Uncertainties In Structural Response Research Articles

Mitigating ground motion duration impact on steel moment-resisting frames using viscous dampers

This paper explores the significant influence of ground motion duration on the seismic performance of steel moment resisting frames. It demonstrates that during long-duration strong earthquakes, the structural response of such frames can be substantially larger than under short-duration ground motions. To address this challenge, viscous dampers, known for their stable hysteretic behavior and resistance to degradation under cyclic loading, are introduced as a retrofitting solution. To evaluate the effectiveness of viscous dampers, incremental dynamic analysis was conducted on three prototype steel moment-resisting frames of varying heights, both before and after retrofitting with viscous dampers. A total of 44 pairs of short-duration and long-duration spectrum-matched ground motions were employed as seismic inputs to isolate the effects of seismic motion duration from those arising from seismic amplitude and acceleration spectral shape. The findings underscore the potential of viscous dampers to significantly enhance the seismic performance of steel moment-resisting frames. Furthermore, these dampers effectively mitigate the impact of ground motion duration, reducing the uncertainty in structural response and facilitating more accurate evaluations of seismic performance.

Risk-targeted hazard for seismic design in New Zealand considering individual and societal risk targets

The promotion of risk-targeted hazard as the basis of seismic design internationally has increased over the past decade. Risk-targeted hazard estimates are derived through convolution of hazard curves with representative fragility functions and provide a means to target uniform risk across a region. Using risk targets also enables performance objectives of building codes that are consistent with other life risks and can include societal input into the expected performance of structures. Current design procedures using a uniform-hazard spectrum are unable to provide equal risk across the country due to variation in the shapes of hazard curves in different locations and uncertainty in structural response. In this article a framework is proposed, which can be used with national seismic hazard models, to produce risk-targeted hazard spectra for seismic design. This study extends the risk-targeted hazard framework through full quantification of epistemic uncertainty in seismic hazard and includes multiple risk targets for individual and societal risk at the building and city scales. The article describes a framework that can be used to adjust current seismic design force levels in New Zealand standards to target uniform seismic risk for buildings considering both the performance of individual buildings and the performance of cities.

Multi-objective optimal design of steel MRF buildings based on life-cycle cost using a swift algorithm

This paper proposed a swift multi-objective optimization algorithm for the performance-based design of steel moment-resisting frame (MRF) buildings considering life-cycle cost (LCC). Two components of the life-cycle cost, including the initial construction cost and the lifetime seismic damage cost of the building, are considered as two separate objectives of the optimization problem and are minimized simultaneously using the proposed algorithm. The proposed algorithm called Multi-objective Uniform Damage Optimization (MUDO) is an adaptive method that utilizes the concept of uniform damage (deformation) theory. MUDO leads to design alternatives for the building that are optimal (minimum) for both mentioned objectives. These alternatives, called Pareto optimal designs, allow decision-makers to choose the optimal investment option according to the project goals and by the trade-off between optimization objectives. The proposed algorithm is used to optimize three steel MRF buildings with 3, 6, and 9 stories. The lifetime seismic damage cost is calculated by assessing seismic losses at several ground motion intensities and using a probabilistic approach presented in HAZUS. A Monte Carlo analysis is used in this research to account for inherent uncertainties in structural response. The results demonstrate that MUDO can find competitive Pareto optimal designs in a much shorter time compared to a well-known metaheuristic algorithm called non-dominated sorting genetic algorithm II (NSGA-II).

