Multi-fidelity Analysis Research Articles

Seismic fragility estimation through real-time hybrid simulation and surrogate-based multi-fidelity Monte Carlo predictor

The intricate dynamic responses of structures, particularly when confronted with uncertainty, poses significant challenges in constructing reliable analytical models, thus resulting in unreliable fragility assessment. This study presents an approach that integrates data-driven techniques with real-time hybrid simulation (RTHS) to achieve reliable fragility analysis. RTHS data and imprecise surrogate models are fused using a multi-fidelity Monte Carlo predictor (MFMC), yielding unbiased estimations for parameters of fragility curve. The MFMC predictor can be considered as an optimized forecasting tool that harnesses the computational efficiency of low-fidelity simulations and the precision of high-fidelity experiments. RTHS is utilized for obtaining high-fidelity experimental data, part of which is leveraged to establish low-fidelity surrogate models, ultimately enabling multi-fidelity analysis through direct data-to-data analysis. A two-story steel moment-resisting frame equipped with self-centering viscous dampers is used as a proof-of-concept to demonstrate the proposed method. Structural and ground motion uncertainties are incorporated to reflect practical engineering environment. The low-fidelity Kriging models were built using portion of high-fidelity RTHS data. Simulation and experimental investigations were conducted to evaluate the effectiveness and efficiency of the proposed approach. The results suggest that the proposed method provides a promising tool for accurately evaluating seismic fragility, particularly when simulation-based methods are not feasible.

Investigating the Functional Mock-up Interface as a Coupling Framework for the multi-fidelity analysis of nuclear reactors

This paper investigates the use of the Functional Mock-up Interface (FMI) for code coupling in nuclear engineering. The FMI is a standard that defines a container and an interface to exchange dynamic simulation models. It has been developed and refined by several actors over the past two decades. This coupling standard allows seamless integrations of independent objects called Functional Mock-up Units (FMU). Since communication among FMUs is standardized, encapsulating a simulation tool and model within an FMU allows this tool and model to be coupled with any other FMU. This approach is opposed to creating dedicated code-to-code coupling interfaces and enables a more sustainable approach to code coupling in nuclear engineering. The paper showcases the utilization of the FMI standard for the simulation of an operational load-follow scenario in a Lead-cooled Fast Reactor. The primary circuit and balance of the plant are modeled using higher and lower-fidelity codes, respectively, with a third tool employed to model a simplified control system. The paper investigates the pros and cons of the proposed approach by exercising it throughout the following workflow: incorporation of the FMI standard into an existing code; setting up of models using different codes; coupling of these codes based on different architectures; simulation and post-processing of results. As an outcome, implementing an FMI interface presents itself as a judicious long-term investment for simulation software. However, users and developers should be aware of the limited FMI capabilities for the coupling of partial differential equations. In addition, a coupling standard by itself cannot address some difficulties, such as simulation restart, that are associated with the handling of a heterogeneous set of tools.

Parametric model of aircraft external geometry as a component of FAST-OAD aircraft preliminary design system.

Rapid evolutions in fields such as aerospace propulsion, materials engineering, geometry modelling tools or optimization tools provide the opportunity to search for novel configurations of future aircraft in an expanding domain. In order to effectively explore the space of variables of constantly expanding size, one needs tools that give the ability to automate this process. Such a tool is the Future Aircraft Sizing Tool for Overall Aircraft Design or FAST-OAD. FAST-OAD allows for rapid estimation of aircraft size, based on set, so-called Top Level Aircraft Requirements (TLARs) by using multi-disciplinary and multi-fidelity analysis and optimization.An essential component of such a system is a module capable of modelling the external geometry of the calculated case. This article describes an attempt to use a powerful commercial Computer Aided Design software, Siemens NX, to model the aircraft external geometry based on the results of the analysis performed by FAST-OAD. This approach, compared to previous works, brings some limitations but, on the other hand, gives the possibility to base the geometry on a mathematically consistent model and helps to better understand the set of parameters necessary to describe the geometry correctly.The main objective of this research is to provide a tool that allows the automatic generation of aircraft exterior geometry based on the output parameters received from the FAST-OAD package.An additional goal of this activity is to determine the parameter set necessary to properly define the external geometry, but at the same time not containing redundant, dependent geometric parameters. The minimum number of independent parameters necessary to completely describe the external geometry is sought.

