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The impact of the objective function in multi-site and multi-variable calibration of the SWAT model

ENVIRONMENTAL MODELLING & SOFTWARE 2017年第Jul.期93卷 255-267页

作者： Molina-Navarro, Eugenio Andersen, Hans E. Nielsen, Anders Thodsen, Hans Trolle, Dennis Aarhus Univ Dept Biosci Vejlsovej 25 DK-8600 Silkeborg Denmark

Automatic calibration of complex hydro-ecological models is an increasingly important issue which involves making decisions. One of the most relevant is the choice of the objective function, but its effects have been scarcely studied in complex models. We have used the SWAT model to assess the impact of the objective function for a multi-site (4 stations) and multi-variable (OrgP, OrgN, NO3-, PO43-) calibration of the Odense catchment (Denmark). Six calibration schemes were tested, varying the objective function and the nutrient fractions targeted. The best performance metrics (R2, NSE, PBIAS) were obtained when using NSE as objective function and targeting N-fractions and P-fractions separately. The scheme was validated in another SWAT set-up in northern Denmark. Although NSE is often questioned, we found it as an adequate objective function when addressing a multi-site and multi-variable calibration. Our findings may serve as guideline for hydro-ecological modellers, being useful to achieve watershed management goals. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Catchment model objective function Multi-site calibration Nutrients SWAT Calibration scheme

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A critical analysis of using the dynamic compliance as objective function in topology optimization of one-material structures considering steady-state forced vibration problems

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JOURNAL OF SOUND AND VIBRATION 2019年 444卷 1-20页

作者： Silva, Olavo M. Neves, Miguel M. Lenzi, Arcanjo Univ Fed Santa Catarina Mech Engn Dept Florianopolis SC Brazil Univ Lisbon Inst Super Tecn IDMEC Lisbon Portugal

Material based models for topology optimization in harmonic vibration problems present some inconveniences, especially when the goal is to obtain low vibration monolithic structures for excitation frequencies above the first resonance of the initial design. In this article, the authors study the choice of the vibrational performance function to be minimized. It is shown that it is inadequate to use the dynamic compliance (the most frequently used measure in the literature for vibration optimization) as an objective function for this type of optimization (aiming to obtain one-material structures), even when applying the static compliance as a constraint function or as a weighted part of the objective function. Physical and mathematical characteristics of the dynamic compliance are presented, such as dependence on the excitation frequency, function differentiability, and tendency to a trivial minimum. Several examples are analyzed in order to illustrate the difficulties in using this measure in topology optimization of one-material structures subjected to time-harmonic external loading, even including a constraint on static compliance in an attempt to ensure engineering feasibility. After some discussion, the authors indicate the main features of a vibration measure that makes it a better candidate to represent an objective function in an optimization procedure for harmonic problems, such as the absence of antiresonances in its frequency plot and an adequate capacity of representing the global system's response. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Topology optimization objective function Dynamic compliance Steady-state forced vibration

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Study of Perturbation Designs for the Partially Separable objective function With Gradient-Based Optimizations in History Matching

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SPE JOURNAL 2013年第3期18卷 495-507页

作者： Ding, D. Y. McKee, F. IFP Energies nouvelles F-92852 Rueil Malmaison France

Assisted history matching is widely used to constrain reservoir models by integrating well-production data and/or 4D seismic data. However, history matching generally requires a large number of reservoir simulations, which are very CPU time-consuming, in the optimization procedure. In this paper, we present a new technique that allows us to reduce the number of reservoir simulations for the gradient-based optimization method in history matching. The new method is based on the partial separability of the objective function with local components referred to the wells and/or the seismic zones. How to choose a good perturbation design for the gradient computation is the main issue. In this paper, the graph-coloring algorithm is applied to determine "independent" components and parameters for a partially separable function, and analytical test functions are proposed for the selection of perturbation designs. This method can significantly reduce the number of reservoir simulations for a partially separable objective function in history matching.

