Response Surface Surrogate Models Research Articles

Optimization design of radial inflow turbine combined with mean-line model and CFD analysis for geothermal power generation

It is a considerable challenge to determine the key parameters affecting the efficiency and propose an accurate loss prediction model for radial flow turbine design. In current investigation, a one-dimensional mean-line model combined with particle swarm optimization algorithm and Kriging response surface surrogate model based on 3D numerical results were proposed to optimize radial flow turbines and evaluate performance. The loss model was carried out to analyze the relationship between geometric parameters, operating conditions and turbine performance. CFD numerical simulations were employed to revealed the mechanism of enhancing the turbine performance. The total-static efficiency was increased from 88.5 % to 91.7 %, and the clearance loss and passage loss were reduced by 18.4 % and 35.8 %, respectively,by optimized design. It is attributed to mitigate the curvature-induced boundary layer separation and vortex at the outlet, which reduces the secondary flow losses.The correlation between the predicted values of the Kriging response surface and the numerical results was up to 98.3 %. The results showed that the angle of attack was in the range of -10-0°, the blade has less influence on the flow loss. The current study effectively combined the flow path structure parameters and flow characteristics to realize the efficient optimization of ORC turbine.

Reliability analysis and optimization design of hydrogen storage composite pressure vessel with hybrid random-fuzzy uncertainties

In this study, a progressive failure model for hydrogen storage composite pressure vessel (CPV) burst is established. The burst pressure and progressive damage behavior of the CPV are analyzed. Besides, kriging and response surface (RS) surrogate models for CPV burst are established. The verification and the comparative analysis of the surrogate models are carried out. Then, the reliability of the CPV is analyzed with hybrid random-fuzzy uncertainties, and the influence of longitudinal tensile strength, hoop layer thickness, and helical layer thickness on the hybrid reliability is explored. Finally, a unified reliability index is established with hybrid random-fuzzy uncertainties, and the modified particle swarm optimization (PSO) algorithm is applied to carry out reliability-based optimization design. The minimum weight of the composite shell is set as the objective, and the reliability of the CPV with hybrid random-fuzzy uncertainties is set as the constraint. The results show that the hoop layer of the CPV is the main load-bearing structure. The kriging and RS surrogate models are effectiveness to surrogate the burst pressure of the CPV, and the RS model is simpler and more computationally efficient than kriging model, which is more suitable for reliability analysis and optimization design. Under the condition of hybrid random-fuzzy uncertainties, the reliability of the hydrogen storage CPV exhibits fuzzy uncertainty, and there is a possibility of reliability equal to 0 under the low λ-cut level, making it difficult to meet reliability requirements. Increasing the longitudinal tensile strength, the hoop layer thickness and the helical layer thickness can improve the reliability of the hydrogen storage CPV. Furthermore, the optimization method proposed in this study improves its reliability from 0.7043 to 1. This study establishes reliability analysis and optimization design methods for hydrogen storage CPV with hybrid random-fuzzy uncertainties, which contributes to further improvement on the safety of CPV.

Off-design performance of micro-scale solar Brayton cycle

A novel methodology to design a micro-scale, solar-only, air-breathing, open Brayton cycle and assess its on- and off-design performance. The methodology is applied to generate and assess six thermodynamic layouts over a range of solar irradiation levels. All plants have the same on-design requirements to create a baseline to compare their off-design performance. PyCycle, a thermodynamic cycle modeling library to model jet engine performance, is revised to transform the jet engine performance modeling to solar thermal plant performance modeling and used to create a volumetric receiver component. A response surface surrogate model of the receiver is created for design optimization to maximize the component-level efficiency. The compressor and turbine maps are scaled for the balance of the plant. Off-design efficiency, mass flow rate, operation range, turbomachinery maps, and maximum power output are presented. Since the methodology can be adapted to all plant sizes, the results are normalized to on-design condition. The outcome of this study demonstrates the impact of the thermodynamic configuration on off-design performance and provides a methodology to design plants that are more robust across a range of solar irradiation levels and can be operated in a more flexible manner. Compared to single shaft configuration, solar radiation operation range is improved by 5%, with 6% less mass flow, and operates more efficiently than the benchmark case over 85% of the operating regime.

A Parametric Physics-Informed Deep Learning Method for Probabilistic Design of Thermal Protection Systems

Precise and efficient calculations are necessary to accurately assess the effects of thermal protection system (TPS) uncertainties on aerospacecrafts. This paper presents a probabilistic design methodology for TPSs based on physics-informed neural networks (PINNs) with parametric uncertainty. A typical thermal coating system is used to investigate the impact of uncertainty on the thermal properties of insulation materials and to evaluate the resulting temperature distribution. A sensitivity analysis is conducted to identify the influence of the parameters on the thermal response. The results show that PINNs can produce quick and accurate predictions of the temperature of insulation materials. The accuracy of the PINN model is comparable to that of a response surface surrogate model. Still, the computational time required by the PINN model is only a fraction of the latter. Considering both computational efficiency and accuracy, the PINN model can be used as a high-precision surrogate model to guide the TPS design effectively.

