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Готові списки джерел за темами / Multiscale optimization / Статті в журналах

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Статті в журналах з теми "Multiscale optimization"

Автор: Grafiati

Опубліковано: 19 жовтня 2024

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1

Xu, Fan, Peter Wai Tat TSE, Yan-Jun Fang, and Jia-Qi Liang. "A fault diagnosis method combined with compound multiscale permutation entropy and particle swarm optimization–support vector machine for roller bearings diagnosis." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 233, no. 4 (July 20, 2018): 615–27. http://dx.doi.org/10.1177/1350650118788929.

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A method based on compound multiscale permutation entropy, support vector machine, and particle swarm optimization for roller bearings fault diagnosis was presented in this study. Firstly, the roller bearings vibration signals under different conditions were decomposed into permutation entropy values by the multiscale permutation entropy and compound multiscale permutation entropy methods. The compound multiscale permutation entropy model combined the different graining sequence information under each scale factor. The average value of each scale factor was regarded as the final entropy value in the compound multiscale permutation entropy model. The compound multiscale permutation entropy model suppressed the shortcomings of poor stability caused by the length of the original signals in the multiscale permutation entropy model. Validity and accuracy are considered in the numerical experiments, and then compared with the computational efficiency of the multiscale permutation entropy method. Secondly, the entropy values of the multiscale permutation entropy/compound multiscale permutation entropy under different scales are regarded as the input of the particle swarm optimization–support vector machine models for fulfilling the fault identification, the classification accuracy is used to verify the effectiveness of the multiscale permutation entropy/compound multiscale permutation entropy with particle swarm optimization–support vector machine. Finally, the experimental results show that the classification accuracy of the compound multiscale permutation entropy model is higher than that of the multiscale permutation entropy.

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2

Murphy, Ryan, Chikwesiri Imediegwu, Robert Hewson, and Matthew Santer. "Multiscale structural optimization with concurrent coupling between scales." Structural and Multidisciplinary Optimization 63, no. 4 (January 8, 2021): 1721–41. http://dx.doi.org/10.1007/s00158-020-02773-3.

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AbstractA robust three-dimensional multiscale structural optimization framework with concurrent coupling between scales is presented. Concurrent coupling ensures that only the microscale data required to evaluate the macroscale model during each iteration of optimization is collected and results in considerable computational savings. This represents the principal novelty of this framework and permits a previously intractable number of design variables to be used in the parametrization of the microscale geometry, which in turn enables accessibility to a greater range of extremal point properties during optimization. Additionally, the microscale data collected during optimization is stored in a reusable database, further reducing the computational expense of optimization. Application of this methodology enables structures with precise functionally graded mechanical properties over two scales to be derived, which satisfy one or multiple functional objectives. Two classical compliance minimization problems are solved within this paper and benchmarked against a Solid Isotropic Material with Penalization (SIMP)–based topology optimization. Only a small fraction of the microstructure database is required to derive the optimized multiscale solutions, which demonstrates a significant reduction in the computational expense of optimization in comparison to contemporary sequential frameworks. In addition, both cases demonstrate a significant reduction in the compliance functional in comparison to the equivalent SIMP-based optimizations.

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3

Mjolsness, E., C. D. Garrett, and W. L. Miranker. "Multiscale optimization in neural nets." IEEE Transactions on Neural Networks 2, no. 2 (March 1991): 263–74. http://dx.doi.org/10.1109/72.80337.

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4

Han, Zhenyu, Shouzheng Sun, Zhongxi Shao, and Hongya Fu. "Multiscale Collaborative Optimization of Processing Parameters for Carbon Fiber/Epoxy Laminates Fabricated by High-Speed Automated Fiber Placement." Advances in Materials Science and Engineering 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/5480352.

