Multidimensional Response Surface Research Articles

Surrogate methods for determining profiles of material properties of planar test objects with accumulation of apriori information about them

New methods for identifying the material properties of planar objects as a result of measurements by the eddy current method are proposed. The methods are based on the latest surrogate strategies and advanced optimization techniques that improve efficiency and reduce resource consumption of problem solutions, and balance computational complexity with the accuracy of the results. High-performance metamodels for global surrogate optimization are based on deep truly meaningful fully connected neural networks, serving as an additional function of accumulating apriori information about objects. High accuracy of the approximation of the multidimensional response surface, which is determined by the “exact” electrodynamic model of the testing process, is ensured by performing calculations according to the computer design of a homogeneous experiment with a low weighted symmetric centered discrepancy. The results of numerical experiments performed for full and reduced dimensional search spaces, which can be obtained by linear transformations using the principal component method, are presented. The verification of the methods proved their sufficiently high accuracy and computational performance.

Diet Quality, Microbial Lignan Metabolites, and Cardiometabolic Health among US Adults.

The gut microbiome has been shown to play a role in the relationship between diet and cardiometabolic health. We sought to examine the degree to which key microbial lignan metabolites are involved in the relationship between diet quality and cardiometabolic health using a multidimensional framework. This analysis was undertaken using cross-sectional data from 4685 US adults (age 43.6 ± 16.5 years; 50.4% female) participating in the National Health and Nutrition Examination Survey for 1999-2010. Dietary data were collected from one to two separate 24-hour dietary recalls and diet quality was characterized using the 2015 Healthy Eating Index. Cardiometabolic health markers included blood lipid profile, glycemic control, adiposity, and blood pressure. Microbial lignan metabolites considered were urinary concentrations of enterolignans, including enterolactone and enterodiol, with higher levels indicating a healthier gut microbial environment. Models were visually examined using a multidimensional approach and statistically analyzed using three-dimensional generalized additive models. There was a significant interactive association between diet quality and microbial lignan metabolites for triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, insulin, oral glucose tolerance, adiposity, systolic blood pressure, and diastolic blood pressure (all p < 0.05). Each of these cardiometabolic health markers displayed an association such that optimal cardiometabolic health was only observed in individuals with both high diet quality and elevated urinary enterolignans. When comparing effect sizes on the multidimensional response surfaces and model selection criteria, the strongest support for a potential moderating relationship of the gut microbiome was observed for fasting triglycerides and oral glucose tolerance. In this study, we revealed interactive associations of diet quality and microbial lignan metabolites with cardiometabolic health markers. These findings suggest that the overall association of diet quality on cardiometabolic health may be affected by the gut microbiome.

Influence of the Longitudinal and Tree-Shaped Fin Parameters on the Shell-and-Tube LHTES Energy Efficiency

Changes in the energy sector, associated with the move away from fossil fuels, pose a challenge for appropriate thermal energy management in residential buildings. The important element to deal with the variability of renewable energy in thermal systems is latent heat thermal energy storage. Due to the low thermal conductivity of phase change materials, a number of techniques are proposed to enhance the heat transfer process. In this research, the global sensitivity of fin geometrical parameters on the melting and solidification times and energy efficiency of these processes was investigated. The computational model of the phase change was developed using the finite volume method with the enthalpy-porosity model and Boussinesq approximation. Numerical simulations were carried out according to the design of experiments technique. The multi-dimensional response surface was developed, and the multi-objective optimisation was done. The research shows that the melting process is most influenced by the position of the top fin (α angle) and the solidification process by the position of the bottom fin (γ angle). The angle of the tree fin (β) has a different effect on both processes, with the energy efficiency decreasing during melting and increasing during solidification. Maximum values for the energy efficiencies of melting (ηm=0.973) and solidification (ηs=0.988) were obtained for α=18.2°, β=89.0°, L=10.7 mm and γ=21.0°.

Uncertainty quantification of kinetic models using adjoint-driven active subspace algorithms

Simulations of chemically reacting flows are particularly sensitive to kinetic models, which in turn depend on a large number of parameters. Therefore, quantifying parametric uncertainties is essential in order to assess the applicability and performance of such models. The size of the parameter space renders conventional methods in quantifying uncertainties impractical. The active subspace methodology has proven to be very effective in such applications and has been adopted here to analyze ignition delay time in an isochoric adiabatic reactor. This method has been augmented with an adjoint-based algorithm to provide low-cost access to gradient information, necessary for dimensionality reduction. In addition, the predictions of the active subspace method have been compared to a linear approximation using the adjoint model (LAAM), where depending on the case, a satisfactory estimation is achieved at a fraction of the cost. Moreover, a strategy is presented for constructing a multi-dimensional response surface for cases, where contrary to previous studies, a single dominant direction is insufficient in predicting the corresponding PDF. Finally, the uncertainties with respect to initial conditions are analyzed, highlighting the limitations of the linear approach (LAAM) in cases with strong nonlinearities.

