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Efficient continuous piecewise linear regression for linearising univariate non-linear functions

IISE TRANSACTIONS 2025年第3期57卷 231-245页

作者： Warwicker, John Alasdair Rebennack, Steffen Karlsruhe Inst Technol Inst Operat Res Stochast Optimizat Karlsruhe Germany

Due to their flexibility and ability to incorporate non-linear relationships, Mixed-Integer Non-linear Programming (MINLP) approaches for optimization are commonly presented as a solution tool for real-world problems. Within this context, piecewise linear (PWL) approximations of non-linear continuous functions are useful, as opposed to non-linear machine learning-based approaches, since they enable the application of Mixed-Integer linear Programming techniques in the MINLP framework, as well as retaining important features of the approximated non-linear functions, such as convexity. In this work, we extend upon fast algorithmic approaches for modeling discrete data using PWL regression by tuning them to allow the modeling of continuous functions. We show that if the input function is convex, then the convexity of the resulting PWL function is guaranteed. An analysis of the runtime of the presented algorithm shows which function characteristics affect the efficiency of the model, and which classes of functions can be modeled very quickly. Experimental results show that the presented approach is significantly faster than five existing approaches for modeling non-linear functions from the literature, at least 11 times faster on the tested functions, and up to a maximum speedup of more than 328,000. The presented approach also solves six benchmark problems for the first time.

关键词： piecewise linear function continuous function function fitting piecewise linear regression convex function

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Optimal scheduling of an integrated energy system considering carbon trading mechanism and multi-energy supply uncertainties in a real-time price environment

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2024年 38卷

作者： Zhu, Gang Gao, Yan Liu, Huiran Univ Shanghai Sci & Technol Sch Management Shanghai 200093 Peoples R China

This research presents an optimized scheduling model for Integrated Energy Systems (IES) that harmonizes economic efficiency with low carbon emissions in a Real -Time Price (RTP) environment. Integrating a laddertype carbon tax approach, this model adeptly addresses the unpredictability of renewable energy generation and IES load demands. It introduces a carbon trading mechanism for efficient emission control, complemented by an RTP model that manages interactions between the IES and the main power grid through piecewise linear functions. The model also proposes an adaptable operation strategy for thermoelectric and electric cooling ratios, enhancing the IES's economic and operational flexibility. The objective function, crafted on a deviation preference optimization basis, reflects the diverse goals of decision -makers, and the model is skillfully translated into a mixed -integer linear programming format through a series of mathematical transformations. Simulation results demonstrate the model's efficacy in achieving an optimal balance between cost-effectiveness and reliability, particularly by setting a strategic confidence level for spinning reserves. Additionally, incorporating a ladder -type carbon tax and Electric Vehicle (EV) charging within the IES underscores its significant environmental benefits, marking a stride towards a low -carbon future.

关键词： Integrated energy system Ladder-type carbon tax Real-time price piecewise linear function Adaptable operation strategy

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Ethylenediaminetetraacetic acid intercalated MgAl-layered double-hydroxides nanocomposite as an efficient platform in the development of electrochemical sensor for the detection of iron (II)

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JOURNAL OF APPLIED ELECTROCHEMISTRY 2024年第2期54卷 309-321页

作者： Sankarlinkam, Shruthee Suresh, Indhu Hariharan, G. Nesakumar, Noel Kulandaisamy, Arockia Jayalatha Rayappan, John Bosco Balaguru SASTRA Deemed Univ Sch Chem & Biotechnol SCBT Thanjavur 613401 Tamil Nadu India SASTRA Deemed Univ Sch Elect & Elect Engn SEEE Thanjavur 613 401 Tamil Nadu India SASTRA Deemed Univ Sch Humanities & Sci Thanjavur 613401 Tamil Nadu India SASTRA Deemed Univ Ctr Nanotechnol & Adv Biomat CeNTAB Thanjavur 613401 Tamil Nadu India

