Randomness Of Structural Parameters Research Articles

Stochastic force identification for uncertain structures based on matrix equilibration and improved Tikhonov regularization method

Accurate identification and estimation of stochastic forces applied to in-service engineering structures play a vital role in structural safety assessments. This study devised an effective force power spectral density (PSD) identification method to address the challenge of identifying multipoint stationary stochastic forces in uncertain structures. Initially, a probability model was employed to characterize structural uncertainties. Subsequently, an integral relationship was established between the probability density function (PDF) of the random structural parameters and that of the stochastic force PSD. By employing a point-selection technique based on the generalized F-discrepancy and a smoothing method, the uncertainty problem was transformed into a finite number of stochastic force PSD identification problems for deterministic structures. Simultaneously, based on the inverse pseudo-excitation method, a matrix equilibration approach and an improved Tikhonov regularization method were used to address the problem of large identification errors near structural natural frequencies. In comparison to the traditional weighting matrix method, the proposed method further reduces the condition number of frequency response function matrices, thereby enhancing the accuracy of force PSD identification. Finally, numerical examples were presented to validate the effectiveness of the proposed method in solving the stochastic force identification problem.

Dynamic reliability calculation of random structures by conditional probability method

For the composite random reliability problem, based on the Markov hypothesis of the dynamic response spanning action, two procedures of conditional probability explanation are accomplished: to derive the 2nd-order approximate expression for the calculation of the dynamic reliability of the random structure based on Taylor expansion method; secondly is to determine a mathematical sampling technique based on the Kriging model derive from the statistical analysis. Between them, the sampling procedure by the Kriging interpolation model meets the nonlinear correlation among dynamic reliability and structural random boundaries. Consequently, the finite element results can be used instantly to anatomize the significance of random structural parameters on dynamic reliability, avoiding the tedious and cumbersome theoretical derivation. The numerical example outcomes demonstrate that the numerical sampling method established upon the Kriging model is inconsiderate to the ratio to represent the dispersion and has additional benefits in computational verisimilitude and calculation productivity

Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges

It is known that the extradosed cable-stayed bridge, a hybrid bridge, possesses the virtues of both classic cable-stayed bridges and girder bridges in mechanical behaviors. In this paper, the sensitivity of seismic fragility demand parameters (SFDP) of a high-speed railway extradosed cable-stayed bridge is studied systematically along with the consideration of structural parameter uncertainty. Based on the probability distribution and correlation of random parameters, the Latin hypercube sampling method is adopted herein. The dynamic 3D finite element model of the employed bridge is established by using powerful and attractive OpenSEES nonlinear software. A nonlinear incremental dynamic analysis is performed to consider the randomness of structural parameters using sampling analysis. Some important conclusions are drawn indicating that the structural design parameter uncertainty predominantly has influence on the SFDP for fragility analysis of bridge structures. The design parameters of extradosed cable-stayed bridges are categorized and identified as primary, secondary and insensitive parameters. The high sensitivity parameters of extradosed cable-stayed bridges for fragility analysis include friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. Additionally, the strength and strain of unconfined concrete cannot be ignored. Furthermore, the uncertainty of structural design parameters fails to be responsible for the cable force responses due to larger girder stiffness. The structural design parameter uncertainty has a significant influence on the responses of extradosed cable-stayed bridges for seismic fragility analysis.

A probabilistic method for dynamic force identification of uncertain structures

To address the dynamic force identification problem of uncertain structures with random parameters, this study proposes a novel approach to describe the probabilistic properties of the identified forces. First, the integral equation for the force probability density function (PDF) is derived from the mathematical mapping relationship between the identified force and random structural parameters. Next, the sample space of the random parameters is partitioned into non-overlapping subdomains using a point selection technique based on the generalized F-discrepancy. Meanwhile, the function fitting technique and Tikhonov regularization method are applied to identify the force samples under the corresponding partitioned subdomains. Thus, the integral equation of the force PDF is transformed into a summation of the force probabilities for all the subdomains. Subsequently, a smoothing technique is introduced to obtain the expression of the identified force PDF. Finally, the confidence interval over the entire time domain is constructed from the force cumulative distribution function, which effectively quantifies the influence of random structural parameters on the identified results. The efficiency and superiority of the proposed method are verified using an example of a plane truss structure with multiple random structural parameters, and force identification for a simplified launch vehicle model with connection uncertainties is discussed.