Seismic fragility and uncertainty mitigation of cable restrainer retrofit for isolated highway bridges incorporated with deteriorated elastomeric bearings

Overcoming the deterioration of aging infrastructure has aroused increasing concern in recent years, particularly, problem of deteriorated elastomeric bearings has emerged as one of the greatest challenges in maintenance and reliability strategies for isolated highway bridges. Though the abundant applications of cable restrainers to provide alternative measure against bearing deterioration and reduce the risk of bridge collapse due to deck unseating, the performance of cable restrainer retrofit is not well understood because of the complicated and nonuniform deterioration process of elastomeric bearings. This paper presents an in-depth seismic fragility and variation analysis to evaluate cable restrainer retrofit for isolated highway bridges, with a special emphasis on the introduction and mitigation of structural response uncertainty caused by the deteriorated lead rubber bearings (LRBs) and cable restrainer retrofit. Firstly, the mechanical properties of deteriorated LRBs and cable restrainers including the associated parameter uncertainty were modeled based on the consideration of past relevant researches. Subsequently, seismic response of a simplified model of a typical continuous girder isolated highway bridge subjected to various scaled earthquake ground motions was computed to statistically evaluate the effect of typical uncertainties of the mechanical behavior of deteriorated LRBs and cable restrainers upon the risk of global seismic failure of the bridge. Finally, the contribution of cable restrainer retrofit in mitigating the vulnerability and response uncertainty of structural components is quantitatively assessed by comparing the cases with and without the application of cable restrainers. The statistical assessments not only reveal the effect of restrainer cable retrofit at the earthquake levels for design standards, but also consider the levels of seismic events greater than consideration in the design, incorporating the seismic performance uncertainty introduced and enlarged by the aging deterioration of LRBs.

Effect of modeling uncertainty on multi-limit state performance of controlled rocking steel braced frames

Quantifying and propagating uncertainties in structural response is critical to robust performance-based seismic assessments. This paper evaluates the influence of structural model parameter uncertainty on the seismic response and limit state assessment of controlled rocking steel braced frames (CRSBFs). The dead load on the rocking frame, fuse yield strength, initial post-tension (PT) force and yield strength of the braced frame elements are the random variables considered. Realizations of 3-, 6- and 9-story CRSBF nonlinear structural models are constructed using the random variable instances generated by Latin Hypercube Sampling (LHS). The structural model realizations are subjected to multiple stripe analyses using six sets of hazard-consistent ground motions. Three limit states are considered including immediate occupancy, repairability and collapse prevention. The probability distribution of maximum transient and residual story drift ratios, PT strain and fuse shear deformation are also established. These four engineering demand parameters also serve as the basis for the limit state assessments. The effect of modeling uncertainty is examined by comparing the dispersion of the responses and limit state performance from “mean models” (i.e., models constructed based on mean values of random variables) with those obtained from the LHS-generated models. The results showed that model uncertainty had the greatest impact on the response and performance of the 9-story CRSBF.

An efficient non-probabilistic importance analysis method based on MDRM and Taylor series expansion

The input variable of engineering structure inevitable has certain uncertainty. How to quantify the influence of those uncertainties on the uncertainty of structural response is an important issue in structural design. Non-probabilistic reliability importance analysis is one of the methods to quantify this influence when variable data information is insufficient. Although the method has great advantages for variables with insufficient data information, there is no efficient calculation method at present, and the excessive computational cost seriously hinders its application in actual engineering structures. In this paper, the multiplicative dimensional reduction method, Taylor series expansion and unary quadratic function are combined to put forward an efficient algorithm to estimate two non-probabilistic reliability importance indices. With the proposed method, all the calculation processes used to solve the extreme value of function are replaced by an approximate analytical solution. Since the proposed method is an approximate analytical solution, the calculation efficiency is extremely high. Three examples are investigated to verify the accuracy and efficiency of the proposed method.

Uncertainty propagation analysis in free vibration of uncertain composite plate using stochastic finite element method

Material uncertainty is more widespread in composite material than the other engineering materials. This uncertainty makes response of these types of structures to be nondeterministic. In order to predict structural reliability, uncertainty in structural responses must be quantified. There is not a reported research in the literature studing free vibration of composite plate with spatially stochastic material properties. In this research, physical and mechanical properties of composite plate including tensile and shear modulus and density of the plate are modeled as stochastic Gaussian fields. Assuming exponential auto covariance kernels for aforementioned stochastic fields, they are discretized to two parts, including deterministic and stochastic parts employing Karhunen-Loeve theorem. Assuming linear form of strains, mechanical strains are defined applying first order shear deformation theory. Kinetic and potential energy of the composite plate is extracted using finite element formulation. Stochastic finite element formulation is derived employing Hamilton’s principle and Euler-Lagrange and equations are verified with the results in the literature for deterministic case. After verification of formulation, material uncertainty effects on uncertainty of natural frequencies are investigated using Monte Carlo simulation. Results show that there is a linear relation between coefficient of variation of uncertain properties and coefficient of variation of stochastic natural frequencies.

