Response Sensitivity Analysis Research Articles

Probabilistic assessment of structural seismic performance influenced by the characteristics of hysteretic energy dissipating devices

The seismic performance of a structure with hysteretic energy dissipation devices (HEDDs) is significantly influenced by their cyclic structural characteristics. This is due to the fact that the acceleration and displacement responses of the structure mainly depend on the dissipating capacities of HEDDs. Hence, it is important to verify the cyclic characteristics of the HEDDs in designing the structure. Recognizing this importance, a current ASCE/SEI 7 requires prototype tests of energy dissipating systems that consist of HEDDs and their connecting components with a seismic-force-resisting system. The codified requirements for the prototype tests prescribe the acceptance criteria of energy dissipating systems, so called as a 15 percent rule. However, there is little information on the reliability of such acceptance criteria. As a part of research efforts to figure out this problem, this paper carries out sensitivity analysis of the seismic responses of steel moment-resisting frames influenced by the cyclic characteristics of damping systems employing HEDDs. Throughout the sensitivity analyses using probabilistic approaches, this study numerically assesses the influence of HEDD’s cyclic characteristics on the seismic response of steel moment-resisting frames. The analysis results show that the change of HEDD’s design parameters significantly affects the seismic response and of the HEDD’s design parameters, the initial stiffness and yield strength are the most influential parameters. Furthermore, the variation of the important structural engineering parameters is similar to or smaller than 10% of their mean values if all design parameters of HEDDs are satisfied with the prototype testing requirements prescribed in ASCE/SEI 7.

A suite of metrics for assessing the performance of solar power forecasting

Forecasting solar energy generation is a challenging task because of the variety of solar power systems and weather regimes encountered. Inaccurate forecasts can result in substantial economic losses and power system reliability issues. One of the key challenges is the unavailability of a consistent and robust set of metrics to measure the accuracy of a solar forecast. This paper presents a suite of generally applicable and value-based metrics for solar forecasting for a comprehensive set of scenarios (i.e., different time horizons, geographic locations, and applications) that were developed as part of the U.S. Department of Energy SunShot Initiative’s efforts to improve the accuracy of solar forecasting. In addition, a comprehensive framework is developed to analyze the sensitivity of the proposed metrics to three types of solar forecasting improvements using a design-of-experiments methodology in conjunction with response surface, sensitivity analysis, and nonparametric statistical testing methods. The three types of forecasting improvements are (i) uniform forecasting improvements when there is not a ramp, (ii) ramp forecasting magnitude improvements, and (iii) ramp forecasting threshold changes. Day-ahead and 1-hour-ahead forecasts for both simulated and actual solar power plants are analyzed. The results show that the proposed metrics can efficiently evaluate the quality of solar forecasts and assess the economic and reliability impacts of improved solar forecasting. Sensitivity analysis results show that (i) all proposed metrics are suitable to show the changes in the accuracy of solar forecasts with uniform forecasting improvements, and (ii) the metrics of skewness, kurtosis, and Rényi entropy are specifically suitable to show the changes in the accuracy of solar forecasts with ramp forecasting improvements and a ramp forecasting threshold.

A two-step approach for damage Identification in plates

This paper presents a two-step approach based on modal strain energy and response sensitivity analysis to identify the local damages in isotropic plates with moderate thickness. The first step focuses on detection of damage location. The local damage is simulated by a reduction in the elemental Young’s modulus of the plate. It is determined from the modal strain energy change ratio approach. A method to weaken the “vicinity effect” is proposed to reduce the false alarms in the localization of damage. In the second step, an approach based on response sensitivity-based finite element model updating is used to further identify the locations and extents of the local damages in time domain. The identified results are obtained iteratively with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single and multiple damages can be identified successfully and the effect of measurement noise on the identification results is investigated. Good identified results can be obtained from the short time histories of a few number of measurement points.

Concurrent design of composite macrostructure and cellular microstructure under random excitations

In this paper, a method for the concurrent topology optimization of macrostructural material distribution and periodic microstructure under random excitations is proposed. The sensitivity analysis of dynamic response with respect to design variables in two scales, i.e., macro and micro scales, is presented. The corresponding concurrent topology optimization of macrostructure and microstructure is established, where the objective function is to minimize the displacement response mean square (RMS) of the prescribed degree of freedom while volume constraints are applied to the macromaterial distribution and phase materials. The optimization problem is solved using a bi-directional evolutionary structural optimization (BESO) method. Several examples are presented to demonstrate the effectiveness of the proposed method.

