Surrogate Optimization Method Research Articles

Determining the Drucker-Prager Cap model constants using experimental, numerical and optimization for compacted Mg powders at different strain rates

This article investigates an inverse approach to determine the coefficients of the Drucker-Prager model for magnesium powder. The approach involves conducting finite element simulations of the powder compression process within LS-DYNA software, employing the Drucker-Prager material model. The goal is to minimize the disparity between force-displacement outcomes derived from simulations and experimental data using a surrogate optimization method. Experimental data were obtained through a uniaxial compression test and served as a basis for adjusting the Cap model coefficients. A random selection of coefficients was made using the Latin cube method and simulations were performed based on the initial coefficients. The optimization was then performed using the particle swarm algorithm over 20 iterations. The optimized coefficients were validated against experimental data, demonstrating close agreement. By utilizing the extracted coefficients, the relative density of the samples was calculated at three different compaction speeds, i.e., 15.5 m s−1 (using a Hopkinson bar), 8 m s−1 (using a drop weight), and 1 mm min−1 (using an Instron machine). The analysis revealed the highest relative density and stress in the densified sample via the Hopkinson bar method, reaching 99.83% and 1.1 GPa, respectively.

DETERMINATION OF CONCRETE RHEOLOGICAL PARAMETERS USING NONLINEAR OPTIMIZATION METHODS

The article proposes a method for processing concrete creep curves based on the nonlinear equation of V.M. Bondarenko. The experimental data of A.V. Yashin is used. The problem of finding rheological parameters and the nonlinearity function is posed as a nonlinear optimization problem. The objective function represents the sum of the squared deviations of the experimental values of the creep strain from the theoretical values for all creep curves for one concrete at different stress levels. The minimum of the objective function is found using the interior point method, the surrogate optimization method, the pattern search method, the genetic algorithm, and the particle swarm method. It has been established that the first of these methods has the greatest efficiency. The proposed approach provides high quality approximation of experimental curves at all stress levels. It is shown that for concrete the nonlinearity of creep deformations is more pronounced than the nonlinearity of instantaneous deformations, and the same function cannot be used to describe these two types of nonlinearity.

An optimization method of electrostatic sensor array based on Kriging surrogate model and improved non-dominated sorting genetic algorithm with elite strategy algorithm

Array-type electrostatic monitoring is gradually becoming an effective tool for aero-engine fault diagnosis. In this paper, we innovatively apply the surrogate optimization method to the optimization of the sensor array structure in order to meet the need of improving the particle information recognition capability of the electrostatic sensor array (ESA). A structure optimization method of ESA based on the Kriging surrogate model and improved NSGA-II algorithm is proposed. In this paper, a finite element simulation model of ESA is established, and the array optimization problem is abstracted as the solution of a mixed-integer optimization problem. This paper reduces the large-scale numerical simulations in the full-variable space with the help of the Kriging surrogate model. In addition, an improved NSGA-II algorithm for mixed-integer optimization is proposed. The simulation experiment verified that the average absolute error of the sensor before and after optimization for the identification of particle position and charge quantity was reduced by 69.88% and 49.68%, respectively. The array structure optimization method proposed in this paper facilitates the acceleration of the design process of electrostatic sensors and provides a scientific design method for their specific design for airborne application.

Data-driven surrogate optimization for deploying heterogeneous multi-energy storage to improve demand response performance at building cluster level

Energy storage such as battery and thermal energy storage is an effective approach to shift building peak load and alleviate grid stress at a building cluster level. However, due to the heterogeneous performance of different types of storage (e.g., response speed, charge/discharge efficiency and rate, storage capacity) and highly diversified energy use patterns of individual buildings, the multi-energy storage should be properly selected and optimally designed for individual buildings to achieve effective load shifting. The optimal deployment of multi-energy storage at a cluster level is a challenging optimization problem due to the nonlinear dynamic performance of the multi-energy storage and the high dimensionality as a result of a large number of buildings. To tackle the challenges, this study proposes a data-driven surrogate optimization method that optimally deploys multi-energy storage at a cluster level to minimize the building cluster energy bill under demand response programs. The method utilizes data-driven surrogate models to accurately predict demand response performance of individual buildings with multi-energy storage. An iterative optimization with automated energy-storage-option screening is developed to optimize the multi-energy storage configurations and design parameters. For a case study including 21 buildings, by optimally deploying multi-energy storage including battery, cooling TES tank, and building-integrated TES, the method reduced the building cluster energy bill by 8%–181% as compared to baseline cases. The optimal deployment method effectively identifies the buildings with better potential to adopt demand-side management and balances the pros and cons of the energy storage options, increasing demand response incentives by 12%–31%. The proposed method can be used in practice to facilitate the deployment of energy storage and improve engagement of buildings in demand response.

