Uncertainties In Structural Parameters Research Articles

Generalized system restoration models of ductility bridges for seismic resilience analysis

System restoration models are usually adopted for seismic resilience analysis of bridges. However, no analytical process can be found in the existing literature to develop the restoration models for bridges. This paper proposed a new Monte Carlo-based method to derive the generalized system restoration models for ductility highway bridges. In the proposed method, a large number of random samples for ductility bridges were generated by considering uncertainty of structural parameters. The IDA was adopted for producing the damaged bridge samples at different damage states. The repair time of each bridge sample was estimated to generate the actual restoration curve. The Monte Carlo simulations were then adopted to estimate the expected mean functionality curves, which were used to derive the generalized system restoration models by using mathematical functions. Finally, seismic resilience analysis based on the derived generalized system restoration models was conducted and compared with the traditional method to illustrate the effectiveness of the proposed method. It is concluded that the proposed Monte Carlo-based method is an efficient and reliable method for developing the restoration models for ductility highway bridges.

Dynamic uncertainty propagation analysis framework for nonlinear control problem based on manifold learning and optimal polynomial method and its application on active suspension system

A novel uncertainty propagation method based on manifold learning and optimal polynomial model is proposed to quantify and analyze the dynamic uncertainties of the nonlinear feedback control system. To deal with the multiple objectives and constraints of the nonlinear control problem, a barrier Lyapunov-function-based nonlinear filtered backstepping controller is developed and applied to active suspension system to obtain superior ride comfort performance under limited structural constraints. Considering the errors in the production, manufacturing, and assembly, the probability density function is employed to quantify the structural parameter uncertainties in the nonlinear control system. Moreover, to reveal the dynamic propagation mechanism of uncertainties in the system with nonlinearity, the manifold learning method is proposed to reduce the dimensionality of the dynamic system to avoid the complexity of uncertainty propagation. Simultaneously, data-driven optimal polynomial model is utilized to accurately approximate the internal mechanism of nonlinear filtered backstepping control system. Based on that, the response uncertainties of the nonlinear control system are accurately and quickly quantified through dynamic moment information and uncertain fluctuation space. Finally, an active suspension system with nonlinearities and uncertainties is developed to verify the effectiveness of the controller with improved ride comfort and better handling safety and the superiority of the framework in terms of efficiency and accuracy of the dynamic uncertainty propagation analysis for nonlinear control problem.

Fragility evaluation of bridge shallow foundation piers under floods by coupling simulation in structural and hydraulic fields

The erosion of soil around bridge shallow foundation piers can substantially increase the fragility of bridges during flood events. The available research for assessing the fragility of shallow foundation piers under floods is predominantly qualitative, while ignoring the influence of coupling effects arising from complex hydrodynamic-soil-structure interactions. To fill these gaps, a numerical solver for coupled simulations accounting for hydrodynamic-soil-structure interaction is developed, facilitating boundary conversions for different physical fields and updating them over time. The numerical solver is validated in terms of subgrade reactions, pier displacements and scour extent based on the results of open-channel tests of a reference shallow foundation pier. The validation results show that the developed coupled solver has satisfactory accuracy in predicting the morphology of scour-hole and failure process of shallow foundation piers. Then all potential failure modes of shallow foundation piers under floods are analyzed within the framework of deterministic analysis. Finally, a probabilistic fragility analysis using the coupled solver accounting for uncertainties in hydraulic, structural, and geological parameters is performed through the Latin Hypercube Sampling method. The study concludes that the deterministic analysis without considering the uncertainties in model parameters leads to underestimating the risk due to overturning failure and vertical failure.

Dynamic Seismic Probabilistic Risk Assessment of Nuclear Power Plants Using Advanced Structural Methodologies

The conditional core damage probability (CCDP) of a representative nuclear power plant is estimated for a beyond design basis earthquake (BDBE) using state-of-the-art structural models within a dynamic probabilistic risk assessment (DPRA) framework. Randomness of seismic excitation and uncertainty of structural parameters are considered using a simulation-based approach. Finite element models are developed for the structure and a liquid container (hydro-accumulator), and fluid–structure interaction is considered with the arbitrary Lagrangian-Eulerian method. The CCDP is evaluated through a time-dependent event tree. Also, correlation among multiple hydro-accumulators is investigated. The results show that operator action and implementation time of mobile safety equipment are critical under BDBE in case of loss of offsite power following an earthquake. It was also found necessary to adopt a DPRA approach to determine the available time for action and core damage timing probabilistically.

