Piecewise Linear Technique Research Articles

Optimization of the electric vehicle charging strategy problem for sustainable intercity travels with multiple refueling stops

Electric vehicle (EV) drivers considering long-distance trips still face range anxiety due to the limited range of EVs and the scarcity of charging stations. Thus, it becomes important to ensure the feasibility of the selected route and determine an optimal charging strategy. As a crucial aspect of decision support for EV drivers, this study proposes a mixed integer linear programming (MILP) approach for the EV charging strategy problem (EVCSP), incorporating a piecewise linear approximation technique to address the challenges posed by nonlinear charging times. The proposed optimization model, namely CSPM determines where, when, and how much to charge an EV for a specified route to minimize travel time and cost. The solution time of large-scale test problems and a case study on Türkiye reveal the robustness and reliability of the CSPM. Furthermore, two multi-objective optimization methods (the weighted sum and the lexicographic method) are applied to the case study, and the results are analyzed. The results indicate that the travel cost is more sensitive to the selected charging strategy, with a range of 46.09 % across the applied charging strategies, whereas travel time remains more resilient, with a maximum fluctuation of 19.77 %. A comparative analysis with a full charging strategy reveals that the CSPM reduces the travel time by 60.1 % and improves the cost efficiency by 105.72 %.

Efficient Sleep Stage Identification Using Piecewise Linear EEG Signal Reduction: A Novel Algorithm for Sleep Disorder Diagnosis.

Sleep is a vital physiological process for human health, and accurately detecting various sleep states is crucial for diagnosing sleep disorders. This study presents a novel algorithm for identifying sleep stages using EEG signals, which is more efficient and accurate than the state-of-the-art methods. The key innovation lies in employing a piecewise linear data reduction technique called the Halfwave method in the time domain. This method simplifies EEG signals into a piecewise linear form with reduced complexity while preserving sleep stage characteristics. Then, a features vector with six statistical features is built using parameters obtained from the reduced piecewise linear function. We used the MIT-BIH Polysomnographic Database to test our proposed method, which includes more than 80 h of long data from different biomedical signals with six main sleep classes. We used different classifiers and found that the K-Nearest Neighbor classifier performs better in our proposed method. According to experimental findings, the average sensitivity, specificity, and accuracy of the proposed algorithm on the Polysomnographic Database considering eight records is estimated as 94.82%, 96.65%, and 95.73%, respectively. Furthermore, the algorithm shows promise in its computational efficiency, making it suitable for real-time applications such as sleep monitoring devices. Its robust performance across various sleep classes suggests its potential for widespread clinical adoption, making significant advances in the knowledge, detection, and management of sleep problems.

A Robust Zero-Watermarking Scheme in Spatial Domain by Achieving Features Similar to Frequency Domain

In recent years, there has been a substantial surge in the application of image watermarking, which has evolved into an essential tool for identifying multimedia material, ensuring security, and protecting copyright. Singular value decomposition (SVD) and discrete cosine transform (DCT) are widely utilized in digital image watermarking despite the considerable computational burden they involve. By combining block-based direct current (DC) values with matrix norm, this research article presents a novel, robust zero-watermarking approach. It generates a zero-watermark without attempting to modify the contents of the image. The image is partitioned into non-overlapping blocks, and DC values are computed without applying DCT. This sub-image is further partitioned into non-overlapping blocks, and the maximum singular value of each block is calculated by matrix norm instead of SVD to obtain the binary feature matrix. A piecewise linear chaotic map encryption technique is utilized to improve the security of the watermark image. After that, the feature image is created via XOR procedure between the encrypted watermark image and the binary feature matrix. The proposed scheme is tested using a variety of distortion attacks including noise, filter, geometric, and compression attacks. It is also compared with the other relevant image watermarking methods and outperformed them in most cases.

