Neural Network Surrogate Model Research Articles

Reliability‐Based Fatigue Life Prediction for Complex Structure with Time‐Varying Surrogate Modeling

To improve the computational efficiency and accuracy of reliability‐based fatigue life prediction for complex structure, a time‐varying particle swarm optimization‐ (PSO‐) based general regression neural network (GRNN) surrogate model (called as TV/PSO‐GRNN) is developed. By integrating the proposed space‐filling Latin hypercube sampling technique and PSO‐GRNN regression function, the mathematical model of TV/PSO‐GRNN is studied. The reliability‐based fatigue life prediction framework is illustrated in respect of the TV/PSO‐GRNN surrogate model. Moreover, the reliability‐based fatigue life prediction of an aircraft turbine blisk under multiphysics interaction is performed to validate the TV/PSO‐GRNN model. We obtain the distributional characteristics, reliability degree, and sensitivity degree of fatigue failure cycle, which are useful for the turbine blisk design. By comparing the direct simulation (FE/FV model), RSM, GRNN, PSO‐GRNN, and TV/PSO‐GRNN, we observe that the TV/PSO‐GRNN surrogate model is promising to perform the reliability‐based fatigue life prediction of the turbine blisk and enhance the computational efficiency while ensuring an acceptable computational accuracy. The efforts of this study offer a useful insight for the reliability‐based design optimization of complex structure.

Optimized Blade Design of Counter-Rotating-Type Pump-Turbine Unit Operating in Pump and Turbine Modes

In this study, a counter-rotating-type pump-turbine unit was optimized to improve the pump and turbine mode efficiencies simultaneously. Numerical analysis was carried out by solving three-dimensional Reynolds-averaged Navier–Stokes equations using the shear stress turbulence model. The hub and tip blade angles of the rear impeller (in the pump mode) were selected as the design variables by conducting a sensitivity test. An optimization process based on steady flow analysis was conducted using a radial basis neural network surrogate model with Latin hypercube sampling. The pump and turbine mode efficiencies of the unit were selected as the objective functions and they combined into a single specific objective function with the weighting factors. Consequently, the pump and turbine mode efficiencies of the optimum design increased simultaneously at overall range of flow rate, except for low flow rate of turbine mode, compared to the reference design.

Surrogate based modeling and optimization of plasmonic thin film organic solar cells

In this study, we demonstrate that surrogate models can be trained and used to accurately predict the optical properties of thin film solar cells and to optimize their structures. We consider organic an active thin film poly(3-hexylthiophene):(6,6)-phenyl-C61-butyric-acid-methyl ester (P3HT:PCBM) layer coated by indium-free highly conductivepolymer poly (3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT:PSS) on top with aluminum as cathode, and study optical absorptivity enhancement of such a structure when embedded with periodic spherical silver nano-particles. Metallic nano-structures, including textures, gratings and particles are known to induce plasmonic effects on the surface and inside absorbing semiconductors, thereby increasing light trapping in thin film cells. However, design of such structures requires precise characterization of the dependencies of electromagnetic field distribution to geometry parameters and material choices. Optical properties of structures at sub-wavelength scales are measured by numerically solving first principle electromagnetic equations, e.g., by means of finite difference time domain (FDTD) method. These methods are time-consuming, and therefore limit the possibility of exhaustive optimization. Surrogate modeling can be used to overcome this challenge. In the present work, we design a two-layer neural network (NN) surrogate model to estimate the optical absorptivity of the cell for any given geometry vector as well as any radiation wavelength and incident angle. Training of the network is done using the Levenberg–Marquardt (LM) method with generalization techniques such as early stopping and Bayesian regularization using a pool of training and validation data. The resulting surrogate model is first demonstrated to yield accurate out-of-sample estimation of absorptivity. Then, the model is used to investigate the individual contributions of each input by means of sensitivity analysis. In addition, optimization of the parameters is efficiently done using the surrogate model for different source light irradiance spectra and incident angles. Resulting optimizations are very efficient. At the end, solutions found by surrogate-based optimization demonstrate enhancement factors greater than 270% for optical absorptivity.