Hierarchical and mixed uncertainty quantification for simulation-based structural seismic fragility analysis

Seismic fragility assessments (SFA) encompass significant uncertainties, including ground motions, materials, geometry, boundaries, and modeling, which impart inherent uncertainties to the fragility curve. Quantifying these uncertainties is essential for informed decision-making in earthquake disaster mitigation. This paper presents a hierarchical uncertainty quantification (UQ) framework for simulation-based SFA, which can address mixed aleatory and epistemic uncertainties. The framework comprises two levels: At Level 1, ground motion uncertainties are accounted for through record-to-record variation, while structural parameter uncertainties are captured using well-defined probability distributions. The quantification of uncertainty in seismic fragility is accomplished using mean and quantile fragility curves, representing the average outcome and the dispersion of structural fragility, respectively. Fuzziness is also introduced to enhance the objectivity of failure determination. Level 2 addresses uncertainties in the distribution hyper-parameters of structural variables through evidence theory, facilitating an understanding of their influence on the seismic fragility curve and quantifying uncertainty in mean and quantile fragility curves. This UQ framework builds upon the multivariate seismic fragility analysis method, integrating Kriging regression for seismic demand prediction and logistic regression for generating multivariate seismic fragility functions. The proposed framework is validated numerically on an existing three-span reinforced concrete continuous girder bridge, affirming its practical utility and reliability.

Propagation of Modelling Uncertainties for Seismic Risk Assessment: The Effect of Sampling Techniques on Low-Rise Non-Ductile RC Frames

ABSTRACT Quantifying the impact of modelling uncertainty on seismic performance assessment of existing buildings is non-trivial when considering the partial information available on material properties, construction details, and the uncertainty in the capacity models. This task is further complicated when uncertainty related to ground motion representation is considered. To address this issue, record-to-record variability, uncertainties in structural model parameters, and fragility model parameters due to limited sample size are propagated herein by employing a nonlinear dynamic analysis procedure based on recorded ground motions. A one-to-one sampling approach is adopted in which each recorded ground motion is paired up with a different structural model realization. Uncertainty propagation is explored by measuring the impact of different sampling techniques, such as Monte Carlo simulation with standard random sampling and Latin Hypercube sampling (with Simulated Annealing) in the presence of three alternative nonlinear dynamic analysis procedures: Incremental Dynamic Analysis (IDA), Modified Cloud Analysis (MCA), and Cloud to IDA (a highly efficient IDA-like procedure). This is all illustrated through application to an existing reinforced-concrete school building in southern Italy. It is shown that with a small subset of records, both MCA and Cloud to IDA can provide reliable structural fragility (and risk) estimates for three considered limit states, comparable to the results of more resource-intensive schemes.

Efficient strategy for topology optimization of stochastic viscoelastic damping structures

In this study, the dynamic topology optimization (TO) of stochastic viscoelastic damping structures (VDSs) is performed for the first time. However, the expensive computation cost seriously hinders the TO process. To address this problem, an efficient strategy is proposed. On the one hand, in the stochastic structural response analysis, a fully adaptive method based on direct probability integral method is presented to determine the number and locations of samples. Meanwhile, to improve the computational efficiency of structural response for each sample, a piecewise model-order reduction method based on Krylov subspace is adopted to generate the orthonormal basis and project the original large-scale system onto a low-order system. On the other hand, to overcome the optimization challenge arising from large number of design variables in the density-based topology method, a material-field series-expansion method is employed to describe the topology layout and significantly reduce the number of design variables. Moreover, the sensitivity of the optimization model is derived by the adjoint method and the method of moving asymptotes (MMA) is used to efficiently update the design variables. Some numerical examples comprehensively demonstrate the effectiveness and efficiency of the proposed strategy. The results indicate that the uncertainty of structural parameters greatly affect both the topology layout of VDS and vibration damping capacity.