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Processing optimization is an important means to inhibit manufacturing defects efficiently. However, processing optimization used by experiments or macroscopic theories in high-speed automated fiber placement (AFP) suffers from some restrictions, because multiscale effect of laying tows and their manufacturing defects could not be considered. In this paper, processing parameters, including compaction force, laying speed, and preheating temperature, are optimized by multiscale collaborative optimization in AFP process. Firstly, rational model between cracks and strain energy is revealed in order that the formative possibility of cracks could be assessed by using strain energy or its density. Following that, an antisequential hierarchical multiscale collaborative optimization method is presented to resolve multiscale effect of structure and mechanical properties for laying tows or cracks in high-speed automated fiber placement process. According to the above method and taking carbon fiber/epoxy tow as an example, multiscale mechanical properties of laying tow under different processing parameters are investigated through simulation, which includes recoverable strain energy (ALLSE) of macroscale, strain energy density (SED) of mesoscale, and interface absorbability and matrix fluidity of microscale. Finally, response surface method (RSM) is used to optimize the processing parameters. Two groups of processing parameters, which have higher desirability, are obtained to achieve the purpose of multiscale collaborative optimization.

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5

Sivapuram, Raghavendra, Peter D. Dunning, and H. Alicia Kim. "Simultaneous material and structural optimization by multiscale topology optimization." Structural and Multidisciplinary Optimization 54, no. 5 (July 1, 2016): 1267–81. http://dx.doi.org/10.1007/s00158-016-1519-x.

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6

Fritzen, Felix, Liang Xia, Matthias Leuschner, and Piotr Breitkopf. "Topology optimization of multiscale elastoviscoplastic structures." International Journal for Numerical Methods in Engineering 106, no. 6 (October 6, 2015): 430–53. http://dx.doi.org/10.1002/nme.5122.

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7

Boucard, P. A., S. Buytet, and P. A. Guidault. "A multiscale strategy for structural optimization." International Journal for Numerical Methods in Engineering 78, no. 1 (April 2, 2009): 101–26. http://dx.doi.org/10.1002/nme.2484.

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8

Zhao, Ang, Pei Li, Yehui Cui, Zhendong Hu, and Vincent Beng Chye Tan. "Multiscale topology optimization with Direct FE2." Computer Methods in Applied Mechanics and Engineering 419 (February 2024): 116662. http://dx.doi.org/10.1016/j.cma.2023.116662.

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9

Oliveira, D. F., and A. C. Reynolds. "Hierarchical Multiscale Methods for Life-Cycle-Production Optimization: A Field Case Study." SPE Journal 20, no. 05 (October 20, 2015): 896–907. http://dx.doi.org/10.2118/173273-pa.

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Summary We apply hierarchical multiscale techniques previously developed by the authors to estimate the well controls that maximize the net present value of the long-term production from a real field offshore Brazil. This field has been in production for several years, and it represents a significant share of the overall oil production for the country. The production-optimization step is preceded by a 10-year historical period, where seismic and production data were history matched by use of ensemble-based approaches. The well controls on a sequence of control steps (time intervals) are optimized for the next 10 years of production by use of the hierarchical-multiscale-optimization and the refinement-indicator-based hierarchical-multiscale-optimization techniques, which refine the control steps as the optimization proceeds. The performance of our approaches is compared with that of a reference case, which applies the well rates used to forecast the production of the real field, as well as with the performance of a standard optimization procedure that uses a fixed set of well controls and a simple procedure to refine control steps.

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10

Pal, Saloni, Richard Clare, Andrew Lambert, and Stephen Weddell. "Multiscale optimization of the geometric wavefront sensor." Applied Optics 60, no. 25 (August 23, 2021): 7536. http://dx.doi.org/10.1364/ao.423536.

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11

Kato, Junji, Daishun Yachi, Shinsuke Takase, Kenjiro Terada, and Takashi Kyoya. "1903 Material Design using Multiscale Topology Optimization." Proceedings of The Computational Mechanics Conference 2013.26 (2013): _1903–1_—_1903–2_. http://dx.doi.org/10.1299/jsmecmd.2013.26._1903-1_.

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12

Yourdkhani, Mostafa, Damiano Pasini, and Francois Barthelat. "Multiscale mechanics and optimization of gastropod shells." Journal of Bionic Engineering 8, no. 4 (December 2011): 357–68. http://dx.doi.org/10.1016/s1672-6529(11)60041-3.