关键词： Artificial Intelligence Upstream Oil & Gas optimization problem Optimization Result seismic data principal parameter Reservoir Characterization history matching objective function Computation

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Optimal objective function for simulating endurance time excitations

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SCIENTIA IRANICA 2020年第4期27卷 1728-1739页

作者： Mashayekhi, M. Estekanchi, H. E. Vafai, A. Sharif Univ Technol Dept Civil Engn POB 11155-9313 Tehran Iran

Endurance Time (ET) method is a dynamic analysis procedure in which increasing excitations are imposed on structures;these excitations are known as Endurance Time Excitation functions (ETEF). This study presents a method to determine an optimal objective function for simulating ETEFs including unconstrained optimization problems. In optimization problems, equations are defined in terms of an objective function. In the problem of simulating ETEFs, the objective function can be defined in many different ways regarding the considered intensity measures and respective weighting factors. In addition, the type of calculating residuals (absolute way or relative way) diversifies the objective function definitions. The proposed method for determining the optimal objective function includes quantifying the accuracy of ETEFs in a scalar quantity regardless of their objective functions and introducing an approach to attenuate the dependence of results on the initial points of optimizations. The proposed method is applied, and results are then presented. It is observed that considering only acceleration spectra and calculating residuals in a relative way lead to more accurate ETEFs. (C) 2020 Sharif University of Technology. All rights reserved.

关键词： Endurance time method Optimization objective function Response spectra Time history dynamic analysis

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Effect of the objective function in the design of concentration plants

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MINERALS ENGINEERING 2014年 63卷 16-24页

作者： Cisternas, Luis A. Lucay, Freddy Galvez, Edelmira D. Univ Antofagasta Mineral Proc & Chem Eng Dept Antofagasta Chile CICITEM Antofagasta Chile Univ Catolica Norte Dept Met Eng Antofagasta Chile

Different objective functions have been used in the design of concentration plants. The frequently used functions correspond to the maximization of revenue or profit. However, there is no study examining the effect of the type of objective function on the design of these plants. This manuscript analyzes the effect of various objective functions, including the maximization of profits, the return on investment and the net present worth and the minimization of the payback period, among other functions. Additionally, the procedure for a flotation circuit design is presented that is based on a flexible superstructure, where the designer can choose the set of alternatives. Two cases were considered: the equipment design for a given circuit structure and the circuit structure design given the equipment. The generated models correspond to mixed integer nonlinear programming and nonlinear programming problems. The results indicate that the objective function has a significant effect on the obtained solution, as well as the concentration circuit structure. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Concentration plant Process design Optimization objective function

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Development of objective function-based ensemble model for streamflow forecasts

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JOURNAL OF HYDROLOGY 2024年 632卷

作者： Lin, Yongen Wang, Dagang Zhu, Jinxin Sun, Wei Shen, Chaopeng Wei, Shangguan Sun Yat Sen Univ Sch Geog & Planning Guangzhou Peoples R China Sun Yat Sen Univ Guangdong Key Lab Urbanizat & Geosimulat Guangzhou Peoples R China Penn State Univ Civil & Environm Engn University Pk PA 16802 USA Sun Yat Sen Univ Sch Atmospher Sci Zhuhai Peoples R China

The objective function plays an important role in hydrological model calibrations/training, since it largely determines the values of the model parameters and consequently influences the model performance. In this study, we establish two application-orientated objective functions, namely high flow balance error (HFBE) and mean squared percentage error (MSPE), for the forecasts of high flows and low flows, respectively. We examine the strengths and weaknesses of these streamflow forecast models trained with HFBE, MSPE and mean square error (MSE). Furthermore, we develop an objective function-based ensemble model (OEM) framework that can integrate the models trained with different objective functions. Our results in 273 catchments over USA show that the models trained on MSE have obvious underestimation in high-flow prediction. The models trained on HFBE can alleviate this underestimation and thus perform remarkably better for high-flow forecast. In addition, the models trained on MSPE outperform the other two models in low-flow forecast, but with an expense of the deterioration in the forecasting performance for high-flow. By incorporating the models trained on HFBE, MSPE and MSE, our proposed OEM performs well under all streamflow levels, with a median KGE of 0.96 and a median logNSE of 0.95. OEM realistically captures the mean and the variability of the observational streamflow under different scenarios with a variety of hydrometeorological conditions. This study highlights the necessity of applying objective functions that are appropriate for the modeling goal and the potential of ensemble learning methods for multi-objective optimization in hydrological modeling.