Mapping Daily Air Temperature Over the Hawaiian Islands From 1990 to 2021 via an Optimized Piecewise Linear Regression Technique

AbstractGridded air temperature data are required in various fields such as ecological modeling, weather forecasting, and surface energy balance assessment. In this work, a piecewise multiple linear regression model is used to produce high‐resolution (250 m) daily maximum (Tmax), minimum (Tmin), and mean (Tmean) near‐surface air temperature maps for the State of Hawaiʻi for a 32‐year period (1990–2021). Multiple meteorological and geographical variables such as the elevation, daily rainfall, coastal distance index, leaf area index, albedo, topographic position index, and wind speed are independently tested to determine the most well‐suited predictor variables for optimal model performance. During the mapping process, input data scarcity is addressed first by gap‐filling critical stations at high elevation using a predetermined linear relationship with other strongly‐correlated stations, and second, by supplementing the training dataset with station data from neighboring islands. Despite the numerous covariates physically linked to temperature, the most parsimonious model selection uses elevation as its sole predictor, and the inclusion of the additional variables results in increased cross‐validation errors. The mean absolute error of resultant estimated Tmax and Tmin maps over the Hawaiian Islands from 1990 to 2021 is 1.7°C and 1.3°C, respectively. Corresponding bias values are 0.01°C and −0.13°C, respectively for the same variables. Overall, the results show the proposed methodology can robustly generate daily air temperature maps from point‐scale measurements over complex topography.

Real-Time Implementation of a Frequency Shifter for Enhancement of Heart Sounds Perception on VLIW DSP Platform

Auscultation of heart sounds is important to perform cardiovascular assessment. External noises may limit heart sound perception. In addition, heart sound bandwidth is concentrated at very low frequencies, where the human ear has poor sensitivity. Therefore, the acoustic perception of the operator can be significantly improved by shifting the heart sound spectrum toward higher frequencies. This study proposes a real-time frequency shifter based on the Hilbert transform. Key system components are the Hilbert transformer implemented as a Finite Impulse Response (FIR) filter, and a Direct Digital Frequency Synthesizer (DDFS), which allows agile modification of the frequency shift. The frequency shifter has been implemented on a VLIW Digital Signal Processor (DSP) by devising a novel piecewise quadratic approximation technique for efficient DDFS implementation. The performance has been compared with other DDFS implementations both considering piecewise linear technique and sine/cosine standard library functions of the DSP. Piecewise techniques allow a more than 50% reduction in execution time compared to the DSP library. Piecewise quadratic technique also allows a more than 50% reduction in total required memory size in comparison to the piecewise linear. The theoretical analysis of the dynamic power dissipation exhibits a more than 20% reduction using piecewise techniques with respect to the DSP library. The real-time operation has been also verified on the DSK6713 rapid prototyping board by Texas Instruments C6713 DSP. Audiologic tests have also been performed to assess the actual improvement of heart sound perception. To this aim, heart sound recordings were corrupted by additive white Gaussian noise, crowded street noise, and helicopter noise, with different signal-to-noise ratios. All recordings were collected from public databases. Statistical analyses of the audiological test results confirm that the proposed approach provides a clear improvement in heartbeat perception in noisy environments.

Выявление и учет дрейфа нуль-пункта относительного гравиметра приливного типа

Thorough study of the equipment is essential before any measurements are made. Relative tidal gravimeters are complex technical devices; they enable measuring gravity time variations with high accuracy (1 μGal). The main source of systematic errors is their instrumental drift. Value and nonlinearity of the drift for each unit is individual. There are plenty of considering methods; they depend on material and technical opportunities. The simplest and less resource-consuming algorithm is to take the drift into account using the piecewise linear approximation technique. This research deals with assessing the accuracy of accounting the instrumental drift of the gPhoneX#117 (Micro-g LaCoste, USA) tidal gravimeter using the specified means. For this purpose, the drift was obtained through approximation by polynomials of the first and second degree was estimated in comparison with the results of reference (absolute) observations. It is concluded that the method of piecewise linear approximation can only be used for rejecting poor quality measurements. It is recommended to identify, control and accounting the instrumental drift by comparing measurements with the data of regular absolute monitoring.