Efficient Sensitivity Analysis for Enhanced Heat Transfer Performance of Heat Sink with Swirl Flow Structure under One-Side Heating

Excellent heat transfer performance has increasingly become a key issue that needs to be solved urgently in the development process of large-scale fusion equipment. The study of heat transfer performance improvement to scientifically and reasonably determine the design parameters of the high heat flow (HHF) components of fusion reactors based on the efficient in-depth analysis of the heat transfer mechanism and its sensitive factors is of great significance. In this paper, a liquid-vapor two-phase flow model with subcooled boiling for a large length-diameter ratio swirl tube structure in the HHF calorimeter component is proposed to analyze the effects of key design parameters (such as inlet temperature of cooling water flow, swirl tube structure parameters, etc.) on its heat transfer performance. Then, considering the high computational cost of the liquid-vapor two-phase flow model, and in order to improve the efficiency of the sensitivity analysis of these design parameters, the polynomial response surface surrogate model of heat transfer performance function was constructed based on Latin hypercube sampling. On this basis, by combining the proposed surrogate model, the sensitivity index of each design parameter could be obtained efficiently using the Sobol global sensitivity analysis method. This method could greatly improve the calculation efficiency of the design parameter sensitivity analysis of HHF components in the fusion reactor, which provides vital guidance for the subsequent rapid design optimization of related components.

Solution to the problem of bridge structure damage identification by a response surface method and an imperialist competitive algorithm

To increase the efficiency of structural damage identification (SDI) methods and timeously and accurately detect initial structural damage, this research develops an SDI method based on a response surface method (RSM) and an imperialist competitive algorithm (ICA). At first, a Latin hypercube design method is used for experimental design and selection of sample points based on RSM. Then, a high-order response surface surrogate model for the target frequency response and stiffness reduction factor is established. Finally, analysis of variance is performed to assess the overall goodness-of-fit and prediction accuracy of the established model. Then the results obtained are combined with structural dynamic response data to construct objective functions; furthermore, the optimal solution of parameter vector in the objective function is solved based on the ICA. Then damage positioning and quantification can be achieved according to location and degree of change in each parameter; finally, the RSM-ICA-based SDI method proposed is applied to damage identification of high-dimensional damaged simply-supported beam models. To verify the effectiveness of the proposed method, the damage identification results are compared with the results obtained from traditional optimization algorithms. The results indicate that: average errors in the structural stiffness parameters and natural frequency that are identified by the proposed method are 6.104% and 0.134% respectively. The RSM-ICA-based SDI method can more accurately identify the location and degree of damages with more significantly increased identification efficiency and better precision compared to traditional algorithms. This approach provides a novel means of solving SDI problems.

Optimization Design of Holding Poles Based on the Response Surface Methodology and the Improved Arithmetic Optimization Algorithm

The computation consumption of finite element analysis for structural optimization design of holding pole is large, and it is difficult to determine the feasible region. The response surface method (RSM) was used to simulate the real response of the holding pole, and an improved arithmetic optimization algorithm (IAOA) was proposed to optimize the holding pole. Fractional-order calculus was introduced into arithmetic optimization algorithm (AOA) to improve the exploitation ability of AOA. Latin hypercube sampling was applied to select the test samples of each member of the holding pole, and the least square method was employed to analyze the sample points. Then, the second-order response surface surrogate model of the stress and displacement of the holding pole on the cross-sectional size of each member was established. An optimization model was constructed with the minimum mass as the optimization objective and the allowable stress and displacement as constraints, and the IAOA was implemented to solve the model. The results show that the second-order response surface model can accurately predict the response value of the holding pole. The solution accuracy of the IAOA is significantly improved. The surrogate model can greatly decrease the calculation cost of finite element analysis. The mass of the holding pole is reduced 8.2% after optimization. The RSM and the IAOA can be combined to solve the optimization design problem of large spatial truss structures effectively.

GPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.

Optimization of Nonlinear Lamb Wave Detection System Parameters in CFRP Laminates.