Trihedral Lattice Towers Optimization with a Limitation on the Resonant Vortex Excitation Occurrence

Trihedral lattice towers are widely used as transmission line supports, wind turbine supports, cell towers, and floodlight towers. The aim of this work is to develop a technique for optimizing trihedral lattice supports to reduce their weight, taking into account the limitation on resonant vortex excitation. At the same time, restrictions are also introduced on the maximum stress, as well as the ultimate slenderness of the elements. Thus, with a minimum weight, the tower must meet all the requirements of the design codes. A lattice tower used as a floodlight mast is considered. The tower consists of two sections, the upper of which is of constant width, and the width of the lower section varies according to a linear law. The elements of the tower are made from pipes with an annular cross section. The sections’ widths and heights, the dimensions of elements’ cross-sections, and the number of panels are the variable parameters. The solution of the nonlinear optimization problem is implemented in MATLAB software. Internal forces in the tower and natural frequencies are calculated by the finite element method. The tower is subjected to the action of ice and wind loads, dead weight and the weight of the equipment. The wind load is considered as the sum of the average and pulsation components. To solve the problem of nonlinear optimization, the surrogate optimization method and the genetic algorithm are used. One of the serially used designs was chosen as the initial approximation. The design obtained as a result of optimization compared to the initial approximation has a mass more than two times less and at the same time satisfies all design requirements.

A wide-speed-range aerodynamic configuration by adopting wave-riding-strake wing

The wide-speed-range characteristics of aerodynamic configuration are critical to the design of the horizontal take-off and landing aircraft. To address this problem, the work proposes a wide-speed-range aerodynamic configuration by assembling a waverider to the aircraft with arrow-shaped wing. To enhance the aerodynamic performance of this configuration, surrogate optimization method is applied to the airfoil of the arrow-shaped wing. Thus, the optimized airfoil with double “S” cambers on the lower surface, and a small leading-edge radius is obtained. The aerodynamic performance of the whole aircraft in the wide-speed range has been investigated numerically by means of the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations coupled with the SST k-omega turbulence model. At subsonic conditions, the waverider can act as a strake-wing to induce vortex from the leading edge of the upper surface. With the large sweep arrow-wing, the subsonic aerodynamic performance is improved by utilizing the vortex lift. At supersonic conditions, wave-riding characteristics as well as the small leading-edge radius wing can effectively reduce the wave-drag. Overall, the lift-to-drag ratio of this configuration is not less than 5.4 at 4-degree angle of attack within Mach number 0.5–7, indicating that this configuration provides outstanding hypersonic aerodynamic performance as well as fairly acceptable subsonic aerodynamic characteristics.

Surrogate Global Optimization for Identifying Cost‐Effective Green Infrastructure for Urban Flood Control With a Computationally Expensive Inundation Model

AbstractOptimization algorithms and urban inundation models are powerful tools to identify cost‐effective designs of urban green infrastructures such as low‐impact developments (LIDs). Most previous LID design optimization studies are based on one‐dimensional (1D) inundation models, which cannot provide spatial information of flooding. The LID design optimization on two‐dimensional (2D) models or coupled 1D‐2D models was rarely explored due to the expensive computing time. This work investigates the effectiveness of surrogate optimization methods for LID design, which have not been used for the LID design problems. We propose a general LID design optimization framework that searches the optimal LID configurations based on both the spatial flood damage under a series of probable flood events and the life cycle costs (LCCs) of LID. We demonstrate the framework using a case study for an urban catchment with 55 sub‐catchments and 103 LID decision variables. We tested two different surrogate optimization methods designed for high‐dimensional problems: DYnamic COordinate search using Response Surface models (DYCORS) and Trust Region Bayesian Optimization (TuRBO), and one popular non‐surrogate method particle swarm (PSO). The result indicates that: (a) DYCORS is a promising method (significantly faster than TuRBO and PSO) for identifying the optimal LID design to minimize the flood damage cost and LID LCC; (b) Optimized LID design could reduce damage cost by as much as $12.14 million for the urban catchment after eliminating its own LCC compared with no LID implementation; (c) LID is effective in reducing the imperviousness of lands in urban areas.