Dynamic reliability analysis of stochastic structures under non-stationary random excitations based on an explicit time-domain method

For the analysis of the dynamic reliability of stochastic structures subjected to non-stationary random excitations, an effective hybrid approach is proposed. In this approach, the explicit time-domain method is employed to obtain the dynamic responses of each deterministic structure. Dynamic responses for the explicit time-domain method can be expressed as a series of products of deterministic coefficient matrices and random load vectors, which can significantly enhance computational efficiency. For the issue of stochastic structures, the double-hidden-layer backpropagation neural network is introduced as a surrogate model for reconstructing the coefficient matrices to avoid repeated construction of the coefficient matrices for each sample with different structural parameters using the extremely time-intensive regular method. For more effective training of the backpropagation neural network, the Latin hypercube sampling technique is introduced to generate representative samples of random structural parameters. In consideration of the intrinsic benefit of the explicit time-domain method, parallel computation is incorporated into the method. Finally, the explicit time-domain method is used to perform the Monte Carlo simulation in conjunction with the parallel computing technique to resolve the problem of small failure probabilities. To demonstrate the efficacy of the proposed method, numerical examples are presented.

Simultaneous layout and size optimization of nonlinear viscous dampers for frame buildings under stochastic seismic excitation

Viscous dampers, as effective energy-dissipation devices, have been widely used for seismic mitigation of building structures. Due to the intrinsic uncertainties of structural parameters and earthquake ground motions, to obtain an optimal performance of structural control, the stochastic design optimization of viscous dampers for buildings is essential. This paper establishes a new dynamic reliability-based optimization framework to address the simultaneous layout and size design of nonlinear viscous dampers in frame buildings, considering the dual randomness of both nonstationary seismic excitations and uncertain structural model parameters. Firstly, a mixed integer optimization problem for nonlinear viscous dampers, including discrete and continuous design variables, is formulated, and the design target is to minimize the cost of the dampers subjected to performance constraints on dynamic reliability of building structures. Then, sequential approximate mixed integer programming with trust region is proposed to solve the optimization problem. Moreover, direct probability integral method is suggested to assess the dynamic reliability and its sensitivity with respect to design variables. Finally, accounting for both stochastic nonstationary seismic excitations and random structural parameters, the optimized results of two numerical examples indicate that the proposed method is a competitive choice for realizing the layout and size optimization of limiting types of nonlinear viscous dampers in frame buildings. To ensure the same target performance of buildings in terms of the probability of exceeding the target value of inter-story drift, the larger peak ground acceleration of stochastic ground motions is, the more cost of dampers is required for seismic protection of buildings.

Reliability index based strategy for the probability-damage approach in fail-safe design optimization (β-PDFSO)

This research proposes a new formulation for fail-safe size optimization, considering the probability of occurrence of each failure scenario and the random structural parameters as sources of uncertainty. Essentially, the fail-safe reliability-based design optimization is reformulated, where the term “damaged structure” coalesces information of the whole set of damaged configurations. Thus, a single random reliability index is defined, representing the reliability of a limit-state of the damaged structure, which accounts for the safety level of the entire set of damaged configurations. The method provides the optimum design for which the reliability indices of the damaged structure are achieved at the confidence level the designer demands. The first application example corresponds to an academic analytical problem. The second and third application examples correspond to practical engineering cases: a 2D truss structure with stress constraints as well as the tail section of an aircraft fuselage with stress and buckling constraints. Results show a considerable reduction of the objective function compared to the fail-safe RBDO, which could lead to oversized designs. In this sense, mass savings up to 13.6% are achieved for the industrial-like application example.