关键词： Streamflow forecast objective function Ensemble learning Multi-optimization USA

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Protection coordination of directional overcurrent relays: new time current characteristic and objective function

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第1期12卷 190-199页

作者： Yazdaninejadi, Amin Naderi, Mehdi S. Gharehpetian, Gevork B. Talavat, Vahid Urmia Univ Elect Engn Dept Orumiyeh Iran Amirkabir Univ IGSORC Tehran Iran Amirkabir Univ Elect Engn Dept Tehran Iran

Clearing power grid faults swiftly and selectively offers higher security, reliability and sustainability. Accomplishing this aim by deploying directional overcurrent relays (DOCRs) is one of the major challenges in meshed and multisource distribution networks. To overcome this challenge, the current study elaborates a new coordination strategy which concentrates on minimising overall operation time of relays. In this strategy, an auxiliary variable is added to classical operation time model of each DOCR. All the auxiliary variables are considered as coordination constraints which help to yield new and well-defined time current characteristics (TCCs). In other words, more flexibility is attained in adjusting relay's characteristic which helps to alleviate clearing time of faults. The obtained TCCs can be easily performed by numerical relays. In addition, a new objective function is defined to steer the relay settings towards optimal solutions conveniently. It was shown that the proposed approach not only reduces the operation time of relays, but also prevents miscoordinations. This approach demonstrates a non-linear programming model tackled by particle swarm optimisation algorithm. The effectiveness of the proposed approach is verified via 8-bus and IEEE 14-bus test systems and results are discussed in depth.

关键词： relay protection overcurrent protection power grids fault diagnosis power distribution protection nonlinear programming numerical analysis protection coordination directional overcurrent relays DOCR time current characteristic objective function power grid faults meshed distribution networks multisource distribution networks classical operation time model auxiliary variables coordination constraints TCC numerical relays operation time nonlinear programming model particle swarm optimisation algorithm 8-bus test systems IEEE 14-bus test systems

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On the objective function for Topology Optimization of Heat Sinks

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IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY 2021年第11期11卷 1776-1782页

作者： Lee, Gilho Joo, Younghwan Kim, Sung Jin Korea Adv Inst Sci & Technol Dept Mech Engn Daejeon 34141 South Korea Korea Inst Energy Res Energy Management Syst Lab Daejeon 34129 South Korea

In topology optimization, the optimal layout of the structure is obtained through an iterative update of the geometry. Since this update procedure utilizes the gradient of the objective function, it is important to select an appropriate objective function in order to obtain a meaningful geometry. From this point of view, the mathematical definition and physical meaning of the objective functions for topology optimization of heat sinks are reviewed in this article. For this, studies from conductive heat transfer problems to recent computational fluid dynamics (CFD)-based conjugate heat transfer problems are covered. In most of the studies, the objective functions are defined in order to minimize the thermal resistance of the heat sink or to minimize the maximum temperature of the heat source. In place of thermal resistance, thermal compliance is commonly used as the objective function. However, it is worth noting that minimization of the thermal compliance may lead to considerable deviation of the design from that based on the minimum thermal resistance. This is because the thermal compliance is linearly proportional to the average temperature of the heat source in the computational domain, and the average temperature of the heat source is usually different from the maximum temperature of the heat source. In heat conduction problems, the difference between the maximum temperature and the average temperature becomes large when the thermal conductivity of the solid material becomes low. In convection problems, the difference becomes large when the streamwise fluid temperature variation becomes large due to the low heat capacity rate of the fluid.