A new method for ensemble combination based on adaptive decision making

Ensemble classifiers methods are considered as one of the strongest classification approaches in different applications. A key factor in creating a successful ensemble is to design an optimal combiner that minimizes classification errors. Unfortunately, finding the best fusion methodology that maximizes ensemble performance is a challenge. Most popular ensemble classifiers systems use fixed fusion methods such as average and majority voting. For a given application, there is no clear understanding of why a fusion method might work better than other methods. In this work, decision-making based on Adaptive Power Mean Combiner (APMC) is investigated. A mathematical and experimental framework for ensemble classifier systems based on APMC is proposed. The theoretical results explain why a given algebraic combiner such as average, product, maximum, minimum, and others works best for a given dataset while providing poor results on other datasets. It was shown that selecting an optimal fusion method is strongly dependent on the statistics of base learners’ outputs. Theoretical results for a given ensemble condition show that an improvement in classification accuracy of ∼8% compared to the average fusion method is achieved. Guided by theoretical results, we propose an experimental ensemble-learning algorithm based on surrogate optimization method for searching fusion methods for a given ensemble condition. The performance trend predicted by the mathematical model is validated through several datasets and compared against different fusion methods. Experimental results show the proposed algorithm achieves notable classification results compared to several fusion methods.

Optimal bidding and scheduling of AA-CAES based energy hub considering cascaded consumption of heat

The increasing level of uncertainty caused by high penetration of renewable energy and the widening gap of peak-valley demands call for the deployment of energy storage in power systems. Advanced-adiabatic compressed air energy storage (AA-CAES) is a large-scale physical energy storage technology with the merits of long lifetime, low environmental impact, and no emission. Moreover, AA-CAES works with electricity and heat, making it an excellent choice to realize the framework of energy hub. This paper proposes a cogeneration and storage architecture of an AA-CAES based energy hub in an industrial park. Particularly, the cascaded use of thermal energy to supply heat demands with different temperatures is modeled. A bi-level optimization model is established to study the optimal bidding and scheduling of AA-CAES based energy hub in the day-ahead market. The upper level is the power purchase and self-scheduling of the energy hub, aiming at minimizing the daily operation cost; the lower level represents the market clearing problem which determines the electricity price based on alternating-current optimal power flow. A radial basis function based surrogate optimization method is developed to solve the bi-level model with a nonlinear lower level problem. The problem is decomposed into second-order cone programs and a nonlinear surrogate model which can be solved without much computational effort. Numerical examples verify the effectiveness of the proposed method.

Trihedral lattice towers geometry optimization

The problem of trihedral lattice towers geometry optimization, the width of which varies linearly with height, has been considered. The variable parameters were the support width at the base and top point, as well as the cross-sectional areas of the lattice and chords. A restriction was introduced on the mass constancy. The objective function was the potential strain energy, the maximum displacement and the first frequency of natural vibrations. In the first and second cases the optimum corresponds to the minimum of the objective function, and in the third - to the maximum. The solution was performed by the finite element method in combination with four nonlinear optimization methods: the interior point method, surrogate optimization method, genetic algorithm and pattern search method. The efficiency of each of the listed optimization methods has been compared by the authors.

Topological surrogates for computationally efficient seismic robustness optimization of water pipe networks

AbstractThe criticality of seismic robustness of the water pipe networks cannot be overstated. Current methodologies for optimizing seismic robustness of city‐scale water pipe networks are scarce. A very few studies that can be found are also prone to long optimization runtimes due to the requirement of repeated hydraulic analysis. Hence, there is a critical need for the identification of computationally efficient surrogate optimization methods for maximizing seismic robustness of water pipe networks. To address this need, this research was conducted to identify, for the first time, computationally efficient topological surrogates for hydraulic simulation‐based optimization. The computational efficiency of surrogate optimization was measured in terms of solution quality (i.e., post‐earthquake serviceability) and computational runtime. Ten different topological connectivity metrics were evaluated out of which five were considered computationally infeasible due to their prohibitive optimization runtime. Five remaining metrics were then used to formulate five surrogate objective functions for seismic robustness of water pipe networks. Each of these functions was optimized using a simulated annealing‐based algorithm. Application of the proposed approach to city‐level benchmark networks helped to identify two metrics out of ten that offered a substantial reduction in optimization runtime with a minimal loss in solution quality. These findings will be highly valuable to water distribution network managers for identifying economical rehabilitation policies for enhancing the seismic robustness at a city‐scale within a reasonable amount of time.