Additive neural network approximation of multidimensional response surfaces for synthesis of eddy-current probes

Wydawnictwo SIGMA-NOT wydaje czasopisma fachowe informujące swoich czytelników o najnowszych osiągnięciach naukowych i nowoczesnych rozwiązaniach technicznych w Polsce i na świecie, popularyzuje problemy techniczne oraz poszerza wiedzę i kulturę techniczną.

The prediction profiler at 30

The prediction profiler as it is now called in the statistical software, JMP, was introduced at a talk with discussion entitled, “An Interactive Graph for Exploring Multidimensional Response Surfaces.” The talk was part of a session at the Joint Statistics Meetings in Atlanta, Georgia in 1991. The original intent of the plot was to provide a graph to display the fitted response surface from a designed experiment even if that experiment had many responses and more than two factors. In the last 30 years, however, the prediction profile plot has transcended its original use in displaying the results of response surface experiments. It has shown its utility in displaying the prediction functions coming from classification or regression trees or neural nets among other modern analytical tools for the study of observational data. There are also pedagogical uses of the plot for developing intuition about mathematical functions having multiple inputs. This article provides a detailed description of the plot and examples of its various uses.

Control strategy of genetic algorithm for a hybrid electric container loader

A genetic algorithm is applied to optimise the control parameters of a hybrid electric loader. Based on the optimal control parameters, a multidimensional response surface model for control parameters was established by a response surface method. The simulation shows that under multiple loads, battery temperatures and initial SOCs, the fuel saving of the hybrid loader is significant, the battery maintains the charge sustain or reaches within the optimal range, the battery temperature rise is kept within a reasonable range, and the battery charge and discharge rate is controlled within 1C. The fuel consumption of the hybrid electric loader is reduced by more than 20% compared with the traditional loader under the full load conditions. Compared with the original calculation model optimised by genetic algorithms and the dynamic programming, it was verified that the calculation accuracy and fuel saving significance of the response surface model for control parameters.

Framework for probabilistic leakage resistance envelopes of casing connections

Probabilistic well casing design is a recent trend in Oil & Gas exploration, especially for ultra-deep and HPHT wells. Reliability-based design allows safety margins to be optimized, while managing the corresponding risks. Statistics for pipe body geometry and strength are today widely available, but most reported incidents are related to connection failures. In this context, a methodology is proposed herein to construct probabilistic leakage resistance envelopes for casing connections. The methodology is based on extensive axisymmetric Finite Element analysis, considering geometric variabilities resulting from manufacturing tolerance. Maximum internal pressure is found for different values of axial load. Multi-dimensional response surfaces are constructed to take into account individual effects, and cross-effects for the most relevant variables. Regression analysis is used to construct failure envelopes for pre-defined probability levels. These are also converted into probabilistic envelopes for arbitrary combinations of axial load and internal pressure. The API 8 Round 5½ J55 14 lb/ft LTC connection is employed as study object, but the methodology can be readily extended to other connections with metal-to-metal seal. To the best of our knowledge, this is the first time such a probabilistic framework for leakage resistance of casing connections is presented in the literature. This framework, and the resulting models, are fundamental for the proper reliability-based design of well casing.

Time-variant reliability modeling based on hybrid non-probability method

In this paper, an innovative time-variant reliability analysis method based on non-probabilistic theory is developed for structures, which combines the interval model with the elliptical model. The coordinate transformation method is adopted to eliminate the correlation between variables for improving the accuracy of the reliability analysis results. An improved multi-dimensional response surface method is selected to solve the reliability problem based on the hybrid model. Finally, taking the cantilever beam structure as a case study, which is used to shed a light on the validity of the presented measure. The results show that in the early and the middle stage of service period, the dispersion of the uncertainty variable has a significant impact on the reliability. At the later stage, the moment degradation is the main factor affecting the reliability.