Carbon fiber reinforced polymer (CFRP) laminates, as unique multifunctional materials, are widely applied in various aircraft, such as airliners, fighter planes, and space shuttles. To ensure aircraft safety during the production and application of CFRP laminates, it is necessary to improve the accuracy of nonlinear Lamb wave nondestructive testing to assess the damage in CFRP laminates caused by impact, high temperature, friction, corrosion, etc. In this study, the accuracy of nonlinear ultrasonic nondestructive testing was found to highly depend on the cycle number, output level and gain of the nonlinear ultrasonic detection system. Based on a single-factor experiment that considered the cycle number, output level, and gain of the amplifier as independent variables, a regression analysis was carried out on the fundamental wave amplitude value (A1) and second harmonic amplitude value (A2). Two response surface surrogate models were established to improve the accuracy of nonlinear Lamb wave nondestructive testing and to optimize the detection system parameters. The response surface models were verified via an analysis of variance (ANOVA), significance tests and an error statistical analysis. The results revealed the significant influence of these three factors on A1 and A2. Optimization of the response surface was achieved at eight cycles, an output level of 42 and a gain of 32 dB. Moreover, the nonlinear ultrasonic detection system achieved good operational stability, high accuracy and reliability under the above optimal parameter conditions. This approach provides scientific guidance for the accurate assessment of CFRP laminate damage.

Saltwater scavenging optimization under surrogate uncertainty for a multi-aquifer system

Surrogate-assisted simulation-optimization technique is an effective approach for identifying aquifer remediation strategies. Using surrogate models to replace high-fidelity groundwater simulation models is key to reduce computing time. Inevitably, uncertainties persist in surrogate model structure and parameters and may lead to poor accuracy in prediction. However, past studies often adopt one surrogate to capture the original model response and rarely investigate uncertainties and approximation accuracy of surrogate models. In this study, we present an ensemble surrogate modeling approach to address uncertainty in surrogate model predictions for saltwater intrusion mitigation designs using a hypothetical horizontal scavenger well. Firstly, polynomial response surface surrogate models are constructed to capture the relationship between chloride concentrations and saltwater extraction rates of a horizontal well. Secondly, a stochastic optimization model that includes multiple ensemble surrogates is developed to determine the optimal saltwater extraction schedule. Chance-constrained (CC) programming is used to account for model selection uncertainty in probabilistic nonlinear concentration constraints. Akaike information criterion correction (AICc) based Bayesian model averaging (BMA) method is adopted to determine required statistics of concentrations in the chance constraints. Finally, a set of saltwater intrusion mitigation strategies are obtained through an interior point optimization algorithm. The proposed methodology is applied to the saltwater intrusion problem in Baton Rouge, Louisiana. A high-fidelity flow and solute transport model is developed, but requires 16 h for one model run. The study shows that the developed surrogate models perform well and have strong predictive capabilities with respect to the solute transport model response, while considerably reducing computation time. Including model selection uncertainty through multimodel inference and model averaging provides more reliable remediation strategies compared with the single-surrogate assisted approach.

Performance comparison of several response surface surrogate models and ensemble methods for water injection optimization under uncertainty

In this paper we defined a relatively complex reservoir engineering optimization problem of maximizing the net present value of the hydrocarbon production in a water flooding process by controlling the water injection rates in multiple control periods. We assessed the performance of a number of response surface surrogate models and their ensembles which are combined by Dempster–Shafer theory and Weighted Averaged Surrogates as found in contemporary literature works. Most of these ensemble methods are based on the philosophy that multiple weak learners can be leveraged to obtain one strong learner which is better than the individual weak ones. Even though these techniques have been shown to work well for test bench functions, we found them not offering a considerable improvement compared to an individually used cubic radial basis function surrogate model. Our simulations on two and three dimensional cases, with varying number of optimization variables suggest that cubic radial basis functions-based surrogate model is reliable, outperforms Kriging surrogates and multivariate adaptive regression splines, and if it does not outperform, it is rarely outperformed by the ensemble surrogate models.

Robust optimization of well location to enhance hysteretical trapping of CO2: Assessment of various uncertainty quantification methods and utilization of mixed response surface surrogates

AbstractThe paper aims to solve a robust optimization problem (optimization in presence of uncertainty) for finding the optimal locations of a number of CO2 injection wells for geological sequestration of carbon dioxide in a saline aquifer. The parametric uncertainties are the interfacial tension between CO2 and aquifer brine, the Land's trapping coefficient and the boundary aquifer's absolute permeability. The spatial uncertainties are due to the channelized permeability field which exhibits a binary channel‐non‐channel system. The objective function of the optimization is the amount of residually trapped CO2 due to the hysteresis of the relative permeability curves. A risk‐averse value derived from the cumulative density function of the distribution of the amount of trapped gas is chosen as the objective function value. In order to ensure that the uncertainties are effectively taken into account, Monte Carlo simulation and Polynomial Chaos Expansion (PCE)‐based methods are used and compared with each other. For different cases of parametric and spatial uncertainties, the most accurate uncertainty quantification (UQ) method is chosen to be integrated within the optimization algorithm. While for parametric uncertainty cases of up to two uncertain variables, PCE‐based methods computationally outperform Monte Carlo simulations, it is shown that for the multimodal distributions of the function of trapped gas occurring for the spatial uncertainty case, Monte Carlo simulations are more reliable than PCE‐based UQ methods. For the discrete (integer) optimization problem, various mixed response surface surrogate models are tested and the robust optimization resulted in optimal CO2 injection well locations.