Response analysis of asymmetric monostable energy harvester with an uncertain parameter

The nonlinear piezoelectric vibration energy harvesting system offers a solution to the power supply challenge for low-power sensors. However, In practical engineering, structural parameter uncertainties arise from manufacturing errors, environmental temperature fluctuations, and changes in material properties. Besides, due to inherent flaws in the structure and materials, asymmetry may occur in the potential well, which leads to the complexity of the dynamic behavior exhibited in energy harvesting system. In this paper, in order to investigate the dynamics of the asymmetric monostable piezoelectric energy harvesting system under an uncertain parameter, the orthogonal polynomial approximation method is applied to transform the stochastic system into an equivalent deterministic system. Then, the responses of the equivalent deterministic system are used to reveal the stochastic behavior of the uncertainty system. The results indicate that, when the uncertainty intensity of the cubic nonlinear coefficient is 0, an increase in the asymmetry level of the potential well leads to an increase in the output voltage. Increasing the other parameters, the output voltage is reduced. In addition, as the uncertainty intensity increases, the parameter intervals of chaotic response become wider and the energy harvesting efficiency decreases. Moreover, as the potential well asymmetry increases, the sensitivity of energy harvesting system to uncertain parameter increases.

Mechanical analysis for deepwater drilling riser system with structural parameters uncertainty

Uncertain structural parameters increase the mechanical failure risk of the drilling riser system. The effect of uncertain structural parameters on the mechanical characteristics of the drilling riser system is unclear. Therefore, the mechanical characteristics of the drilling riser system with structural parameter uncertainty are analyzed. A mechanical model with uncertain structural parameters is established based on the basic analysis model and the local average theory. The basic analysis model takes into account the combined effects of platform motion, tensioner, riser string, and marine environment. The local average theory is suitable for situations where there is a lack of uncertainty information. A solution approach is proposed using the second-order central perturbation method and the Newmark-β method. The solution method reduces the load by simplifying degrees of freedom and random variables. The correctness of the solution method is verified using the Monte Carlo method. The analysis results indicate that uncertain structural parameters significantly affect the static response, while the dynamic response is less affected. The failure risk due to static axial stress and static shear stress is heightened by uncertain structural parameters. The failure risk arising from static shear stress at the bottom of the riser system experiences a significant increase.

Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings

This paper presents a comprehensive study on the spectral properties of mimetic finite-difference operators and their application in the robust fluid–structure interaction (FSI) analysis of aircraft wings under uncertain operating conditions. By delving into the eigenvalue behavior of mimetic Laplacian operators and extending the analysis to stochastic settings, we develop a novel stochastic mimetic framework tailored for addressing uncertainties inherent in the fluid dynamics and structural mechanics of aircraft wings. The framework integrates random matrix theory with mimetic discretization methods, enabling the incorporation of uncertainties in fluid properties, structural parameters, and coupling conditions at the fluid–structure interface. Through spectral and localization analysis of the coupled stochastic mimetic operator, we assess the system’s stability, sensitivity to perturbations, and computational efficiency. Our results highlight the potential of the stochastic mimetic approach for enhancing reliability and robustness in the design of aircraft wings, paving the way for optimization algorithms that integrate uncertainties directly into the design process. Our findings reveal a significant impact of stochastic perturbations on the spectral radius and eigenfunction localization, indicating heightened system sensitivity. The introduction of randomized singular value decomposition (RSVD) within our framework not only enhances computational efficiency but also preserves accuracy in low-rank approximations, which is critical for handling large-scale systems. Moreover, Monte Carlo simulations validate the robustness of our stochastic mimetic framework, showcasing its efficacy in capturing the nuanced dynamics of FSI under uncertainty. This study contributes to the fields of numerical methods and aerospace engineering by offering a rigorous and scalable approach for conducting uncertainty-aware FSI analysis, which is crucial for the development of safer and more efficient aircraft.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Bayesian finite element model updating techniques have found widespread application in the structural health monitoring. The conventional Bayesian modeling framework (CBMF) identifies the posterior distribution of structural parameters using data from a single experiment. However, structural parameters exhibit variability due to changes in environmental or experimental conditions, an aspect overlooked by CBMF. In recent years, the hierarchical Bayesian modeling framework (HBMF) has gradually attracted attention. This framework incorporates an additional layer of hyperparameters and utilizes multiple sets of experimental data to describe the variability in structural parameters caused by changes in experimental conditions. Unfortunately, the increase in hyperparameters and data size leads the HBMF to face the dilemma of exceedingly high computational costs. To address this issue, this study proposes an improved hierarchical Bayesian modeling framework (IHBMF). To enhance the computational efficiency of IHBMF, the importance sampling method is employed to simplify the computation of the likelihood function for hyperparameters. Subsequently, a surrogate model based on arbitrary polynomial chaos expansion is introduced to further reduce the computational cost of IHBMF. The framework's accuracy and efficiency were validated through analysis of a simply supported beam and a steel pedestrian bridge. The results demonstrate that IHBMF not only delivers a more accurate quantification of structural parameter uncertainty than CBMF but also exhibits higher computational efficiency compared to HBMF, showcasing its superior capability in structural health monitoring applications.

