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piecewise linear approximation of Battery Open-Circuit Voltage Characteristics Using Dynamic Programming

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Sunil, Sooraj Pattipati, Krishna R. Balasingam, Balakumar Univ Windsor Dept Elect & Comp Engn Windsor ON N9B 3P4 Canada Univ Connecticut Dept Elect & Comp Engn Storrs CT 06269 USA

An open-circuit voltage (OCV) model, which represents OCV as a function of state of charge (SOC), is essential for estimating the state of a battery. Typically, the OCV-SOC characteristic is approximated using empirical functions, such as polynomials or lookup tables, and stored in a battery management system (BMS). However, polynomial approximations have several limitations: they are sensitive to floating-point errors, can be noninvertible, and require a high-precision computing system for numerical inverse lookups (determining the SOC for a given OCV). Moreover, many OCV models fail to maintain the monotonicity of the OCV-SOC relationship, especially in resource-constrained environments. While table-based (or piecewise linear) approaches have been explored, existing methods often fall short of preserving the accuracy of the OCV-SOC curve with a minimal number of breakpoints. This article introduces a novel dynamic programming approach to model the OCV-SOC characteristic as piecewise line segments. Compared to existing piecewise models, the proposed approach is more resource-efficient in systematically reducing the required table breakpoints while maintaining optimal accuracy. Experimental validation across various lithium-ion chemistries at four ambient temperatures consistently demonstrated a root mean square error below 5 mV. Additionally, differential feature extraction and segmented correlation analysis highlight the model's effectiveness in estimating the battery's state of health (SOH).

关键词： Computational modeling State of charge Batteries Numerical models Polynomials Accuracy piecewise linear approximation Data models Dynamic programming Splines (mathematics) Battery management systems (BMSs) battery modeling dynamic programming lithium-ion batteries open-circuit voltage (OCV) model piecewise linear approximation state of charge (SOC) state of health (SOH)

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Bi-attribute utility preference robust optimization: A continuous piecewise linear approximation approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第1期323卷 170-191页

作者： Wu, Qiong Wang, Wei Zhang, Sainan Xu, Huifu Nanjing Normal Univ Sch Math Sci Nanjing 210046 Peoples R China Huazhong Univ Sci & Technol Sch Math & Stat Luoyu Rd 1037 Wuhan 430074 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong 999077 Peoples R China

In this paper, we consider a bi-attribute decision making problem where the decision maker's (DM's) objective is to maximize the expected utility of outcomes with two attributes but where the true utility function which captures the DM's risk preference is ambiguous. To tackle this ambiguity, we propose a maximin bi-attribute utility preference robust optimization (BUPRO) model where the optimal decision is based on the worst- case utility function in an ambiguity set of plausible utility functions constructed using partially available information such as the DM's specific preference for certain lotteries. Specifically, we consider a BUPRO model with two attributes, where the DM's risk attitude is bivariate risk-averse and the ambiguity set is defined by a linear system of inequalities represented by the Lebesgue-Stieltjes integrals of the DM's utility functions. To solve the inner infinite-dimensional minimization problem, we propose a continuous piecewise linear approximation approach to approximate the DM's unknown true utility. Unlike the univariate case, we partition the domain of the utility function into a set of small non-overlapping rectangles and then divide each rectangle into two triangles by either the main diagonal (Type-1) or the counter diagonal (Type-2). The inner minimization problem based on the piecewise linear utility function can be reformulated as a mixed-integer linear program and the outer maximization problem can be solved efficiently by the derivative-free method. In the case that all the small triangles are partitioned either in Type-1 or in Type-2, the inner minimization can be formulated as a finite dimensional linear program and the overall maximin as a single mixed-integer program. To quantify the approximation errors, we derive, under some mild conditions, the error bound for the difference between the BUPRO model and the approximate BUPRO model in terms of the ambiguity set, the optimal value and the optimal solutions. Finally, we c

关键词： Decision analysis BUPRO Preference elicitation piecewise linear approximation Mixed-integer program

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APLASE: Compression using Adaptive piecewise linear approximation and Sparse Encoding

APLASE: Compression using Adaptive Piecewise Linear Approxim...

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2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025

作者： Saxena, Ravi Raj Prabhakar, T.V. Kuri, Joy Murthy, Chandra R. Dept. of Electronic System Engineering Indian Institute of Science Bengaluru India Dept. of Electrical Communication Engineering Indian Institute of Science Bengaluru India

ISBN: (纸本)9798350368741

This work focuses on compressing vast amounts of time series data from IoT sensors while achieving low reconstruction error, at a low compression ratio (ratio of output data size to input data size), for efficient storage and transmission. We investigate two lossy compression techniques: Adaptive piecewise linear approximation (APLA) and Sparse Encoding (SE). APLA reduces data volume by leveraging the temporal correlation in time series data, while SE captures small, complex variations that APLA might miss. We identify a signal characteristic parameter, denoted by σd, which is used to derive error bounds for SE using σd, the dictionary used, and the input compression parameters. We also introduce APLASE, a novel compression technique that combines the two techniques by applying SE to the reconstruction error generated by APLA. We evaluate APLA, SE and APLASE using data from the NASA flight data recorder database consisting of recordings from 116 sensors. Our results show that APLASE consistently outperforms both APLA and SE individually, as well as the recent QoZ algorithm, particularly at lower compression ratios. © 2025 IEEE.

