Potential of Surrogate Modelling for Probabilistic Fire Analysis of Structures

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

This research work deals with aspects concerned with delamination detection in composite structures as revealed by an approach based on vibration measurements. Variations in vibration characteristics generated in composite laminates indicate the existence of delaminations because degradation due to delamination causes reduction in flexural stiffness and strength of the material and as a result vibration parameters like natural frequency responses are changed. Hence, it is possible to monitor the variation in natural frequencies to identify the presence of delamination, and assess its size and location for online structural health monitoring (SHM). The approach to this paper, therefore, typically depends on undertaking the analysis of structural models implemented by finite element analysis (FEA). The numerical solutions using FE models known as the simulator computes the natural frequencies for the delaminated and undelaminated specimens of composite laminates. However, these FE models are computationally expensive, and surrogate (approximation) models are introduced to curtail the computational expense. The simulator is employed to solve the inverse problem using algorithms based on computational intelligence concepts. An artificial neural network (ANN) model is developed to also solve the inverse problem for delamination detection directly and to provide surrogate models integrated with optimization algorithms (the gradient-based local search and non-dominated sorting genetic algorithm-II) to contain the computationally expensive simulations by FEA. This approach is termed as surrogate assisted optimization and it is seen that the engagement of surrogate models in lieu of the FE models in the optimization loop greatly enhances the accuracy of delamination detection results within an affordable computational cost and provides control over handling different variables. Meanwhile, to aid with the building of effective surrogate models using substantial number of training datasets, K-means clustering algorithm is harnessed and this effectively reduces the large training datasets usually required for ANN training. This paper demonstrated that ANN and optimization algorithms with surrogates show immense potentialities for use in delamination damage detection scenarios. Prediction errors of the algorithms were quantified and they were shown to be satisfactory when applied to previously experimental data. The algorithms in their inverse formulations are capable of predicting accurately delamination parameters. Hence, these algorithms should be employed for application in the domain of SHM where their small computational requirements could be exploited for online damage detection.

This study demonstrates an efficient and precise surrogate model to probabilistically analyze the helical soil nailed walls (HSNWs) under seismic conditions. The modified pseudo-dynamic (MPD) approach is employed which produces realistic results in comparison to its former counterparts. The unit weight (γ), internal friction angle of soil (ϕ), and shear wave velocity (Vs ) are chosen as random variables. The influence of the normalized frequency, damping ratio, and size of the helix on the reliability of HSNW is presented in detail. The plots reveal that the proposed surrogate model is an accurate method with the value of coefficient of determination (R2 ) as 0.99 for the present study. In addition to it, it is 99 times more efficient when compared to the direct Monte-Carlo Simulation (MCS) (50000 iterations). For the same input parameters, the minimum number of helical nails required for a safe reinforced wall are less than the grouted and the driven ones, given their larger pull-out capacity. Moreover, the required number of helical soil nails (HSNs) computed from probabilistic analysis are 42.85% more than the deterministic one for a given set of input parameters which lay a strong base for performing the probabilistic analysis for a precise measure of stability.

Surrogate modeling of joint flood risk across coastal watersheds

Soils show inherent variability due to various physio-chemical, geological and environmental processes. It is necessary to consider soil spatial variability in evaluation and probabilistic design of foundations. However probabilistic frameworks become computationally expensive and infeasible for a complex realistic scenario. This study develops an approach to evaluate the bearing capacity factor of strip footing resting on a spatially varying clayey slope using a Sparse polynomial chaos expansion (SPCE) surrogate model. Non-stationary soil condition is adopted in this study. Initially random fields are generated using KL expansion method considering 95% energy variance terms. This helps to reduce the terms for a random field as input to the SPCE model. The combined model of SPCE with Global Sensitivity analysis (GSA) reduced computational time and cost. This approach is very efficient because the predicted bearing capacity factor is accurate and needs only a smaller number of realizations to train. This makes it computationally time efficient. Meanwhile using any traditional approach, the probabilistic analysis is computationally inefficient in terms of cost and time.

The reliability of a simple turbomachinery model was calculated to demonstrate the application of a newly developing system integration tool, Probabilistic Design and Analysis Framework(PRODAF), along with efficient probabilistic methods using a response surface method. The model represents a system consisting of hypothetical turbine components. The parts include a blade, disk, and shaft with an applied angular velocity. All the components were modeled with the properties of the nickel alloy, Inconel 718. A response surface was calculated for the system of components to improve probabilistic computational efficiency. In addition, a fast probability integration method, Advanced First Order Reliability Method (AFORM), was used for the probabilistic analysis in order to provide an efficient analysis as possible. Geometric dimensions, the applied load, and material yield strength were varied for this study. The probability of failure was determined using the maximum first principal stress response and the material yield strength. A simple G function using the difference between strength and loading stress was used to determine failure limits. The probabilistic sensitivity of the failure response relative to the individual variables was determined also with material yield strength having the greatest influence. The model was recreated with every iteration of the probabilistic analysis in order to vary the geometry. As a result, the response surface method has a significant impact on improving computational efficiency and enabling reliability analysis with rapid turnaround.