A novel State of Charge and State of Health estimation technique for Lithium-ion cells using machine learning based Pseudo-Random Binary Sequence method

Lithium-Ion batteries are electrochemical storage devices with State of Charge (SOC) and State of Health (SOH) sensitive operations. The accurate estimation of these two parameters is vital for the battery's optimum usage for different applications. Electrochemical Impedance Spectroscopy (EIS) is a benchmark technique that measures the cell internal impedance for online estimation of these parameters. Recent studies have used EIS with Discrete Fourier Transform, neural networks, and other machine learning algorithms for improving the accuracy and reliability of these parameters. However, such methods also increase system complexity, time interval, and cost of the estimation system. Few researchers have also used Pseudo-Random Binary Sequence (PRBS) techniques to improve the speed of EIS estimations. However, they have lower accuracy due to frequency harmonics, and the continued requirement of simultaneous measurements of physical parameters introduces complexity in designing an online estimator. This paper proposes a novel hybrid method of estimating these parameters using a combination of a PRBS and an online piecewise linear machine learning technique. A hardware prototype is developed to validate the proposed method resulting in a cost-effective and simpler method with an estimation accuracy of 98 % at 5-sec intervals.

Finite element analysis of nonlinear reaction–diffusion system of Fitzhugh–Nagumo type with Robin boundary conditions

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper.

Global algorithm for a class of multiplicative programs using piecewise linear approximation technique

Global algorithm for a class of multiplicative programs using piecewise linear approximation technique

Nonlinear Modeling Analysis and Arc High-Impedance Faults Detection in Active Distribution Networks With Neutral Grounding via Petersen Coil

For Arc High-Impedance Faults (AHIFs) in Active Distribution Networks (ADNs) with neutral grounding via Petersen coil, both nonlinear characteristics caused by arc and the influence of zero-input response have been not considered in previous research. Quantitative analysis methods based on the threshold setting comparison is mostly adopted in current field applications, which cannot balance the detection reliability and sensitivity simultaneously. In response to this problem, a higher precision nonlinear AHIF equivalent model is established based on the logarithmic arc model. State equations describing the occurrences of AHIFs are solved by using piecewise linear fitting technique, and analytical expressions of zero-sequence voltage and currents are present in paper. Furthermore, the regular volt-ampere characteristic dynamic trajectory between the zero-sequence voltage and current in characteristic frequency band is analyzed, and a tangent-inverse method is proposed to extract the direction of dynamic trajectory, then an effective fault detection algorithm is designed. The validity of the proposed nonlinear equivalent model and detection algorithm are verified by various cases’ simulations and field test data.

Interjoint Coordination in Kicking a Moving Target: A Comparison Between Elite and Nonelite Taekwondo Players.

Patterns of interjoint coordination in the kicking legs of taekwondo players were investigated to understand movement pattern variability as a functional property of skill level. Elite and nonelite players performed roundhouse kicks against a custom-built moving target fitted with an accelerometer, and movements were recorded by motion capture. Average foot segment velocities of 13.6 and 11.4m/s were recorded for elite and nonelite players, respectively (P < .05), corresponding to target accelerations of 87.5 and 70.8g (P < .05). Gradient values derived from piecewise linear regression of continuous relative phase curves established the comparative incoordination of nonelite taekwondo players in the form of an overshoot behavior during the crucial period leading to target impact (P < .05). This overshoot was apparent in both knee-hip and ankle-knee continuous relative phase curves. Elite players generated greater limb speed and impact force through more effective limb segment coordination. The combination of continuous relative phase and piecewise linear regression techniques allowed identification of alternate joint control approaches in the 2 groups.

Stochastic single allocation hub location problems with balanced utilization of hub capacities

This paper presents a stochastic formulation for capacitated single allocation hub location problems with uncertain demands, in which the balanced utilization of hub capacities is considered in the strategic decision making process. The demands are assumed to be independent random variables with known normal probability distributions. A stochastic programming model with joint chance constraints is established and then transformed into a second-order mixed-integer cone programming model. Furthermore, the proposed model is approximated by using piecewise tangent approximation and piecewise linear approximation techniques. For the approximated models, alternative reformulations are developed, and valid inequalities are employed to add to alternative reformulations. Extensive numerical experiments with CAB and AP data sets are conducted to evaluate the performance of the proposed methods, and analyze the configuration of hub-and-spoke networks and the utilization of hub capacities. Experimental results show that the optimal solution of proposed models can be obtained by using the two approximation techniques with a small number of tangent and linear segments. The developed alternative reformulations and valid inequalities can significantly improve computational efficiency. The entire unbalanced utilization degree of hub capacities can be greatly reduced with a small rise in the traditional operating cost.