Improved Prediction of Aerodynamic Loss Propagation as Entropy Rise in Wind Turbines Using Multifidelity Analysis

Several physics-based enhancements are embedded in a low-fidelity general unducted rotor design analysis tool developed, py_BEM, including the local Reynolds number effect, rotational corrections to airfoil polar, stall delay model, high induction factor correction, polar at large angle of attack, exergetic efficiency calculation and momentum-based loss. A wind turbine rotor is analyzed in high fidelity designed from py_BEM using a 3D blade generator. It is a design derived from the NREL Phase VI rotor. Three design variations are analyzed using steady 3D CFD solutions to demonstrate the effect of geometry on aerodynamics. S809 and NACA 2420 airfoil properties are used for calculating the aerodynamic loading. Momentum, vorticity and energy transport are explained in depth and connected to entropy production as a measure of performance loss. KE dissipation downstream of the rotor is shown to be a significant contributor of entropy rise. Wake analysis demonstrates mixing with the free stream flow, which begins after 3 diameters downstream of the rotor and extends to about 25 diameters until the decay is very small. Vorticity dynamics is investigated using a boundary vorticity flux technique to demonstrate the relationship between streamwise vorticity and lift generated in boundary layers. Drag components are accounted as well. It is demonstrated using rothalpy that shaft power is not only torque multiplied by rotational velocity but a viscous power loss term must also be included. A multifidelity analysis of wind turbine aerodynamics is demonstrated by capturing flow physics at several levels.

Multifidelity Analysis of a Solo Propeller: Entropy Rise Using Vorticity Dynamics and Kinetic Energy Dissipation

Propellers for electric aviation are used in solo- and multirotor applications. Multifidelity analysis with reduced cycle time is crucial to explore several designs for energy minimization and range maximization. A low-fidelity design tool, py_BEM, is developed for design and analysis of a reverse-engineered solo 2-bladed propeller using blade-element momentum theory with physics enhancements including local Reynolds number effect, boundary-layer rotation, airfoil polar at large AoAs and stall delay. Spanwise properties from py_BEM are converted into 3D blade geometry using T-Blade3. S809 and NACA airfoil polar are utilized, obtained by XFOIL. Lift, drag, performance losses, wake analysis, comparison of 3D steady CFD with low fidelity tool, kinetic energy dissipation, entropy and exergy through irreversibility are analyzed. Spanwise thrust and torque comparison between low and high fidelity reveals the effect of blade rotation on the polar. Vorticity dynamics and boundary-vorticity flux methods describe the onset of flow separation and entropy rise. Various components of drag and loss are accounted. The entropy rise in the boundary layer and downstream propagation and mixing out with freestream are demonstrated qualitatively. Irreversibility is accounted downstream of the rotor using the second-law approach to understand the quality of available energy. The performance metrics are within 5% error for both fidelities.

Enhancement of light aircraft 6 DOF simulation using flight test data in longitudinal motion

Abstract This paper proposes a procedure to improve the accuracy of the light aircraft 6 DOF simulation model by implementing model tuning and aerodynamic database correction using flight test data. In this study, the full-scale flight testing of a 2-seater aircraft has been performed in specific longitudinal manoeuver for model enhancement and simulation validation purposes. The baseline simulation model database is constructed using multi-fidelity analysis methods such as wind tunnel (W/T) test, computational fluid dynamic (CFD) and empirical calculation. The enhancement process starts with identifying longitudinal equations of motion for sensitivity analysis, where the effect of crucial parameters is analysed and then adjusted using the model tuning technique. Next, the classical Maximum Likelihood (ML) estimation method is applied to calculate aerodynamic derivatives from flight test data, these parameters are utilised to correct the initial aerodynamic table. A simulation validation process is introduced to evaluate the accuracy of the enhanced 6 DOF simulation model. The presented results demonstrate that the applied enhancement procedure has improved the simulation accuracy in longitudinal motion. The discrepancy between the simulation and flight test response showed significant improvement, which satisfies the regulation tolerance.

Rapid design generation and multifidelity analysis of aircraft structures

There is a huge demand for automation in geometry creation within aerospace industry for multidisciplinary design optimization. Currently, every model is being built independently for each discipline. Thus, any changes in design parameters require updates on all of the models, which is inefficient, time-consuming and prone to deficiencies. A parametric software called ‘Engineering Sketch Pad’ (ESP) is used to resolve this issue. It provides the user with the ability to generate new design concepts through modifying a text file. Another highly demanded feature is data transfer between different fidelity models automatically. The need to transfer loads and/or deformations data from one model to another in order to perform the multi-fidelity analysis. In this project, the load is transferred from the stick model to ribs of the wing to perform static optimization and deformation data from ribs and spars is transferred to stiffened panels to perform buckling optimization. This paper focuses on a novel concept of single click weight optimization of aircraft structural parts and components using a parametric design modeler (i.e., ESP) and the analysis solver (i.e., Nastran). The interface code has been done via a C-program.

