response Analysis of Structure Subjected to Non-Stationary Seismic Excitation

The evolutionary power spectrum which can reflect the non-stationary characteristics of earthquake ground motion is estimated by the Hilbert-Huang Transform (HHT), and with reference to the experiential statistical method, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 121 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U S. The pseudo excitation method is adopted to acquire the solution for structure random response under specific non-stationary seismic excitation. The results demonstrate that the non-stationary contents included in seismic excitation will enlarge greatly the random response of structure in comparison with uniform modulation random excitation.

Sensitivity and Hessian Matrix Analysis of Evolutionary PSD Functions for Nonstationary Random Seismic Responses

AbstractThis paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniforml...