Seismic Response Of Structures Research Articles

Seismic fragility assessment of multistory precast concrete parking structures

In this study, fragility and collapse mechanisms of multistory precast concrete parking structures were assessed. The variation of a set of structural parameters was considered, including shear stiffness and tensile stiffness of connectors, number of stories, and two orthogonal directions of the seismic action. A probabilistic analysis based on fragility curves was regarded a robust technique for assessing the influence of these parameters on the expected seismic performance. Additionally, fragility curves were obtained using the SPO2FRAG procedure. The results indicate that variation of the considered parameters significantly affects the seismic response and seismic fragilities of precast concrete parking structures.

Genetic algorithm model of PEC column-steel plate shear wall with flush end-plate joints based on component method

The partially encased concrete (PEC) column-steel beam frame steel plate shear wall (SPSW) structure of semi-rigid joint has good cooperative working performance and seismic performance. In this paper, based on the EC3 component model, considering the contribution of the new concrete components in the PEC column to the initial rotational stiffness of the joint domain, the component model of the flush end-plate PEC column joint was established. A 1/3-scale two-story single-span flush end-plate PEC column-steel beam frame SPSW structure was tested under quasi-static cyclic loading. The OpenSees model of this structure was established, which was validated by test results. Parametric analysis of the additional damping ratio for semi-rigid joints was conducted using OpenSees. The suggested value of additional damping ratios for semi-rigid joints was given. Finally, based on Matlab and OpenSees, the model was input in the form of tool command language (TCL), an optimal arrangement model of flush end-plate PEC column joints with the genetic algorithm (GA) as the main procedure was designed. The effects of different arrangement schemes of semi-rigid joints on the seismic response of PEC column-steel beam frame SPSW structures were analyzed. The results show that the seismic performance of the flush end-plate PEC column-steel beam frame SPSW structures is reliable. The results of the finite element (FE) are in good agreement with the test results, which indicates that the established OpenSees model is effective. The contribution of the new concrete components to the initial rotational stiffness of the middle joints, top and bottom joints is 45.02% and 49.68%, respectively. The optimal arrangement scheme of semi-rigid joints can be efficiently computed by the proposed GA model.

Effects of tuned liquid dampers on the nonlinear seismic responses of high-rise structures using real-time hybrid simulations

Tuned liquid dampers (TLDs) are effective passive-control devices used to suppress wind-induced vibrations and the seismic responses of high-rise structures. However, investigations on the effects of TLDs on nonlinear structural responses are limited; thus, this study explored the influence of a TLD on the nonlinear seismic response of a high-rise structure based on a real-time hybrid simulation. The effects of the TLD on the nonlinear seismic response were evaluated in terms of the characteristics of seismic excitations, the TLD mass ratio, and the structural damping ratio. The experimental results revealed that the TLD was helpful in reducing hysteretic energy dissipation of the controlled structure. Moreover, when the structure entered the nonlinear state, the damping frequency band of the TLD became narrower, aggravating the effect of the TLD on structural damping relative to that in the linear case. Meanwhile, the results also indicated that structural nonlinearity could increase the possibility of adverse effects on the structural dynamic response.

Nonparametric probabilistic seismic demand model and fragility analysis of subway stations using deep learning techniques

A novel and computationally efficient method for developing a nonparametric probabilistic seismic demand model (PSDM) is proposed to conduct the fragility analysis of subway stations accurately and efficiently. The probability density evolution method (PDEM) is used to calculate the evolutionary probability density function of demand measure (DM) without resort to any assumptions of the distribution pattern of DM. To reduce the computational cost of a large amount of nonlinear time history analyses (NLTHAs) in the PDEM, the one-dimensional convolutional neural network (1D-CNN) is used as a surrogate model to predict the time history of structural seismic responses in a data-driven fashion. The proposed nonparametric PSDM is adopted to conduct the fragility analysis of a two-story and three-span subway station, and the results are compared with those from two existing parametric PSDMs, i.e., two-parameter lognormal distribution model and probabilistic neural network (PNN)-based PSDM. The results show that the PDEM-based PSDM has the best performance in describing the probability distribution of seismic responses of underground structures. Different from the fragility curves, the time-dependent fragility surface of the subway station shows how the exceedance probability of damage state changes over time. It can be used to estimate the escape time and thus the number of casualties in an earthquake, which are important indexes when conducting the resilience-based seismic evaluation.

The optimum design of particle tuned mass damper for structural seismic control considering soil-structure interaction

Particle tuned mass damper has received considerable attention on mitigating structural seismic responses recently. However, soil-structure interaction effects have not been considered for the optimization design of particle tuned mass damper in the previous studies yet, which may play significant roles in particle tuned mass damper’s effectiveness. This paper investigates the seismic control performance of particle tuned mass damper for tall buildings considering SSI effects. A 40-story benchmark structure is adopted as the primary structure, and different soil conditions including soft, medium, dense soil, and the fixed-base case are considered. Based on the Cuckoo Search algorithm, an optimum design approach for the particle tuned mass damper implemented in SSI system under earthquake excitations is proposed, and the optimum parameters of particle tuned mass damper are obtained from the optimum design process. The optimum results indicate that the optimized particle tuned mass damper can effectively decrease the displacement response without the increase of peak acceleration, and the reduction rates could exceed 30% in some cases. Compared with other soil type cases, under soft soil condition, the optimum parameters of particle tuned mass damper are especially different, and the mitigation effects of the optimized particle tuned mass damper on maximum displacement weaken. Hence, it is necessary to consider the SSI effects for particle tuned mass damper’s seismic design. Furthermore, the interaction effects between the primary structure and particle tuned mass damper in SSI system are also evaluated through energy analysis. The results show that considering SSI effects, the optimized particle tuned mass damper device dissipates the overwhelming majority of the input energy, and it greatly decreases the structural energy, displaying excellent energy dissipation performance on seismic vibration control of structure.

Combination of physics‐based and data‐driven modeling for nonlinear structural seismic response prediction through deep residual learning

AbstractDespite great progress in seeking accurate numerical approximator to nonlinear structural seismic response prediction using deep learning approaches, tedious training process and large volume of structural response data under earthquakes for training and validation are often prohibitively accessible. In our methodology, the main innovation can be seen in the incorporation of deep neural networks (DNNs) into a classical numerical integration method by using a hybridized integration time‐stepper. In this way, the linear physics information of the structure and the obscure nonlinear dynamics are smoothly combined. We propose to use residual network (ResNet) to learn time‐stepping schemes specifically for the nonlinear state variables of the system. Our Physics‐DNN hybridized integration (PDHI) time‐stepping scheme provides important advantages over current pure data‐driven approaches, including (i) a flexible framework incorporating known time‐invariant physics information, (ii) requirement of structural seismic response data being circumvented by simple short bursts of trajectories collected from underlying nonlinear components, and (iii) efficiency in training and validation process. Besides, our results indicate that a simple feedforward or convolutional architecture outperforms recurrent networks to fulfill the requirement of prediction accuracy as well as long‐range memory in structural dynamic analysis. Several numerical and experimental examples are presented to demonstrate the performance of the method.

Nonlinear gas-spring DVA for seismic response control: Experiment and numerical simulation

A gas-spring with adjustable nonlinear capacity is introduced into a conventional linear dynamic vibration absorber (DVA), thus forming a nonlinear gas-spring dynamic vibration absorber for structural seismic response control, which is a nonlinear energy sink with a fundamental tuning function. The mechanical properties of the symmetrical combined gas-spring system are studied first by theoretical analysis and model tests. A series of shaking table tests are designed and conducted to systematically investigate the control effect and nonlinear damping mechanism of the gas-spring DVA for a 5-story structure. A numerical model of the nonlinear gas-spring DVA attached to the structure is established and validated by the experimental results. The experimental results show that the proposed nonlinear gas-spring DVA can effectively mitigate the structural dynamic responses and has a wide damping bandwidth with good stability. The presented system has amplitude-frequency characteristics, and the sensitivity of its control performance to amplitude is significantly reduced by introducing a fundamental tuning mechanism. The nonlinear DVA vibrates in a broadband mode and is capable of resonating with the structure at multiple frequencies so that the nonlinear restoring force of the gas-spring DVA redistributes the structure’s vibration energy from its low-order modes to high-order modes. Compared with the optimum tuning DVA, the reasonably designed nonlinear gas-spring DVA has a similar control effect and shorter working stroke, possessing the advantage of flexible parameter configuration capabilities. Moreover, the experimental and numerical simulation results are in good agreement, indicating that the proposed numerical model is accurate in predicting the behaviors of the nonlinear gas-spring DVA.

Seismic damage characteristics and evaluation of aboveground-underground coupled structures

Aboveground-underground coupled structures (AUCSs) integrate aboveground multitowers, podiums, and large underground structures. The complex structural composition and connection forms enhance structure-structure and soil-structure interactions and result in a complicated structural seismic damage condition. The different dynamic characteristics of aboveground and underground structures make it difficult to select optimal seismic intensity measures (IMs) for the seismic damage evaluation of the AUCS. A refined nonlinear finite element model of the AUCS considering soil-structure interactions is established in this paper. Near-fault pulse-type and far-field ground motions are selected as seismic inputs. The structural seismic failure and its influencing factors, including ground motion characteristics and structural coupling interactions, are thoroughly examined. Numerical results demonstrated that structural seismic damage and weak positions are associated with the embedded effects induced by the podium and the underground structure. The structural failure begins at the column of the podium, and the failure modes are associated with the ground motion characteristics. The coupling interactions between towers are beneficial for reducing the seismic response of the AUCS. The wave scattering caused by the underground structure amplifies the seismic response of the aboveground structure as seismic intensity increases. A stability criterion for optimal IM selection is proposed, which evaluates changes in seismic response dispersion after the structure enters the plastic stage and can reflect the influence of dynamic characteristics of the AUCS on IM selection. Statistical results showed that the peak ground velocity and the root mean square velocity are optimal IMs for the evaluation of seismic damage of the AUCS.

Shake table tests on 1:2 reduced scale masonry house with the application of horizontal seismic bands

The safety of people's lives is crucial in structures that provide shelter. Earthquakes are a major natural disaster that have claimed thousands of lives over the years, but other factors can also cause damage to these structures. Building collapses are often due to their inability to endure the seismic loading, not the earthquake itself. Most residential buildings are masonry structures. There are many strategies for enhancing structural behavior, but very little research has been done on masonry structures, which house about 1/3rd of the world's population. This study focuses on characterization of seismic response using shake table tests to assess the dynamic behavior of masonry structures when horizontal seismic bands are applied. Horizontal seismic band is one of the traditional techniques used in masonry structure. Three reduced scale models were constructed with one using a reinforced concrete band, one with a timber band, and one without a band. All models were constructed using extruded earth block and mud mortar, common building materials in developing nations. The models were tested on a shake table using the same loading signal to compare their response behavior. A high-speed camera was also used to capture images; accelerometers and displacement sensors were installed to record the response. Digital Image Correlation (DIC), which provides non-contact optical measurement, has been essential in obtaining full-field measurement. The results showed significant improvement in the seismic response of structures with horizontal seismic bands. The behaviors are compared in terms of natural frequency, damping, energy dissipation, and crack propagation patterns using two types of materials as seismic bands.

Stochastic Optimization of Dissipation Structures Based on Lyapunov Differential Equations and the Full Stress Design Method

This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for the damping system under the excitation of a nonstationary stochastic process using two types of modulation functions: g(t)=1 and g(t)=t. Finally, the optimal damping arrangement is achieved using this method with a six-layer non-eccentric planar frame. In addition, the optimization results of this study are verified with those in the literature using time-history analysis, which verifies the feasibility and effectiveness of the proposed method. This study provides a method for the optimal configuration of dampers for seismic response of structures, which is beneficial for engineering applications and the protection of seismic structures.

Shaking table test study of nuclear power plant model considering soil-structure interaction effect

The influence analysis of site condition is fundamental to the seismic design of nuclear power plants. In this paper, a series of shaking table tests were performed to investigate the Soil-Structure Interaction (SSI) effect on the seismic response of nuclear power structures. An AP1000 nuclear power plant was taken as the objective structure, lead rubber bearings (LRBs) were used as the isolators and Shanghai silty clay was selected as the model soil. Test results show that (1) The soil has different effects on the dynamic characteristics of isolated and non-isolated model structures. (2) During the shaking table test, the foundation edge is subject to the highest soil pressure, and a contact surface separation between the foundation and the soil begins to occur under the seismic-margin earthquake (SME) seismic input level. (3) Both for the rigid and soil foundation, seismic isolation bearings can effectively reduce the acceleration response of the superstructure. (4) For the non-isolated model, the SSI effect significantly amplifies the seismic response at the bottom floor of the structure in the low frequency range, and an obvious rocking behavior occurs at the operating basis earthquake (OBE) seismic input level. (5) For the isolated model, the SSI effect reduces the hysteresis capacity of the seismic isolation system and amplifies the seismic response at the bottom floor, especially in the vertical direction. The site condition and the use of an isolation system have a significant impact on the seismic response of a nuclear power structure. Therefore, in the design and safety assessment of nuclear power plants, the influences of soil characteristics and isolation equipment in the soil-structure interaction system should be fully considered.

Prediction of nonlinear seismic response of underground structures in single- and multi-layered soil profiles using a deep gated recurrent network

A deep learning method consisting of the gated recurrent (GRU) neural network is proposed to predict the seismic responses of underground structures in single-layered soil and multi-layered soil. The proposed neural network employed ground motion as the input, and the acceleration time history of underground structure acquired by a finite element method (FEM) to be the output. The distribution of the normalized errors and the error of the peak value of the predicted acceleration time history are adopted to evaluate the prediction performance and extrapolating ability of the proposed GRU architecture. The GRU network showed better prediction performance in the seismic response of a tunnel in a homogeneous sand layer than in a clay layer, as sand has a higher shear modulus representing lower nonlinearity of the soil-structure system. The peak acceleration of a two-story three-span subway station in multi-layered soil exhibited similar prediction accuracy to the tunnel in single-layered clay. The proposed GRU neural network generally displayed satisfactory prediction performances on the acceleration responses of underground structures in various soil conditions.

Effect of parameters associated with soil-to-structure relative stiffness on seismic fragility curves of subway station

Seismic response and vulnerability of subway station underground structures are greatly influenced by kinematic soil-structure interaction, which is a function of soil properties and stiffness. Therefore, this paper investigates the influence of parameters associated with soil-to-structure relative stiffness (F) on the seismic fragility curves of underground structures. Incremental dynamic analysis method is conducted employing finite element analysis to establish the fragility curves of the station structure considering 44 earthquake records. The soil was simulated as a two-dimensional (2D) finite element domain and its nonlinear behavior is described employing the Davidenkov constitutive model. Appropriate plasticity models simulated the nonlinearity of concrete and reinforcing rebars. It was found that the failure probability of the structure decreases significantly as soil shear wave velocity increases, and the change of probability of structural failure was quantified for changes in shear wave velocity within the range 200 m/s to 600 m/s. It was also found that the failure probability of subway station in heterogeneous soil is significantly higher than that of a structure buried in homogeneous soil. On the other hand, the cross-section type of the structure has less influence on its seismic vulnerability. The seismic performance of the structure with higher F is relatively better, while there are special cases where some structures with high F that are more susceptible to failure under earthquake than structures with lower F. The findings can provide helpful guide for the performance-based seismic design of underground structures.

Time-Frequency Feature-Based Seismic Response Prediction Neural Network Model for Building Structures

Currently, machine learning techniques are widely used in structural seismic response studies. The developed network models for various types of seismic response provide new ways to analyse seismic hazards. However, it is not easy to balance the applicability of the input, accuracy, and computational efficiency for existing network models. In this paper, a neural network model containing an efficient self-adaptive feature extraction module (AFEM) is designed. It can recognize time-frequency features from ground motion (GM) inputs for structural seismic response prediction tasks while considering the model’s computational accuracy and computational cost. The self-adaptive feature extraction module is constructed based on the MFCCs feature extraction process in NLP. AFEM recognizes time-frequency features closely related to structures’ behaviour and response under dynamic loads. Taking the seismic response prediction of a typical building as the target task, the neural network configuration, including a baseline model M0 and three comparison models (M1, M2, and M3) with AFEM, is systematically analysed. The results demonstrate that the proposed M1 model with initial AFEM, the M2 model with combined amplitude and phase features, and the M3 model with a complex-valued network are more adaptable than the baseline model to the target task. The extracted amplitude and phase features by the M3 model’s AFEM significantly improve model validation accuracy by 8.6% while reducing computation time by 11.4%. It could provide the basis for future research on regional earthquake damage intelligence assessment systems.

Effect of a symmetric V‐shaped canyon on the seismic response of an adjacent building under oblique incident SH waves

AbstractTo elucidate whether an irregular topography affects the seismic response of nearby structures, an analytical solution to the dynamic interaction between a symmetric V‐shaped canyon and an adjacent building under the incidence of SH waves is proposed by using the wave function expansion method. The dynamic canyon‐soil‐structure interaction is decomposed into two problems of scattering and radiation. The building is idealized as a shear wall supported by a semicircular rigid foundation. The analytical solution can be degenerated theoretically to the canonical model of a shear wall embedded in a half‐space for either a zero depth‐to‐width ratio of the canyon or an infinite canyon‐building distance. Through a numerical comparison with two past exact solutions to the sole shear wall model as well as the sole V‐shaped canyon model, the correctness of the method in this paper is verified. A systematic parametrical analysis in both frequency and time domains is performed. It is found that the seismic response of the building may be amplified when it is on the wave‐facing side of the canyon. The degree of amplification is closely related to the size and depth‐to‐width ratio of canyon, the wave velocity of half‐space, and the incident angle and frequency content of seismic waves. The potential adverse effects of the V‐shaped canyon on the ground motion input of adjacent buildings should be considered in the seismic design.

Comparative Assessment of Variable Loads and Seismic Actions on Bridges: A Case Study in Italy Using a Multimodal Approach

The structural safety of the infrastructure stock is an important issue in modern seismic performance assessments. Following recent seismic events, reports have highlighted the increased vulnerability of physical infrastructural assets, particularly for many bridges across the Italian road and motorway network. Italy possesses one of the most complex and intricate road systems in Europe which was constructed across irregular territories in terms of plan and elevation and of varying dimensions. As such, a comparative case study is presented herein. This case study aims to characterise the seismic vulnerability of the Vizzana-Zampogna viaduct which is part of the A15 Parma-La Spezia motorway, near the locality of Selva Bocchetto. The viaduct is considered representative of the 1970s construction period. It is approximately 342 m in length and is characterized by a flat curvilinear prestressed concrete deck consisting of 15 spans simply supported on reinforced concrete piers. To better understand the seismic structural response of the individual piers of the viaduct, a “multi-modal” nonlinear static analysis was developed, which allows the effects of sectional stresses relative to the variable load profiles of the single modes to be combined through the quadratic modal combination, and to be compared with the relevant limit state. The research aims to qualitatively identify the piers most vulnerable to seismic action and to study the effects that are induced by introducing variable loads and intensity scenarios of different earthquakes.

Seismic performance and fragility of two-story and three-span underground structures using a random forest model and a new damage description method

This paper proposes a new method for evaluating the seismic performance and fragility of large underground structures. A typical underground subway station consisting of a two-story and three-span structure was used as the research subject. Considering the variation of sites and the uncertainty of input ground motions, we developed a finite element model of a nonlinear dynamic soil-underground structure interaction system. Based on the incremental dynamic analysis method, the nonlinear seismic responses of the subway station structure were calculated for 900 cases. Python (software) was used to accelerate the processing of the large number of numerical simulation data. Based on the seismic damage characteristics of an underground structure, this paper proposes a new concept of average seismic damage value to evaluate the damage condition of the underground structure to overcome the inadequacies induced by an expert’s intuitive judgment. Meanwhile, the random forest prediction model was adopted to predict the seismic performance levels (SPLs) of the underground structure, and a non-parametric test was performed to verify the correlation between the degree of seismic damage and the inter-story drift ratios (IDR) of the large underground structure. This proved that the IDR could describe the seismic damage of shallow-buried underground structures; we advanced a precise quantification system of the SPL for shallow-buried subway station structures with two-story and three-span using probability statistics. The peak ground velocity (PGV) is more suitable than the peak ground acceleration (PGA) for use as the seismic intensity measure (IM) for large underground structures when the stiffness of the soil foundation becomes soft. In addition, the seismic fragility curves of the shallow-buried subway station structure were constructed and analyzed using the developed quantification system for the SPL.

Ranking method of the severest input ground motion for underground structures based on composite ground motion intensity measures

Underground structure seismic response analyses and structural safety seismic designs are based on the scientific and reasonable selection of ground motion records. Different input ground motions lead to varies seismic response due to the strong randomness of ground motion. The severest input ground motion for the seismic analysis of underground structures cannot be obtained via a single intensity measure (IM). For this purpose, a ranking method is proposed based on composite IM for the severest input ground motion for underground structures. Four composite ground motion IMs constructed using the partial least squares regression (PLSR) method are proposed as representative ground motion IMs of the seismic failure potential of underground structures. These composite ground motion IMs correspond to the evaluation of four engineering demand parameters (EDPs), including the moment, shear force, axial force, and relative displacement of the central column of a subway station. Elastic-plastic time-history analyses of a two-story three-span subway station are performed given 64 ground motion records to provide the necessary data samples. After the construction, a bilinear logarithmic regression analysis is carried out. The results show that the proposed composite ground motion IMs have a higher correlation with the seismic dynamic responses than single IMs with respect to effectiveness, practicability, and proficiency. Finally, a ranking method for the severest input ground motion based on these composite ground motion intensity parameters is proposed. This method can be used to obtain the severest design ground motion of underground structures for seismic design.

The Effect of Soil-Structure Interaction on the Seismic Response of Structures Using Machine Learning, Finite Element Modeling and ASCE 7-16 Methods.

Seismic design of structures taking into account the soil-structure interaction (SSI) methods is considered to be more efficient, cost effective, and safer then fixed-base designs, in most cases. Finite element methods that use direct equations to solve SSI problems are very popular, but the prices of the software are very high, and the analysis time is very long. Even though some low-cost and efficient software are available, the structures are mostly analyzed for the superstructure only, without using the geotechnical properties of the ground and its interaction effects. The reason is that a limited number of researchers have the knowledge of both geotechnical and structural engineering to model accurately the coupled soil-structure system. However, a cost-effective, less time-consuming and easy-to-implement technique is to analyze the structure along with ground properties using machine learning methods. The database techniques using machine learning are robust and provide reliable results. Thus, in this study, machine learning techniques, such as artificial neural networks and support vector machines are used to investigate the effect of soil-structure interactions on the seismic response of structures for different earthquake scenarios. Four frame structures are investigated by varying the soil and seismic properties. In addition, varying sample sizes and different optimization algorithms are used to obtain the best machine learning framework. The input parameters contain both soil and seismic properties, while the outputs consist of three engineering demand parameters. The network is trained using three and five-story buildings and tested on a three-story building with mass irregularity and a four-story building. Furthermore, the proposed method is compared with the dynamic responses obtained using fixed-base and ASCE 7-16 SSI methods. The proposed machine learning method showed better results compared with fixed-base and ASCE 7-16 methods with the nonlinear time history analysis results as a reference.

Surrogate modeling of structural seismic response using probabilistic learning on manifolds

AbstractNonlinear response history analysis (NLRHA) is generally considered to be a reliable and robust method to assess the seismic performance of buildings under strong ground motions. While NLRHA is fairly straightforward to evaluate individual structures for a select set of ground motions at a specific building site, it becomes less practical for performing large numbers of analyses to evaluate either (1) multiple models of alternative design realizations with a site‐specific set of ground motions, or (2) individual archetype building models at multiple sites with multiple sets of ground motions. In this regard, surrogate models offer an alternative to running repeated NLRHAs for variable design realizations or ground motions. In this paper, a recently developed surrogate modeling technique, called probabilistic learning on manifolds (PLoM), is presented to estimate structural seismic response. Essentially, the PLoM method provides an efficient stochastic model to develop mappings between random variables, which can then be used to efficiently estimate the structural responses for systems with variations in design/modeling parameters or ground motion characteristics. The PLoM algorithm is introduced and then used in two case studies of 12‐story buildings for estimating probability distributions of structural responses. The first example focuses on the mapping between variable design parameters of a multidegree‐of‐freedom analysis model and its peak story drift and acceleration responses. The second example applies the PLoM technique to estimate structural responses for variations in site‐specific ground motion characteristics. In both examples, training data sets are generated for orthogonal input parameter grids, and test data sets are developed for input parameters with prescribed statistical distributions. Validation studies are performed to examine the accuracy and efficiency of the PLoM models. Overall, both examples show good agreement between the PLoM model estimates and verification data sets. Moreover, in contrast to other common surrogate modeling techniques, the PLoM model is able to preserve correlation structure between peak responses. Parametric studies are conducted to understand the influence of different PLoM tuning parameters on its prediction accuracy.