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Proposal of a facet-to-facet multiple flow direction algorithm based on geometrical and mathematical analysis of physical dispersion over triangle facet

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GEOMORPHOLOGY 2024年 466卷

作者： Li, Zhenya Lai, Xijun Shi, Pengfei Yang, Tao Chinese Acad Sci Nanjing Inst Geog & Limnol Key Lab Lake & Watershed Sci Water Secur Nanjing 210008 Peoples R China Hohai Univ Ctr Global Change & Water Cycle State Key Lab Hydrol Water Resources & Hydraul Eng Nanjing 210098 Peoples R China Hohai Univ Natl Cooperat Innovat Ctr Water Safety & Hydrosci Nanjing 210098 Peoples R China

flow direction algorithms have been widely used to extract crucial terrain attributes of great hydrological and geomorphological significance. However, essential distinctions between the empirically-designed strategies of typical algorithms and the natural rules of physical dispersions bring various problems (e.g. parallel channel, artificial dispersion), leading to the low size and extent precisions of estimated results. In this work, geometrical and mathematical analysis is conducted on the inherent characteristics of physical dispersions along slope lines on local terrains. On each 3 x 3 window of digital elevation model (DEM), center pixel is divided into eight nonoverlapping sub-facets. Necessary and sufficient (NS) conditions of size relationships between the elevations of adjacent pixels are summarized to directly identify the receiving facets of a sub-facet. Then, strict mathematical relations are derived between slope direction of a sub-facet and flow proportions allocated to receiving facets. A strategy is designed to re-adjust receiving facets and flow proportions for the boundary flow of adjacent facets. Lastly, a multiple-flow-direction algorithm called TFGA is proposed with the NS condition of size relationships, mathematical relation of slope direction with flow proportion, and adjustment strategy of boundary flow. Case studies are conducted for investigating the total contributing areas (TCA) and specific contributing areas (SCA) estimated by TFGA. Results reveal all-side superiorities of TFGA to typical algorithms in spatial patterns, error indicators and statistic characteristics of estimated TCAs and SCAs. Particularly, TFGA improves size precision of estimated results by approximately one order of magnitude. In a conclusion, we highly recommend TFGA for digital elevation analysis.

关键词： flow direction algorithm Digital elevation model (DEM) Geometric and mathematic analysis Total contributing area (TCA) Multiple-flow-direction algorithm based on Triangular Facet and Geometrical Analysis (TFGA)

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Enhanced flow direction Arithmetic Optimization algorithm for mathematical optimization problems with applications of data clustering

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年第0期138卷 13-29页

作者： Abualigah, Laith Almotairi, Khaled H. Abd Elaziz, Mohamed Shehab, Mohammad Altalhi, Maryam Amman Arab Univ Fac Comp Sci & Informat Amman 11953 Jordan Univ Sains Malaysia Sch Comp Sci George Town 11800 Malaysia Umm Al Qura Univ Comp Engn Dept Mecca Saudi Arabia Galala Univ Fac Comp Sci & Engn Suze 435611 Egypt Zagazig Univ Fac Sci Dept Math Zagazig Egypt Ajman Univ Artificial Intelligence Res Ctr AIRC Ajman 346 U Arab Emirates World Islamic Sci & Educ Univ Informat Technol Amman Jordan Taif Univ Coll Business Adm Dept Management Informat Syst POB 11099 Taif 21944 Saudi Arabia

Data clustering is one of the most common and challenging problems in the machine learning domain. It requires an efficient method to be addressed. This paper proposed a new version of the flow direction algorithm (FDA) to solve various optimization problems. The proposed method is called FDAOA, which enhanced the performance of the original flow direction algorithm by the arithmetic operators that have been used in the Arithmetic Optimization algorithm (AOA). The main aim of the proposed FDAOA is to avoid the recognized weaknesses in the original methods;stuck in the local area, premature convergence, and weak equilibrium between the exploration and exploitation search mechanisms. The proposed method is tested on two sets of various problems to validate its performance. In the first set, twenty-three benchmark functions are used, which belong to three categories;seven unimodal functions, six multimodal functions, and ten fixed dimension functions. In the second set, eight common data clustering problems are used to prove the ability of the proposed FDAOA to deal with real-world optimization problems. The results of the proposed method are compared with other well-established methods, and the proposed FDAOA achieved promising output compared to the other methods on various tested problems. The proposed method got the optimal clustering solutions almost in all the tested data clustering problems with clear significant improvements against the other comparative methods.