Investigations on a mega–sub isolation system under near-fault ground motions

The failure mechanism of the mega–sub isolation system under near-fault ground motions is studied in this article. 90 suites of near-fault ground motions collected from 23 earthquakes are adopted to investigate the ground motion intensity indices applicable for the mega–sub isolation system. Then, the sensitivities of the stochastic responses to the structural parameters are analyzed to determine the representative random structural parameters. Furthermore, considering the uncertainties of ground motion characteristics and structural parameters, the seismic fragility is analyzed by the response surface method in order to obtain the failure mechanism of this system under near-fault ground motions. Results show that different intensity indices have various correlation coefficients with the peak responses of the mega–sub isolation system. The correlations of acceleration-related intensity indices are the worst, whereas the correlations of displacement-related intensity indices show high linearity. The sensitivities of the structural responses are weaker to the sub-structure story stiffness but more sensitive to the sub-structure story mass and the stiffness and damping ratio of the isolation layer. The failure probability of the sub-structure is higher than that of the mega-structure under near-fault ground motion. While in the collapse state, the failure probability of the isolation layer is greater than that of the sub-structure.

Efficient reliability-based optimization of linear dynamic systems with random structural parameters

Efficient reliability-based optimization of linear dynamic systems with random structural parameters

Modeling and analysis of high aspect ratio wing considering random structural parameters

With the application of advanced composite materials in High-Aspect-Ratio wings (HARW), the randomness of structural parameters, such as elastic modulus and Poisson's ratio, is enhanced. Hence, in order to explore the whole picture of aeroelastic problems, it is of great significance to study the role of random structural parameters in aeroelastic problems. In this paper, the dynamic response of flexible HARW considering random structural parameters is analyzed. An aeroelastic model of a one-dimensional cantilevered Euler–Bernoulli beam considering aerodynamic forces acting on the wing is established based on Hamilton's principle. Adopted the idea of simplifying calculation, the effect of random structural parameters is analyzed. Then, considering the elastic modulus and torsional stiffness as continuously one-dimensional random field functions, and discretized by local method. The first and second order recursive stochastic nonlinear finite element equations of wing are derived by using perturbation method. Based on it, statistical expression of aeroelastic effects of the wing is derived. Monte Carlo method is adopted to verify the effectiveness of the method. Numerical simulations indicate that the method proposed can well mirror the statistical characteristics of aeroelastic response.

Toward confident regional seismic risk assessment of spatially distributed structural portfolios via entropy-based intensity measure selection

Intensity measure (IM) selection is a crucial step in regional seismic risk assessment (RSRA) of spatially distributed structural portfolios. In order to facilitate more confident regional seismic risk estimates, this study proposes an entropy-based IM selection methodology, offering the first systematic and quantitative regional-level IM selection approach. By conceptualizing the spatially distributed structural portfolio as an integrated multi-response structural system, the joint entropy of the system’s unconditional seismic demands is leveraged as an IM evaluation criterion. Owing to the adaptation of a newly developed advanced IM co-simulation method and multivariate surrogate demand modeling techniques, this entropy-based IM selection approach is able to holistically incorporate uncertainties rising from the spatial IM random field, structural parameters, and surrogate demand models, during the course of uncertainty propagation in RSRA. The efficacy of the proposed methodology is demonstrated along with practical heuristics for alleviating the computational burden, based on a hypothetical highway bridge portfolio. Different application cases in the context of RSRA are considered, including pre-event RSRA considering a single scenario-earthquake as well as a stochastic earthquake catalog, and post-event RSRA considering record updating. The results consistently highlight the significance of the proposed IM selection method in facilitating more confident regional seismic risk estimates. Moreover, this study also provides valuable insights into record updating in reducing the level of uncertainty of the spatial IM random field, and its implication on IM selection in post-event RSRA.