Hydropower Optimization Using Artificial Neural Network Surrogate Models of a High‐Fidelity Hydrodynamics and Water Quality Model

AbstractHydropower operations optimization subject to environmental constraints is limited by challenges associated with dimensionality and spatial and temporal resolution. The need for high‐fidelity hydrodynamic and water quality models within optimization schemes is driven by improved computational capabilities, increased requirements to meet specific points of compliance with greater resolution, and the need to optimize operations of not just single reservoirs but systems of reservoirs. This study describes an important advancement for computing hourly power generation schemes for a hydropower reservoir using high‐fidelity models, surrogate modeling techniques, and optimization methods. The predictive power of the high‐fidelity hydrodynamic and water quality model CE‐QUAL‐W2 is successfully emulated by an artificial neural network, then integrated into a genetic algorithm optimization approach to maximize hydropower generation subject to constraints on dam operations and water quality. This methodology is applied to a multipurpose reservoir near Nashville, Tennessee, USA. The model successfully reproduced high‐fidelity reservoir information while enabling 6.8% and 6.6% increases in hydropower production value relative to actual operations for dissolved oxygen (DO) limits of 5 and 6 mg/L, respectively, while witnessing an expected decrease in power generation at more restrictive DO constraints. Exploration of simultaneous temperature and DO constraints revealed capability to address multiple water quality constraints at specified locations. The reduced computational requirements of the new modeling approach demonstrated an ability to provide decision support for reservoir operations scheduling while maintaining high‐fidelity hydrodynamic and water quality information as part of the optimization decision support routines.

Optimization design of energy deposition on single expansion ramp nozzle

Optimization design has been widely used in the aerodynamic design process of scramjets. The single expansion ramp nozzle is an important component for scramjets to produces most of thrust force. A new concept of increasing the aerodynamics of the scramjet nozzle with energy deposition is presented. The essence of the method is to create a heated region in the inner flow field of the scramjet nozzle. In the current study, the two-dimensional coupled implicit compressible Reynolds Averaged Navier–Stokes and Menter's shear stress transport turbulence model have been applied to numerically simulate the flow fields of the single expansion ramp nozzle with and without energy deposition. The numerical results show that the proposal of energy deposition can be an effective method to increase force characteristics of the scramjet nozzle, the thrust coefficient CT increase by 6.94% and lift coefficient CN decrease by 26.89%. Further, the non-dominated sorting genetic algorithm coupled with the Radial Basis Function neural network surrogate model has been employed to determine optimum location and density of the energy deposition. The thrust coefficient CT and lift coefficient CN are selected as objective functions, and the sampling points are obtained numerically by using a Latin hypercube design method. The optimized thrust coefficient CT further increase by 1.94%, meanwhile, the optimized lift coefficient CN further decrease by 15.02% respectively. At the same time, the optimized performances are in good and reasonable agreement with the numerical predictions. The findings suggest that scramjet nozzle design and performance can benefit from the application of energy deposition.

Surrogate-enhanced stochastic search algorithms to identify implicitly defined functions for reliability analysis

The paper proposes two adaptive stochastic search algorithms to locate and trace an implicitly defined function with samples that are used to construct a surrogate model for reliability analysis. Both methods begin by propagating a series of surrogate-informed stochastic processes toward the implicit performance function. Having located the function, the first method conducts a “global” tracing of the function while the second traces the function by propagating samples locally. A key feature of both proposed algorithms is that the surrogate model evolves continuously with the sample selection and is used to inform the selection of new samples such that it converges rapidly to an accurate representation of the limit surface. In the present implementation, an artificial neural network surrogate model is employed but the method can, in principle, be applied with any surrogate model form. Performance of the algorithms is illustrated through problems with highly nonlinear limit state functions and high dimensional non-Gaussian random variables.