Multi-fidelity analysis and uncertainty quantification of beam vibration using co-kriging interpolation method

In this paper, a multi-fidelity surrogate model is created using co-kriging methodology to determine the natural frequencies of beams by combining the fidelities of Euler-Bernoulli (low-fidelity) and Timoshenko (high-fidelity) beam finite element models. This study of free vibration of beams involves uncertainties in material properties. The sampling space for the co-kriging surrogate model is created using an optimal latin hypercube sampling technique. It is shown that the co-kriging surrogate model predicts the natural frequencies with high computational efficiency and accuracy, in the entire design space. The computational efficiency and utility of the multi-fidelity model is demonstrated through its application to a problem of quantifying uncertainties in the natural frequencies of a tapered beam using Monte Carlo Simulation.

A generalized methodology for multidisciplinary design optimization using surrogate modelling and multifidelity analysis

The advantages of multidisciplinary design are well understood, but not yet fully adopted by the industry where methods should be both fast and reliable. For such problems, minimum computational cost while providing global optimality and extensive design information at an early conceptual stage is desired. However, such a complex problem consisting of various objectives and interacting disciplines is associated with a challenging design space. This provides a large pool of possible designs, requiring an efficient exploration scheme with the ability to provide sufficient feedback early in the design process. This paper demonstrates a generalized optimization framework with rapid design space exploration capabilities in which a Multifidelity approach is directly adjusted to the emerging needs of the design. The methodology is developed to be easily applicable and efficient in computationally expensive multidisciplinary problems. To accelerate such a demanding process, Surrogate Based Optimization methods in the form of both Radial Basis Function and Kriging models are employed. In particular, a modification of the standard Kriging approach to account for Multifidelity data inputs is proposed, aiming to increasing its accuracy without increasing its training cost. The surrogate optimization problem is solved by a Particle Swarm Optimization algorithm and two constraint handling methods are implemented. The surrogate model modifications are visually demonstrated in a 1D and 2D test case, while the Rosenbrock and Sellar functions are used to examine the scalability and adaptability behaviour of the method. Our particular Multiobjective formulation is demonstrated in the common RAE2822 airfoil design problem. In this paper, the framework assessment focuses on our infill sampling approach in terms of design and objective space exploration for a given computational cost.

Multi-fidelity analysis and uncertainty quantification of beam vibration using correction response surfaces

A multi-fidelity model for beam vibration is developed by coupling a low-fidelity Euler-Bernoulli beam finite element model with a high-fidelity Timoshenko beam finite element model. Natural frequencies are used as the response measure of the physical system. A second order response surface is created for the low-fidelity Euler-Bernoulli model using the face centered design. Correction response surfaces for multi-fidelity analysis are created by utilizing the high-fidelity finite element predictions and the low-fidelity finite element predictions. It is shown that the multi-fidelity model gives accurate results with high computational efficiency when compared to the high-fidelity finite element model.

Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis

Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis

Multifidelity Analysis of Acoustic Streaming in Forced Convection Heat Transfer

Abstract This research effort is related to the detailed analysis of the temporal evolution of thermal boundary layer(s) under periodic excitations. In the presence of oscillations, the nonlinear interaction leads to the formation of secondary flows, commonly known as acoustic streaming. However, the small spatial scales and the inherent unsteady nature of streaming have presented challenges for prior numerical investigations. In order to address this void in numerical framework, the development of a three-tier numerical approach is presented. As a first layer of fidelity, a laminar model is developed for fluctuations and streaming flow calculations in laminar flows subjected to traveling wave disturbances. At the next level of fidelity, two-dimensional (2D) U-RANS simulations are conducted across both laminar and turbulent flow regimes. This is geared toward extending the parameter space obtained from laminar model to turbulent flow conditions. As the third level of fidelity, temporally and spatially resolved direct numerical simulation (DNS) simulations are conducted to simulate the application relevant compressible flow environment. The exemplary findings indicate that in certain parameter space, both enhancement and reduction in heat transfer can be obtained through acoustic streaming. Moreover, the extent of heat transfer modulations is greater than alterations in wall shear, thereby surpassing Reynolds analogy.