The analyses of dynamic response and reliability for failure-dependent stochastic micro-resonator with thermoelastic coupling effects

A crucial measure for the design of high-performance micro-resonators is to consider the randomness of structural parameters when analyzing the structural system reliability. In this work, the stochastic dynamic response analysis and subsequently, a dynamic reliability assessment of the random micro-resonators are originally presented, where the thermoelastic coupling effects are freshly incorporated in the models proposed. The dynamic characteristics equation of the deterministic micro-resonator is firstly established based on the finite element method. The random dynamic characteristics of the resonator are then solved by implementing the left and right eigenvectors and the block Lanczos algorithm, and the random temperature field and structural random dynamic stress are also tackled. Afterwards, the overall structural reliability is investigated with a comprehensive consideration of the strength failure and frequency resonance failure, in which the Copula function is used for describing the dynamic correlation between two failure modes. Finally, the feasibility and rationality of the method put forward are demonstrated via a practically motivated example.

Effect of random structural damage on vehicle–track–bridge coupled response

With the rapid development of high-speed railway construction around the world, the structural damage problem of tracks and bridges has attracted more and more attention. In this paper, considering the random structural damages of tracks and bridges, an efficient computational procedure is developed based on the probability density evolution method to systematically investigate the random characteristics of the dynamic responses varying with the damages in vehicle–track–bridge time-dependent systems. Firstly, a vehicle–track–bridge dynamic model with random structural damage parameters is established, and the random motion equations are derived based on the generalized energy principle. Then, the probability density evolution equation for each random response is established and the random feature is investigated by the proposed computational procedure. Finally, the representative numerical examples are applied and some conclusions for the effects of the random structural damages on the dynamic responses of the vehicle–track–bridge systems are presented.

Variance‐based global sensitivity analysis for fuzzy random structural systems

AbstractThere have been increasing advances in the sophisticated approaches like fuzzy randomness to handle different uncertainties in civil engineering; however, less attention has been paid to the formulation of a sensitivity analysis for fuzzy random structural systems. In this study, the main objective is to present the formulation of fuzzy Sobol sensitivity indices to quantify the influence of fuzzy random structural parameters. Meanwhile, uncertainty in derivation of limit states and acceptance criteria in collapse analysis is addressed briefly and treated using fuzzy model parameters. To show the application of the established sensitivity test, the collapse behavior of a steel moment frame subjected to sudden column removal is evaluated thoroughly. The proposed fuzzy sensitivity indices are determined for the problem and the overall influence of fuzzy acceptance criteria on the collapse assessment is shown using fragility analysis. The results show that the presented fuzzy sensitivity analysis can give detailed insight into the characteristics of fuzzy random systems, and the epistemic uncertainty in derivation of limit states can have significant effects on the reliability‐based collapse analysis. It is worth mentioning that to alleviate high computational demands in fuzzy probabilistic collapse analysis, a neural network metamodel is applied in conjunction with the genetic algorithm which is also of practical value to engineers and researchers.

Reliability analysis and optimization design on equilibrium elbow

Equilibrium elbow is a key mechanical component in the self-propelled artillery system and the reliability analysis of the component is necessary to the safety of the whole system. In this paper, the equilibrium elbow model is established to analyze the reliability and reliability sensitivity of arbitrary distribution parameters. Three main failure modes and the times of loading action have been taken into account when analyzing the reliability sensitivity. Numerical method for reliability calculation is presented based on four moment method and the reliability sensitivity model of mean and variance values with random structural parameters were established. Based on the results of the reliability sensitivity analysis, reliability robust optimization design has been studied to enhance the reliability of equilibrium elbow and decrease the reliability sensitivity of mean and variance value. Application of the proposed approach could provide a practical routine for mechanical optimization and design.

Prediction of sound absorption property of metal rubber using general regression neural network

Metal rubber (MR) is an excellent sound absorption material which can be utilized in extremely harsh environments. Traditional experimental studies are incomplete for MR with random structural parameters. In this article, the general regression neural network (GRNN) method is developed to comprehensively predict the sound absorption behaviors of MR with random structural parameters. Sixty samples are utilized and divided into training and test set. Training set contains 50 samples to establish the GRNN model. Input training parameters include the porosity, wire diameter and thickness, while the target dates consist of sound absorption coefficients at six central frequencies as well as their average values. The remaining 10 samples constitute the testing set; sound absorption coefficients can be obtained by inputting their structure parameters. Results indicate that the proposed approach is reliable to design and predict the sound absorption properties of MR in engineering field. © 2018 Institute of Noise Control Engineering.