Performance of the Boost Converter Controlled with ZAD to Regulate DC Signals

This paper presents the performance of a boost converter controlled with a zero average dynamics technique to regulate direct current signals. The boost converter is modeled in a compact form, and a variable change is performed to depend only on the γ parameter. A new sliding surface is proposed, where it is possible to regulate both the voltage and the current with low relative errors with respect to the reference signals. It is analytically demonstrated that the approximation of the switching surface by a piecewise linear technique is efficient in controlling the system. It is shown numerically that for certain operating conditions, the system is evolved into a chaotic attractor. The zero average dynamics technique implemented in the boost converter has good regulation, due to the presence of zones in the bi-parametric space. Furthermore, the zero average dynamics technique regulates the voltage well and presents a chaotic attractor with low steady-state error.

An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

AbstractIn this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L2 norm of the error is derived to determine the errors for the approximate solution. The accuracy of four piecewise linear reconstruction techniques, namely, Frink, Holmes‐Connell, Green‐Gauss, and least‐squares methods are investigated on structured triangular grids. Numerical evidence shows that the least‐squares method is the most accurate of all methods for smooth initial condition problems. For discontinuous initial condition problems, the Frink and the Holmes‐Connell methods give a spurious oscillating solution in the vicinity of the discontinuity upstream of the discontinuity, and the Green‐Gauss and least‐squares methods give a spurious oscillating solution in the vicinity of the discontinuity downstream of the discontinuity. Moreover, the amplitude of the oscillation could be amplified on the finer grid sizes.

FastSW: Efficient Piecewise Linear Approximation of Quaternion-Based Orientation Sensor Signals for Motion Capturing with Wearable IMUs.

In the past decade, inertial measurement sensors have found their way into many wearable devices where they are used in a broad range of applications, including fitness tracking, step counting, navigation, activity recognition, or motion capturing. One of their key features that is widely used in motion capturing applications is their capability of estimating the orientation of the device and, thus, the orientation of the limb it is attached to. However, tracking a human’s motion at reasonable sampling rates comes with the drawback that a substantial amount of data needs to be transmitted between devices or to an end point where all device data is fused into the overall body pose. The communication typically happens wirelessly, which severely drains battery capacity and limits the use time. In this paper, we introduce fastSW, a novel piecewise linear approximation technique that efficiently reduces the amount of data required to be transmitted between devices. It takes advantage of the fact that, during motion, not all limbs are being moved at the same time or at the same speed, and only those devices need to transmit data that actually are being moved or that exceed a certain approximation error threshold. Our technique is efficient in computation time and memory utilization on embedded platforms, with a maximum of 210 instructions on an ARM Cortex-M4 microcontroller. Furthermore, in contrast to similar techniques, our algorithm does not affect the device orientation estimates to deviate from a unit quaternion. In our experiments on a publicly available dataset, our technique is able to compress the data to of its original size, while achieving an average angular deviation of approximately 2° and a maximum angular deviation below 9°.

An Efficient Hardware Approach for Approximate Logarithmic Computation

In this work, we present a technique that combines piecewise linear interpolation technique with a look-up table-based method in a novel way resulting in a logarithmic converter with higher accuracy. The piecewise linear interpolation function is obtained using a new algorithm, which aids in reducing the interpolation error. The algorithm helps in obtaining an optimized interpolation function which tracks the slope of log[Formula: see text] function more accurately. As a consequence, the size of the look-up table used to correct this interpolation error reduces significantly. Further, precision of the logarithmic converter can be improved by adding additional memory without changing the overall hardware. The method of combining linear interpolation with look-up results in high accuracy with less hardware complexity compared to similar existing techniques. The proposed and existing logarithmic converter designs are synthesized on FPGA and compared for their performance. Results indicate that the proposed approach achieves an improvement of 12% to 22% in memory for accuracies ranging from 10-bit to 20-bit.