关键词： Arithmetic Optimization algorithm flow direction algorithm Meta-heuristics Mathematical benchmark problems Data clustering problems

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A novel hybrid flow direction optimizer-dynamic oppositional based learning algorithm for solving complex constrained mechanical design problems

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MATERIALS TESTING 2023年第1期65卷 134-143页

作者： Yildiz, Betul S. Pholdee, Nantiwat Mehta, Pranav Sait, Sadiq M. Kumar, Sumit Bureerat, Sujin Yildiz, Ali Riza Uludag Univ Bursa Uludag Univ Dept Mech Engn TR-16059 Bursa Turkiye Khon Kaen Univ Dept Mech Engn Khon Kaen 40002 Thailand Dharmsinh Desai Univ Dept Mech Engn Nadiad 387001 Gujarat India King Fand Univ Petr & Minerals Dhahran Saudi Arabia Univ Tasmania Launceston Tas 7250 Australia

In this present work, mechanical engineering optimization problems are solved by employing a novel optimizer (HFDO-DOBL) based on a physics-based flow direction optimizer (FDO) and dynamic oppositional-based learning. Five real-world engineering problems, viz. planetary gear train, hydrostatic thrust bearing, robot gripper, rolling bearing, and multiple disc clutch brake, are considered. The computational results obtained by HFDO-DOBL are compared with several newly proposed algorithms. The statistical analysis demonstrates the HFDO-DOBL dominance in finding optimal solutions relatively and competitiveness in solving constraint design optimization problems.

关键词： dynamic oppositional based learning flow direction algorithm hydrostatic thrust bearing mechanical design planetary gear train robot gripper

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Evaluating the area and position accuracy of surface water paths obtained by flow direction algorithms

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JOURNAL OF HYDROLOGY 2020年第0期583卷 124619-000页

作者： Li, Zhenya Yang, Tao Xu, Chong-Yu Shi, Pengfei Yong, Bin Huang, Ching-sheng Wang, Chao Hohai Univ Ctr Global Change & Water Cycle State Key Lab Hydrol Water Resources & Hydraul En Nanjing 210098 Peoples R China Hohai Univ Sch Earth Sci & Engn Nanjing 210098 Peoples R China Univ Oslo Dept Geosci POB 1047 Blindern N-0316 Oslo Norway Hohai Univ Natl Cooperat Innovat Ctr Water Safety & Hydrosci Nanjing 210098 Peoples R China New Mexico Inst Min & Technol Dept Earth & Environm Sci Hydrol Program Socorro NM 87801 USA

The surface water path (SWP) extracted from digital elevation model (DEM) by flow direction algorithms is widely employed to obtain a variety of topographic variables used in hydrological modeling. Accurate SWPs can facilitate understanding the underlying mechanisms of water movement on Earth's surface. However, the accuracy of extracted SWPs by different flow direction algorithms has not been systematically studied. In this work, two indicators are developed to measure the area and position errors of extracted SWPs relative to theoretical SWPs on four synthetic surfaces representing typical terrains of natural watersheds. Based on the formulas of the synthetic surfaces, theoretical true SWP can be derived for any grid cell on the DEM discretized from the synthetic surfaces. Several widely used flow direction algorithms including three single flow direction (SFD) algorithms (i.e. D8, Rho8 and D8-LTD approaches) and three multiple flow direction (MFD) algorithms (i.e. FDFM, MFD-md and D8 approaches) are implemented to extract SWPs. Results suggest that significant distinctions can be detected in SWPs extracted by different flow direction algorithms. The SWPs extracted by SFD algorithms are always one-dimensional non-dispersive lines because SFD algorithms allow only one flow direction at each grid cell. In contrast, the SWPs extracted by MFD algorithms show excessive artificial dispersion. The average area error of extracted SWPs ranges from 16.3% to 75.2% on different synthetic surfaces and the minimum is obtained by FDFM approach for all synthetic surfaces. The average position error falls in the range of 46.0% to 161.4%. The maximum is gained by D8 or FDFM approach, and the minimum by D8-LTD or D8 approach. The cross compensation of SWP area induced by artificial dispersion leads to relatively high area accuracy but relatively low position accuracy of MFD algorithms. In addition, increasing DEM resolution without capturing more topographic variability can decrease