Probabilistic safety analysis for urgent situations following the accidental release of a pollutant in the atmosphere

Various sources of uncertain parameters at multiple levels, from design steps to manufacturing processes, are often involved in composite structures. Probabilistic modeling and analysis of the composite structure and its manufacturing processes can provide underlying information to assess uncertainties and improve the quality of the developed composite structures. This paper presents a stochastic multi-level modeling framework considering material, structural, modeling parameters as well as the manufacturing process based on a surrogate model. An enhanced laminate theory is employed to determine the elastic constants of the composite materials considering imperfect bonding among filaments in the manufacturing process. To improve the computational efficiency in simulation-based reliability approach, the evaluation of the structure properties is approximated by employing surrogate models based upon the physics model. To apply the present framework, a case study with a composite laminate beam under three-point bending, which is made through fused deposition modeling, is conducted, and the case study results demonstrate the efficacy of the presented modeling scheme and analysis methodology.

Thermal protection system (TPS) is one of the most important subsystems for vehicle reentry. Because of the uncertainties in thermal loads, material properties, and manufacture tolerances, the thermal response of TPS has strong randomness, which brings great challenges to the engineering design and reliability evaluation. Because the uncertain aerodynamic heating loads are stochastic processes in time history, it is difficult to model them in the conventional surrogate models that usually take scalar random variables as input. This paper thus proposes an effective characterization method that can represent the uncertainties of aerodynamic heating by a set of random variables using Karhunen–Loève expansion. The random variables that describe the uncertainty of thermal loads, material properties, and geometric thickness are taken as inputs for probabilistic analyses. A kriging surrogate model is constructed to solve the transient heat conduction with high accuracy. Taking a typical multilayer TPS as an example, the probabilistic thermal analyses are carried out considering different degrees of heat rate uncertainties. The results show that the uncertainties of aerodynamic heating intensify the randomness of the thermal response of TPS, and thus have a great impact on the thermal reliability. The sensitivities of temperature response to various uncertain parameters are investigated as well, which provide a reference for system design and reliability improvement.

With ever-increasing complexity in Upstream project planning, to ensure decision quality, the dynamics of subsurface resources need to be embedded into concept screening to maintain consistency between the production forecast and development plan. We developed a decision-driven subsurface surrogate model that encapsulates key reservoir dynamics into the machine augmented mathematical technologies for holistic decision recommendation in concept selection and development planning under uncertainties. The surrogate model replicates the essential subsurface dynamics by using a hybrid-approach that takes into accounts both reservoir simulation data and physical first principle. In addition to standalone usage on production forecast for rapid profile screening under resource uncertainties, the subsurface surrogate model is incorporated into mathematical optimization models that simultaneously consider surface network, commercial obligation and project economics etc. to provide alternative concepts under various uncertainties. Our subsurface surrogate model has been applied for decision making on gas gathering system design, field development optimization, field-management timing and sequencing, and field tie-back study etc. Results not only show the capability of surrogate models to enable large scale rapid decision screening, but also bear a close resemblance between the predicted production profiles and the reservoir simulation results when fed with the field operating strategy recommended by our decision models with surrogate dynamics. The study demonstrates the reliability of our surrogate modeling technology on ensuring decision quality and helps build business’ confidence on technology adoption. By further incorporating subsurface uncertainties into surrogate models, the decision makers are provided with: probabilistic analysis of the outcomes, value of information analysis, cost of optionality and flexibility, and holistic project outlook etc. Our decision-driven surrogate modeling technology incorporated in mathematical decision models is the first of its kind for holistic decision support in concept selection and development planning in oil and gas industry, and has full potentials in a variety of asset lines with reliable subsurface performance prediction under uncertainties.

In this paper, an efficient approach is presented for probabilistic power flow analysis of complex structures with parameter uncertainties. A component-based technique is used to generate Reduced-Order Models (ROMs) of low- to mid-frequency vibration and power flow. Using this framework, two techniques are employed for probabilistic vibration power flow analysis: (1) a Locally Linear Interpolation (LLI) method, which is a new response surface construction method that has been specifically developed for probabilistic vibration analysis and (2) the Advanced Mean Value (AMV) method, which is a more general technique from the reliability literature. The advantages and limitations of the LLI method are examined and compared to those of the AMV method with respect to probabilistic power flow analysis. Numerical results are shown for a simple example system, an L-shaped plate, and for an important engineering application, a ground vehicle structure.

Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

Machine learning-based bridge cable damage detection under stochastic effects of corrosion and fire

Using Bayesian deep learning approaches for uncertainty-aware building energy surrogate models

The next edition of the ASCE/SEI 7 standard commences a new and groundbreaking industry-consensus standard of care for structural fire protection in the USA, and other adopting jurisdictions. The default option is termed standard fire resistance design, and is based on a long-standing empirical indexing system that excludes consideration of realistic thermal demands and structural system response. The only permitted alternative to standard fire resistance design is structural fire engineering (SFE), as constituted in the new Appendix E. SFE explicitly evaluates the demand and capacity of structural systems under fire loading in a similar manner as other design loads are treated in structural engineering practice. Due to common misconceptions and lack of industry guidance, designers often erroneously intermingle these two approaches in order to justify structural fire protection variances. To combat this poor practice, recent industry efforts in the USA have focused on formally bifurcating these two design options, and providing specific requirements for the SFE approach.