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13

Wang, Yingjun, Hang Xu, and Damiano Pasini. "Multiscale isogeometric topology optimization for lattice materials." Computer Methods in Applied Mechanics and Engineering 316 (April 2017): 568–85. http://dx.doi.org/10.1016/j.cma.2016.08.015.

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14

XU, Zhao, Weihong ZHANG, Ying ZHOU, and Jihong ZHU. "Multiscale topology optimization using feature-driven method." Chinese Journal of Aeronautics 33, no. 2 (February 2020): 621–33. http://dx.doi.org/10.1016/j.cja.2019.07.009.

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15

Hu, Nan, and Jacob Fish. "Enhanced ant colony optimization for multiscale problems." Computational Mechanics 57, no. 3 (January 2, 2016): 447–63. http://dx.doi.org/10.1007/s00466-015-1245-z.

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16

Chandrasekhar, Aaditya, Saketh Sridhara, and Krishnan Suresh. "Graded multiscale topology optimization using neural networks." Advances in Engineering Software 175 (January 2023): 103359. http://dx.doi.org/10.1016/j.advengsoft.2022.103359.

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17

Deng, Jiadong, Claus B. W. Pedersen, and Wei Chen. "Connected morphable components-based multiscale topology optimization." Frontiers of Mechanical Engineering 14, no. 2 (January 12, 2019): 129–40. http://dx.doi.org/10.1007/s11465-019-0532-3.

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18

Christofides, Panagiotis D., and Antonios Armaou. "Control and optimization of multiscale process systems." Computers & Chemical Engineering 30, no. 10-12 (September 2006): 1670–86. http://dx.doi.org/10.1016/j.compchemeng.2006.05.025.

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19

Yang, Jianghong, Hailiang Su, Xinqing Li, and Yingjun Wang. "Fail-safe topology optimization for multiscale structures." Computers & Structures 284 (August 2023): 107069. http://dx.doi.org/10.1016/j.compstruc.2023.107069.

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20

Xiao, Mi, Wei Sha, Yan Zhang, Xiliang Liu, Peigen Li, and Liang Gao. "CMTO: Configurable-design-element multiscale topology optimization." Additive Manufacturing 69 (May 2023): 103545. http://dx.doi.org/10.1016/j.addma.2023.103545.

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21

Zhou, Fuming, Xiaoqiang Yang, Jinxing Shen, and Wuqiang Liu. "Fault Diagnosis of Hydraulic Pumps Using PSO-VMD and Refined Composite Multiscale Fluctuation Dispersion Entropy." Shock and Vibration 2020 (August 24, 2020): 1–13. http://dx.doi.org/10.1155/2020/8840676.

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Анотація:

Multiscale fluctuation dispersion entropy (MFDE) has been proposed to measure the dynamic features of complex signals recently. Compared with multiscale sample entropy (MSE) and multiscale fuzzy entropy (MFE), MFDE has higher calculation efficiency and better performance to extract fault features. However, when conducting multiscale analysis, as the scale factor increases, MFDE will become unstable. To solve this problem, refined composite multiscale fluctuation dispersion entropy (RCMFDE) is proposed and used to improve the stability of MFDE. And a new fault diagnosis method for hydraulic pumps using particle swarm optimization variational mode decomposition (PSO-VMD) and RCMFDE is proposed in this paper. Firstly, PSO-VMD is adopted to process the original vibration signals of hydraulic pumps, and the appropriate components are selected and reconstructed to get the denoised vibration signals. Then, RCMFDE is adopted to extract fault information. Finally, particle swarm optimization support vector machine (PSO-SVM) is adopted to distinguish different work states of hydraulic pumps. The experiments prove that the proposed method has higher fault recognition accuracy in comparison with MSE, MFE, and MFDE.

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22

Krogstad, S., V. L. L. Hauge, and A. F. F. Gulbransen. "Adjoint Multiscale Mixed Finite Elements." SPE Journal 16, no. 01 (August 23, 2010): 162–71. http://dx.doi.org/10.2118/119112-pa.

