Over the past few years, there has been substantial interest and research activity surrounding the application of Convolutional Neural Networks (CNNs) for post-filtering in video coding. Most current research efforts have focused on using CNNs with various kernel sizes for post-filtering, primarily concentrating on High-Efficiency Video Coding/H.265 (HEVC) and Versatile Video Coding/H.266 (VVC). This narrow focus has limited the exploration and application of these techniques to other video coding standards such as AV1, developed by the Alliance for Open Media, which offers excellent compression efficiency, reducing bandwidth usage and improving video quality, making it highly attractive for modern streaming and media applications. This paper introduces a novel approach that extends beyond traditional CNN methods by integrating three different self-attention layers into the CNN framework. Applied to the AV1 codec, the proposed method significantly improves video quality by incorporating these distinct self-attention layers. This enhancement demonstrates the potential of self-attention mechanisms to revolutionize post-filtering techniques in video coding beyond the limitations of convolution-based methods. The experimental results show that the proposed network achieves an average BD-rate reduction of 10.40% for the Luma component and 19.22% and 16.52% for the Chroma components compared to the AV1 anchor. Visual quality assessments further validated the effectiveness of our approach, showcasing substantial artifact reduction and detail enhancement in videos.
{"title":"Multi-Type Self-Attention-Based Convolutional-Neural-Network Post-Filtering for AV1 Codec","authors":"Woowoen Gwun, Kiho Choi, Gwang Hoon Park","doi":"10.3390/math12182874","DOIUrl":"https://doi.org/10.3390/math12182874","url":null,"abstract":"Over the past few years, there has been substantial interest and research activity surrounding the application of Convolutional Neural Networks (CNNs) for post-filtering in video coding. Most current research efforts have focused on using CNNs with various kernel sizes for post-filtering, primarily concentrating on High-Efficiency Video Coding/H.265 (HEVC) and Versatile Video Coding/H.266 (VVC). This narrow focus has limited the exploration and application of these techniques to other video coding standards such as AV1, developed by the Alliance for Open Media, which offers excellent compression efficiency, reducing bandwidth usage and improving video quality, making it highly attractive for modern streaming and media applications. This paper introduces a novel approach that extends beyond traditional CNN methods by integrating three different self-attention layers into the CNN framework. Applied to the AV1 codec, the proposed method significantly improves video quality by incorporating these distinct self-attention layers. This enhancement demonstrates the potential of self-attention mechanisms to revolutionize post-filtering techniques in video coding beyond the limitations of convolution-based methods. The experimental results show that the proposed network achieves an average BD-rate reduction of 10.40% for the Luma component and 19.22% and 16.52% for the Chroma components compared to the AV1 anchor. Visual quality assessments further validated the effectiveness of our approach, showcasing substantial artifact reduction and detail enhancement in videos.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"15 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tanuj Joshi, Abhinav Gupta, Om Parkash, Ralph Kristoffer B. Gallegos, Nay Lin Oo, Gopal Krishan
The study establishes two mathematical formulations to predict the pressure drop in a solid–liquid slurry flowing through a straight pipe. Employing the Eulerian–Eulerian RNG k-ε model, the computational investigation uses water as the carrier fluid and glass beads as solid particles. The analysis spans various particle sizes (d50 = 75–175 μm), volumetric concentrations (Cvf = 10–50%), and velocities (Vm = 1–5 m/s). The first model, developed using the MATLAB curve-fitting tool, is complemented by a second empirical equation derived through non-polynomial mathematical formulation. Results from both models are validated against existing experimental and computational data, demonstrating accurate predictions for d50 = 75–175 µm particles within a Reynolds number range of 20,000 ≤ Re ≤ 320,000.