Evaluation of the variability contribution due to epistemic uncertainty on constitutive models in the definition of fragility curves of RC frames

In the framework of uncertainty propagation in seismic analyses, most of the research efforts were devoted to quantifying and reducing uncertainties related to seismic input. However, also uncertainties associated to the definition of constitutive models must be taken into account, in order to have a reliable estimate of the total uncertainty in structural response. The present paper, by means of incremental dynamic analyses on reinforced concrete frames, evaluates the effect of the epistemic uncertainty for plastic-hinges hysteretic models selection. Eleven different hysteretic models, identified based on literature data, were used and seismic fragility curves were obtained for three different levels of maximum interstorey drift ratio. Finally, by means of analysis of variance techniques, the paper shows that the uncertainty associated to the hysteretic model definition has a magnitude similar to that due to record-to-record variability.

Predicting probabilistic distribution functions of response parameters using the endurance time method

SummaryThe main objective of this study is the development of endurance time (ET) excitations in order to take structural response uncertainty into account for use in performance‐based earthquake engineering. There are several uncertainties in earthquake engineering, including earthquake occurrence, structural response, damage, and loss. In the current research, structural response uncertainty is directly included in the ET method, which is an analysis method used for performing structural behavior assessment under seismic actions. Conventional practice of the ET method does not provide any information about seismic response distribution. Despite the simplicity of the ET method, it is an accurate dynamic analysis approach in which structures are subjected to predesigned intensifying acceleration functions, also known as ET excitation functions (ETEFs). In this study, the ETEF generating procedure is modified in order to include the exceedance probability of structural responses observed at an intensity measure. This proposed method is applied to generate new ETEFs; then they are utilized in assessing distribution responses in three structure case studies. Finally, response distributions obtained by the ET method are compared with incremental dynamic analysis so as to investigate the proposed method efficiency. Results show that response probabilistic distributions that are predicted using the ET method match those obtained by incremental dynamic analysis.

The influence of uncertain local subsoil conditions on the response of buildings to ground vibration

This paper examines the influence of imperfect knowledge of the local subsoil conditions on the prediction of building response to ground-borne vibration. The focus is on problems of environmental ground vibration in the wide frequency range between 1 Hz and 80 Hz. A probabilistic finite element-perfectly matched layers model is developed for the analysis of the dynamic soil-structure interaction problem where the shear modulus of the soil is modeled as a conditional random field. A subdomain formulation is employed to impose loading by an incident wave field in the model. The uncertainty on the subsoil properties is propagated to the response of a building by means of Monte Carlo simulation. A case study is considered to investigate the influence of the spatial correlation length of the random field representing the shear modulus of the subsoil, and the foundation type of the building. The structural response uncertainty varies over frequency bands but as a general trend increases with frequency. The foundation type of the building is a crucial parameter determining the structural response and the associated uncertainty bounds.

An approach to quantify the influence of ground motion uncertainty on elastoplastic system acceleration in incremental dynamic analysis

Inclusion of ground motion–induced uncertainty in structural response evaluation is an essential component for performance-based earthquake engineering. In current practice, ground motion uncertainty is often represented in performance-based earthquake engineering analysis empirically through the use of one or more ground motion suites. How to quantitatively characterize ground motion–induced structural response uncertainty propagation at different seismic hazard levels has not been thoroughly studied to date. In this study, a procedure to quantify the influence of ground motion uncertainty on elastoplastic single-degree-of-freedom acceleration responses in an incremental dynamic analysis is proposed. By modeling the shape of the incremental dynamic analysis curves, the formula to calculate uncertainty in maximum acceleration responses of linear systems and elastoplastic single-degree-of-freedom systems is constructed. This closed-form calculation provided a quantitative way to establish statistical equivalency for different ground motion suites with regard to acceleration response in these simple systems. This equivalence was validated through a numerical experiment, in which an equivalent ground motion suite for an existing ground motion suite was constructed and shown to yield statistically similar acceleration responses to that of the existing ground motion suite at all intensity levels.