Bladelets—Winglets on Blades of Wind Turbines: A Multiobjective Design Optimization Study

The work presented in this paper used rigorous 3D flow-field analysis combined with multi-objective constrained shape design optimization for the design of complete blade + bladelet configurations for a three-blade horizontal-axis wind turbine. The fluid flow analysis in this work was performed using Openfoam software. The 3D, steady, incompressible, turbulent flow Reynolds-Averaged Navier–Stokes equations were solved in the rotating frame of reference for each combination of wind turbine blade and bladelet geometry. The free stream uniform wind speed in all cases was assumed to be 9 m s−1. The three simultaneous design optimization objectives were as follows: (a) maximize the coefficient of power, (b) minimize the coefficient of thrust force, and (c) minimize twisting moment around the blade axis. The bladelet geometry was fully defined by using a small number of parameters. The optimization was carried out by creating a multidimensional response surface for each of the simultaneous objectives. The response surfaces were based on radial basis functions, where the support points were designs analyzed using the high-fidelity computational fluid dynamics (CFD) analysis of the full blade + bladelet geometry. The response surfaces were then coupled to an optimization algorithm in modefrontier software. The predicted values of the objective functions for the optimum designs were then again validated using Openfoam high-fidelity analysis code. Results for a Pareto-optimized bladelet on a given blade indicate that more than 4% increase in the coefficient of power at minimal thrust force penalty is possible at off-design conditions compared to the same wind turbine rotor blade without a bladelet.

Sealing reliability modeling of aviation seal based on interval uncertainty method and multidimensional response surface

Many variables affect the sealing performance, and their distribution characteristics are difficult to obtain with probabilistic methods owing to the high cost involved. Numerous problems in engineering are similar due to the appearance of small-sample parameters. In this study, the sealing reliability of an aviation seal was defined as the research object, and an interval uncertainty method and multidimensional response surface were proposed to calculate the sealing reliability. Based on this, we first analyzed the failure mechanism of the aviation seal and established a leakage rate model. Then, based on the non-probabilistic interval model, an interval uncertainty method was proposed to construct the analytical model. With reference to the limit state equation from the structural reliability theory, the multidimensional response surface was used for fast calculation. Then, we chose the single-cylinder gas steering gear used in aircraft as the case study, its sealing reliability in working and non-working statuses were calculated, and the results were verified with the actual maintenance records. By analyzing the sensitivity of some variables, we can improve the sealing reliability of the aviation seal by improving the surface roughness only if the cost allows. Finally, we consider that the method proposed in this study realizes the application of small-sample uncertainty analysis in reliability analysis, and could provide a feasible way to solve the similar problems in engineering with multidimensional and small-sample parameters.

Global sensitivity analysis of borehole thermal energy storage efficiency on the heat exchanger arrangement

Global sensitivity analysis of the efficiency of borehole thermal energy storage (BTES) during long-term operation on the borehole heat exchanger (BHE) arrangement was investigated to advance understanding of the system’s thermal performance. Three parameters were assessed to determine the BHE arrangement: the first parameter designate the distance between BHE axis in x direction, the second in y direction and the third an angle between top surface of the rock mass and boreholes axis. Conducting research on the real system is extremely expensive, so it was decided to conduct simulation studies utilising a finite element method. The ANSYS software with a newly implemented heat and mass transport model in BHE was used. Based on conducted numerical simulations, and according to the design of the experiment, a multidimensional response surface was achieved. The global sensitivity was conducted based on a response surface model. It was found that the BHE inclination (SEeffP3=0.97 – FAST algorithm) has a crucial impact for the BTES efficiency. The area on response surface, where the optimal BHE arrangement to maximise BTES efficiency could be reached, is an inclination P3=0° and BHE spacing in the range of P1=P2=(1.5–3m).

Optimizing fin design for a PCM-based thermal storage device using dynamic Kriging

A key challenge in the development of a practical thermal storage device (TSD) is the low thermal conductivity of common phase change materials (PCM). This low conductivity impedes both heat input and extraction. The most common solution is to use conductive metal fins to spread heat through the device. However, optimizing the effectiveness of the container and the fin arrangement is difficult due to the large number of potential design parameters. This paper develops a strategy to make simulation-based optimization process affordable and accurate. First, numerical techniques are designed to accurately and efficiently compute heat and mass transport in a variety of geometries without generating grids to conform to each geometry. This facilitates rapid prototyping and mitigates the expense of individual simulations. Second, a pre-screening process identifies the independent variables with the largest and most nonlinear effect on the objective function in the optimization process, thus narrowing the parameter space. Finally, a dynamic Kriging-based optimization approach constructs a multidimensional response surface using sparse input datasets; the response surface is then used to identify an optimal design. The combination of the above three strategies is shown to result in an approach that can aid in the design of optimal thermal storage devices that rely on a mixture of PCM and metal fins.