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Summary We develop an adjoint model for a simulator consisting of a multiscale pressure solver and a saturation solver that works on flow-adapted grids. The multiscale method solves the pressure on a coarse grid that is close to uniform in index space and incorporates fine-grid effects through numerically computed basis functions. The transport solver works on a coarse grid adapted by a fine-grid velocity field obtained by the multiscale solver. Both the multiscale solver for pressure and the flow-based coarsening approach for transport have shown earlier the ability to produce accurate results for a high degree of coarsening. We present results for a complex realistic model to demonstrate that control settings based on optimization of our multiscale flow-based model closely match or even outperform those found by using a fine-grid model. For additional speed-up, we develop mappings used for rapid system updates during the timestepping procedure. As a result, no fine-grid quantities are required during simulations and all fine-grid computations (multiscale basis functions, generation of coarse transport grid, and coarse mappings) become a preprocessing step. The combined methodology enables optimization of waterflooding on a complex model with 45,000 grid cells in a few minutes.

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23

Wang, Peng, Kun Cheng, Yan Huang, Bo Li, Xinggui Ye, and Xiuhong Chen. "Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization." Computational Intelligence and Neuroscience 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/8430175.

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This paper presents a variant of multiscale quantum harmonic oscillator algorithm for multimodal optimization named MQHOA-MMO. MQHOA-MMO has only two main iterative processes: quantum harmonic oscillator process and multiscale process. In the two iterations, MQHOA-MMO only does one thing: sampling according to the wave function at different scales. A set of benchmark test functions including some challenging functions are used to test the performance of MQHOA-MMO. Experimental results demonstrate good performance of MQHOA-MMO in solving multimodal function optimization problems. For the 12 test functions, all of the global peaks can be found without being trapped in a local optimum, and MQHOA-MMO converges within 10 iterations.

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24

Li, Keyu, Chao Yang, Xiaozhe Wang, Zhiqiang Wan, and Chang Li. "Multiscale Aeroelastic Optimization Method for Wing Structure and Material." Aerospace 10, no. 10 (October 2, 2023): 866. http://dx.doi.org/10.3390/aerospace10100866.

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Microstructured materials, characterized by their lower weight and multifunctionality, have great application prospects in the aerospace field. Optimization methods play a pivotal role in enhancing the design efficiency of both macrostructural and microstructural topology (MMT) for aircraft. This paper proposes a multiscale aeroelastic optimization method for wing structure and material considering realistic aerodynamic loads for large aspect ratio wings with significant aeroelastic effects. The aerodynamic forces are calculated by potential flow theory and the aeroelastic equilibrium equations are solved through finite element method. The parallel design of the wing MMT is achieved by utilizing the optimization criterion (OC) method based on sensitivity information. The optimization results indicate that wing elastic effects reinforce the outer section of the wing structure compared with the optimization results obtained under rigid aerodynamic forces. As the optimization constraints become more rigorous, the optimization results show that the components with larger loads are strengthened. Furthermore, the method presented in this paper can effectively optimize the wing structure under complex boundary conditions to achieve a reasonable stiffness distribution in the wing.

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25

Glanzer, Martin, and Georg Ch Pflug. "Multiscale stochastic optimization: modeling aspects and scenario generation." Computational Optimization and Applications 75, no. 1 (October 11, 2019): 1–34. http://dx.doi.org/10.1007/s10589-019-00135-4.

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Abstract Real-world multistage stochastic optimization problems are often characterized by the fact that the decision maker may take actions only at specific points in time, even if relevant data can be observed much more frequently. In such a case there are not only multiple decision stages present but also several observation periods between consecutive decisions, where profits/costs occur contingent on the stochastic evolution of some uncertainty factors. We refer to such multistage decision problems with encapsulated multiperiod random costs, as multiscale stochastic optimization problems. In this article, we present a tailor-made modeling framework for such problems, which allows for a computational solution. We first establish new results related to the generation of scenario lattices and then incorporate the multiscale feature by leveraging the theory of stochastic bridge processes. All necessary ingredients to our proposed modeling framework are elaborated explicitly for various popular examples, including both diffusion and jump models.

