Response Surface Metamodels Research Articles

Building portfolio seismic fragility analysis: incorporating building-to-building variability to carry out seismic fragility analysis for reinforced concrete buildings in a city

Predicting how future earthquakes will affect structural performance in a particular region is a challenge due to the unpredictable nature of earthquakes and inherent uncertainties in construction materials and the geometry of structures. This study considers building-to-building variabilities as inputs in an existing Response Surface Methodology (RSM) that are based on the Design of Experiment (DoE) technique to quickly determine the structural fragility of a region. As it is impractical to analyse each individual structure in a region in detail, this study addresses the issue by collecting a set of building parameters and using screening design to evaluate the most significant building parameters in the overall seismic performance. Instead of performing building-to-building analyses, the propagation of uncertainty in building-to-building variability can now be performed using a polynomial response surface metamodel. The metamodel is a function of the response of the building, and a set of significant parameters. This study aims to obtain the fragility of a collection of buildings with the help of the existing RSM by considering variability in structural parameters that can represent the overall structural geometric and material properties within a region. A case study is conducted for the collection of reinforced concrete (RC) buildings in the city of Silchar, located in Northeast India, which is one of the most seismically active regions of the country. The fragility curve developed with significant building parameters from RSM has been compared with that of the conventional method using Incremental Dynamic Analysis (IDA), and the match of the result confirms the accuracy of fragility assessment using RSM.

Multi-Hazard Fragility Analysis of Offshore Wind Turbine Portfolios using Surrogate Models

This paper deals with a surrogate modeling-based fragility estimate of monopile offshore wind turbine (OWT) towers subjected to wind and wave loadings. The monopile 5-MW OWT specified by the National Renewable Energy Laboratory (NREL), United States was used as the base model for this study. Aero- and hydrodynamic simulations of the OWT were first performed via Fatigue, Aerodynamics, Structures, and Turbulence (FAST) developed by the NREL to determine its critical wave-and-wind responses, to determine peak tower top deflections, flexural moments, and shear forces. Through least squares regression with the simulation data, two surrogate models, Response Surface Metamodel (RSM) and Stepwise Multiple Linear Regression (SMLR) were developed to predict the critical OWT responses caused by both wind and wave loads and to develop its fragility curves at a low computational cost. Responses and fragility curves resulting from each of the surrogate models were compared to those from the FAST simulation, demonstrating the effectiveness of the RSM in terms of accuracy to replicate the FAST results. As a result of the comparison, the RSM was adopted as the final model to estimate the multi-wind-and-wave vulnerability of the OWT in terms of fragility surfaces considering uncertainties in a broad spectrum of its loads and capacities. Major findings indicated that the wind speed was observed to be the most critical load parameter for peak tower top deflections with response observed in the range of 2.2 5 m at a wind speed of 5 m/s to 5.5 m at 70 m/s, while the wave height appeared to be the major contributor to the vulnerability on flexural moments with the observed peak value of 1.75 × 108 Nm at a wave height of 1 m increased to 5.75 × 108 Nm at 20 m. It was also found that structural characteristics parameters related to the OWT's capacities, including hub height, rotor diameter, and monopile thickness have a significant impact on the overall vulnerability with one-quarter exceeding probability for mudline flexure was noted at 83.26 m, 151 m, and 0.133 m, respectively.

Welding versus adhesive bonding strength investigation

This paper was intended to investigate the strength of adhesive and welded connections to be used in a dynamic message sign (DMS). The tensile strength and shear strength were studied for both of the adhesive and welded specimens. A number of tensile specimens and shear specimens with variations in width and temperature were tested until failure according to the ASTM D638 and ASTM D1002, respectively. The specimens with a range of width from 13 mm to 38 mm were conditioned with temperatures between −56.67 °C and 93.33 °C. The effects of temperature and width on each of the strengths were evaluated by analysing the testing data in a graphical and statistical manner. As expected, all the tests revealed that the welded specimens have significantly higher strength compared to the adhesive specimens in tensile and shear loadings. For the adhesive specimens, due to the increment of temperature, the highest increments were found to be 31.9% and 30.4%. In addition to the tests, Response Surface Metamodels (RSMs) and practical design equations were developed with regression analysis of the testing data, so as to predict tensile and shear stresses of both adhesive and welded specimens in an efficient way. 3D plots generated from the RSMs showed a higher effect of the temperature and width on the ultimate tensile and shear strength for both adhesive and welded specimens, and the practical design equations were founded to be more reliable for the overall tensile and shear stress prediction compared to the RSMs.

Optimizing resiliency of train operations in an underground metro: A hybrid discrete-event simulation and response surface methodology

Avoiding the passengers extra waiting time is a vital task for rail planners. The current research focused on minimizing the passenger waiting time on the presence of real frequently random occurred disturbances. Details of the proposed model are on the 1st line of Tehran underground rail rapid transit. All fitness functions are validated using the analysis of variance (ANOVA) by applying the hypothesis testing method. Also, a validated discrete-event computer simulation model is applied to examine the average waiting time per passenger as the key performance measure under different scenarios generated using full factorial design of experiments. The validity of the obtained optimal solution, i.e., train headway times is confirmed at a 95% level of reliability. Also, simulation outcomes indicated that the proposed response surface meta-model could efficiently provide a more reliable train operation plan to ensure a desirable level of system resiliency on the presence of random disturbances. The numerical results indicated that wait time could be reduced by 14.8% for passengers as compared with the baseline train headway plan.

Expected seismic performance of gravity dams using machine learning techniques

Methods for the seismic analysis of dams have improved extensively in the last several decades. Advanced numerical models have become more feasible and constitute the basis of improved procedures for design and assessment. A probabilistic framework is required to manage the various sources of uncertainty that may impact system performance and fragility analysis is a promising approach for depicting conditional probabilities of limit state exceedance under such uncertainties. However, the effect of model parameter variation on the seismic fragility analysis of structures with complex numerical models, such as dams, is frequently overlooked due to the costly and time-consuming revaluation of the numerical model. To improve the seismic assessment of such structures by jointly reducing the computational burden, this study proposes the implementation of a polynomial response surface metamodel to emulate the response of the system. The latter will be computationally and visually validated and used to predict the continuous relative maximum base sliding of the dam in order to build fragility functions and show the effect of modelling parameter variation. The resulting fragility functions are used to assess the seismic performance of the dam and formulate recommendations with respect to the model parameters. To establish admissible ranges of the model parameters in line with the current guidelines for seismic safety, load cases corresponding to return periods for the dam classification are used to attain target performance limit states.

Tensile- and Shear-Strength Tests with Adhesive Connections in Dynamic Message Signs

A dynamic message sign (DMS) is made up of a display, cabinet sheet aluminum skin, and internal structure along with electrical components. The aluminum skin is connected to the internal structure usually with a welded connection; however, adhesive or chemical bonding can be used instead for the connection between these two components. The goal of this paper is to examine the tensile and shear strengths along with other mechanical properties of adhesives used in the DMS under varying environmental and geometrical conditions. Adhesive tensile and shear specimens with different widths were tested according to accepted standards after conditioning them in different temperature and humidity conditions. Numerous data resulting from the tests were analyzed through graphical comparisons and statistical analysis so as to explore the effect of the considered parameters on tensile and shear strengths. As part of the statistical analysis, response surface metamodels (RSMs) were utilized not only to determine statistically significant parameters affecting the strengths, but also to develop separate regression models for the tensile and shear strengths. The highest decrement in the tensile stress was found to be 7.1%, 19.9%, and 7.9% with the increase in conditioning temperature, conditioning humidity, and specimen’s width, respectively. Owing to the effect of increases in conditioning temperature, conditioning humidity, and specimen width, the shear stress was increased most by 10%, 7%, and 19.3%, correspondingly. Key findings revealed that an increase in conditioning humidity decreases the tensile strength. The RSM model–based analysis also found conditioning humidity to be the most significant parameter negatively affecting the tensile stress because a probability value of 2.529% was observed from the RSM model. Finally, this work found adhesive or chemical bonding to be a possible substitute to welding for assembly of the DMS.

Mathematical sustainability assessment framework of earthquake-induced steel building population

The ability to estimate the probability a building population under seismic events will be sustainable is timely, useful in appropriately allocating earthquake mitigation funds earmarked for repair, rehabilitation, and replacement. A building population is considered sustainable if actual cost incurred is less than a target cost at a given ground motion intensity level such as a certain level of spectral accelerations. The purpose of this study is to construct a mathematical framework coupled with Gompertz and power functions to determine the probability of sustainability of building population subjected to seismic events as a function of target repair-cost ratios. The framework accounts for the exceedence probability of certain earthquake occurrence in 50 years and the fragility data created by joint response surface metamodels (RSMs) and Monte Carlo Simulation (MCS). The fragility data for a population of L-shaped Steel Moment-Frame (LSMF) buildings located in the Central United States and the probability of spectral acceleration exceedence for the target region are used for this study. The probability of sustainability of the LSMF buildings built from pre-1970, between 1970 and 1990, and post-1990 are determined through the developed framework. The mathematical and graphical relationship between the probability of sustainability of the building population under a broad range of spectral accelerations and its target repair-cost ratio are determined. Key findings show that the buildings built in the post-1990 are more sustainable than those built from the pre-1970.

Peel and cleavage strength tests with adhesive connections in dynamic message signs

This paper aims to examine the mechanical properties of the adhesive focusing on peel strength and cleavage strength for varying environmental and geometrical conditions. To that end, peel and cleavage specimens with variations in width were fabricated and examined according to American Society for Testing and Materials (ASTM) after conditioning them in different environmental conditions, including temperature (20 °C, 52.5 °C, and 85 °C) and humidity (48%, 71,5%, and 95%). The specimens were conditioned in the temperature-humidity controlled chamber for at least 96 h for moisture saturation at each humidity level. The effect of temperature, humidity, and width on peel and cleavage strengths were graphically and statistically examined by analyzing the testing data. As part of the statistical analysis, regression models, encompassing multiple linear regression (MLR) and response surface metamodels (RSM), were established to predict the peel and cleavage strengths. Through evaluation of R-squared values and graphs of the predicted values against the testing data, it was found that the RSM was more accurate than MLR. Key results indicated that the peel strength of tested adhesive specimens was increased with the increment in humidity up to 30.1% and was decreased by the maximum reduction of 28.2% with increment in specimen's width, while the cleavage strength of the tested specimens improved with the peak increment of 27.4% and 28.5% when the temperature and specimen's width was increased, respectively. The cleavage strength, however, was decreased up to 13.7% with the increment in humidity. Findings from 3-D surfaces generated from the RSM to observe the effect of different parameters on the peel and cleavage strength of adhesive joints were in agreement to the testing results. The statistical analysis indicated that the width was a significant parameter affecting the peel strength.

Multiobjective performance optimisation of a new differential steering concept

Differential steering is an emerging steering concept based on traction force differences between left and right sides of vehicles equipped with independently actuated wheels. Actually, this concept is only used to support classical vehicle designs utilising rack and pinion steering components. However, it may fully substitute such devices to reduce complexity and cut down costs. Since we do not have well-established design rules for such kind of vehicles, this paper will overcome the missing experience and explore the general applicability of such a new steering concept by using multiobjective optimisation. Three design objectives and three constraints are defined with respect to the dynamic, steady-state and low-speed steering performance of the vehicle. Since mechanical and control parts are strongly coupled, their parameters are optimised simultaneously by a multiobjective genetic algorithm aided by iteratively updated neural network-based response surface metamodels. Optimisation results in a variety of technically feasible Pareto-optimal designs. Investigation of a particular optimal design shows that a vehicle with differential steering is able to provide convincing steering performance.

Optimal Scheduling for Integrated Energy System Considering Scheduling Elasticity of Electric and Thermal Loads

Reasonable scheduling is the basic guarantee for an integrated energy system (IES) to achieve coordinated and efficient operation of multi-energies. For an IES including electric and thermal loads, a demand response (DR) model based on a compensation mechanism is established in this article, and scheduling elasticity (SE) of different types of loads is analyzed to guide users to use energies reasonably and economically. On this basis, an optimization model is established for an IES in accordance with the energy consumption and system operation characteristics. In accordance with the dynamic demands of multi-energies, this model aims at meeting all energy demands with the lowest operation cost. It performs the coordinated optimization for the device output power and the power transmission between multi-energies. To solve the problems of the complex solving process and long computation time, a global optimization algorithm based on a polynomial response surface (PRS) metamodel is proposed in this article. The proposed algorithm adopts a response surface method to fit the optimization model and construct a PRS metamodel to estimate the function values instead of the optimization model, thereby avoiding repeatedly calling the original complex objective function and reducing the computation time. The test results verify the effectiveness of the proposed model and algorithm.

Efficient Method of Firing Angle Calculation for Multiple Launch Rocket System Based on Polynomial Response Surface and Kriging Metamodels

Aiming at solving the problem of firing angle calculation for the multiple launch rocket system (MLRS) under both standard and actual atmospheric conditions, an efficient method based on large sample data and metamodel is proposed. The polynomial response surface, Kriging, and the ensemble of metamodels are used to establish the functional relations between the firing angle, the maximum range angle, the maximum range, and various influencing factors under standard atmospheric conditions, and related processes are described in detail. On this basis, the initial values for the first two iterations are determined with the meteorological data being made full use of in the six degrees of freedom trajectory simulation, and then the firing angle corresponding to a specific range is automatically and iteratively calculated. The efficient method of firing angle calculation for the typical MLRS has been extensively tested with three cases. The results show that the high-order polynomial response surface, the Kriging predictors with Cubic, Gauss, and Spline correlation functions, and the ensemble of above four individual metamodels have better performances for predicting the firing angle under standard atmospheric conditions compared with those of other metamodels under identical conditions, and execution times of the above four individual metamodels with a training sample size of 9000 are all less than 0.9ms, which verifies the effectiveness and feasibility of the proposed method for calculating the firing angle under standard atmospheric conditions. Moreover, the number of iterations is effectively reduced by using the proposed iterative search approach under actual atmospheric conditions. This research can provide guidance for designing the fire control and command control system of the MLRS.

Efficient seismic reliability analysis of large-scale coupled systems including epistemic and aleatory uncertainties

Reliability analysis of large coupled systems is a challenging task in dam safety. Not only the number of random variables is increased, but also a complex numerical model makes the simulations computationally expensive. To overcome this problem, an efficient analytical model should be developed which does not affect the accuracy of reliability analysis. In this paper, a gravity dam-foundation-reservoir coupled system is taken as a vehicle for the numerical simulations. Epistemic (i.e. material) uncertainties, as well as the ground motion record-to-record variability (i.e. aleatory) are incorporated in the simulations. A new reliability technique is proposed and its efficiency is compared to the Latin Hypercube Sampling (LHS). In this technique, a continuous probability density function is replaced by a finite number of fractional moments. Furthermore, an improved bivariate dimension reduction method is developed for dynamic systems. Several parametric simulations are performed to investigate the impact of the reservoir water level and the dam size. Results of the proposed method are in good agreement with the LHS. Finally, a response surface meta-model is proposed to estimate the dam behavior as a function of ground motion intensity measures.

A Consistent Procedure Using Response Surface Methodology to Identify Stiffness Properties of Connections in Machine Tools.