{"title":"Mathematical Formulations for Predicting Pressure Drop in Solid–Liquid Slurry Flow through a Straight Pipe Using Computational Modeling","authors":"Tanuj Joshi, Abhinav Gupta, Om Parkash, Ralph Kristoffer B. Gallegos, Nay Lin Oo, Gopal Krishan","doi":"10.3390/math12182879","DOIUrl":"https://doi.org/10.3390/math12182879","url":null,"abstract":"The study establishes two mathematical formulations to predict the pressure drop in a solid–liquid slurry flowing through a straight pipe. Employing the Eulerian–Eulerian RNG k-ε model, the computational investigation uses water as the carrier fluid and glass beads as solid particles. The analysis spans various particle sizes (d50 = 75–175 μm), volumetric concentrations (Cvf = 10–50%), and velocities (Vm = 1–5 m/s). The first model, developed using the MATLAB curve-fitting tool, is complemented by a second empirical equation derived through non-polynomial mathematical formulation. Results from both models are validated against existing experimental and computational data, demonstrating accurate predictions for d50 = 75–175 µm particles within a Reynolds number range of 20,000 ≤ Re ≤ 320,000.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"24 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Signifiable computability aims to separate what is theoretically computable from what is computable through performable processes on computers with finite amounts of memory. Real numbers and sequences thereof, data types, and instances are treated as finite texts, and memory limitations are made explicit through a requirement that the texts be stored in the available memory on the devices that manipulate them. In Part I of our investigation, we define the concepts of signification and reference of real numbers. We extend signification to number tuples, data types, and data instances and show that data structures representable as tuples of discretely finite numbers are signifiable. From the signification of real tuples, we proceed to the constructive signification of multidimensional matrices and show that any data structure representable as a multidimensional matrix of discretely finite numbers is signifiable.
{"title":"On Signifiable Computability: Part I: Signification of Real Numbers, Sequences, and Types","authors":"Vladimir A. Kulyukin","doi":"10.3390/math12182881","DOIUrl":"https://doi.org/10.3390/math12182881","url":null,"abstract":"Signifiable computability aims to separate what is theoretically computable from what is computable through performable processes on computers with finite amounts of memory. Real numbers and sequences thereof, data types, and instances are treated as finite texts, and memory limitations are made explicit through a requirement that the texts be stored in the available memory on the devices that manipulate them. In Part I of our investigation, we define the concepts of signification and reference of real numbers. We extend signification to number tuples, data types, and data instances and show that data structures representable as tuples of discretely finite numbers are signifiable. From the signification of real tuples, we proceed to the constructive signification of multidimensional matrices and show that any data structure representable as a multidimensional matrix of discretely finite numbers is signifiable.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hon Yiu So, Man Ho Ling, Narayanaswamy Balakrishnan
One-shot devices are products that can only be used once. Typical one-shot devices include airbags, fire extinguishers, inflatable life vests, ammo, and handheld flares. Most of them are life-saving products and should be highly reliable in an emergency. Quality control of those productions and predicting their reliabilities over time is critically important. To assess the reliability of the products, manufacturers usually test them in controlled conditions rather than user conditions. We may rely on public datasets that reflect their reliability in actual use, but the datasets often come with missing observations. The experimenter may lose information on covariate readings due to human errors. Traditional missing-data-handling methods may not work well in handling one-shot device data as they only contain their survival statuses. In this research, we propose Multiple Imputation with Unsupervised Learning (MIUL) to impute the missing data using Hierarchical Clustering, k-prototype, and density-based spatial clustering of applications with noise (DBSCAN). Our simulation study shows that MIUL algorithms have superior performance. We also illustrate the method using datasets from the Crash Report Sampling System (CRSS) of the National Highway Traffic Safety Administration (NHTSA).