关键词： Surface water path (SWP) flow direction algorithm Synthetic surfaces Artificial dispersion Area and position precision

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Implementing a radial basis function model to anticipate the outcomes of the gasification

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CHEMICAL PRODUCT AND PROCESS MODELING 2025年第1期20卷 57-78页

作者： Cui, Hongfang Su, Ning Cui, Hongyan Hebei Armed Police Corps Shijiazhuang 050000 Peoples R China Hengshui Univ Sch Math & Comp Sci Hengshui 053000 Peoples R China Hegang Digital Technol Co Ltd Shijiazhuang 050000 Peoples R China

Hydrogen (H-2) and nitrogen (N-2) are both critical components in gasification processes, making efficient conversion of carbonaceous feedstocks into valuable gases with reduced environmental impact indispensable. This study demonstrates a state-of-the-art approach to predictive modeling for these quantities at high accuracy while allowing cost-effective solutions under a variety of operational conditions, enhancing safety, and enabling data-driven optimization. This work develops a new framework that incorporates the radial basis function model with two state-of-the-art optimization algorithms, namely the Zebra Optimization algorithm (ZOA) and flow direction algorithm (FDA), to enhance the predictive accuracy of gasification processes. This is a new frontier in optimizing the sustainable conversion of carbonaceous feedstocks, demonstrating the potential of data-driven methodologies in process efficiency and environmental sustainability. The RBFD model resulted in outstanding anticipation capability for H2, reaching an exceptional R2 value of 0.997 during the whole period of testing. On the other hand, the RBZO framework proved to be the strongest predictor for N2 anticipation, presenting an outstanding R2 of 0.994 during the testing and validation phases. The RBFD and RBZO frameworks showed significantly higher productivity compared to the conventional RBF model, as evidenced by accuracy metrics like MSE, RMSE, and WAPE.

关键词： hydrogen nitrogen machine learning radial basis function Zebra Optimization algorithm flow direction algorithm

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Comparison of flow direction algorithms in the Application of the CTI for Mapping Wetlands in Minnesota

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WETLANDS 2014年第3期34卷 513-525页

作者： Rampi, Lian P. Knight, Joseph F. Lenhart, Christian F. Univ Minnesota St Paul MN 55108 USA Dept Forest Resources St Paul MN 55108 USA

Topography has been traditionally used as a surrogate to model spatial patterns of water distribution and variation of hydrological conditions. In this study, we investigated the use of light detection and ranging (lidar) data to derive two Single flow direction (SFD) and five Multiple flow direction (MFD) algorithms in the application of the compound topographic index (CTI) for mapping wetlands. The CTI is defined here as ln [(alpha)/(tan (beta)], where alpha represents the local upslope contributing area and beta represents the local slope gradient. We evaluated the following flow direction algorithms: D8, Rho8, DEMON, D-a MD-a, Mass Flux, and FD8 in three ecoregions in Minnesota. Numerous studies have found that MFD algorithms better represent the spatial distribution of water compared to SFD algorithms. CTI maps were compared to field collected and image interpreted reference data using traditional remote sensing accuracy estimators. Overall accuracy results for the majority of CTI based algorithms were in the range of 81-92 %, with low errors of wetland omission. The results of this study provide evidence that 1) wetlands can be accurately identified using a lidar derived CTI, and 2) MFD algorithms should be preferred over SFD algorithms in most cases for mapping wetlands.

关键词： Wetland mapping Lidar flow direction algorithm Compound topographic index

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Artificial surfaces simulating complex terrain types for evaluating grid-based flow direction algorithms

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2013年第6期27卷 1055-1072页

作者： Qin, Cheng-Zhi Bao, Li-Li Zhu, A-Xing Hu, Xue-Mei Qin, Biao Chinese Acad Sci Inst Geog Sci & Nat Resources Res State Key Lab Resources & Environm Informat Syst Beijing Peoples R China Univ Wisconsin Dept Geog Madison WI 53706 USA