Structural damage identification based on power spectral density sensitivity analysis of dynamic responses

A new method is proposed to identify locations and severities of structural damages based on the power spectral density sensitivity analysis. Firstly, the structural responses and power spectral density under stationary and random excitations are calculated using pseudo excitation method. Then, the sensitivities of power spectral density with respect to the structural damage parameters are obtained. Finally, the finite element model updating method is adopted to identify the structural damages from the calculated and the simulated measured power spectral density. Two numerical examples demonstrate the satisfactory identification results obtained from the present method.

Structural damage identification based on residual force vector and response sensitivity analysis

A two-stage approach based on residual force vector and response sensitivity analysis is proposed for structural damage identification in this study. Local damage is represented by a perturbation in the elemental stiffness parameter of the structural finite element model. Primarily, the difference between the virtual residual force vector of an intact and damaged structure is used to localize the damage. Then, a response sensitivity-based method is adopted to identify the perturbation of the stiffness parameter (i.e., the extent of the local damage) from the measured dynamic responses. Numerical simulations are conducted to identify both single and multiple structural damages under sinusoidal or impulsive excitation. The proposed approach gives satisfactory results with artificial measurement noise.

Tidal-scale flow routing and sedimentation in mangrove forests: Combining field data and numerical modelling

Tidal-scale biophysical interactions establish particular flow routing and sedimentation patterns in coastal mangroves. Sluggish water flows through the mangrove vegetation and enhanced sediment deposition are essential to maintain these valuable ecosystems, thereby enabling their contribution to coastal protection and stabilization. Spatially explicit field observations of tidal-scale flow routing and sediment deposition were obtained in an elevated mangrove stand dissected by tidal creeks, located in the Trang river estuary at the Thai Andaman coast. An accurate and efficient depth-averaged process-based numerical model of this field site was developed in Delft3D to study the contributions of various biogeophysical mangrove settings to the observed tidal dynamics and to study the impacts of changes of these environmental conditions. The creeks are found to form the major pathway for the tidal inflow during the lower tides, while the sheltered interior of the forest is an effective sediment sink during the higher tides. A numerical sensitivity analysis of the initial response—or adaptive capacity—of the studied mangrove system to instantaneous environmental changes reveals the stable state of the study site: deposition rates are largely imposed by the topography and relative elevation, while they are rather independent of the vegetation density. Deeper inundations of the mangroves favor sheet flows through the forest and spatially averaged deposition rates decrease, particularly when this coincides with decreasing vegetation densities. Moreover, the sediment trapping efficiency is found to reduce significantly with diminishing sediment inputs and with mangrove area losses. These results clearly indicate the sensitivity of mangroves' ecosystem engineering ability—in terms of sedimentation—to climate change and anthropogenic threats.

Direct differentiation method for response sensitivity analysis of structures in fire

Response sensitivity is an important quantity in structural reliability calculations, parameter importance studies, and design optimization. In the response sensitivity analysis of structures at ambient temperature, prior research has shown that the direct differentiation method provides improved accuracy and efficiency in comparison to the finite difference method. The direct differentiation method is extended here to the analysis of structures in fire, in which parameters exist in the fire, thermal and structural domains. Analytical expressions for the response sensitivities are derived for nonlinear heat transfer and structural finite elements, with specific consideration for the interdependencies between the physical domains. Numerical analyses were conducted for a steel beam exposed to natural fire conditions. Comparisons between the finite difference and direct differentiation methods demonstrate that the proposed formulations offer much promise for assessing response gradients of fire-exposed structures in a robust and computationally efficient manner.

APSTRACT: Development and validation of sensitivity analysis code

This paper deals with the application of the perturbation theory in the field of nuclear reactor research. In order to determine the sensitivity coefficients the code APSTRACT was developed. We describe adopted methodology and its connection to common calculation tools. The reliability of developed code was validated by direct perturbation calculation in terms of integral values for isotopes and reactions of interest. The shapes of sensitivity profiles were compared with sensitivities adopted from the International Subgroup 33 of NEA Paris and calculated by TSUNAMI-3D to also ensure the within-group validity. Finally, the applicability of APSTRACT was shown in reactivity response sensitivity analysis.

Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates

The generation of reliable quantitative precipitation estimations (QPEs) through use of raingauge and radar data is an important issue. This study investigates the impacts of radar QPEs with different densities of raingauge networks on rainfall–runoff processes through a semi-distributed parallel-type linear reservoir rainfall–runoff model. The spatial variation structures of the radar QPE, raingauge QPE and radar-gauge residuals are examined to review the current raingauge network, and a compact raingauge network is identified via the kriging method. An analysis of the large-scale spatial characteristics for use with a hydrological model is applied to investigate the impacts of a raingauge network coupled with radar QPEs on the modelled rainfall–runoff processes. Since the precision in locating the storm centre generally represents how well the large-scale variability is reproduced; the results show not only the contribution of kriging to identify a compact network coupled with radar QPE, but also that spatial characteristics of rainfalls do affect the hydrographs.Editor Z.W. Kundzewicz; Guest editor R.J. MooreCitation Pan, T.-Y., Li, M.-Y., Lin, Y.-J., Chang, T.-J., Lai, J.-S., and Tan, Y.-C., 2014. Sensitivity analysis of the hydrological response of the Gaping River basin to radar-raingauge quantitative precipitation estimates. Hydrological Sciences Journal, 59 (7), 1335–1352. http://dx.doi.org/10.1080/02626667.2014.923969

Adjoint design sensitivity analysis of molecular dynamics in parallel computing environment

An adjoint design sensitivity analysis method is developed for molecular dynamics using a parallel computing scheme of spatial decomposition in both response and design sensitivity analyses to enhance the computational efficiency. Molecular dynamics is a path-dependent transient dynamic problem with many design variables of high nonlinearity. Adjoint variable method is not appropriate for path-dependent problems but employed in this paper since the path is readily available from response analysis. The required adjoint system is derived as a terminal value problem. To compute the interaction forces between atoms in different spatial boxes, only atomic positions in the neighboring boxes are required to minimize the amount of data communications. Through some numerical examples, the high nonlinearity of the selected design variables is discussed. Also, the accuracy of the derived adjoint design sensitivity is verified by comparing with finite difference sensitivity and the efficiency of parallel adjoint variable method is demonstrated.

Sensitivity analysis of structural response to position of external applied load: in plane stress condition

Procedures for sensitivity analysis of the structural responses, i.e., nodal displacement, mean compliance and local stresses within an element, with respect to the location of an external applied load are developed. This is mainly because the external loads are often of some freedom to change their application positions in the structural preliminary design. Apart from the structural response evaluation, the finite element method is employed in this work for the sensitivity analysis implementation of a plane stress continuum structure. First, an external load is transformed into the equivalent nodal forces such that the influence of an external load shift is represented completely by the magnitude variation of the associated nodal forces, upon which the first- and second-order derivatives of an external load to its location change are performed respectively in a closed form by the aid of the features of the element shape functions. Then, the relevant sensitivities of the structural responses aforementioned are formulated readily with the discrete method. Finally, two typical examples are provided to demonstrate the validity of the sensitivity formulations presented, and the numerical results show a perfect accuracy of calculation of the response sensitivity.

Damage Identification Based on Power Spectral Density Sensitivity Analysis of Structural Responses

A new method is proposed to identify structural damages based on the power spectral density sensitivity analysis. The responses of the structure under stationary and random excitations are obtained using pseudo excitation method, and then the sensitivities of power spectral density with respect to the structural damage parameters are obtained similarly. Finite element model updating method is adopted to identify the structural damages. A numerical example of a shearing structure demonstrates the satisfactory results obtained from the present method.