一次性设备是只能使用一次的产品。典型的一次性装置包括安全气囊、灭火器、充气救生衣、弹药和手持信号弹。它们大多是救生产品，在紧急情况下应具有高度可靠性。对这些产品进行质量控制并预测其在一段时间内的可靠性至关重要。为了评估产品的可靠性，制造商通常会在受控条件下而非用户条件下对产品进行测试。我们可以依靠公共数据集来反映产品在实际使用中的可靠性，但这些数据集往往会丢失观测数据。实验人员可能会因为人为失误而丢失协变量读数信息。传统的缺失数据处理方法可能无法很好地处理一次性设备数据，因为这些数据只包含其存活状态。在这项研究中，我们提出了 "无监督学习多重估算"（Multiple Imputation with Unsupervised Learning，MIUL）方法，利用层次聚类、k-原型和基于密度的带噪声应用空间聚类（DBSCAN）来估算缺失数据。我们的模拟研究表明，MIUL 算法性能优越。我们还使用美国国家公路交通安全管理局（NHTSA）的碰撞报告采样系统（CRSS）数据集对该方法进行了说明。
{"title":"Imputing Missing Data in One-Shot Devices Using Unsupervised Learning Approach","authors":"Hon Yiu So, Man Ho Ling, Narayanaswamy Balakrishnan","doi":"10.3390/math12182884","DOIUrl":"https://doi.org/10.3390/math12182884","url":null,"abstract":"One-shot devices are products that can only be used once. Typical one-shot devices include airbags, fire extinguishers, inflatable life vests, ammo, and handheld flares. Most of them are life-saving products and should be highly reliable in an emergency. Quality control of those productions and predicting their reliabilities over time is critically important. To assess the reliability of the products, manufacturers usually test them in controlled conditions rather than user conditions. We may rely on public datasets that reflect their reliability in actual use, but the datasets often come with missing observations. The experimenter may lose information on covariate readings due to human errors. Traditional missing-data-handling methods may not work well in handling one-shot device data as they only contain their survival statuses. In this research, we propose Multiple Imputation with Unsupervised Learning (MIUL) to impute the missing data using Hierarchical Clustering, k-prototype, and density-based spatial clustering of applications with noise (DBSCAN). Our simulation study shows that MIUL algorithms have superior performance. We also illustrate the method using datasets from the Crash Report Sampling System (CRSS) of the National Highway Traffic Safety Administration (NHTSA).","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"116 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiu Shu, Feng Huang, Zhaobing Qiu, Xinming Zhang, Di Yuan
The limited availability of thermal infrared (TIR) training samples leads to suboptimal target representation by convolutional feature extraction networks, which adversely impacts the accuracy of TIR target tracking methods. To address this issue, we propose an unsupervised cross-domain model (UCDT) for TIR tracking. Our approach leverages labeled training samples from the RGB domain (source domain) to train a general feature extraction network. We then employ a cross-domain model to adapt this network for effective target feature extraction in the TIR domain (target domain). This cross-domain strategy addresses the challenge of limited TIR training samples effectively. Additionally, we utilize an unsupervised learning technique to generate pseudo-labels for unlabeled training samples in the source domain, which helps overcome the limitations imposed by the scarcity of annotated training data. Extensive experiments demonstrate that our UCDT tracking method outperforms existing tracking approaches on the PTB-TIR and LSOTB-TIR benchmarks.