Cooldown procedure success criteria map for the full break size spectrum of SBLOCA

A success criteria map defining successful implementation of a cooldown procedure to mitigate small-break loss of coolant accident (SBLOCA) with failed high pressure safety injection system for the OPR1000 is generated for the full break size spectrum from 0.5 in to 2.5 in diameter breaks. The success criteria map is a multi-dimensional response surface that gives the expected peak clad temperature (PCT) as a function of break size and operator action time to start the 55.6 °C/hr reactor coolant system cooldown and depressurization involving secondary side steam dump through manual manipulation of the atmospheric dump valves (ADV). The PCT response surface is constructed through a regression analysis using a Gaussian process model (GPM) coupled to an adaptive sampling procedure that greatly reduces the computational cost and analysis time by limiting the number of required best estimate simulations of the SBLOCA with the MARS code to approximately 100. Break flow rates and times to core heat up each span several orders of magnitude when considering the full break size spectrum so an innovative solution of transforming the break size and ADV actuation time input variables using exponential and logarithm functions was implemented such that the regression could be performed on the scaled and transformed input space.

Design and optimization of a natural gas-fired thermoelectric generator by computational fluid dynamics modeling

The paper reports the results of the computational part of an ongoing research and development project aimed at designing and optimization of a thermoelectric generator fired with natural gas. The idea of the project is to provide an independent and reliable source of power in the power range of 50–100W for island-mode supply, tailored for remote objects of the natural gas distribution infrastructure which, for economic reason, are not connected to the electric grid. The device includes a burner as a heat source, flow channels for air and for exhaust gases and a set of thermoelectric modules generating electric current if subject to temperature difference. The pre-selected design configuration (type E) was subject to parametric optimization. A corresponding numerical model based on the Ansys/Fluent computational fluid dynamics code was built. The optimization procedure aims to maximize the temperature difference across the thermoelectric module in order to maximize the generated power output. Simultaneously, it is essential to maintain the hot-side temperature below the required technical limit of 320°C. First, thirteen design parameters (most of them concerning geometry) influencing the target function were identified. A central value and a possible range for each parameter have been set. Next, the partial impact of each parameter on the target function was found, and the set of the design parameters was limited to eight. Finally, only five parameters were estimated to be non-monotonically related to the generated power. The impact of the selected five parameters on the target function was investigated using a central composite design optimization plan. The set of points obtained in the multi-dimensional response surface was then limited to points meeting the imposed limitation of maximum temperature. Eventually, three candidate points (i.e. three sets of design parameters) have been proposed for the next stage of the project involving an experimental set-up for the design of the prototype.

Nonlinear, interacting responses to climate limit grassland production under global change

Global changes in climate, atmospheric composition, and pollutants are altering ecosystems and the goods and services they provide. Among approaches for predicting ecosystem responses, long-term observations and manipulative experiments can be powerful approaches for resolving single-factor and interactive effects of global changes on key metrics such as net primary production (NPP). Here we combine both approaches, developing multidimensional response surfaces for NPP based on the longest-running, best-replicated, most-multifactor global-change experiment at the ecosystem scale-a 17-y study of California grassland exposed to full-factorial warming, added precipitation, elevated CO2, and nitrogen deposition. Single-factor and interactive effects were not time-dependent, enabling us to analyze each year as a separate realization of the experiment and extract NPP as a continuous function of global-change factors. We found a ridge-shaped response surface in which NPP is humped (unimodal) in response to temperature and precipitation when CO2 and nitrogen are ambient, with peak NPP rising under elevated CO2 or nitrogen but also shifting to lower temperatures. Our results suggest that future climate change will push this ecosystem away from conditions that maximize NPP, but with large year-to-year variability.