The significance of iron in maintaining physiological homeostasis in the human body is well recognized. However, the presence of unbound iron, specifically the non-transferrin bound iron (NTBI), can potentially induce tissue damage in crucial organs, such as the heart, kidney, and liver. Consequently, there arises a critical need to establish a sensing platform with the capability of detecting exceedingly low concentrations of iron (II). To address this imperative, a layered double-hydroxide (LDH) structure comprising Mg2+ and Al3+ with ethylenediaminetetraacetic acid (EDTA) intercalated between the layers has been successfully synthesized. The proposed methodology involves the utilization of a differential pulse voltammetric detection approach to identify Fe2+ on an EDTA-MgAl LDHs composite-modified glassy carbon electrode. Scanning Electron Microscopy (SEM) analysis of the EDTA-MgAl LDHs revealed the stratified structure of sheets with thicknesses ranging from 95 to 160 nm. Voltammetry studies further demonstrated the effective Fe2+ capturing ability of EDTA and confirmed the existence of multi-layered MgAl LDHs, which contribute to the electrocatalytic oxidation of Fe2+ to Fe3+. The developed sensor exhibited an elevated sensitivity (0.061 & mu;A & mu;M-1) towards Fe2+ and a wide linear detection ranges from 0.1 to 102.1 & mu;M, with an exceptionally low detection limit of 50 nM. Furthermore, the applicability of a two-segmented piecewise linear function to estimate the breakpoint Fe2+ concentration, above and below which the sensor's response behaviour changes, was assessed for the direct determination of Fe2+ in a 0.1 M KCl solution. In conclusion, the developed sensor possesses several advantageous attributes, including a rapid response time, effective Fe2+ capturing ability, electrocatalytic capability, wide linearity, and resistance to interference from other metal ions. These characteristics collectively render it a highly promising and efficient sensing pl

关键词： Layered double hydroxides Electrochemical sensor Iron (II) Differential pulse voltammetry Ethylenediaminetetraacetic acid piecewise linear function

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Modeling of TVS Diode Harmonic Distortion Using piecewise linear Capacitance

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2024年第9期72卷 5051-5059页

作者： Petzel, Leonhard Pommerenke, David Holland, Steffen Graz Univ Technol Inst Elect A-8010 Graz Austria Nexperia Germany GmbH Inst Elect D-22529 Hamburg Germany

When used in RF applications, TVS diodes exhibit harmonic distortion due to their nonlinear capacitance and other effects. This article presents an approach to modeling harmonic distortion caused by TVS diodes using nonlinear capacitance. The approach is novel in the sense that it is highly automatable, computationally cheap, and generic. First, the harmonic distortion measurements are described. Then, the capacitor model is introduced and its harmonic distortion is analyzed analytically. A fitting procedure is described to convert the observed harmonic distortion into the coefficients of the model. Finally, the process is demonstrated on real data and the models were tested against an experiment.

关键词： ESD protection harmonic distortion nonlinear device modeling piecewise linear function TVS diodes

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Complexity-Optimized Adaptive Model for Multiband Digital Predistortion of RF Power Amplifiers

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2024年第6期72卷 3410-3422页

作者： Han, Renlong Jiang, Chengye Yang, Guichen Zhang, Qianqian Liu, Falin Univ Sci & Technol China Dept Elect Engn & Informat Sci Hefei 230027 Peoples R China

In this article, we present a low-complexity adaptive digital predistortion (DPD) model for concurrent multiband (MB) power amplifiers (PAs). A novel MB basis function space is constructed for the proposed MB vector combination search (MB-VCS) model by performing multidimensional extensions and adding piecewise linear functions to the Polar Volterra series. The proposed basis function multiplexing-based model search algorithm also helps the MB-VCS model to balance model performance and complexity. The MB-VCS model contains novel in-band and cross-band terms to characterize complex interactions between different band signals and can adaptively construct intermodulation (IMD) terms to handle arbitrary carrier configurations. In order to further exploit the advantages of the MB-VCS model, the MB piecewise VCS (MB-PVCS) model with MB-VCS as a submodel based on the piecewise modeling technique is proposed in this article, and an efficient classification controller construction strategy is designed for the MB-PVCS model. The experimental test results confirm that the MB-VCS and MB-PVCS models achieve a better performance-complexity tradeoff than the state-of-the-art MB single and MB piecewise models.