Optimization of Economic Efficiency in Distribution Grids Using Distribution Locational Marginal Pricing

Distribution locational marginal pricing (DLMP) is an increasingly popular pricing signal that can be used to incentivize grid-friendly behavior of distributed energy resources (DER) to optimize economic efficiency in distribution grids. In this paper, a lossy direct-current optimal power flow (DCOPF) is utilized to obtain the iterative calculation framework for DLMPs. The two-stage algorithm iterates between the transmission system optimal power flow (OPF) and the distribution system OPF until no significant changes in DLMPs are observed. Real power losses are estimated using a static piecewise linear approximation technique. A sampling algorithm is proposed to minimize the possible convergence issues associated with the proposed mathematical model. DLMPs are calculated for the i) contemporary, ii) enhanced, and iii) meshed distribution grids using an IEEE 34-bus test feeder. The test transmission system is modeled using an IEEE 30-bus system. Finally, the calculated DLMPs in the enhanced grid are compared against three existing pricing mechanisms via three case studies to prove its validity and superiority, especially in congested systems with high penetration of price-responsive loads (PRLs).

Communication reliability-restricted energy sharing strategy in active distribution networks

With the development of information and communication technology (ICT), massive distributed energy resources (DERs) are aggregated to share the surplus energy across a community. Contingencies on the communication side may lead to incorrect control commands, which could influence the physical operation of power systems. However, the existing literature has ignored the extent to which communication reliability (CR) influences energy sharing in active distribution networks (ADNs). Therefore, we propose a tri-layer framework integrating decision-making and a cyber-physical system (CPS). In this framework, a number of microgrids (MGs) aggregating demand-side energy and a communication base station (BS), are connected in an ADN. Due to the interference and noise among MGs, CR is modelled as a nonlinear function of the transmit power of the different BSs, which is linearized by the least-squares method and piecewise linear (PWL) technique. The proposed energy sharing scheme minimizes the overall distribution network costs considering DER sharing under the premise that each MG meets its physical and CR constraints. Case studies based on IEEE 33- and 141-bus feeder systems validate the effectiveness of the proposed framework and method. Adjustable BS transmit power and CR constraints could effectively reduce the total cost, and all MGs could share energy via reliable communication services.

A Fast Semi-Analytic Approach for Combined Electromigration and Thermomigration Analysis for General Multisegment Interconnects

Considering temperature gradient or thermomigration (TM) impacts on electromigration (EM) due to Joule heating was less studied in the past. In this article, we propose a new semi-analytical stress transient analysis method to consider both EM and TM effects for general multisegment interconnects. The new method is based on the separation of variables (SOVs) approach to find the analytic solution of coupled EM-TM partial differential equation (PDE). The algorithm consists of several steps. We first develop analytic solutions to compute the steady-state temperature distribution of multisegment wires. Based on this, we derive closed-form solutions for steady-state hydrostatic stress distribution in the context of thermal gradients due to Joule heating for multisegment interconnect wires. With the steady-state stress distribution, the coupled EM-TM PDE can be homogenized and solved by the SOV method. To deal with temperature/position-dependent diffusivity of metal migration process due to nonuniform temperature distribution, we utilize a piecewise linear technique to approximate the position-dependent diffusivity. The numerical results on multisegment interconnects show that the proposed method has negligible error loss compared to commercial finite element analysis software COMSOL but is about an order of magnitude faster than COMSOL with $10\times $ less memory footprint. The numerical results further show that temperature gradient due to Joule heating indeed has significant impacts on the EM failure process.

Optimal Offering Strategy of a Price-Maker Hydro Producer Considering the Effects of Crossing the Forbidden Zones

The phenomenon of crossing the forbidden zone is unavoidable and wasteful when scheduling the hydro units. In this paper, the effect of crossing the forbidden zone is taken into account using the strategic offering model to help the price-maker hydro producers (PMHPs) devise more economic offering strategies in this paper. This effect is economically quantified and formulated in the form of the mixed integer linear program (MILP) with the use of the big M method and the piecewise linear technique. Therefore, the effect of crossing the forbidden zone therefore can easily be incorporated into the strategic offering model. Based on the residual demand curve (RDC) scenarios, the strategic offering model, which consists of offering and self-scheduling models, is established according to the real-world data from the Three Gorges Project (TGP). The whole optimization model is then converted into the form of MILP formulations by properly discretizing the net head. A test case based on the TGP is presented, in which the strategic offering model is set as a comparable test while ignoring the effect of crossing the forbidden zone. The results provide insight on the offering strategy and physical system operations during a single day. The outcomes indicate that the model that incorporates the effect of crossing the forbidden zone will effectively prevent the crossing phenomenon from happening and that the proposed strategic offering model is more useful for assisting a PMHP in developing profitable offering strategy.