This article presents a set of artificial surfaces simulating complex terrain types for evaluating the performances of grid-based flow direction algorithms. The proposed artificial surfaces were developed based on sine and cosine functions and thus can simulate four complex terrain types: a convex-centred slope, concave-centred slope, saddle-centred slope and straight-ridge slope;such features are typical and widespread in real landscapes. We analytically solved the theoretical values of specific catchment area (SCA) for the proposed artificial surfaces. Compared with existing artificial surfaces for evaluating flow direction algorithms, the proposed artificial surfaces provide a better representation of common terrain types in the real world. To analyse the feasibility of the proposed artificial surfaces, two sets of artificial digital elevation models (DEMs) were created by sampling the proposed artificial surfaces with different reliefs at a series of resolutions (i.e. 1, 5, 10 and 20m). Four representative flow direction algorithms were applied to these artificial DEMs: D8, D-inf, FD8 and MFD-md. The root mean square error, mean error and standard deviation in the computed SCA from flow direction algorithm show that MFD-md generally yielded lower error under simulated terrain conditions than D8, D-inf and FD8. The cumulative frequency distributions of errors from the tested flow direction algorithms with the proposed artificial DEMs can effectively reflect the inherent characteristics of each algorithm. MFD-md performed more similarly to FD8 in low-relief terrains and more similarly to D-inf in high-relief terrains. The map of errors from each tested algorithm is available for a spatially explicit evaluation of the occurrence of errors. Over most of the area, the D-inf algorithm underestimated the SCA when FD8 overestimated the SCA.

关键词： artificial surface error assessment specific catchment area flow direction algorithm gridded digital elevation models

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Assessing the Precision of Total Contributing Area (TCA) Estimated by flow direction algorithms Based on the Analytical Solution of Theoretical TCA on Synthetic Surfaces

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WATER RESOURCES RESEARCH 2021年第4期57卷 e2020WR028546-e2020WR028546页

作者： Li, Zhenya Yang, Tao Wang, Chao Shi, Pengfei Yong, Bin Song, Ying Hohai Univ Ctr Global Change & Water Cycle State Key Lab Hydrol Water Resources & Hydraul En Nanjing Peoples R China Hohai Univ Sch Earth Sci & Engn Nanjing Peoples R China Hohai Univ Natl Cooperat Innovat Ctr Water Safety & Hydrosci Nanjing Peoples R China New Mexico Inst Min & Technol Dept Earth & Environm Sci Hydrol Program Socorro NM 87801 USA

Total contributing area (TCA) has important hydrological, geological, and geomorphological implications in digital terrain analysis. Currently, the validity of estimated TCA is challenged by the approximation error of digital elevation models (DEMs) to real-world terrains, the choice of flow direction algorithms and the difficulty in a quantitative evaluation. To solve these problems, this work employs a range of synthetic surfaces for free from approximation errors. Theoretical TCA for any cell on synthetic surfaces is analytically solved by using subsection integral and L'Hospital's rule based on the topographical definition of TCA. The impacts of grid discretization on the spatial patterns of theoretical TCA are explained mathematically and geometrically. In case studies, the analytically solved theoretical TCA is treated as a benchmark to quantitatively evaluate the TCAs estimated by three SFD algorithms (i.e., D8, Rho8, and D8-LTD) and three MFD algorithms (i.e., FDFM, MFD-md, and D infinity). Results show that (1) SFD algorithms obtain unsmooth and discontinuous spatial patterns of estimated TCA, due to the existence of source cells caused by the basic hypothesis of allowing only one receiving cell;(2) Cross compensation induced by artificial dispersion in MFD algorithms leads to a less error in the quantity of estimated TCA but a larger error in the physical position of estimated TCA;(3) The addition of contour length errors does not promise larger specific contributing area errors than TCA errors. To summarize, this work offers a theoretical and quantitative evaluation on the precision of the TCAs estimated by flow direction algorithms.