Accurate finite element models of mechanical systems are fundamental resources to perform structural analyses at the design stage. However, uncertainties in material properties, boundary conditions, or connections give rise to discrepancies between the real and predicted dynamic characteristics. Therefore, it is necessary to improve these models in order to achieve a better fit. This paper presents a systematic three-step procedure to update the finite element (FE) models of machine tools with numerous uncertainties in connections, which integrates statistical, numerical, and experimental techniques. The first step is the gradual application of fractional factorial designs, followed by an analysis of the variance to determine the significant variables that affect each dynamic response. Then, quadratic response surface meta-models, including only significant terms, which relate the design parameters to the modal responses are obtained. Finally, the values of the updated design variables are identified using the previous regression equations and experimental modal data. This work demonstrates that the integrated procedure gives rise to FE models whose dynamic responses closely agree with the experimental measurements, despite the large number of uncertainties, and at an acceptable computational cost.

MCS-based response surface metamodels and optimal design of experiments for gravity dams

Deterministic seismic analysis of dam-foundation-water does not usually reflect the true behavior of the system due to presence of different epistemic uncertainties. On the other hand, the crude Monte Carlo simulation (CMCS) of such a system is computationally expensive and often practically impossible. This paper investigates the potential application of so-called design of experiments (DOE) in order to develop appropriate metamodels and present an explicit expression of dam response. More than ten DOE techniques are compared and contrasted. Accuracy of metamodels is evaluated using about 120,000 finite element simulations from CMCS. Furthermore, the application of several sampling reduction techniques (i.e. Latin Hypercube, Sobol, and Halton) is evaluated. Next, the impact of polynomial degree is studied for an actual gravity dam with five random variables. Results are generalised for 12 different dam classes where the displacements, stresses and failure modes are quantified. Last but not least, a metamodel is proposed for seismic uncertainty of gravity dam in which the dam response is estimated using different features of the input ground motions.

Taguchi design-based seismic reliability analysis of geostructures

ABSTRACTThis paper presents a methodology to evaluate the seismic reliability of geostructures in an optimal way. Taguchi design of experiments are adopted to find the most efficient and cost-effective combination of material properties in the uncertainty domain. Twelve uniform and mixed design models are tested. A polynomial-based response surface meta-model is built for each one and the accuracy of perdition is examined using 10,000 Monte Carlo simulations. A two-dimensional gravity dam is used as a vehicle for probabilistic transient analyses. The ground motion record-to-record variability is added as well using over one hundred earthquake records selected based on probabilistic seismic hazard analysis. Dynamic sensitivity of epistemic random variables are evaluated for the first time. Finally, an efficient and practical procedure is proposed in order to determine the reliability index of the geostructures. This approach, in fact, can be generalised for any type of engineering structures dealing with multi-hazard problems.

Response surface approach to robust design of assembly cells through simulation

PurposeThis paper aims to present a multi-response robust design (RD) optimization approach for U-shaped assembly cells (ACs) with multi-functional walking-workers by using operational design (OD) factors in a simulation setting. The proposed methodology incorporated the design factors related to the operation of ACs into an RD framework. Utilization of OD factors provided a practical design approach for ACs addressing system robustness without modifying the cell structure.Design/methodology/approachTaguchi’s design philosophy and response surface meta-models have been combined for robust simulation optimization (SO). Multiple performance measures have been considered for the study and concurrently optimized by using a multi-response optimization (MRO) approach. Simulation setting provided flexibility in experimental design selection and facilitated experiments by avoiding cost and time constraints in real-world experiments.FindingsThe present approach is illustrated through RD of an AC for performance measures: average throughput time, average WIP inventory and cycle time. Findings are in line with expectations that a significant reduction in performance variability is attainable by trading-off optimality for robustness. Reductions in expected performance (optimality) values are negligible in comparison to reductions in performance variability (robustness).Practical implicationsACs designed for robustness are more likely to meet design objectives once they are implemented, preventing changes or roll-backs. Successful implementations serve as examples to shop-floor personnel alleviating issues such as operator/supervisor resistance and scepticism, encouraging participation and facilitating teamwork.Originality/valueACs include many activities related to cell operation which can be used for performance optimization. The proposed framework is a realistic design approach using OD factors and considering system stochasticity in terms of noise factors for RD optimization through simulation. To the best of the authors’ knowledge, it is the first time a multi-response RD optimization approach for U-shaped manual ACs with multi-functional walking-workers using factors related to AC operation is proposed.