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26

Wang, Yani, Jinfang Dong, and Bo Wang. "Feature Matching Optimization of Multimedia Remote Sensing Images Based on Multiscale Edge Extraction." Computational Intelligence and Neuroscience 2022 (June 2, 2022): 1–7. http://dx.doi.org/10.1155/2022/1764507.

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In order to solve the problem of low efficiency of image feature matching in traditional remote sensing image database, this paper proposes the feature matching optimization of multimedia remote sensing images based on multiscale edge extraction, expounds the basic theory of multiscale edge, and then registers multimedia remote sensing images based on the selection of optimal control points. In this paper, 100 remote sensing images with a size of 3619 ∗ 825 with a resolution of 30 m are selected as experimental data. The computer is configured with 2.9 ghz CPU, 16 g memory, and i7 processor. The research mainly includes two parts: image matching efficiency analysis of multiscale model; matching accuracy analysis of multiscale model and formulation of model parameters. The results show that when the amount of image data is large, feature matching takes more time. With the increase of sampling rate, the amount of image data decreases rapidly, and the feature matching time also shortens rapidly, which provides a theoretical basis for the multiscale model to improve the matching efficiency. The data size is the same, 3619 × 1825, which makes the matching time between images have little difference. Therefore, the matching time increases linearly with the increase of the number of images in the database. When the amount of image data in the database is large, a higher number of layers should be used; when the amount of image data in the database is small, the number of layers of the model should be reduced to ensure the accuracy of matching. The availability of the proposed method is proved.

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27

Yu, Chen, Qifu Wang, Chao Mei, and Zhaohui Xia. "Multiscale Isogeometric Topology Optimization with Unified Structural Skeleton." Computer Modeling in Engineering & Sciences 122, no. 3 (2020): 779–803. http://dx.doi.org/10.32604/cmes.2020.09363.

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28

Acar, Pınar, Veera Sundararaghavan, and Nicholas Fasanella. "Multiscale Optimization of Nanocomposites with Probabilistic Feature Descriptors." AIAA Journal 56, no. 7 (July 2018): 2936–41. http://dx.doi.org/10.2514/1.j056791.

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29

Yan, Minghan, Jian Zhou, Cong Luo, Tingfa Xu, and Xiaoxue Xing. "Multiscale Joint Optimization Strategy for Retinal Vascular Segmentation." Sensors 22, no. 3 (February 7, 2022): 1258. http://dx.doi.org/10.3390/s22031258.

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The accurate segmentation of retinal vascular is of great significance for the diagnosis of diseases such as diabetes, hypertension, microaneurysms and arteriosclerosis. In order to segment more deep and small blood vessels and provide more information to doctors, a multi-scale joint optimization strategy for retinal vascular segmentation is presented in this paper. Firstly, the Multi-Scale Retinex (MSR) algorithm is used to improve the uneven illumination of fundus images. Then, the multi-scale Gaussian matched filtering method is used to enhance the contrast of the retinal images. Optimized by the Particle Swarm Optimization (PSO) algorithm, Otsu algorithm (OTSU) multi-threshold segmentation is utilized to segment the retinal image extracted by the multi-scale matched filtering method. Finally, the image is post-processed, including binarization, morphological operation and edge-contour removal. The test experiments are implemented on the DRIVE and STARE datasets to evaluate the effectiveness and practicability of the proposed method. Compared with other existing methods, it can be concluded that the proposed method can segment more small blood vessels while ensuring the integrity of vascular structure and has a higher performance. The proposed method has more obvious targets, a higher contrast, more plentiful detailed information, and local features. The qualitative and quantitative analysis results show that the presented method is superior to the other advanced methods.

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30

Nafati, N. M., S. Antonczak, J. Topin, and J. Golebiowski. "Multiscale Convergence Optimization in Constrained Molecular Dynamics Simulations." International Journal of Energy 16 (March 9, 2022): 45–51. http://dx.doi.org/10.46300/91010.2022.16.7.