Influence of modelling strategies on uncertainty propagation in the alternate path mechanism of reinforced concrete framed structures

Reliable performance-based evaluation of structures subjected to extreme loading scenarios, which is a function of structural response uncertainty characterization is a vital question. This paper aims to study the major sources of uncertainty in the alternate path response quantities of reinforced concrete framed structures subjected to sudden column removal scenarios. Using global variance-based sensitivity analysis, influence of nonlinear modelling approaches on uncertainty propagation is studied. Sensitivity of structural response quantities to the input uncertainties using plastic analysis with lumped plastic hinges found to be quite distinct compared with those of obtained using fibre-based modelling approaches, where axial–flexural deformation interaction, and in turn, compressive arching action is taken into account. Moreover, uncertainty propagation at different load levels is investigated using nonlinear incremental dynamic analysis (NIDA). Results obtained from displacement-based element (DBE) formulation, and force-based element (FBE) formulation were in good agreement at low to moderate load factors, where use of DBE formulation found to be computationally more efficient. However, at high load factors, where the structure is prone to progressive collapse, FBE formulation provides more reliable solution as the DBE formulation underestimates local response quantities, and in turn, underestimates the probability of failure. Finally, as uncertainty evaluation using fibre-based modelling approaches is computationally expensive, a substructure technique is applied, and influence of structural idealization on uncertainty propagation in structural response quantities is investigated. Results show that structural idealization is an efficient technique for reducing computational costs in terms of probabilistic analysis, especially when hundreds or thousands of simulations are needed to be performed.

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM) is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.

A computational framework for life-cycle management of wind turbines incorporating structural health monitoring

The integration of structural health monitoring into life-cycle management strategies can help facilitating a reliable operation of wind turbines and reducing the life-cycle costs significantly. This article presents a life-cycle management framework for online monitoring and performance assessment of wind turbines, enabling optimum maintenance and inspection planning at minimum associated life-cycle costs. Incorporating continuously updated monitoring data (i.e. structural, environmental, and operational data), the framework allows capturing and understanding the actual wind turbine condition and, hence, reduces uncertainty in structural responses as well as load effects acting on the structure. As will be shown in this article, the framework integrates a variety of heterogeneous hardware and software components, including sensors and data acquisition units, server systems, Internet-enabled user interfaces as well as finite element models for system identification, and a multiagent system for self-detecting sensor malfunctions. To validate its capabilities and to demonstrate its practicability, the framework is deployed for continuous monitoring and life-cycle management of a 500-kW wind turbine. Remote life-cycle analyses of the monitored wind turbine are conducted, and case studies are presented investigating both the structural performance and the operational efficiency of the wind turbine.

Variance decomposition of the seismic response of structures

The reliability of structures is dependent on the variability in random characteristics of strong ground motion. In this paper, the influence of the variability of ground motion variables on the variability of structural response has been accessed by sensitivity analysis. The Variance-Based Sensitivity Analysis (VBSA) is considered using the Monte Carlo based procedure, for computing the set of first order sensitivity indices of variables to estimate the contribution that each uncertain input makes to variance in the model output. The variables that have a dominant influence on the uncertainty of structural response are identified. The analytical results show that the formulation of dynamic structural response in the frequency domain, based on the seismological information of excitation, can be used in some countries, such as Iran, with lack of recorded strong motion.