关键词： Digital predistortion (DPD) intermodulation (IMD) model complexity multiband (MB) piecewise linear function piecewise model Polar Volterra power amplifiers (PAS)

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Robust Parametric Programming for Adaptive piecewise linear Control of Photovoltaic Inverters to Regulate Voltages in Power Distribution Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第2期39卷 3685-3700页

作者： Gao, Yuanhai Xu, Xiaoyuan Yan, Zheng Shahidehpour, Mohammad Wang, Han Ping, Jian Shanghai Jiao Tong Univ Key Lab Control Power Transmiss & Convers Minist Educ Shanghai 200240 Peoples R China Shanghai Noncarbon Energy Convers & Utilizat Inst Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Coll Smart Energy Shanghai 200240 Peoples R China IIT Galvin Ctr Elect Innovat Chicago IL 60616 USA

This article proposes a robust parametric programming (RPP) method to adaptively obtain piecewise linear control functions of photovoltaic (PV) inverters for real-time voltage regulation in distribution systems. First, the voltage regulation problem is designed as a multi-parametric programming problem, which is transformed into single-parametric linear programming (sp-LP) problems for realizing local control of a PV inverter while considering the maximum voltage deviation caused by other PV units. Second, an alternating iterative algorithm is developed to solve the sp-LP problem of each PV unit and obtain the control functions of all the PV units. Third, considering the information on PV power correlation, a two-level parametric programming problem is established to enhance the voltage regulation performance of PV inverters. A geometric method is developed to solve the inner-level problem, and breakpoint reduction with robust interpolation is developed to improve the computational efficiency in solving the outer-level problem. Four distribution systems integrated with PV units are used to validate the effectiveness of the proposed method. Numerical results show that the performance of the proposed PV inverter control strategy is close to that of the ideal optimal solution and superior to existing piecewise linear control strategies.

关键词： Photovoltaic inverter robust parametric programming uncertainty distribution system voltage regulation piecewise linear function

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Exploring the Nonlinearity of Commute-Time Utility Considering Individual Ideal Preferences and Tolerance ThresholdsC: ase Study in Kunming

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TRANSPORTATION RESEARCH RECORD 2023年第6期2677卷 812-826页

作者： Yang, Jiankun He, Min He, Mingwei Shi, Zhuangbin Liu, Yang Li, Jianbo Kunming Univ Sci & Technol Fac Transportat Engn Kunming Peoples R China Kunming Univ Fac Mech & Elect Engn Kunming Peoples R China

Exploring the nonlinearity of commute-time utility is useful in predicting urban travel demand. However, existing studies assume that commute utility decreases linearly with commute time. This ignores the influence of commuters' ideal preferences and tolerance thresholds on commute utility. To reveal the nonlinear variation of commute utility with commute time and its influence on the choice of commute mode, the ideal commute time (ICT) and the tolerance threshold for commute time (TTCT) were introduced. Three-piecewise linear utility models (Models 2, 3, 4) were constructed and compared with the linear utility multinomial logit model (Model 1). The results of empirical study showed that: (a) the goodness of fit of these three modified models is higher than that of Model 1, indicating that the fitting effect of the commute-time utility model can be improved with either or both the ICT and TTCT;(b) there is a nonlinear relationship between the commute utility and the commute time. The commute-time utility decreases slowly before ICT, declines steadily between the ICT and the TTCT, and falls significantly after TTCT;and (c) when the commute time exceeds the TTCT, the perceived utility of commuters traveling by walking or cycling decreases significantly, and there are few changes in the perceived utility of commuters by car, which increases the probability that commuters who use active modes will transfer to commuting by car. The research results have implications for improving the prediction capacity of commute mode choice model and could guide commuters to switch to more sustainable commute modes.

关键词： commute mode choice commute utility ideal commute time commute time tolerance threshold nonlinear utility piecewise linear function

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Generic Hardware Integrating Multiple Activation functions for Deep Learning Applications 11

Generic Hardware Integrating Multiple Activation Functions f...