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The energy analysis is essential for studying chemical or biochemical reactions but also for characterizing interactions between two protagonists. Molecular Dynamics Simulations are well suited to sampling interaction structures but under minimum energy. To sample unstable or high energy structures, it is necessary to apply a bias-constraint in the simulation, in order to maintain the system in a stable energy state. In MD constrained simulations of ""Umbrella Sampling"" type, the phenomenon of ligand-receptor dissociation is divided into a series of windows (space sampling) in which the simulation time is fixed in advance. A step of de-biasing and statistical processing then allows accessing to the Potential Force Medium (PMF) of the studied process. In this context, we have developed an algorithm that optimizes the DM computation time regarding each reaction coordinate (distance between the ligand and the receptor); and thus can dynamically adjust the sampling time in each US-Window. The data processing consists in studying the convergence of the distributions of the coordinate constraint and its performance is tested on different ligand-receptor systems. Its originality lies in the used processing technique which combines wavelet thresholding with statistical-tests decision in relation to distribution convergence. In this paper, we briefly describe a Molecular Dynamic Simulation, then by assumption we consider that distribution data are series of random-variables vectors obeying to a normal probality law. These vectors are first analyzed by a wavelet technique, thresholded and in a second step, their law probability is computed for comparison in terms of convergence. In this context, we give the result of PMF and computation time according to statistic-tests convergence criteria, such as Kolmogorov Smirnov, Student tTest, and ANOVA Tests. We also compare these results with those obtained after a preprocessing with Gaussian low-pass filtering in order to follow the influence of thresholding. Finally, the results are discussed and analyzed regarding the contribution of the muli-scale processing and the more suited criteria for time optimization.

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31

Abdulle, Assyr, Orane Jecker, and Alexander Shapeev. "An Optimization Based Coupling Method for Multiscale Problems." Multiscale Modeling & Simulation 14, no. 4 (January 2016): 1377–416. http://dx.doi.org/10.1137/15m105389x.

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32

Gratton, Serge, Annick Sartenaer, and Philippe L. Toint. "Recursive Trust-Region Methods for Multiscale Nonlinear Optimization." SIAM Journal on Optimization 19, no. 1 (January 2008): 414–44. http://dx.doi.org/10.1137/050623012.

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33

Luo, Lingai, and Daniel Tondeur. "Multiscale optimization of flow distribution by constructal approach." China Particuology 3, no. 6 (December 2005): 329–36. http://dx.doi.org/10.1016/s1672-2515(07)60211-5.

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34

Wang, Guannan, and Marek-Jerzy Pindera. "Elasticity-based microstructural optimization: An integrated multiscale framework." Materials & Design 132 (October 2017): 337–48. http://dx.doi.org/10.1016/j.matdes.2017.07.003.

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35

White, Daniel A., William J. Arrighi, Jun Kudo, and Seth E. Watts. "Multiscale topology optimization using neural network surrogate models." Computer Methods in Applied Mechanics and Engineering 346 (April 2019): 1118–35. http://dx.doi.org/10.1016/j.cma.2018.09.007.

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36

Pun, Chi Seng, and Hoi Ying Wong. "Robust investment–reinsurance optimization with multiscale stochastic volatility." Insurance: Mathematics and Economics 62 (May 2015): 245–56. http://dx.doi.org/10.1016/j.insmatheco.2015.03.030.

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37

Andreasen, C. S., and O. Sigmund. "Multiscale modeling and topology optimization of poroelastic actuators." Smart Materials and Structures 21, no. 6 (May 11, 2012): 065005. http://dx.doi.org/10.1088/0964-1726/21/6/065005.

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38

Lucia, Angelo, Peter A. DiMaggio, and Praveen Depa. "Funneling Algorithms for Multiscale Optimization on Rugged Terrains." Industrial & Engineering Chemistry Research 43, no. 14 (July 2004): 3770–81. http://dx.doi.org/10.1021/ie030636+.