Uncertainties Quantification of Effective Thermal Conductivity for Ceramic Fiber Blanket

In the present paper, a probabilistic propagation model for assessing the uncertainty of the effective thermal conductivity was developed based on a combined conduction and radiation heat transfer model of a ceramic fiber blanket composite. The Monte Carlo technique was used to cope with the uncertainties in the material density, radiative properties, and boundary temperatures observed in experimental tests. The calculated effective thermal-conductivity distribution for the sample was compared with the experimental measurements performed on multiple samples, and the predicted mean values were in good agreement with the measured data. The result validates the thermal predictive model and demonstrates the suitability of the stochastic model containing statistical distributions in the input variables. Statistical information also indicates that the uncertainty effect can be enlarged at high temperatures. Response sensitivity analysis between the random inputs and the effective thermal conductivity demonstrates that the randomness in the hot-side temperature, the cold-side temperature, and extinction coefficient of the sample has a significant influence on the variability of thermal-conductivity properties. The extinction coefficient becomes more and more important with an increase of temperature due to the dominant radiative heat transfer contribution at high temperature. The analysis provides good insight into the scattering control in the experimental measurement and theoretical prediction of the effective thermal conductivity of a ceramic fiber composite.

A 2D finite element based on a nonlocal constitutive model describing localization and propagation of phase transformation in shape memory alloy thin structures

Here, the effects of localization and propagation of martensitic phase transformation on the response of SMA thin structures subjected to thermo-mechanical loadings are investigated using nonlocal constitutive model in conjunction with finite element method. The governing equations are derived based on variational principle considering thermo-mechanical equilibrium and the spatial distribution of the nonlocal volume fraction of martensite during transformation. The nonlocal volume fraction of martensite is defined as a weighted average of the local volume fraction of martensite over a domain characterized by an internal length parameter. The local version of the thermo-mechanical behavior model derived from micromechanics considers the local volume fraction of martensite and the mean transformation strain. A 4-noded quadrilateral plane stress element with three degrees of freedom per node accounting for in-plane displacements and the nonlocal volume fraction of martensite is developed. Numerical simulations are conducted to bring out the influence of material and geometrical heterogeneities (perturbations/defects) on the localization and propagation of phase transformation in SMA thin structures. Also, a sensitivity analysis of the material response due to the localization and the other related model parameters is carried out. The detailed investigation done here clearly shows that the localization of phase transformation has significant effect on the response of shape memory alloys.

Design sensitivity analysis of dynamic response of nonviscously damped systems

The sensitivity problem of dynamic analysis of linear nonviscously damped systems is considered. The assumed nonviscous damping forces depend on the past history of motion via convolution integrals over some kernel functions. The nonviscous damping model can be alternatively chosen from familiar viscoelastically damping structures and is considered as a further generalization of the familiar viscous damping. The computations of dynamic responses are reviewed for the purpose of design sensitivity analysis development. The dynamic response can be easily calculated using direct frequency response method and modal superposition method when the dynamic equation of motion of nonviscously damped systems is transformed into the frequency domain using the Laplace transform. It is shown that the dynamic response of nonviscously damped systems can be obtained using traditional modal analysis in a familiar manner used in undamped or viscously damped systems. The discrete Fourier transform and inverse discrete Fourier transform algorithms are also suggested to obtain the displacement in the time domain. Based on these expressions of dynamic response, the adjoint variable and direct differentiation methods, originally presented to obtain the dynamic response sensitivity of undamped or viscously damped systems, are both developed for efficiently and accurately calculating the sensitivity of dynamic response of nonviscously damped systems. Finally, some case studies are used to show the application, effectiveness and some characters of the derived formulas. The numerical sensitivity results show the sensitivity obtained using the developed methods are in excellent agreement with the finite difference results. However, the finite difference method suffers from computational inefficiency and possible errors.