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11th IEEE International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan) - Empower of Innovative Consumer Technology

作者： Yu, Chu Hung, Yi-Ching Natl Ilan Univ Dept Elect Engn Yilan Taiwan

ISBN: (纸本)9798350386851;9798350386844

The activation function is an indispensable part of artificial neural networks, introducing nonlinearity into the network to enable learning of nonlinear relationships, mimicking natural world problems. This paper proposes a generic hardware implementation that combines commonly used activation functions, coupled with convolutional computation and batch normalization, capable to construct accelerators for various artificial neural network models. The proposed scheme utilizes the piecewise linear function to approximate nonlinear activation functions. Because the slope values for each segment are constants, fixed-point numbers are converted into canonic signed digit multipliers to replace larger-area multipliers, thereby reducing hardware area and power consumption. Furthermore, to further reduce area, common terms are isolated within each segment of the linear function, allowing synthesis of the required piecewise linear functions with fewer hardware components, and employing Horner's rule to reduce the arithmetic error. According to simulation and logic synthesis results using TSMC 90nm process, our proposed generic hardware achieves a 12.7x reduction in area and a 13.8x reduction in power consumption compared to the original unsimplified version.

关键词： activation function deep learning piecewise linear function

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An Improved Min-Sum Polar Code Decoding Algorithm 3

An Improved Min-Sum Polar Code Decoding Algorithm

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3rd Asia-Pacific Conference on Communications Technology and Computer Science (ACCTCS)

作者： Fang, Mingyuan Univ Manchester Manchester Lancs England

ISBN: (纸本)9798350310801

In 2009, the presentation of polar code, the first theory to approach the Shannon limit of communication channel coding schemes. Thus, academics and business have focused on Polar codes. Research and worldwide standards have been offered one after another, establishing the groundwork for its real-world *** paper proposes a min-sum decoding technique for enhanced Polar codes and revises the node update formula in the min-sum decoding algorithm by using the piecewise linear function to approximate the function In cosh (x) in the belief propagation decoding algorithm. Compared to the min-sum decoding algorithm, the enhanced approach improves decoding performance while somewhat increasing complexity. Compared to the belief propagation decoding algorithm, this approach decreases computational complexity significantly and is simpler to implement in hardware. Based on the min-sum method and the belief propagation algorithm, this approach is offered as a balance between complexity and performance. The simulation results demonstrate that the enhanced min-sum decoding algorithm performs similarly to its predecessor. The performance of the degree propagation decoding method is almost identical to that of the min-sum decoding technique, which is superior.

关键词： Polar Code Belief Propagation Algorithm Min-Sum Algorithm piecewise linear function

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Interactive Generalized Additive Model and Its Applications in Electric Load Forecasting 23

Interactive Generalized Additive Model and Its Applications ...

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29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD)

作者： Yang, Linxiao Ren, Rui Gu, Xinyue Sun, Liang Alibaba Grp DAMO Acad Hangzhou Peoples R China

ISBN: (纸本)9798400701030

Electric load forecasting is an indispensable component of electric power system planning and management. Inaccurate load forecasting may lead to the threat of outages or a waste of energy. Accurate electric load forecasting is challenging when there is limited data or even no data, such as load forecasting in holiday, or under extreme weather conditions. As high-stakes decision-making usually follows after load forecasting, model interpretability is crucial for the adoption of forecasting models. In this paper, we propose an interactive GAM which is not only interpretable but also can incorporate specific domain knowledge in electric power industry for improved performance. This boosting-based GAM leverages piecewise linear functions and can be learned through our efficient algorithm. In both public benchmark and electricity datasets, our interactive GAM outperforms current state-of-the-art methods and demonstrates good generalization ability in the cases of extreme weather events. We launched a user-friendly web-based tool based on interactive GAM and already incorporated it into our eForecaster product, a unified AI platform for electricity forecasting.

关键词： electric load forecasting generalized additive model interpretability piecewise linear function

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