Aerodynamic and aeroacoustic optimization for design of a forward-curved blades centrifugal fan

This paper presents a multidisciplinary optimization procedure for enhancing the aerodynamic and aeroacoustic performance of a forward-curved blade centrifugal fan for residential ventilation. Flow analysis in a forward-curved blade centrifugal fan was conducted by solving three-dimensional steady and unsteady Reynolds-averaged Navier–Stokes equations using the shear stress transport turbulence model. On the basis of the aerodynamic sources extracted from the unsteady flow, aeroacoustic analysis was implemented in a finite/infinite element method by solving the variational formulation of Lighthill’s analogy. Experiments were performed to obtain aerodynamic and aeroacoustic measurements for validation of numerical results. The single- and multi-objective optimizations were performed sequentially. The single-objective optimization was carried out to improve the efficiency of the fan using a radial basis neural network surrogate model with four design variables defining the scroll cut-off angle, scroll diffuser expansion angle, diameter ratio of the impeller, and blade exit angle. Multi-objective optimization based on the single-objective optimization result was carried out to simultaneously improve the efficiency and reduce the sound pressure through a hybrid multi-objective evolutionary algorithm coupled with a response surface approximation surrogate model with two design variables defining the scroll cut-off radius and distance. These objective functions were accessed numerically through three-dimensional aerodynamic and aeroacoustic analyses at the design points sampled by Latin hypercube sampling in the design space. Arbitrary selected optimum designs in the Pareto-optimal solutions yielded significant increases in efficiency and decreases in the sound pressure level compared to the reference design.

Optimization of ejection angles of double-jet film-cooling holes using RBNN model

The effects of the ejection and lateral ejection angles of double-jet film-cooling holes on the film-cooling effectiveness was evaluated, and the shape of the double-jet film-cooling holes was optimized using three-dimensional Reynolds-averaged Navier–Stokes equations with a shear stress transport turbulence model and a radial basis neural network surrogate model. The numerical results for the film-cooling effectiveness were validated by a comparison with experimental data. To optimize the double jet film-cooling holes, the spatially-averaged, film-cooling effectiveness was considered as the objective function. Latin hypercube sampling was performed to determine the design points in the design space. A radial basis neural network model was constructed using the objective function values calculated at the design points. The optimal point was obtained from the constructed surrogate using sequential quadratic programming. The cooling performance of the double-jet film-cooling holes was improved considerably by optimization compared to the reference geometry. The constructed surrogate model was found to be sufficiently reliable.

Hydrodynamic performance enhancement of a mixed-flow pump

This paper presents an optimization procedure based on a radial basis neural network surrogate model for design of a vaned diffuser in a mixed-flow pump. Numerical analysis of fluid flow in a mixed-flow pump has been carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model. The optimization processes have been performed twice to investigate the coupled effects of diverse variables. The first optimization process has been conducted with two design variables defining the straight vane length ratio and the diffusion area ratio, and the second one has been conducted with four design variables, i.e., the angle at the diffuser vane tip, the distance between the impeller blade trailing edge and the diffuser vane leading edge, and the two design variables used in the first optimization. The efficiency as a hydrodynamic performance parameter has been selected as the objective function for optimizations. The objective function values have been assessed through three-dimensional flow analysis at design points sampled by Latin hypercube sampling in the design space. The first and second optimizations with the coupled effects of diverse variables have yielded maximum increases in efficiency of 7.16% and 9.75%, respectively, compared to the reference shape. The off-design performance has been also improved in most of the optimum shapes except in the shut-off flow region.

A warpage optimization method for injection molding using artificial neural network with parametric sampling evaluation strategy

A sequential optimization design method based on artificial neural network (ANN) surrogate model with parametric sampling evaluation (PSE) strategy is proposed in this paper. The quality index, such as warpage deformations, thickness uniformity, and so on, is a nonlinear, implicit function of the process conditions, which are typically evaluated by the solution of finite element (FE) equations, a complicated task which often involves huge computational effort. The ANN model can build an approximate function relationship between the design variables and quality index, replacing the expensive FE reanalysis of the quality index in the optimization. Moldflow Corporation’s Plastics Insight software is used to analyze the quality index of the injection-molded parts. The optimization process is performed by a Parametric Sampling Evaluation (PSE) function. PSE is an infilling sampling criterion. Although the design of experiment size is small, this criterion can take the relatively unexpected space into consideration to improve the accuracy of the ANN model and quickly tend to the global optimization solution in the design space. As examples, a scanner, a TV cover, and a plastic lens are investigated. The results show that the sequential optimization method based on PSE sampling criterion can converge faster and effectively approach to the global optimization solution.