Buckling surrogate-based optimization framework for hierarchical stiffened composite shells by enhanced variance reduction method

The surrogate-based optimization of hierarchical stiffened composite shells against buckling is a typical multimodal and multivariables optimization problem. To improve the computational efficiency and global optimizing ability of the surrogate-based optimization of hierarchical stiffened composite shells, an enhanced variance reduction method based on Latinized partially stratified sampling and multifidelity analysis methods is proposed in this paper and then integrated into the surrogate-based optimization framework. In the offline step of the optimization framework, candidate pairing strategies of design variables are generated by Latinized partially stratified sampling and compared by performing priori optimizations based on the low-fidelity analysis method, and the optimal pairing strategy is therefore determined. On the basis of the optimal pairing strategy, the surrogate-based optimization is carried out using the high-fidelity analysis method in the online step. With less computational cost in the offline step, the proposed enhanced variance reduction method overcomes the limitation of Latinized partially stratified sampling that the optimal pairing strategy is not obvious in complex problems. Then, extensive optimization examples are carried out to verify the efficiency and effectiveness of the proposed optimization framework. Given an approximate computational cost, the optimal buckling result of the proposed framework using enhanced variance reduction method increases by 18.2% than that of the traditional framework based on Latin hypercube sampling. In particular, the advantage of enhanced variance reduction method in the space-filling ability is highlighted in comparison to Latin hypercube sampling. When achieving an approximate global optimal solution, the proposed framework reduces the total computational cost by 76.3% than the traditional framework. Finally, the numerical implementation of asymptotic homogenization method is used herein for the accurate prediction of effective stiffness coefficients of the initial design and optimal results. Through comparison, it is concluded that the high axial stiffness and bending stiffness are the main mechanism for the high load-carrying capacity of optimal results.

Multi-fidelity modeling framework for nonlinear unsteady aerodynamics of airfoils

• Unsteady multi-fidelity framework for nonlinear aerodynamics is proposed. • Data fusion is introduced to improve the efficiency of model construction. • The correction term is represented by a neural network model. • The framework gives accurate prediction with data from only three harmonic motions . • The framework outperforms reduced-order models when high-fidelity data is limited. Aerodynamic data can be obtained from different sources, which vary in fidelity, availability and cost. As the fidelity of data increases, the cost of data acquisition usually becomes higher. Therefore, to obtain accurate unsteady aerodynamic model with very low cost and the desired level of accuracy, this paper proposes an unsteady multi-fidelity aerodynamic modeling framework. The approach integrates ideas from data fusion, multi-fidelity modeling, nonlinear system identification and machine learning. Data fusion reduces the total cost of data generation for model construction, while multi-fidelity modeling with a nonlinear autoregressive with exogenous input (NARX) description provides a general framework for unsteady aerodynamics. The correction term from the low-fidelity model to the high-fidelity result is then identified by a machine learning approach, i.e., a multi-kernel neural network. To validate the proposed method, unsteady aerodynamics of a NACA0012 airfoil pitching at Mach number 0.8 is modeled. The high-fidelity data is obtained from a Navier–Stokes-equation-based solver, while the low-fidelity solution is taken from an Euler-equation-based flow solver. The main difference between two types of data is that the high-fidelity solution takes into account the viscous effect, while the low-fidelity solution is based the invisicid flow assumption. Besides, to mimic the practical situation where high-fidelity data are limited in amount and diversity due to high cost (e.g., the experimental condition), only three high-fidelity unsteady aerodynamic solutions from harmonic motion are available. After performing a multi-fidelity analysis on a typical harmonic motion, the model is applied to the prediction of aerodynamic loads from either new harmonic motions or random motions. The multi-fidelity model shows a good agreement with the high-fidelity solution, indicating that by using only a few high-fidelity data and a low-fidelity model, high-fidelity results can be accurately reproduced. Furthermore, the model convergence with respect to increasing training data, and the comparison with a single high-fidelity reduced-order model (ROM) are also studied. The proposed approach becomes more accurate as the number of high-fidelity samples increases, and outperforms a single aerodynamic ROM in most of test cases. Compared with ROM method, additional computational cost for the proposed approach is small, therefore the total time cost of model training is still low.

Model-Based Verification of Security and Non-Functional Behavior using AADL

Modeling of system quality attributes, including security, is often done with low fidelity software models and disjointed architectural specifications by various engineers using their own specialized notations. These models are typically not maintained or documented throughout the life cycle and make it difficult to obtain a system view. However, a single-source architecture model of the system that is annotated with analysis-specific information allows changes to the architecture to be reflected in the various analysis models with little effort. We describe how model-based development using the Architecture Analysis and Design Language (AADL) and compatible analysis tools provides the platform for multi-dimensional, multi-fidelity analysis and verification. A special emphasis is given to analysis approaches using Bell-LaPadula, Biba, and MILS approaches to security and that enable a system designer to exercise various architectural design options for confidentiality and data integrity prior to system realization.

Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems.

Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

陽的縮約に基づくマルチフィデリティ解析モデルによる複合領域配置設計最適化法（放熱特性を考慮した配置設計問題への適用）

Multi-fidelity analysis has been used for reducing the calculation cost of evaluating the design solution, which is the most costly process in design optimization. In general, multi-fidelity analysis is applied to problems with continuous design variables, which are suitable to construct an approximate model of design space such as the response surface. On the other hand, combinatorial optimization problems, e.g., layout design, are difficult to apply the conventional multi-fidelity analysis, since the response surface cannot be constructed due to the property of the design variables. In this paper, we propose a multi-fidelity optimization method independent of the response surface and a simple analysis model for the method, and apply them to multi-disciplinary optimal layout design problem which is a complicated combinatorial optimization problem. The proposed analytical model, which adopts the concept of the explicit method, realizes for reducing the calculation time by simplifying the physical phenomenon. Then, the multi-fidelity optimization method is constructed by combining the proposed analysis model with the thermal network method which is a well-known thermal analysis method. We confirm that there is a strong correlation between the calculation result of the proposed analysis model and of a CAE software, and show that the proposed analysis model is suitable as a low fidelity model. The effectiveness of the proposed optimization method is demonstrated through numerical experiments.

An efficient low-speed airfoil design optimization process using multi-fidelity analysis for UAV flying wing

This paper proposes an efficient low-speed airfoil selection and design optimization process using multi-fidelity analysis for a long endurance Unmanned Aerial Vehicle (UAV) flying wing. The developed process includes the low speed airfoil database construction, airfoil selection and design optimization steps based on the given design requirements. The multi-fidelity analysis solvers including the panel method and computational fluid dynamics (CFD) are presented to analyze the low speed airfoil aerodynamic characteristics accurately and perform inverse airfoil design optimization effectively without any noticeable turnaround time in the early aircraft design stage. The unconventional flying wing UAV design shows poor reaction in longitudinal stability. However, It has low parasite drag, long endurance, and better performance. The multi-fidelity analysis solvers are validated for the E387 and CAL2463m airfoil compared to the wind tunnel test data. Then, 29 low speed airfoils for flying wing UAV are constructed by using the multi-fidelity solvers. The weighting score method is used to select the appropriate airfoil for the given design requirements. The selected airfoil is used as a baseline for the inverse airfoil design optimization step to refine and obtain the optimal airfoil configuration. The implementation of proposed method is applied for the real flying-wing UAV airfoil design case to demonstrate the effectiveness and feasibility of the proposed method.

Enhanced multi-fidelity model for flight simulation using global exploration and the Kriging method

Using the global exploration and Kriging-based multi-fidelity analysis methods, this study developed a multi-fidelity aerodynamic database for use in the performance analysis of flight vehicles and for use in flight simulations. Athena vortex lattice, a program based on vortex lattice method, was used as the low-fidelity analysis tool in the multi-fidelity analysis method. The in-house high-fidelity AADL-3D code was based on the Navier–Stokes equations. The AADL-3D code was validated by comparing the data and the analysis results of the Onera M-6 wing and NACA TN 3649. The design of experiment method and the Kriging method were applied to integrate low- and high-fidelity analysis results. General data tendencies were established from the low-fidelity analysis results. The high-fidelity analysis results and the Kriging method were used to generate a surrogate model, from which the low-fidelity analysis results were interpolated. To reduce repeated calculations, three design points were simultaneously added for each calculation. The convergence of three design points was avoided by considering only the peak points as additional design points. The reliability of the final surrogate model was determined by applying the leave-one-out cross-validation method and by obtaining the cross-validation root mean square error. Using the multi-fidelity model developed in this study, a multi-fidelity aerodynamic database was constructed for use in the three degrees of freedom flight simulation of flight vehicles.

Application of Multidisciplinary Systems‐of‐Systems Optimization to an Aircraft Design Problem

ABSTRACTA generic mathematical formulation for Systems‐of‐Systems (SoS) optimization problems is presented. SoS optimization problems resemble the structure of a tree of Multidisciplinary Design Optimization (MDO) problems with additional unique features. The framework for solving such problems involves features from evolutionary computing, platform‐based design, and evolving design spaces. One important aspect of SoS Engineering, often overlooked, is the role it plays in improving the design of individual systems. In this vein, this work has sought to exemplify such a synergistic approach for aircraft design. A large‐scale SoS optimization problem for designing noise‐optimal aircraft and improved procedures for the approach phase is studied. Modules involving Computational Fluid Dynamics (CFD), noise modeling, multifidelity analysis, topology optimization, and autotuned control systems are used to obtain optimal solutions.