Multi-factors effects analysis of nonlinear vibration of FG-GNPRC membrane using machine learning

Functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) have exhibited significant potential for the development of high-performance and multifunctional structures. In this paper, we present a machine learning (ML) assisted uncertainty analysis of nonlinear vibration of FG-GNPRC membranes under the influence of multi-factor coupling. Effective medium theory (EMT), Mori-Tanaka (MT) model and rule of mixture are utilized to evaluate the effective material properties of the composite membrane. Governing equations are derived via an energy method with the frameworks of the hyperelastic membrane theory, Neo-Hookean constitutive model and the couple dielectric theory. Randomly generated inputs after data pre-processing are fed into governing equations, which are solved by numerical methods for outputs. Three ML models, including artificial neural network (ANN), support vector regression (SVR) and AutoGluon-Tabular (AGT), are adopted to capture the complex relationship between the systematic inputs (i.e., structural dimensions, attributes of GNPs and pores, external electric field, etc.), frequency ratio and dimensionless amplitude of FG-GNPRC membranes. The results demonstrate that all three ML models demonstrate exceptional computational efficiency, and AGT presents higher prediction accuracy compared to the other two models. Based on the Shapley additive explanations (SHAP) approach, the effects of uncertainties of system parameters and multi-factor coupling on the nonlinear vibration of the FG-GNPRC membrane are analyzed. It is found that the uncertainty of structural parameters has the greatest impact on the nonlinear vibration of FG-GNPRC membranes, particularly when the membrane is subjected to a voltage of 10 V and smaller stretching ratio.

Endothelial cells signaling and patterning under hypoxia: a mechanistic integrative computational model including the Notch-Dll4 pathway.

Introduction: Several signaling pathways are activated during hypoxia to promote angiogenesis, leading to endothelial cell patterning, interaction, and downstream signaling. Understanding the mechanistic signaling differences between endothelial cells under normoxia and hypoxia and their response to different stimuli can guide therapies to modulate angiogenesis. We present a novel mechanistic model of interacting endothelial cells, including the main pathways involved in angiogenesis. Methods: We calibrate and fit the model parameters based on well-established modeling techniques that include structural and practical parameter identifiability, uncertainty quantification, and global sensitivity. Results: Our results indicate that the main pathways involved in patterning tip and stalk endothelial cells under hypoxia differ, and the time under hypoxia interferes with how different stimuli affect patterning. Additionally, our simulations indicate that Notch signaling might regulate vascular permeability and establish different Nitric Oxide release patterns for tip/stalk cells. Following simulations with various stimuli, our model suggests that factors such as time under hypoxia and oxygen availability must be considered for EC pattern control. Discussion: This project provides insights into the signaling and patterning of endothelial cells under various oxygen levels and stimulation by VEGFA and is our first integrative approach toward achieving EC control as a method for improving angiogenesis. Overall, our model provides a computational framework that can be built on to test angiogenesis-related therapies by modulation of different pathways, such as the Notch pathway.