Development of level-1 PSA method applicable to Japan Sodium-cooled Fast Reactor

This paper describes a study to develop the level-1 probabilistic safety assessment (PSA) method that is applicable to the Japan Sodium-cooled Fast Reactor (JSFR). This study has been started since August 2010 and aims to provide a new evaluation method of (1) passive safety architectures related to internal events and (2) an advanced seismic isolation system related to a seismic event as a representative external event in Japan. Regarding the internal events evaluation, a quantitative analysis on the frequency of the core damage caused by reactor shutdown failure was conducted. A failure in passive reactor shutdown was taken into account in the event tree model. The failure rate of sodium-cooled fast reactor (SFR) specific components was evaluated based on the operating experience in existing SFRs by applying the Hierarchical Bayesian Method, which can consider a plant-to-plant variability. By conducting an uncertainty analysis, it was found that the assumption about the correlation of the probability parameters between the main and backup reactor shutdown systems (RSSs) is sensitive to the mean value of the frequency of the core damage caused by reactor shutdown failure. As for the seismic event evaluation, seismic response analysis and sensitivity analysis of a seismic isolation system were carried out. Rubber bearings have a hardening property in horizontal direction and a softening property in vertical direction in case of large deformation. Therefore the analyses considered nonlinearity of rubber bearings. Both horizontal and vertical nonlinear characteristics of rubber bearings were explained by multi-linear model. Mass point analytical models were applied. At first, seismic response analysis was executed in order to investigate influence of nonlinearity of rubber bearing upon response of building. Then sensitivity analysis was executed. Parameters of rubber bearings, oil dampers and the building were fluctuated, and influence of dispersion of these parameters upon response of building was investigated. As a result, it was confirmed that nonlinear properties of rubber bearings have influence on response of the building and inner equipment.

Influence of pitching and yawing during frontal passenger vehicle crash tests on driver occupant's kinematics and injury

Vehicle safety has become a major task in the development process of passenger vehicles. Measures for occupant safety are developed by reference to different tests including legal tests and consumer tests. The different load cases for the considered frontal crash tests cause different vehicle kinematics involving all six degrees of freedom. Besides restraint systems, vehicle kinematics shows distinct influence on occupant loading. A sensitivity analysis of the dummy responses due to varied motion fractions has been performed by finite elements simulations of a well-validated simulation model. The influences of particular motion components are determined by objective assessment variables. These are well-known injury criteria as well as geometrical criteria such as distances between dummy and interior. The results of this sensitivity study can be used for additional measures in terms of occupant protection.

Probabilistic sensitivity analysis of suspension bridges to near-fault ground motion

The sensitivities of a structural response due to variation of its design parameters are prerequisite in the majority of the algorithms used for fundamental problems in engineering as system uncertainties, identification and probabilistic assessments etc. The paper presents the concept of probabilistic sensitivity of suspension bridges with respect to near-fault ground motion. In near field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many suspension bridges have significant structural response modes. Two different types of suspension bridges, which are Bosporus and Humber bridges, are selected to investigate the near-fault ground motion effects on suspension bridges random response sensitivity analysis. The modulus of elasticity is selected as random design variable. Strong ground motion records of Kocaeli, Northridge and Erzincan earthquakes are selected for the analyses. The stochastic sensitivity displacements and internal forces are determined by using the stochastic sensitivity finite element method and Monte Carlo simulation method. The stochastic sensitivity displacements and responses obtained from the two different suspension bridges subjected to these near-fault strong-ground motions are compared with each other. It is seen from the results that near-fault ground motions have different impacts stochastic sensitivity responses of suspension bridges. The stochastic sensitivity information provides a deeper insight into the structural design and it can be used as a basis for decision-making.

Probabilistic sensitivity analysis of suspension bridges to near-fault ground motion

The sensitivities of a structural response due to variation of its design parameters are prerequisite in the majority of the algorithms used for fundamental problems in engineering as system uncertainties, identification and probabilistic assessments etc. The paper presents the concept of probabilistic sensitivity of suspension bridges with respect to near-fault ground motion. In near field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many suspension bridges have significant structural response modes. Two different types of suspension bridges, which are Bosporus and Humber bridges, are selected to investigate the near-fault ground motion effects on suspension bridges random response sensitivity analysis. The modulus of elasticity is selected as random design variable. Strong ground motion records of Kocaeli, Northridge and Erzincan earthquakes are selected for the analyses. The stochastic sensitivity displacements and internal forces are determined by using the stochastic sensitivity finite element method and Monte Carlo simulation method. The stochastic sensitivity displacements and responses obtained from the two different suspension bridges subjected to these near-fault strong-ground motions are compared with each other. It is seen from the results that near-fault ground motions have different impacts stochastic sensitivity responses of suspension bridges. The stochastic sensitivity information provides a deeper insight into the structural design and it can be used as a basis for decision-making.