热红外（TIR）训练样本的有限性导致卷积特征提取网络的目标表示不理想，从而对 TIR 目标跟踪方法的准确性产生不利影响。为解决这一问题，我们提出了一种用于 TIR 跟踪的无监督跨域模型 (UCDT)。我们的方法利用 RGB 域（源域）的标记训练样本来训练通用特征提取网络。然后，我们采用跨域模型来调整该网络，以便在 TIR 域（目标域）中有效提取目标特征。这种跨域策略有效地解决了 TIR 训练样本有限的难题。此外，我们还利用无监督学习技术为源域中未标注的训练样本生成伪标签，这有助于克服标注训练数据稀缺所带来的限制。大量实验证明，在 PTB-TIR 和 LSOTB-TIR 基准上，我们的 UCDT 跟踪方法优于现有的跟踪方法。
{"title":"Learning Unsupervised Cross-Domain Model for TIR Target Tracking","authors":"Xiu Shu, Feng Huang, Zhaobing Qiu, Xinming Zhang, Di Yuan","doi":"10.3390/math12182882","DOIUrl":"https://doi.org/10.3390/math12182882","url":null,"abstract":"The limited availability of thermal infrared (TIR) training samples leads to suboptimal target representation by convolutional feature extraction networks, which adversely impacts the accuracy of TIR target tracking methods. To address this issue, we propose an unsupervised cross-domain model (UCDT) for TIR tracking. Our approach leverages labeled training samples from the RGB domain (source domain) to train a general feature extraction network. We then employ a cross-domain model to adapt this network for effective target feature extraction in the TIR domain (target domain). This cross-domain strategy addresses the challenge of limited TIR training samples effectively. Additionally, we utilize an unsupervised learning technique to generate pseudo-labels for unlabeled training samples in the source domain, which helps overcome the limitations imposed by the scarcity of annotated training data. Extensive experiments demonstrate that our UCDT tracking method outperforms existing tracking approaches on the PTB-TIR and LSOTB-TIR benchmarks.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"16 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.
研究了具有交货时间和可变处理时间的单机到期窗口分配调度，其中作业的可变处理时间意味着处理时间是其在序列中的位置和资源分配的函数。目前，到期窗口分配问题有多个优化目标，而对窗口起始时间、拒绝成本和优化调度共同要求的优化问题的研究较少。本文的目标是在可选工作外包（拒绝）的情况下，使调度成本、资源消耗成本和外包措施的权重之和最小化。在两种资源分配模型（即线性资源分配模型和凸资源分配模型）下，调度成本是早迟到作业数量、早迟到惩罚和到期窗口开始时间及大小的加权和，其中权重与位置有关。本文的主要贡献包括对具有学习效应、交货时间和外包成本的单机调度进行了研究和数据模拟。对于调度成本、资源消耗成本和外包成本的权重和，我们证明了问题的多项式可解性。在普通和松弛的到期窗口分配下，通过最优解的理论分析，我们发现四个问题可以在 O(n6) 时间内求解，其中 n 为作业数。
{"title":"Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing","authors":"Bing Bai, Cai-Min Wei, Hong-Yu He, Ji-Bo Wang","doi":"10.3390/math12182883","DOIUrl":"https://doi.org/10.3390/math12182883","url":null,"abstract":"Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"5 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer’s order-allocation decision, leading to a no-relocation strategy as the supply chain’s equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer’s expected profits but benefits the supplier’s expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers.
{"title":"Should Multinational Suppliers Relocate Their Production Capacity to Preferential Tariff Regions with Unreliable Supply under the Impact of Tariffs?","authors":"Zongbao Zou, Yuxin Liang, Lihao Chen","doi":"10.3390/math12182876","DOIUrl":"https://doi.org/10.3390/math12182876","url":null,"abstract":"This paper investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer’s order-allocation decision, leading to a no-relocation strategy as the supply chain’s equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer’s expected profits but benefits the supplier’s expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"3 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Edgar D. Silva-Vera, Jesus E. Valdez-Resendiz, Gerardo Escobar, Daniel Guillen, Julio C. Rosas-Caro, Jose M. Sosa
This article presents a data-driven methodology for modeling lithium-ion batteries, which includes the estimation of the open-circuit voltage and state of charge. Using the proposed methodology, the dynamics of a battery cell can be captured without the need for explicit theoretical models. This approach only requires the acquisition of two easily measurable variables: the discharge current and the terminal voltage. The acquired data are used to build a linear differential system, which is algebraically manipulated to form a space-state representation of the battery cell. The resulting model was tested and compared against real discharging curves. Preliminary results showed that the battery’s state of charge can be computed with limited precision using a model that considers a constant open-circuit voltage. To improve the accuracy of the identified model, a modified recursive least-squares algorithm is implemented inside the data-driven method to estimate the battery’s open-circuit voltage. These last results showed a very precise tracking of the real battery discharging dynamics, including the terminal voltage and state of charge. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions and battery management systems with the interconnection of multiple battery cells.