A Computationally Efficient Methodology for Generating Training Data for a Transient Neural Network of a Tip-Jet Reaction Drive System

This paper presents a computationally efficient methodology for generating training data for a transient neural network model of a tip-jet reaction drive system for potential use as an onboard model in a model based control application. This methodology significantly reduces the number of training points required to capture the transient performance of the system. The challenge in developing an onboard model for a tip-jet reaction drive system is that the model has to operate over the whole flight envelope, to account for the different dynamics present in the system, and to adjust to system degradation or potential faults. In addition, the onboard model must execute in less time than the update interval of the controller. To address these issues, a computationally efficient training methodology and neural network surrogate model have been developed that captures the transient performance of the tip-jet reaction system. As the number of inputs to a neural network becomes large, the computational time needed to generate the number of training points required to accurately represent the range of operating conditions of the system may become quite large also. A challenge for the tip-jet reaction drive system is to minimize the number of neural network training points, while maintaining the high accuracy. To address this issue, a novel training methodology is presented which first trains a steady-state neural network model and uses deviations from steady-state operating conditions to define the transient portion of the training data. The combined results from both the transient and the steady-state training data can then be used to create a single transient neural network of the system. The results in this paper demonstrate that a transient neural network using this new computationally efficient training methodology has the potential to be a feasible option for use as an onboard real-time model for model based control of a tip-jet reaction drive system.

A Layout Optimization Method of Composite Wing Structures Based on Carrying Efficiency Criterion

A two-level layout optimization strategy is proposed in this paper for large-scale composite wing structures. Design requirements are adjusted at the system level according to structural deformation, while the layout is optimized at the subsystem level to satisfy the constraints from system level. The approaching degrees of various failure critical loads in wing panels are employed to gauge the structure's carrying efficiency. By optimizing the efficiency as an objective, the continuity of the problem could be guaranteed. Stiffened wing panels are modeled by the equivalent orthotropic plates, and the global buckling load is predicted by energy method. The nonlinear effect of stringers' support elasticity on skin local buckle resistance is investigated and approximated by neural network (NN) surrogate model. These failure predictions are based on analytical solutions, which could effectively save calculation resources. Finally, the integral optimization of a large-scale wing structure is completed as an example. The result fulfills design requirements and shows the feasibility of this method.

A Framework for Portfolio Management of Renewable Hybrid Energy Sources

An energy systems modeling tool must address variability of ecological and socio-economic sensitivities in order to practically guide policy and budget related decisions. The aim of this effort is to produce an advisory and design tool geared toward aiding entities with robust planning of effective renewable energy solutions based on trusted models. A tool was developed that enables tradeoffs between various energy systems, based on neural network surrogate models of a publicly available power systems modeling tool. These surrogate models enable the higher-level decision-making tool to manipulate surrogate representations of actual engineering models, as opposed to relying on static data or static simulation results. This research will present a decision-maker with the ability to determine which various renewable and nonrenewable energy systems meet annual energy load requirements, acquisition and operation costs, and individual solution attributes.

High-Degree-of-Freedom Engine Modelling for Control Design Using a Crank-Angle-Resolved Flame Propagation Simulation and Artificial Neural Network Surrogate Models

Non-linearity of the engine system creates a challenge in building a reliable control-oriented model (COM). The main source of non-linearity is the complex nature of the combustion process. Modern engine system configurations are increasingly complex and predicting their transient response poses additional difficulty. In the present paper, a COM is developed to address the challenges and capture the behaviour of a high-degree-of-freedom engine system. Engine combustion models are created by utilizing the high-fidelity engine cycle simulation to characterize the effects of main parameters, such as turbulence, air—fuel ratio, and residual fraction, and subsequently capturing the interrelationships with artificial neural networks. Then, system dynamics are accounted for by adding manifold and actuator dynamics models. The capabilities of the proposed COM are demonstrated using a spark-ignition engine with a dual-independent cam phasing as a test case. The results indicate the model's ability to accurately predict engine responses to an arbitrary schedule of engine control inputs over the feasible operating range.