Optimization of Printed Circuit Heat Exchanger Using Exergy Analysis

A printed circuit heat exchanger (PCHE) with zigzag flow channels in a double-faced configuration was optimized to enhance its thermal–hydraulic performance. Using exergy analysis, the objective function was defined as the net exergy gain of the system considering the exergy gain by heat transfer and exergy loss due to friction in the channels. A Reynolds-averaged Navier–Stokes (RANS) analysis and surrogate modeling techniques were used for the optimization. Three geometric variables were selected as the design variables. The objective function was calculated at each design point through RANS analysis in order to construct a response surface surrogate model. Through the optimization, both the thermal and hydraulic performances of the PCHE were improved with respect to the reference geometry by suppressing flow separation in the channels.

Determination of oral mucosal Poisson’s ratio and coefficient of friction from in-vivo contact pressure measurements

Despite their considerable importance to biomechanics, there are no existing methods available to directly measure apparent Poisson’s ratio and friction coefficient of oral mucosa. This study aimed to develop an inverse procedure to determine these two biomechanical parameters by utilizing in vivo experiment of contact pressure between partial denture and beneath mucosa through nonlinear finite element (FE) analysis and surrogate response surface (RS) modelling technique. First, the in vivo denture–mucosa contact pressure was measured by a tactile electronic sensing sheet. Second, a 3D FE model was constructed based on the patient CT images. Third, a range of apparent Poisson’s ratios and the coefficients of friction from literature was considered as the design variables in a series of FE runs for constructing a RS surrogate model. Finally, the discrepancy between computed in silico and measured in vivo results was minimized to identify the best matching Poisson’s ratio and coefficient of friction. The established non-invasive methodology was demonstrated effective to identify such biomechanical parameters of oral mucosa and can be potentially used for determining the biomaterial properties of other soft biological tissues.

Solving Computational Expensive Problems with a Response Surface Surrogate Models

Modern CAE technology is widely used in modern automobile design, engine design and so on. But its computational expense and highly time cost reduce the efficiency of design. The paper studied a respond surface model-based technique for predictive design. Firstly, we study and compare the four kinds of polynomial orders of RSM technique. Then we use Latin Hypercube technique choose enough sample points for approximation. At last, we employed cross-validation error analysis for error analysis. The results of expensive benchmark functions of CEC 2014 tested our predictive methods.

Shape Optimization of Trawl-doors Using Variable-fidelity Models and Space Mapping

Trawl-doors have a large influence on the fuel consumption of fishing vessels. Design and optimization of trawl-doors using computational models are key factors in minimizing the fuel consumption. This paper presents an efficient optimization algorithm for the design of trawl-door shapes using computational fluid dynamic models. The approach is iterative and uses variable-fidelity models and space mapping. The algorithm is applied to the design of a multi-element trawl-door, involving four design variables controlling the angle of attack and the slat position and orientation. The results demonstrate that a satisfactory design can be obtained at a cost of a few iterations of the algorithm. Compared with direct optimization of the high-fidelity model and local response surface surrogate models, the proposed approach requires 79% less computational time while, at the same time, improving the design significantly (over 12% increase in the lift-to-drag ratio).

Steering Torque Optimization of an In-Wheel Motor Vehicle with Double Pivot Suspension Based on Response Surface and Genetic Algorithm

A rigid-elastic coupling multi-body dynamic model of an in-wheel motor vehicle with double pivot suspension was established. The steering effort performance is analyzed. Results showed an excessive steering force of the vehicle with double pivot suspension. By optimizing the suspension parameters using response surface surrogate model and genetic algorithm, the characteristic of steering effort was improved.

HAWAII HURRICANE WAVE AND SURGE MODELING AND FAST FORECASTING

The US Army Corps of Engineers' Surge and Wave Island Modeling Studies developed a fast forecasting system for hurricane waves and inundation in Hawaii. The system is based on coupled high-resolution, high-fidelity simulations of waves and surge applying the SWAN and ADCIRC numerical models on a 2D finite-element grid. Additionally, wave runup is simulated on high-resolution cross-shore transects using the Boussinesq-equation model BOUSS-1D. Approximately 1500 storms were simulated to cover the range of hurricane parameters of landfall location, track angle at landfall, central pressure, forward speed, and radius of maximum winds expected to impact Hawaii. To create a forecast system that is fast and robust, a moving least-squares response surface surrogate model was developed based on the high-fidelity model results. The surrogate model is approximately seven orders of magnitude faster than the high-fidelity simulations. The efficiency of the surrogate model allows both deterministic and probabilistic simulations in seconds to minutes on a personal computer.