Evaluation of Estimation of Distribution Algorithm to Calibrate Computationally Intensive Hydrologic Model

AbstractThe estimation of distribution algorithm (EDA) is a new evolutionary algorithm developed as an alternative to the traditional genetic algorithm (GA). The EDA guides the search by avoiding the crossover and mutation operators of the GA in favor of building and sampling probabilistic distributions of promising candidate solutions. By increasing the probability of generating solutions with better fitness values, the EDA locates the region of the global optimum or its accurate approximation. In this study, EDA was used to calibrate the parameters of the soil and water assessment tool hydrologic model for the Xunhe River Basin in China. The EDA was compared with three other algorithms: (1) the Multistart Local Metric Stochastic Radial Basis Function algorithm (a surrogate optimization method), (2) the Shuffled Complex Evolution algorithm, and (3) the GA. Four metrics are presented to assess the performance of the algorithms: (1) efficiency in terms of the average best objective function value in a limi...

Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration

Optimization of multi-phase transport models is important both for calibrating model parameters to observed data and for analyzing management options. We focus on examples of geological carbon sequestration (GCS) process-based multi-phase models. Realistic GCS models can be very computationally expensive not only due to the spatial distribution of the model but also because of the complex nonlinear multi-phase and multi-component transport equations to be solved. As a result we need to have optimization methods that get accurate answers with relatively few simulations. In this analysis we compare a variety of different types of optimization algorithms to understand the best type of algorithms to use for different types of problems. This includes an analysis of which characteristics of the problem are important in choice of algorithm. The goal of this paper is to evaluate which optimization algorithms are the most efficient in a given situation, taking into account shape of the optimization problem (e.g. uni- or multi-modal) and the number of simulations that can be done. The algorithms compared are the widely used derivative-based PEST optimization algorithm, the derivative-based iTOUGH2, the Kriging response surface algorithm EGO, the heuristics-based DDS (Dynamically Dimensioned Search), and the Radial Basis Function surrogate response surface based global optimization algorithms ‘GORBIT’ and ‘Stochastic RBF’. We calibrate a simple homogeneous model ‘3hom’ and two more realistic models ‘20layer’ and ‘6het’. The latter takes 2h per simulation. Using rigorous statistical tests, we show that while the derivative-based algorithms of PEST are efficient on the simple 3hom model, it does poorly in comparison to surrogate optimization methods Stochastic RBF and GORBIT on the more realistic models. We then identify the shapes of the optimization surface of the three models using enumerative simulations and discover that 3hom is smooth and unimodal and the more realistic models are rough and multi-modal. When the number of simulations is limited, surrogate response surfaces algorithms perform best on multi-modal, bumpy objective functions, which we expect to have for most realistic multi-phase flow models such as those for GCS.

VERSATILE, HIGH-QUALITY MOTIONS AND BEHAVIOR CONTROL OF A HUMANOID SOCCER ROBOT

Autonomous soccer games represent an extraordinary challenge for autonomous humanoid robots which must act fast and stable while carrying all needed onboard computers, sensors and batteries. In this paper, the development and system integration of hardware and software modules of the 55-cm tall, autonomous humanoid soccer robot Bruno is described to cope with this challenge. Although based on a "minimalistic" design which only uses gyroscopes in the hip but not foot-ground contact sensors for control of balance, versatile and high-quality walking motions have been developed. Fast forward walking of about 1.5 km/h has been obtained using an efficient sequential surrogate optimization method and walking through uneven terrain with a newly designed passively compliant foot sole. Further modules of the software and control architecture which are needed for an adaptive selection of different motions and autonomous robot behavior are briefly described. Experimental results are reported, which have been obtained under the conditions of a live competition. The robot's hardware is mainly based on standard components which can therefore be easily adapted by new designers, as no comparable, standard humanoid robot platforms are available.

EGO shape optimization of horn-loaded loudspeakers

Horn-loaded loudspeakers increase the efficiency and control the spatial distribution of sound radiated from the horn mouth. They are often used as components in cinema sound systems where it is desired that the sound be broadcast onto the audience uniformly at all frequencies, improving the listening experience. The sound distribution, or beamwidth, is related to the shape of the horn and can be predicted by numerical methods, such as the boundary-element or source-superposition method, however the cost of evaluating the objective function is high. To overcome this a surrogate optimization method called Efficient Global Optimization (EGO) was used with a spline-based parameterization to find the shape of the horn that gives a frequency-independent beamwidth, thus giving a high quality listening experience.