Systems-of-Systems Analysis of Ballistic Missile Defense Architecture Effectiveness Through Surrogate Modeling and Simulation

Traditionally, the analysis of Ballistic Missile Defense System (BMDS) effectiveness has been limited in fidelity due to the inherent complexity of the subject. Indeed, the BMDS battle management process involves monitoring and controlling the actions of many interacting participants (e.g. radar sensors, communications networks and interceptor missiles) in a process whereby a target moves from launch through sensor detection through intercept kill assessment. Because the actions of each participant may evolve independently, the battle management process functions as a true system-of-systems (SoS). Proper SoS analysis requires architecture level engineering, dealing with component functional allocation and inter-component interaction rather than the internal workings of individual participants. Although prior work has been identified that addresses BMD effectiveness at the SoS level, each method sacrifices analysis fidelity of both process elements and individual participants to enable timely decision making. This paper proposes a modeling and simulation (M&S) framework that supports architecture level analysis of the BMDS. The key innovation is the application of neural network surrogate models, which are representations of other high- or medium-fidelity M&S tools, and can be executed rapidly with negligible loss in fidelity. Surrogate models were created of a BMDS analysis tool that included multisensor target tracking and fusion codes. Results will show the benefit of integrating M&S to architecture level analysis. Specific examples include sensitivity of operational level metrics to formation of an integration tracking picture, and the enabling architecture level decision making.

LANL* V1.0: a radiation belt drift shell model suitable for real-time and reanalysis applications

Abstract. We describe here a new method for calculating the magnetic drift invariant, L*, that is used for modeling radiation belt dynamics and for other space weather applications. L* (pronounced L-star) is directly proportional to the integral of the magnetic flux contained within the surface defined by a charged particle moving in the Earth's geomagnetic field. Under adiabatic changes to the geomagnetic field L* is a conserved quantity, while under quasi-adiabatic fluctuations diffusion (with respect to a particle's L*) is the primary term in equations of particle dynamics. In particular the equations of motion for the very energetic particles that populate the Earth's radiation belts are most commonly expressed by diffusion in three dimensions: L*, energy (or momentum), and pitch angle (the dot product of velocity and the magnetic field vector). Expressing dynamics in these coordinates reduces the dimensionality of the problem by referencing the particle distribution functions to values at the magnetic equatorial point of a magnetic "drift shell" (or L-shell) irrespective of local time (or longitude). While the use of L* aids in simplifying the equations of motion, practical applications such as space weather forecasting using realistic geomagnetic fields require sophisticated magnetic field models that, in turn, require computationally intensive numerical integration. Typically a single L* calculation can require on the order of 105 calls to a magnetic field model and each point in the simulation domain and each calculated pitch angle has a different value of L*. We describe here the development and validation of a neural network surrogate model for calculating L* in sophisticated geomagnetic field models with a high degree of fidelity at computational speeds that are millions of times faster than direct numerical field line mapping and integration. This new surrogate model has applications to real-time radiation belt forecasting, analysis of data sets involving tens of satellite-years of observations, and other problems in space weather.

Homogenisation Metamodelling of Perforated Plates

Abstract: The use of finite element (FE)‐based homogenisation has improved the study of composite material properties. However, it involves enormous computational effort when implemented in engineering design problems. Therefore an artificial neural network (ANN) surrogate model is proposed here to avoid this issue. In this study, a numerical homogenisation code was developed based on a commercial FE package. It is used to develop the ANN metamodel for an individual composite structure. The effectiveness of the metamodel was examined through an analytical optimisation procedure.