{"title":"Data-Driven Modeling and Open-Circuit Voltage Estimation of Lithium-Ion Batteries","authors":"Edgar D. Silva-Vera, Jesus E. Valdez-Resendiz, Gerardo Escobar, Daniel Guillen, Julio C. Rosas-Caro, Jose M. Sosa","doi":"10.3390/math12182880","DOIUrl":"https://doi.org/10.3390/math12182880","url":null,"abstract":"This article presents a data-driven methodology for modeling lithium-ion batteries, which includes the estimation of the open-circuit voltage and state of charge. Using the proposed methodology, the dynamics of a battery cell can be captured without the need for explicit theoretical models. This approach only requires the acquisition of two easily measurable variables: the discharge current and the terminal voltage. The acquired data are used to build a linear differential system, which is algebraically manipulated to form a space-state representation of the battery cell. The resulting model was tested and compared against real discharging curves. Preliminary results showed that the battery’s state of charge can be computed with limited precision using a model that considers a constant open-circuit voltage. To improve the accuracy of the identified model, a modified recursive least-squares algorithm is implemented inside the data-driven method to estimate the battery’s open-circuit voltage. These last results showed a very precise tracking of the real battery discharging dynamics, including the terminal voltage and state of charge. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions and battery management systems with the interconnection of multiple battery cells.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"25 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Igor Fernández de Bustos, Haritz Uriarte, Gorka Urkullu, Ibai Coria
There are several common procedures used to numerically integrate second-order ordinary differential equations. The most common one is to reduce the equation’s order by duplicating the number of variables. This allows one to take advantage of the family of Runge–Kutta methods or the Adams family of multi-step methods. Another approach is the use of methods that have been developed to directly integrate an ordinary differential equation without increasing the number of variables. An important drawback when using Runge–Kutta methods is that when one tries to apply them to differential algebraic equations, they require a reduction in the index, leading to a need for stabilization methods to remove the drift. In this paper, a new family of methods for the direct integration of second-order ordinary differential equations is presented. These methods can be considered as a generalization of the central differences method. The methods are classified according to the number of derivatives they take into account (degree). They include some parameters that can be chosen to configure the equation’s behavior. Some sets of parameters were studied, and some examples belonging to structural dynamics and multibody dynamics are presented. An example of the application of the method to a differential algebraic equation is also included.
{"title":"A Family of Conditionally Explicit Methods for Second-Order ODEs and DAEs: Application in Multibody Dynamics","authors":"Igor Fernández de Bustos, Haritz Uriarte, Gorka Urkullu, Ibai Coria","doi":"10.3390/math12182862","DOIUrl":"https://doi.org/10.3390/math12182862","url":null,"abstract":"There are several common procedures used to numerically integrate second-order ordinary differential equations. The most common one is to reduce the equation’s order by duplicating the number of variables. This allows one to take advantage of the family of Runge–Kutta methods or the Adams family of multi-step methods. Another approach is the use of methods that have been developed to directly integrate an ordinary differential equation without increasing the number of variables. An important drawback when using Runge–Kutta methods is that when one tries to apply them to differential algebraic equations, they require a reduction in the index, leading to a need for stabilization methods to remove the drift. In this paper, a new family of methods for the direct integration of second-order ordinary differential equations is presented. These methods can be considered as a generalization of the central differences method. The methods are classified according to the number of derivatives they take into account (degree). They include some parameters that can be chosen to configure the equation’s behavior. Some sets of parameters were studied, and some examples belonging to structural dynamics and multibody dynamics are presented. An example of the application of the method to a differential algebraic equation is also included.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"14 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Klein–-Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–-Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.
{"title":"Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation","authors":"Guojiang Wu, Yong Guo, Yanlin Yu","doi":"10.3390/math12182867","DOIUrl":"https://doi.org/10.3390/math12182867","url":null,"abstract":"The Klein–-Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–-Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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