关键词： analytical solution flow direction algorithm synthetic surface total contributing area

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A complex synthetic surface for assessing flow direction algorithms based on total contributing area

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GEOMORPHOLOGY 2024年 450卷

作者： Song, Ying Yang, Tao Li, Zhenya Xu, Chong-Yu Hohai Univ Ctr Global Change & Water Cycle State Key Lab Hydrol Water Resources & Hydraul Eng Nanjing 210098 Peoples R China Hohai Univ Natl Cooperat Innovat Ctr Water Safety & Hydrosci Nanjing 210098 Peoples R China Chinese Acad Sci Key Lab Watershed Geog Sci Nanjing Inst Geog & Limnol Nanjing 210008 Peoples R China Univ Oslo Dept Geosci & Hydrol POB 1047 Blindern N-0316 Oslo Norway

flow direction algorithms have important application in attracting geomorphic features and topographic attributes, which serve as inputs for some hydrological and topographical models. Evaluating flow direction algorithms is of great significance and often conducted on synthetic surfaces instead of real digital elevation models for free of approximation errors. However, most widely-used synthetic surfaces are too simplified to represent complex topographical relief of real-world terrains. For this, this work applies a complex synthetic surface of modified Himmelblau's function (HF) to simulate sophisticated terrains encountered in real landscapes. HF surface is spatially smooth and continuous with four hilltops and one valley, where plan curvatures are clustered mainly from -0.1 to 0.1. In addition, a slope line-based discretization numerical (SLDN) approach is designed for obtaining numerical solution to theoretical total contributing area (TCA) on synthetic surfaces of non-integrable slope lines (e.g. HF surface). TCAs estimated by several flow direction algorithms are compared with SLDNderived TCA quantitatively. Results indicate that the largest and smallest mean size errors are obtained by Random eight-node (Rho8) (i.e. 82.6 %) and Freeman multiple flow direction (FMFD) (i.e. 17.9 %), while the largest and smallest mean extent errors by Eight drainage directions (D8) (i.e. 128.2 %) and Eight drainage directions, least transversal deviation (D8-LTD) (i.e.55.4 %). Most mean errors are larger than 20.0 %, which may not be satisfactory in practice. This work can provide a reference for flow direction algorithms application in digital terrain analysis, and therefore improve accuracy of hydrological, geological and geomorphological models.

关键词： Synthetic surface flow direction algorithm Total contributing area flow path Numerical size and spatial extent error assessment Digital elevation model

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flow direction optimizer tuned robust FOPID-(1

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JOURNAL OF ENERGY STORAGE 2024年 83卷

作者： Ansari, Zafar Ayub Raja, G. Lloyds Natl Inst Technol Patna Dept Elect Engn Patna Bihar India Loknayak Jai Prakash Inst Technol LNJPIT Dept Elect & Elect Engn Chapra Bihar India

The incorporation of renewable energy sources (REs) in modern interconnected power systems (PSs) raises concerns about stability, flexibility, and appropriateness. Furthermore, the stochastic nature of REs, load disruptions, physical constraints and system parameter variations escalate the issue of frequency oscillations in modern PSs. Owing to this, load frequency control (LFC) is vital to providing high quality, reliable and stable power supply. Hence, this study offers a novel fractional-order proportional-integral-derivative (FOPID) cascaded with 1 + tilted-derivative (1 + TD) controller (FOPID-(1 + TD)) for LFC of the multi-area renewableintegrated hybrid power system (RIHPS). The parameters of the proposed controller are optimized using the flow direction algorithm (FDA) with integral time square error (ITSE) as the fitness function. To begin with, thermal systems with/without governor dead band (GDB) nonlinearity are used for the validation of the FDA-tuned FOPID-(1 + TD) control strategy. Then suggested control strategy is further expanded to a challenging RIHPS where the hybrid micro-grid (H mu G) is integrated with the utility grid. The H mu G contains wind turbine generator (WTG), organic Rankine cycle (ORC) solar thermal power (STP), biodiesel generator (BDG) and hybrid electrical energy storage (HEES). The superiority in dynamic behavior and robustness of the FDA-tuned FOPID-(1 + TD) strategy is vindicated by simulating various practical scenarios such as step and random load variations, fluctuations in REs generation and aberration of +/- 25 % in PS parameters. The HEES unit which consists of a redox flow battery (RFB) and capacitive energy storage (CES) is included to advance system performance even further by offsetting the load power requirement. With the recommended FOPID-(1 + TD) controller, significant improvement in dynamic performance is obtained at attaining the depletion of 2 % to 90 %, 26 % to 83 % and 50 % to 95 % in settling time, undersho

关键词： flow direction algorithm FOPID-(1 + TD) cascade controller Hybrid electrical energy storage Microgrid Renewables Nonlinearities

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