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39

Podsiadlo, Pawel, and Gwidon W. Stachowiak. "Directional Multiscale Analysis and Optimization for Surface Textures." Tribology Letters 49, no. 1 (October 18, 2012): 179–91. http://dx.doi.org/10.1007/s11249-012-0054-1.

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40

Imediegwu, Chikwesiri, Ryan Murphy, Robert Hewson, and Matthew Santer. "Multiscale structural optimization towards three-dimensional printable structures." Structural and Multidisciplinary Optimization 60, no. 2 (February 26, 2019): 513–25. http://dx.doi.org/10.1007/s00158-019-02220-y.

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41

Zhao, Ang, Vincent Beng Chye Tan, Pei Li, Kui Liu, and Zhendong Hu. "A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE2 Method." Mathematics 11, no. 12 (June 20, 2023): 2779. http://dx.doi.org/10.3390/math11122779.

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Анотація:

The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE2 method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE2 model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.

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42

Summers, R., T. Abdulla, and J.-M. Schleich. "Progress with Multiscale Systems." Measurement and Control 44, no. 6 (July 2011): 180–85. http://dx.doi.org/10.1177/002029401104400605.

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Lien, Martha E., D. Roald Brouwer, Trond Mannseth, and Jan-Dirk Jansen. "Multiscale Regularization of Flooding Optimization for Smart Field Management." SPE Journal 13, no. 02 (June 1, 2008): 195–204. http://dx.doi.org/10.2118/99728-pa.

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Summary Smart fields can provide enhanced oil recovery through the combined use of optimization and data assimilation. In this paper, we focus on the dynamic optimization of injection and production rates during waterflooding. In particular, we use optimal control theory in order to find an optimal well management strategy over the life of the reservoir that maximizes an objective function (e.g., recovery or net present value). Optimal control requires the determination of a potentially large number of (groups of) well rates for a potentially large number of time periods. However, the optimal number of well groups and time steps is not known a priori. Moreover, taking these numbers too large can slow down the optimization process and increase the chance of achieving a suboptimal solution. We investigate the use of multiscale regularization methods to achieve grouping of the control settings of the wells in both space and time. Starting out with a very coarse grouping, the resolution is subsequently refined during the optimization. The regularization is adaptive in that the multiscale parameterization is chosen based on the gradients of the objective function. Results for the numerical examples studied indicate that the regularization may lead to significantly simpler optimum strategies, while resulting in a better or similar cumulative oil production. Introduction We consider the secondary recovery phase of a heterogeneous oil reservoir, where water is injected into the reservoir for pressure maintenance and sweep improvement. In a smart field scenario, we consider injectors and producers with both single and multiple completions. The flow rates of the different well completions can be adjusted individually. In the following, an individual well completion will be referred to as "well segment." This implies that in case of conventional single-completion wells the term "well segment" is therefore equivalent to "well." Ideally, the injected water will displace the remaining oil in the reservoir on its way from the injection wells to the production wells. Rock heterogeneities will, however, influence the path of the injected water. The water will mainly flow in the high-permeability channels, which causes only part of the oil to be produced. Recently, smart field concepts have been proposed as a means to improve control over the waterfront through detailed adjustments of the injection and production rates in time using a combination of model-based flooding optimization and model updating (Brouwer et al. 2004; Sarma et al. 2005b). For the optimization part, these "closed-loop" reservoir management strategies rely on optimal control theory, which has been proposed before as a flooding optimization method by various authors (Asheim 1988; Virnovski 1991; Sudaryanto 1998; Brouwer et al. 2004; Sarma et al. 2005a). However, optimization by means of optimal control theory is computationally expensive, and detailed management of every individual well segment of a smart field at every moment in time is economically and technically demanding. Moreover, there may not be enough information in the system to determine the optimal production strategy uniquely. Hence, we seek to develop management strategies with a restricted number of degrees of freedom, which at the same time maintain the advantages of the smart field technology. In this paper, multiscale estimation techniques are utilized to attempt to find the optimal well management level. These are hierarchical regularization methods where the number of degrees of freedom in the estimation is gradually increased as the optimization proceeds. Multiscale methods were first applied for solving partial differential equations to speed up convergence (Brandt 1977; Briggs 1987). Later, through the development of wavelets, multiscale approaches have also been widely used within inverse problems (Emsellem and de Marsily 1971; Chavent and Liu 1989; Liu 1993; Yoon et al. 2001). The outline of the paper is as follows: First, the theory behind the solution of the problem in terms of optimal control and gradient-based optimization is presented. Thereafter we present methods to regularize the optimization problem in terms of multiscale reparameterization of the control variable. Finally, the performance of the proposed regularization strategies is illustrated through a line of numerical examples before we summarize and conclude.