Seismic resilience assessment of extended pile shaft supported coastal bridges considering scour and uniform corrosion effects

The resilience-informed assessment for coastal highway bridges exposed to multiple hazards plays a crucial role in the decision-making process for their operation, maintenance, and management during the bridge’s long-term service period. This study performs a seismic resilience assessment for a coastal reinforced concrete (RC) bridge under the combined effects of scour and uniform corrosion. Toward this goal, an extended pile shaft supported coastal RC bridge is taken as the benchmark and fifteen scenarios are generated to cover three regular scour conditions and five different corrosion levels. To inform the bridge management, the probabilistic distribution of the bridge service time corresponding to different corrosion levels is developed. Subsequently, the finite element model (FEM) for each scenario of the benchmark coastal highway RC bridge is developed, involving the soil-pile interaction and considering the uncertainty of structural and geotechnical parameters, as well as earthquake ground motions. The failure mode of the corroded extended pile shaft is identified as a flexural failure by comparing their flexural and shear capacities. Finally, a resilience loss ratio is proposed in this study for the first time to quantify the impacts of corrosion level and scour depth changes on seismic resilience across different ground motion intensities. Results indicate that both the seismic fragility and resilience decrease as the corrosion intensifies over time. Specifically, at a given intensity measure (IM) level, the resilience loss ratio increases as the corrosion level intensifies. For the studied benchmark bridge, the scour significantly increases the structural fundamental period, consequently reducing the curvature demand on the pile shaft. As a result, the scour generally decreases the failure probability and the earthquake-induced functionality loss for the extended pile shaft. As scour depth increases, the resilience loss of the bridge at a given corrosion level decreases.

Machine learning aided uncertainty analysis on nonlinear vibration of cracked FG-GNPRC dielectric beam

Functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) have shown significant potential for the development of high-performance and multifunctional materials and structures. Conducting an accurate analysis of the nonlinear vibration of FG-GNPRC dielectric beams can accelerate their application in various engineering fields. To investigate the nonlinear vibration of FG-GNPRC dielectric beams, the effective material properties of a cracked composite beams are evaluated using effective medium theory (EMT) and the rule of mixture. Three ML models adopted in this work, i.e., artificial neural network (ANN), random forest (RF), and AutoGluon (AG), are used to capture the complex relationship between the systematic inputs (i.e., parameters for materials and structure, the attributes of electrical field, etc.) and frequency ratio of the cracked FG-GNPRC beams. Moreover, shapley additive explanations (SHAP) is employed for the analysis of the nonlinear vibration of FG-GNPRC dielectric beams considering the influence of multi-factor coupling and uncertainties. The SHAP analysis suggests that the uncertainty of structural parameters has the greatest impact on the nonlinear vibration of FG-GNPRC dielectric beams, particularly when the structure is subjected to a voltage of 40 V.

Uncertainty of digital fringe projection measurement caused by structural parameters

Digital fringe projection (DFP) has been widely applied in three-dimensional (3D) precision measurement owing to its advantages of non-contact, high-precision, and large-field measurement. The DFP measurement system undergoes a calibration process to define the parameters that reconstruct the surface points from the camera images. As the DFP system is nonlinear, evaluating the measurement uncertainty caused by the calibration deviation of the structural parameters is a great challenge. In this study, we performed an uncertainty analysis based on the binocular vision model of a DFP system. A virtual DFP system based on the structural parameters of the actual system was built to remove the influence of other uncertainty factors. The adaptive Monte Carlo method (AMCM) was used to evaluate the uncertainty caused by the deviation of the parameters during calibration. The model and method for calculating the uncertainty of the DFP system proposed in this study are helpful in better understanding the propagation of the uncertainty of structural parameters, determining the critical factors affecting the measurement uncertainty, and providing a theoretical basis for subsequent error compensation and accuracy improvement for DFP measurement systems.