J191013 ブートストラップ法を用いた宇宙構造の不確定性推定について([J19101]構造・材料の高度化に向けた宇宙工学と材料力学の展開(1))

Design of a very precise space structural system requires an accurate estimation of uncertainties on structural and environmental parameters. For the purpose, high accurate estimations of uncertainties of the structural parameters and the effect of the paremeter uncertainties on the structural response uncertainty are required. Then, the robust design optimization based on the accurate estaimation is required. This study focuses on the former part, a high accurate estimation of the uncertainties. The applicability of a bootstrap method known as a nonparametric technique is investigated to estimate the confidence intervals of the uncertain parameters related to vibration responses of simple structures. The target structure is a cantileverd bow-shaped structure composed of beam and tether that is a breadboard model of a lightweight space reflector. The confidence intervals identified from several numbers of vibration tests is compared by the nonlinear finite-element analysis.

The effects of explosive blast load variability on safety hazard and damage risks for monolithic window glazing

Although the modelling of built infrastructure subject to blast loading has been well developed, considerable uncertainty remains with respect to explosive loading parameters and structural response. This paper focuses on facade glazing – as this poses significant safety hazards when affected by explosive blast loads. A structural reliability analysis is used to calculate probabilities of glazing damage and safety hazards conditional on given threat scenarios. The analysis considers the variability of explosive blast loading; in particular, from variations in explosive weight, explosion effects in terms of pressure, stand-off distance, inherent blast load variability and model error. Uncertainties in structural response (including the variability in glazing stress limits, situational geometry, fragment drag coefficients and modelling error) are then considered in the analysis. This allows the prediction of likelihood and extent of damage and casualties. It was found that damage and safety hazard risks are very sensitive to the accuracy of the blast loading prediction model and the inherent variability of blast loading.

Analysis of a cable-stayed bridge with uncertainties in Young's modulus and load - A fuzzy finite element approach

This paper presents a fuzzy finite element model for the analysis of structures in the presence of multiple uncertainties. A new methodology to evaluate the cumulative effect of multiple uncertainties on structural response is developed in the present work. This is done by modifying Muhanna's approach for handling single uncertainty. Uncertainty in load and material properties is defined by triangular membership functions with equal spread about the crisp value. Structural response is obtained in terms of fuzzy interval displacements and rotations. The results are further post-processed to obtain interval values of bending moment, shear force and axial forces. Membership functions are constructed to depict the uncertainty in structural response. Sensitivity analysis is performed to evaluate the relative sensitivity of displacements and forces to uncertainty in structural parameters. The present work demonstrates the effectiveness of fuzzy finite element model in establishing sharp bounds to the uncertain structural response in the presence of multiple uncertainties.

Sensitivity analysis of structural response uncertainty propagation using evidence theory

Sensitivity analysis for the quantified uncertainty in evidence theory is developed. In reliability quantification, classical probabilistic analysis has been a popular approach in many engineering disciplines. However, when we cannot obtain sufficient data to construct probability distributions in a large-complex system, the classical probability methodology may not be appropriate to quantify the uncertainty. Evidence theory, also called Dempster–Shafer Theory, has the potential to quantify aleatory (random) and epistemic (subjective) uncertainties because it can directly handle insufficient data and incomplete knowledge situations. In this paper, interval information is assumed for the best representation of imprecise information, and the sensitivity analysis of plausibility in evidence theory is analytically derived with respect to expert opinions and structural parameters. The results from the sensitivity analysis are expected to be very useful in finding the major contributors for quantified uncertainty and also in redesigning the structural system for risk minimization.

Probabilistic structural analysis methodology and applications to advanced space propulsion system components

The development of reliability-based design methods requires the development and use of general purpose structural analysis tools that predict the uncertainty of structural response due to uncertainties in a full range of design conditions. The goal of the reported work has been to develop and apply new technology that will enable the designer to efficiently and accurately account for each of the design sources of uncertainty as it might affect structural reliability and risk assessment. The paper discusses the development of the NESSUS ™ (Numerical Evaluation of Stochastic Structures Under Stress) finite element code and its supporting reliability algorithms. The elements of the solution strategy are outlined and application is made to several propulsion system components.