Algorithms for design optimization of chemistry of hard magnetic alloys using experimental data

A multi-dimensional random number generation algorithm was used to distribute chemical concentrations of each of the alloying elements in the candidate alloys as uniformly as possible while maintaining the prescribed bounds on the minimum and maximum allowable values for the concentration of each of the alloying elements. The generated candidate alloy compositions were then examined for phase equilibria and associated magnetic properties using a thermodynamic database in the desired temperature range. These initial candidate alloys were manufactured, synthesized and tested for desired properties. Then, the experimentally obtained values of the properties were fitted with a multi-dimensional response surface. The desired properties were treated as objectives and were extremized simultaneously by utilizing a multi-objective optimization algorithm that optimized the concentrations of each of the alloying elements. This task was also performed by another conceptually different response surface and optimization algorithm for double-checking the results. A few of the best predicted Pareto optimal alloy compositions were then manufactured, synthesized and tested to evaluate their macroscopic properties. Several of these Pareto optimized alloys outperformed most of the candidate alloys on most of the objectives. This proves the efficacy of the combined meta-modeling and experimental approach in design optimization of the alloys. A sensitivity analysis of each of the alloying elements was also performed to determine which of the alloying elements contributes the least to the desired macroscopic properties of the alloy. These elements can then be replaced with other candidate alloying elements such as not-so-rare earth elements.

Study on Multi-objective Optimization of Airbag Landing Attenuation System for Heavy Airdrop

A finite element model of vehicle and its airbag landing attenuation system is established and verified experimentally. Two design cases are selected to constrain the airbag design for extreme landing conditions, while the height and width of airbag and the area of vent hole are chosen as design variables. The optimization is forced to compromise the design variables between the conflicting requirements of the two extremes. In order to optimize the parameters of airbag, the multi-dimensional response surfaces based on extended Latin hypercube design and radial basis function are employed instead of the complex finite element model. Pareto optimal solution sets based on response surfaces are then obtained by multi-objective genetic algorithm. The results show the optimization method presented in this paper is a practical tool for the optimization of airbag landing attenuation system for heavy airdrop.

Modeling microalgal abundance with artificial neural networks: Demonstration of a heuristic ‘Grey-Box’ to deconvolve and quantify environmental influences

An artificial neural network (ANN)-based technology – a ‘Grey-Box’, originating the iterative selection, depiction, and quantitation of environmental relationships for modeling microalgal abundance, as chlorophyll (CHL) a, was developed and evaluated. Due to their robust capability for reproducing the complexities underlying chaotic, non-linear systems, ANNs have become popular for the modeling of ecosystem structure and function. However, ANNs exhibit a holistic deficiency in declarative knowledge structure (i.e. a ‘black-box’). The architecture of the Grey-Box provided the benefit of the ANN modeling structure, while deconvolving the interaction of prediction potentials among environmental variables upon CHL a. The influences of (pairs of) predictors upon the variance and magnitude of CHL a were depicted via pedagogical knowledge extraction (multi-dimensional response surfaces). This afforded derivation of mathematical equations for iterative predictive outcomes of CHL a and together with an algorithmic expression across iterations, corrected for the lack of declarative knowledge within conventional ANNs. Importantly, the Grey-Box ‘bridged the gap’ between ‘white-box’ parametric models and black-box ANNs in terms of performance and mathematical transparency. Grey-Box formulations are relevant to ecological niche modeling, identification of biotic response(s) to stress/disturbance thresholds, and qualitative/quantitative derivation of biota-environmental relationships for incorporation within stand-alone mechanistic models projecting ecological structure.

Stress Corrosion Cracking Resistant Aluminum Alloys: Optimizing Concentrations of Alloying Elements and Tempering

The objective of this study is to develop a new family of aluminum alloys with superior stress corrosion cracking resistance (SCCR) and mechanical properties. This approach uses experimentally obtained stress corrosion resistance, tensile strength, and yield strength data from the literature and then performs hybrid multiobjective evolutionary optimization combined with multidimensional response surfaces. This software has the proven capability to deal with various alloy design applications using minimal amount of experimental data. The selected objectives in this study are superior stress corrosion resistance, tensile strength, and yield strength. The design variables are concentrations of alloying elements and the individual alloy tempers as they are important parameters that directly affect macroscopic properties and microscopic details of the alloy such as grains, phases, precipitates, etc. The computational trials yield optimal alloys' chemical compositions and standard thermal treatment protocols for the best combination of superior stress corrosion resistance and mechanical properties. Single-objective optimization results confirm the known experimental observations that dilute Al alloys yield the best corrosion resistance at the expense of tensile strength. Optimizations with two simultaneous objectives and more alloying elements create better trade-off solutions. Quality and number of initially available experimentally evaluated alloys have decisive effects on accuracy of this alloy design method.