Angle resolved x-ray photoelectron spectroscopy assessment of the structure and composition of nanofilms—including uncertainties—through the multilayer model

The multilayer model (MLM) for assessing the structural and composition parameters of multilayered nanofilms from angle-resolved x-ray photoelectric spectroscopy is described in detail. It is compared with regularized back-transform (RBT) approaches such as the maximum entropy method (MEM) with Tikhonov-type regularizations. The advantages of MLM over MEM, such as the possibility of assessing confidence ranges, modeling structures beyond conformal multilayered nanofilms, and modeling abrupt interfaces, are discussed and exemplified. In contrast with MLM, the RBT methods have shortcomings such as the violation of the conservation of information and the inability to adequately address the dependence of the effective attenuation length on the material. Examples of the application of MLM to conformal films and systems with protrusions are shown. The covariance matrix method (CMM) is described and applied to assess uncertainties in structural parameters and composition under the MLM. The CMM constitutes the canonical method for assessing confidence ranges and adequately accounts for the covariance among structural (e.g., layer thicknesses) and composition parameters.

Uncertainty Inverse Analysis of Positioning Accuracy for Error Sources Identification of Industrial Robots

Uncertainties widely exist in modeling parameters of industrial robots due to wear during service. These uncertainties are too small to be directly measured and may severely affect the positioning accuracy of end-effector through multi-stage propagation. An uncertainty inverse analysis method of positioning accuracy is proposed to identify uncertainty of typical structural parameters with the selected optimal position information. The Denavit–Hartenberg method is employed to establish the kinematic model. For the probability uncertainty of modeling parameters, the inverse analysis model, which reflects propagation mapping between uncertain variables and end-effector position response is obtained by first-order second-moment method. The partial-derivative information is used to improve calculation efficiency through removing low-contributing parameters. To further reduce measurement noise interference, orthogonal matching pursuit strategy is presented to search optimal sensor placement with the objectives of maximum coefficient modulus and minimum correlation, then pseudoinverse matrix method is employed to obtain the exact solution of identification equation. Finally, numerical simulation results for 6 degrees-of-freedom robots indicate that the proposed method with improved solution efficiency can accurately identify uncertainties of joint angles within the error 5% under large measurement errors.

Sliding Mode Controller Based on Genetic Algorithm and Simulated Annealing for Assured Crew Reentry Vehicle

A sliding mode (SM) re-entry control system is proposed for an assured crew re-entry vehicle (ACRV). The vehicle has a low lift/drag ratio (0.3). The trajectory controller drives the ACRV in a predefined track. The reference vectors for the attitude controller are generated by the trajectory controller and navigation system. The feedback SM controller is designed to accommodate the structural parametric uncertainties and environmental disturbances. The SM controller is optimized by both the genetic algorithm (GA) and the simulated annealing (SA) methods. A comparative study is done between both optimization methods and the efficiency of the SA method is proved. The system is subjected to a sensitivity study in terms of various thrust torque profiles. A robustness check is done by changing the system parameters. A pulse width pulse frequency (PWPF) modulator modulates the output torque dictated by the attitude controller. The simulation results demonstrate the proposed method’s effectiveness in achieving the various required parameters.

A two-stage uncertainty quantification framework for reliability and sensitivity analysis of structures using the probability density evolution method integrated with the Fréchet-derivative-based method

In this work, a novel Fréchet-derivative-based global sensitivity analysis is incorporated into the probability density evolution method for the simultaneous reliability and sensitivity analysis of structures. The two methods are synthesized and realized under a two-stage uncertainty quantification framework. Fundamental and numerical algorithms of the method are described, which is validated by a benchmark problem with theoretical solutions. Then it is applied on studying stochastic seismic responses of a real-world reinforced concrete structure of 288 m high. Results demonstrate that the response characteristics of the structure will be greatly changed when both uncertainties from the ground motions and structural parameters are considered, e.g., the failure probability will be enlarged by 1∼2 orders of magnitude. Besides, contrary to the popular opinion that the uncertainty of structural parameters is trivial compared to that of parameters in the ground-motion model, the importance measures of the structural parameters can be greater than those of the parameters in the ground-motion model by a factor of 2. when the coupling effect of randomness and nonlinearity of structural materials becomes dramatic. Some issues to be further outlined are also discussed.