关键词： Compression piecewise linear approximation Sparse Encoding

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APLASE: Compression using Adaptive piecewise linear approximation and Sparse Encoding

APLASE: Compression using Adaptive Piecewise Linear Approxim...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Ravi Raj Saxena T.V. Prabhakar Joy Kuri Chandra R. Murthy Dept. of Electronic System Engineering Indian Institute of Science Bengaluru India Dept. of Electrical Communication Engineering Indian Institute of Science Bengaluru India

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

This work focuses on compressing vast amounts of time series data from IoT sensors while achieving low reconstruction error, at a low compression ratio (ratio of output data size to input data size), for efficient storage and transmission. We investigate two lossy compression techniques: Adaptive piecewise linear approximation (APLA) and Sparse Encoding (SE). APLA reduces data volume by leveraging the temporal correlation in time series data, while SE captures small, complex variations that APLA might miss. We identify a signal characteristic parameter, denoted by σ d , which is used to derive error bounds for SE using σ d , the dictionary used, and the input compression parameters. We also introduce APLASE, a novel compression technique that combines the two techniques by applying SE to the reconstruction error generated by APLA. We evaluate APLA, SE and APLASE using data from the NASA flight data recorder database consisting of recordings from 116 sensors. Our results show that APLASE consistently outperforms both APLA and SE individually, as well as the recent QoZ algorithm, particularly at lower compression ratios.

关键词： Measurement Dictionaries Time series analysis piecewise linear approximation NASA Signal processing algorithms Encoding Sensors Speech processing Standards

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piecewise linear approximation of Gas Flow Function for the Optimization of Integrated Electricity and Natural Gas System

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IEEE ACCESS 2019年 7卷 91819-91826页

作者： Bao, Yu-Qing Wu, Mei Zhou, Xueting Tang, Xiaobo Nanjing Normal Univ Sch Elect & Automat Engn Nanjing 210046 Jiangsu Peoples R China Nanjing Normal Univ Engn Lab Gas Elect Integrated Energy Jiangsu Prov Nanjing 210046 Jiangsu Peoples R China

The development of integrated electricity and natural-gas energy system (LEGS) aims at improving the energy efficiency and realizing complementarity between different energy sources. However, co-optimization of the IEGS suffers from non-convex and nonlinear Weymouth equation. Focusing on the piecewise linear approximation methods of the LEGS, this paper compares with the formation, the computational speed, and accuracy of the existing piecewise linear approximation methods, and proposes a modification method that achieves both fast-processing and high-accuracy. The numeral testing results verify the effectiveness of the proposed method.

关键词： Integrated electricity and natural-gas energy system piecewise linear approximation co-optimization

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piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics

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SOFT COMPUTING 2019年第19期23卷 9491-9505页

作者： Coroianu, Lucian Gagolewski, Marek Grzegorzewski, Przemyslaw Univ Oradea Dept Math & Informat 1 Univ St Oradea 410087 Romania Warsaw Univ Technol Fac Math & Informat Sci Koszykowa 75 PL-00662 Warsaw Poland Polish Acad Sci Syst Res Inst Newelska 6 PL-01447 Warsaw Poland

The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26-51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot (n >= 2) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems.

关键词： approximation of fuzzy numbers Calculations on fuzzy numbers Characteristics of fuzzy numbers Fuzzy number piecewise linear approximation

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piecewise linear approximation methods with stochastic sampling sites

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 329卷 173-178页

作者： Li, Junbin Wang, Renhong Xu, Min Fang, Qin Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Dalian Univ Coll Informat Dalian 116622 Peoples R China

We study a generalization of the classical piecewise linear approximation methods with equally spaced breaks by considering the sampling sites as random variables. The new form methods are motivated by the facts that real-world data collected from what are perceived to be equally spaced sites suffer from random errors due to measurement inaccuracies and other known or unknown factors. We establish error estimates and convergence results under practical assumptions about the distribution of the sampling sites. (C) 2017 Elsevier B.V. All rights reserved.

关键词： piecewise linear approximation Sampling sites Normal distribution

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piecewise linear approximation of Vector-Valued Images and Curves via Second-Order Variational Model

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第9期26卷 4414-4429页

作者： Zanetti, Massimo Bruzzone, Lorenzo Univ Trento Dept Informat Engn & Comp Sci I-38123 Trento Italy

Variational models are known to work well for addressing image restoration/regularization problems. However, most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images (such as RGB or multispectral imagery) by the composition of a simple band-wise processing. This involves suboptimal results and may introduce artifacts. Only in a few cases, variational models are extended to the case of vector-valued inputs. However, the known implementations are restricted to the first-order models, while the secondorder models are never considered. Thus, typical problems of the first-order models, such as the staircasing effect cannot be overtaken. This paper considers a second-order functional model to function approximation with free discontinuities given by Blake-Zisserman (BZ) and proposes an efficient minimization algorithm in the case of vector-valued inputs. In the BZ model, the Hessian of the solution is penalized outside a set of finite length, therefore the solution is forced to be piecewise linear. Moreover, the model allows the formation of free discontinuities and free gradient discontinuities. The proposed algorithm is applied to difficult color image restoration/regularization problems and to piecewise linear approximation of curves in space.

关键词： Multiband image variational methods Blake-Zisserman Mumford-Shah piecewise linear approximation block-coordinate descent method

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piecewise linear approximation of functions of two variables in MILP models

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OPERATIONS RESEARCH LETTERS 2010年第1期38卷 39-46页

作者： D'Ambrosio, Claudia Lodi, Andrea Martello, Silvano Univ Bologna DEIS I-40136 Bologna Italy

We consider three easy-to-implement methods for the piecewise linear approximation of functions of two variables. We experimentally evaluate their approximation quality, and give a detailed description of how the methods can be embedded in a MILP model. The advantages and drawbacks of the three methods are discussed on numerical examples. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Mixed integer linear programming Non-linear functions of two variables piecewise linear approximation

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piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期315卷 50-62页

作者： Ploussard, Quentin Argonne Natl Lab Lemont IL 60439 USA

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

关键词： Integer programming linear programming piecewise linear approximation Hierarchical optimization

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