Optimal Sensor Placement for Spatial Structure Based on Importance Coefficient and Randomness

The current methods of optimal sensor placement are majorly presented based on modal analysis theory, lacking the consideration of damage process of the structure. The effect of different minor damage cases acting on the total spatial structure is studied based on vulnerability theory in structural analysis. The concept of generalized equivalent stiffness is introduced and the importance coefficient of component is defined. For numerical simulation, the random characteristics for both structural parameters and loads are considered, and the random samples are established. The damage path of each sample is calculated and all the important members on the damage failure path are listed; therefore the sensor placement scheme is determined according to the statistical data. This method is extended to dynamic analysis. For every dynamic time‐history analysis, time‐varying responses of the structure are calculated by selecting appropriate calculating interval and considering the randomness of structural parameters and load. The time‐varying response is analyzed and the importance coefficient of members is sorted; finally the dynamic sensor placement scheme is determined. The effectiveness of the method in this paper is certified by example.

Probabilistic analysis of wind-induced vibration mitigation of structures by fluid viscous dampers

The high-rise buildings usually suffer from excessively large wind-induced vibrations, and thus vibration control systems might be necessary. Fluid viscous dampers (FVDs) with nonlinear power law against velocity are widely employed. With the transition of design method from traditional frequency domain approaches to more refined direct time domain approaches, the difficulty of time integration of these systems occurs sometimes. In the present paper, firstly the underlying reason of the difficulty is revealed by identifying that the equations of motion of high-rise buildings installed with FVDs are sometimes stiff differential equations. Thus, an approach effective for stiff differential systems, i.e., the backward difference formula (BDF), is then introduced, and verified to be effective for the equation of motion of wind-induced vibration controlled systems. Comparative studies are performed among some methods, including the Newmark method, KR-alpha method, energy-based linearization method and the statistical linearization method. Based on the above results, a 20-story steel frame structure is taken as a practical example. Particularly, the randomness of structural parameters and of wind loading input is emphasized. The extreme values of the responses are examined, showing the effectiveness of the proposed approach, and also necessitating the refined probabilistic analysis in the design of wind-induced vibration mitigation systems.

Output tracking control for an omnidirectional rehabilitative training walker with incomplete measurements and random parameters

ABSTRACTIn this study, we propose a model and an output feedback tracking control for an omnidirectional rehabilitative training walker (ODW) with unmeasurable speed, incomplete measurements of position output, and random structural parameters. A stochastic model and an incomplete measurement model were proposed to describe the motion of an ODW subject to random structural parameters and to account for any incomplete data transmission phenomenon caused by possible sensor ageing or failures. A speed observer and a state observer were designed to estimate the unmeasurable speed and the incomplete measurements of position output. Moreover, a dynamic output feedback controller was constructed to ensure the exponential stability in mean square of the tracking error system. Furthermore, the results verify that the choice of appropriate design parameters can result in the mean square of the tracking error becoming arbitrarily small. A simulation example was provided to illustrate the effectiveness of the proposed design procedures.

Random seismic response and sensitivity analysis of uncertain multi-span continuous beams subjected to spatially varying ground motions

An analytical method is formulated for the seismic analysis of multi-span continuous beams with random structural parameters subjected to spatially varying ground motions. An earthquake-induced ground motion is modelled as a stationary random process defined by power spectral density function, and the spatial variation is considered. The physical parameters of the multi-span beams are random and modelled as continuous random Gaussian variables. The stationary random responses are determined as approximate explicit functions of the structural parameters. Direct differentiation of these functions with respect to the structural parameters provides analytical expressions of the sensitivities of the stationary responses. On the basis of Taylor expansion, the statistic moments of the random responses are obtained. Taking the four-span beam as an illustrative example, the mean value and standard deviation of the random responses are computed and compared with those from Monte Carlo simulation to demonstrate the accuracy of the proposed method. Results are illustrated for the influence of different structural parameters on the statistic moments of the random responses. It is found that randomness in Young's modulus and the mass per unit length has approximate equivalent and significant influence on the random responses, while that of damping is negligible.