Response Surface Method for Material Uncertainty Quantification of Infrastructures

Recently, probabilistic simulations became an inseparable part of risk analysis. Managers and stakeholders prefer to make their decision knowing the existing uncertainties in the system. Nonlinear dynamic analysis and design of infrastructures are affected by two main uncertainty sources, i.e., epistemic and aleatory. In the present paper, the epistemic uncertainty is addressed in the context of material randomness. An old ultra‐high arch dam is selected as a vehicle for numerical analyses. Four material properties are selected as random variables in the coupled dam‐reservoir‐foundation system, i.e., concrete elasticity, mass density, compressive (and tensile) strength, and the rock modulus of elasticity. The efficient Box‐Behnken experimental design is adopted to minimize the required simulations. A response surface metamodel is developed for the system based on different outputs, i.e., displacement and damage index. The polynomial‐based response surface model is subsequently validated with a large number of simulations based on Latin Hypercube sampling. Results confirm the high accuracy of proposed technique in material uncertainty quantification.

Gradient-Free Trust-Region-Based Adaptive Response Surface Method for Expensive Aircraft Optimization

This paper presents a novel gradient-free trust region assisted adaptive response surface method for aircraft optimization problems with expensive functions. A gradient-free trust region sampling space approach is developed for design space reduction and sequential sampling, and response surface metamodel refitting enables the trust region assisted adaptive response surface method to possess higher optimization efficiency and better global convergence capability. Besides, an election sequential Latin hypercube sampling method is developed to improve the space-filling property and feasibility of the sequential samples. Moreover, the augmented Lagrangian method is employed to handle expensive constraints. The trust region assisted adaptive response surface method outperforms several adaptive response surface metamodel variants in the comparative study on a number of benchmark problems. Additionally, compared with several other well-known metamodel-based global optimization algorithms, the proposed algorithm also shows favorable performance in global convergence, efficiency, and robustness. Next, the trust region assisted adaptive response surface method is successfully applied to solve an airfoil aerodynamic optimization problem based on computational fluid dynamics simulation to demonstrate its effectiveness for real-world engineering problems. Finally, limitations of the proposed method and future work are discussed.

Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation

Stochastic kriging (SK) methodology has been known as an effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. In this paper we provide some theoretical results on the predictive performance of SK, in light of which novel integrated mean squared error-based sequential design strategies are proposed to apply SK for mean response surface metamodeling with a fixed simulation budget. Through numerical examples of different features, we show that SK with the proposed strategies applied holds great promise for achieving high predictive accuracy by striking a good balance between exploration and exploitation.

Probabilistic seismic restoration cost estimation for transportation infrastructure portfolios with an emphasis on curved steel I-girder bridges

This paper develops a rapid probabilistic seismic restoration cost estimate framework for transportation infrastructures (i.e., bridge portfolios) by integrating Response Surface Metamodels (RSMs) coupled with Monte Carlo Simulation (MCS) into seismic restoration cost curve generation. A portfolio of curved steel I-girder bridges located in the Eastern United States is used for this study. As part of the restoration curve generation, joint RSM-MCS models are created and utilized to assess seismic vulnerabilities of the target bridge portfolio and estimate their damage ratios. Probabilistic damage factor models in conjunction with MCS to treat uncertainties in damage ratios, curved bridge characteristics, and volatile construction conditions are simulated with the joint RSM-MCS-based vulnerability functions. Relevant restoration cost curves are then generated based upon average construction cost data of the United States. Findings reveal that characteristics for the restoration curves vary relying on variability in damage ratios and vulnerabilities, emphasizing that an increase in the difference between lower and upper cost bounds occurs as the seismic intensity increases. This evidence highlights the significance of considering variability in both damage ratios and vulnerabilities for more reliable decision-making for seismic restoration on such bridge portfolios.