关键词： Heat sinks Optimization Linear programming Topology Geometry Thermal resistance Temperature distribution Heat sink objective function topology optimization

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Deep-learning optimization using the gradient of a custom objective function: A full-waveform inversion example study on the convolutional objective function

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GEOPHYSICS 2024年第5期89卷 R479-R492页

作者： Fang, Jinwei Zhou, Hui Li, Yunyue Elita Shi, Ying Li, Xu Wang, Enyuan China Univ Min & Technol Sch Safety Engn State Key Lab Intelligent Construct & Hlth Operat Xuzhou Peoples R China China Univ Petr Dept Geophys Beijing Peoples R China Purdue Univ Dept Earth Atmospher & Planetary Sci Sustainabil G W Lafayette IN USA Northeast Petr Univ Sch Earth Sci Daqing Peoples R China Univ Sci & Technol China Dept Informat Sci & Technol Hefei Peoples R China

The integration of conventional high-performance full-waveform inversion (FWI) algorithms with deep-learning frameworks is an innovative and promising research direction with the potential to enhance and broaden the application prospects of this field significantly. Automatic differentiation with back- propagation techniques can derive the gradients of model parameters in an equivalent manner to that of adjoint methods;however, it requires a substantial amount of computer memory, particularly when considering the time-step layers. In addition, some excellent objective functions suitable for FWI are not available in deep-learning frameworks. In comparison, the ad- joint method, based on effective boundary storage technology, offers greater practicality for calculating the gradients of various objective functions. Therefore, this paper develops a novel approach toward FWI that integrates deep-learning optimization with high-performance gradient computation. In particular, our method inputs model parameter gradients from a custom objective function into the deep-learning framework. Herein, we use the acoustic equation with variable density as an example to demonstrate how a convolutional objective function, along with its corresponding velocity and density gradients, can be used for optimized inversion, multiscale inversion, and deep network parameterization-based multiscale inversion within the deep-learning framework. This approach provides a paradigm for deep-learning-optimized FWI, which we apply to synthetic and field data scenarios.

关键词： full-waveform inversion deep learning objective function

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Assessing the transferability of a hybrid Taguchi-objective function method to optimize image segmentation for detecting and counting cave roosting birds using terrestrial laser scanning data

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JOURNAL OF APPLIED REMOTE SENSING 2016年第3期10卷

作者： Idrees, Mohammed Oludare Pradhan, Biswajeet Buchroithner, Manfred F. Shafri, Helmi Zulhaidi Mohd Bejoc, Siti Khairunniza Univ Putra Malaysia Geospatial Informat Sci Res Ctr Fac Engn Dept Civil Engn Upm Serdang 43400 Selangor Malaysia Tech Univ Dresden Inst Cartog Helmholtzstr 10 D-01062 Dresden Germany Univ Putra Malaysia Fac Engn Dept Biol & Agr Engn Upm Serdang 43400 Selangor Malaysia

As far back as early 15th century during the reign of the Ming Dynasty (1368 to 1634 AD), Gomantong cave in Sabah (Malaysia) has been known as one of the largest roosting sites for wrinkle-lipped bats (Chaerephon plicata) and swiftlet birds (Aerodramus maximus and Aerodramus fuciphagus) in very large colonies. Until recently, no study has been done to quantify or estimate the colony sizes of these inhabitants in spite of the grave danger posed to this avifauna by human activities and potential habitat loss to postspeleogenetic processes. This paper evaluates the transferability of a hybrid optimization image analysis-based method developed to detect and count cave roosting birds. The method utilizes high-resolution terrestrial laser scanning intensity image. First, segmentation parameters were optimized by integrating objective function and the statistical Taguchi methods. Thereafter, the optimized parameters were used as input into the segmentation and classification processes using two images selected from Simud Hitam (lower cave) and Simud Putih (upper cave) of the Gomantong cave. The result shows that the method is capable of detecting birds (and bats) from the image for accurate population censusing. A total number of 9998 swiftlet birds were counted from the first image while 1132 comprising of both bats and birds were obtained from the second image. Furthermore, the transferability evaluation yielded overall accuracies of 0.93 and 0.94 (area under receiver operating characteristic curve) for the first and second image, respectively, with p value of <0.0001 at 95% confidence level. The findings indicate that the method is not only efficient for the detection and counting cave birds for which it was developed for but also useful for counting bats;thus, it can be adopted in any cave. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： Taguchi objective function conservation remote sensing ecology terrestrial laser scanning

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