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Chen, Zhenning, Xinxing Shao, Wei Sun, Jie Zhao, and Xiaoyuan He. "Optimization of multiscale digital speckle patterns for multiscale deformation measurement using stereo-digital image correlation." Applied Optics 60, no. 16 (May 25, 2021): 4680. http://dx.doi.org/10.1364/ao.423350.

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45

Zhao, Peiyao, Ziming Cai, Lingling Chen, Longwen Wu, Yu Huan, Limin Guo, Longtu Li, Hong Wang, and Xiaohui Wang. "Ultra-high energy storage performance in lead-free multilayer ceramic capacitors via a multiscale optimization strategy." Energy & Environmental Science 13, no. 12 (2020): 4882–90. http://dx.doi.org/10.1039/d0ee03094e.

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Xin, Gang, Peng Wang, and Yuwei Jiao. "Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization." Expert Systems with Applications 185 (December 2021): 115615. http://dx.doi.org/10.1016/j.eswa.2021.115615.

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Wilhelms, Wenke, Christoph Schwarzbach, Luz Angélica Caudillo-Mata, and Eldad Haber. "The mimetic multiscale method for Maxwell’s equations." GEOPHYSICS 83, no. 5 (September 1, 2018): E259—E276. http://dx.doi.org/10.1190/geo2017-0503.1.

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We have developed a mimetic multiscale method to simulate quasistatic Maxwell’s equations in the frequency domain. This is especially useful for extensive geophysical models that include small-scale features. Applying the concept of multiscale methods, we avoid setting up a large and costly system of equations on the fine mesh where the material parameters are discretized on. Instead, we build and solve a system on a much coarser mesh. For doing that, it is inevitable to interpolate between fine and coarse meshes. The construction of this coarse-to-fine interpolation is done by solving local, frequency-independent optimization problems for the electric field and the magnetic flux on each coarse cell incorporating the fine-mesh features. Hence, the interpolation operators transfer the fine-mesh material properties onto the coarse simulation mesh. To increase the accuracy of the interpolation, we apply oversampling; i.e., the coarse-cell optimization problems are solved on extended local domains. Previous work on multiscale methods for Maxwell’s equations is not capable of keeping the mimetic properties of the discretization. With our method being mimetic, the properties of the continuous differential operators are preserved in their discrete counterparts and thus, the resulting simulations do not contain spurious modes. We determine the effectiveness of our multiscale construction with coarse-mesh simulations for two examples: a vertical borehole and a mine model.

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Zhu, Frank X. X., and Lijun Xu. "Integrating multiscale modeling and optimization for sustainable process development." Chemical Engineering Science 254 (June 2022): 117619. http://dx.doi.org/10.1016/j.ces.2022.117619.

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Lin, Xingcheng, Yifeng Qi, Andrew P. Latham, and Bin Zhang. "Multiscale modeling of genome organization with maximum entropy optimization." Journal of Chemical Physics 155, no. 1 (July 7, 2021): 010901. http://dx.doi.org/10.1063/5.0044150.

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Xia, Liang, and Piotr Breitkopf. "Recent Advances on Topology Optimization of Multiscale Nonlinear Structures." Archives of Computational Methods in Engineering 24, no. 2 (January 19, 2016): 227–49. http://dx.doi.org/10.1007/s11831-016-9170-7.

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