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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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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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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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A linear programming approach to difference-of-convex piecewise linear approximation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期312卷 493-511页

作者： Kazda, Kody Li, Xiang Queens Univ Dept Chem Engn 19 Div St Kingston ON K7L 3N6 Canada

We address the problem of finding continuous piecewise linear (CPWL) approximations of determinis-tic functions of any dimension that satisfy any predefined error-tolerance, while keeping the number of polytopes that partition the approximation domain low. Specifically, we focus on overcoming the major computational bottleneck of the CPWL approximation Algorithm (CPWL-AA) that has been proposed in the recent literature. CPWL-AA uses the difference-of-convex CPWL representation to search CPWL ap-proximations which can partition the approximation domain to have polytopes of any shape. A computa-tional bottleneck of the method is to solve a mixed-integer linear program (MILP) in which the number of binary variables is large for many problems of practical interest. In this paper, we overcome this by intro-ducing a method that obtains a high quality solution of the MILP by iteratively solving a linear program (LP). We further reduce the computational expense by developing a method that treats some constraints in the LP problem as lazy constraints. Through a computational study we demonstrate that the proposed methods substantially reduce the computation time of CPWL-AA, while maintaining high quality CPWL approximations. With this, we demonstrate that we can generate CPWL approximations that satisfy pre-defined error-tolerances on functions of up to five dimensions within reasonable solution times.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Integer programming piecewise linear approximation MILP Difference -of -convex

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A flexible model based on piecewise linear approximation for the analysis of left truncated right censored data with covariates, and applications to Worcester Heart Attack Study data and Channing House data

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STATISTICS IN MEDICINE 2024年第2期43卷 233-255页

作者： Ganguly, Ayon Mitra, Debanjan Balakrishnan, Narayanaswamy Kundu, Debasis Indian Inst Technol Guwahati Dept Math Gauhati Assam India Indian Inst Management Udaipur Quantitat Methods Div Udaipur Rajasthan India McMaster Univ Dept Math & Stat Hamilton ON Canada Indian Inst Technol Kanpur Dept Math & Stat Kanpur Uttar Pradesh India

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data-driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data.

关键词： cumulative hazard function left truncation maximum likelihood estimators piecewise linear approximation prediction proportional hazards model right censoring

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piecewise linear approximation for identifying wind power ramp events

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AUTOMATIKA 2023年第4期64卷 1306-1314页

作者： Jayalakshmi, J. Linda, M. Mary Ponjesly Coll Engn Dept EEE Nagercoil Tamil Nadu India KIT Kalaignar karunanidhi Inst Technol Dept EEE Kannampaalayam Tamil Nadu India

WPREs (wind power ramp events) are one of the most critical factors affecting the security and protection of the electrical system. Accurate ramp event detection may help power systems better manage extreme events and reduce financial damage. In this study, We present an improved piecewise linear approximation for recognizing wind ramps in Kanyakumari district. In practise, wind power ramps can be decreased by properly managing and dispatching flexible reserve and associated services. This necessitates the use of proper ramp detection techniques as well as precise ramp forecasts. The method's plan to break down wind power signal into increasing with increasing ramps, making ramp identification easier and ensuring that all conceivable ramps of varying lengths are identified. Using observed wind power data, the ramp detection method is used to assess the performance of an energy wind farm. The results reveal that identifying wind power ramps using the segmentation method is equivalent to optical ramp identification.

关键词： Wind power ramp event improved optimal ramp detection algorithm piecewise linear approximation

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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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Li-ion Battery SOC Estimation via Gaussian Sum Filtering and piecewise linear approximation 12

Li-ion Battery SOC Estimation via Gaussian Sum Filtering and...

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2024 IEEE Andescon Conference

作者： Alcantara, Ignacio E. Cedeno, Angel L. Silva, Cesar A. Aguero, Juan C. Univ Tecn Federico Santa Maria Dept Elect Valparaiso Chile

ISBN: (纸本)9798350355291;9798350355284

Model-based methods for state of charge estimation in Lithium-Ion batteries have been widely employed. In this paper a novel filtering model-based algorithm is developed to estimate the state of charge. An 1RC equivalent circuit model and a piecewise linear approximation of the relationship between Open Circuit Voltage and State Of Charge are utilized for modelling the system of interest. A simulation study that consideres pulsed current discharge is developed. To validate these results, real battery data are utilized under various dynamic test profiles. The performance of the proposed filtering algorithm is compared with Extended Kalman Filter and Particle Filter.

关键词： Li-ion battery SOC piecewise linear approximation Model-based method Gaussian sum filtering Bayesian estimation EKF Particle Filter

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piecewise linear approximation by the Method of Worst Segment Division

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2021年第12期42卷 2969-2979页

作者： Sukiasyan, H. S. Natl Acad Sci Republ Armenia Inst Math Yerevan 0019 Armenia Natl Polytech Univ Armenia Yerevan Armenia

The finite element method for numerical solving two-dimensional boundary value problem is based on domain triangulation and piecewise linear approximation. The present paper describes how to minimize the number of triangulation vertices without exceeding the given level of the approximation error. The paper proposes a method for constructing piecewise linear approximations for continuous two-dimensional functions by dividing the ''worst'' segment. The possibilities of applying the proposed method in solving boundary value problems are investigated. The main theorem gives a sufficient condition on the minimized functional so that the best mesh would be the Delaunay triangulation. An example of a numerical solution of the Maxwell equation of the electromagnetic field using the method of the worst segment division with Delaunay triangulation is given.

关键词： boundary value problem finite element method piecewise linear approximation Dealaunay triangulation recursive algorithm

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Gait Phase Partitioning and Footprint Detection Using Mutually Constrained piecewise linear approximation with Dynamic Programming

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2021年第11期E104D卷 1951-1962页

作者： Yasukawa, Makoto Makihara, Yasushi Hosoi, Toshinori Kubo, Masahiro Yagi, Yasushi Osaka Univ Ibaraki 5670047 Japan NEC Corp Ltd Kawasaki Kanagawa 2118666 Japan

Human gait analysis has been widely used in medical and health fields. It is essential to extract spatio-temporal gait features (e.g., single support duration, step length, and toe angle) by partitioning the gait phase and estimating the footprint position/orientation in such fields. Therefore, we propose a method to partition the gait phase given a foot position sequence using mutually constrained piecewise linear approximation with dynamic programming, which not only represents normal gait well but also pathological gait without training data. We also propose a method to detect footprints by accumulating toe edges on the floor plane during stance phases, which enables us to detect footprints more clearly than a conventional method. Finally, we extract four spatial/temporal gait parameters for accuracy evaluation: single support duration, double support duration, toe angle, and step length. We conducted experiments to validate the proposed method using two types of gait patterns, that is, healthy and mimicked hemiplegic gait, from 10 subjects. We confirmed that the proposed method could estimate the spatial/temporal gait parameters more accurately than a conventional skeleton-based method regardless of the gait pattern.

关键词： gait phase partitioning piecewise linear approximation dynamic programming footprint detection rehabilitation

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