Piecewise Linear Approximation Technique Research Articles

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.

Sim-Piece: Highly Accurate Piecewise Linear Approximation through Similar Segment Merging

Approximating series of timestamped data points using a sequence of line segments with a maximum error guarantee is a fundamental data compression problem, termed as piecewise linear approximation (PLA). Due to the increasing need to analyze massive collections of time-series data in diverse domains, the problem has recently received significant attention, and recent PLA algorithms that have emerged do help us handle the overwhelming amount of information, at the cost of some precision loss. More specifically, these algorithms entail a trade-off between the maximum precision loss and the space savings achieved. However, advances in the area of lossless compression are undercutting the offerings of PLA techniques in real datasets. In this work, we propose Sim-Piece, a novel lossy compression algorithm for time-series data that optimizes the space requirements of representing PLA line segments, by finding the minimum number of groups we can organize these segments into, to represent them jointly. Our experimental evaluation demonstrates that our approach readily outperforms competing techniques, attaining compression ratios with more than twofold improvement on average over what PLA algorithms can offer. This allows for providing significantly higher accuracy with equivalent space requirements. Moreover, our algorithm, due to the simplicity of its merging phase, imposes little overhead while compacting the PLA description, offering a significantly improved trade-off between space and running time. The aforementioned benefits of our approach significantly improve the efficiency in which we can store time-series data, while allowing a tight maximum error in the representation of their values.

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

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.

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°.

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).

A Low-Error, Memory-Based Fast Binary Logarithmic Converter

This brief presents a memory based fast binary logarithmic converter based on a piecewise linear approximation technique. The proposed method is simple and arithmetic operation-less, which achieves 10−4 to 10−3 maximum absolute error (MAE) while maintaining a high speed. The approach partitions the logarithmic curve of the fractional component into $2^{L}$ uniform regions and a block RAM (size $2^{L} \times $ bits) stores the approximate value of each sub-region. For any number, most significant $L$ bits of the fractional component address the memory location of the logarithmic converter. The hardware synthesis result, implemented with 26 bits fractional precision on Virtex-6 field-programmable gate array device, shows 75% improvement in MAE and 27% decrease in critical path delay compared to the current state-of-the-art techniques in the worst-case scenario. In Otsu’s image thresholding algorithm, the proposed logarithmic converter with 3.08 ( $=2^{8} \times 12$ ) kbits memory size adequately meets the accuracy requirement for improved image segmentation.

Mixed-integer linear programming approach for product design for life-cycle profit

The paper deals with the product design problem where the characteristics of new and remanufactured products must be determined. The objective of the problem is to maximize the total profit taking into account the design specifications and the selling prices for the new and remanufactured products. The amount of new and remanufactured products is to be determined and the take-back rate is considered. The problem representation leads to a mixed-integer nonlinear structure, which makes very hard to deal with the corresponding mathematical formulation. Nevertheless, the problem can be modeled as a mixed-integer linear formulation taking advantage of the high efficiency, both in terms of solution accuracy and computing time of the software tools (solvers) developed for mixed-integer linear programming (MILP). This is explored in this work and a MILP model able to accurately represent the life-cycle design while the profit is maximized is proposed. In particular, the model takes into account the effects on the demand level of specifications and prices of new and remanufactured products. The formulation deals with the representation of demands nonlinear functions (new and remanufactured products) and the existent bilinear terms are handled through piecewise linear approximation and multi-parametric disaggregation techniques. The practical behavior of the formulation is analyzed through computational experiments considering an example of a desktop computer. In addition, the performance of the formulation and the quality of the solution obtained are compared with the performance of a nonlinear approach.

Circuit-Field Coupling Methodology for Incorporation of Power Electronic Devices: A Piecewise-Linear Approach

A new circuit-field coupling methodology for a single-phase transformer connected to a half-wave rectifier is presented. The rectifier is composed of switched electronic devices (EDs) which can be modeled through a piecewise-linear approximation technique. The modified nodal analysis (MNA) is used to solve the circuit where the EDs are represented with stamps that are systematically incorporated into the system of differential equations. The transformer is modeled using a 2-D finite-element (FE) approach, leading to a coupled circuit-field system, which is solved using proprietary software. The system is also implemented experimentally using an xPC-Target data acquisition system, showing close correspondence with simulation results. Thus, this paper provides the basis for implementing multi-level power converters connected to transformers.

Optimization model for long-distance integrated transmission of wind farms and pumped-storage hydropower plants

Long-distance and large-capacity wind power transmission from western and northern China to load centers through ultra-high voltage (UHV) transmission lines is an important and effective measure for large-scale wind power accommodation in China. This paper proposes a novel practical integrated transmission mode for a wind farm (WF) and a pumped-storage hydropower plant (PSHP). In order to cope with additional imbalance costs caused by deviations from the submitted day-ahead schedule and increase the total operational profit, an optimization model for the integrated transmission of a WF and a PSHP has been formulated. The forecast errors for wind power generation are modeled by a scenario analysis technique. Hydraulic constraints and the head effect on the performance of each pumped-storage hydropower unit (PSHU) in both generating and pumping modes have been considered. Through incorporating the nonlinearities, including constraints on the operation status of units and turbine performance curves, the model is converted into a mixed-integer linear programming (MILP) formulation using piecewise linear approximation techniques. Case studies demonstrate that the integrated transmission of the WF and PHSP can efficiently alleviate the negative effect of wind power fluctuations and significantly increase profit. Sensitivity analyses have been carried out to evaluate the effect of the penalty factor for energy imbalance and the electricity price mechanism in the receiving-end power grid on the overall performance of the WF-PSHP union.

Look ahead dynamic security-constrained economic dispatch considering frequency stability and smart loads

Conventional economic dispatch models aim to determine the optimal production of generation units under the steady state operation constraints. Due to the growing integration of low inertia power generation technologies (e.g. wind, solar, etc.), considering stability constraints, in particular, frequency stability, a theme of this work, becomes a crucial need in nowadays security-constrained economic dispatch (SCED) programs. This paper develops a new look ahead dynamic (i.e. multi-period) security-constrained economic dispatch model, further considering frequency stability constraints (DSCED-FSC). The aim of the DSCED-FSC is to optimize the cost of power generation subject to operation and frequency stability constraints under normal and contingency conditions. The proposed DSCED-FSC secures N-1 contingencies for both thermal limits and frequency stability. The system frequency response is included in DSCED-FSC model by linearizing the discretized rotor angle swing equation. The dynamic models of governors and load damping are considered in the discretized system frequency response. The safety of system frequency response under generation outages is provided by activating generators' governors, inertial response and load damping as the primary frequency reserve. In addition to primary frequency reserve, the demand elasticity of smart motor loads is utilized to avoid the activation of under frequency load shedding (UFLS) relays under severe generation outages. The proposed DSCED-FSC model is formulated as a mixed integer linear programming (MILP) problem. The nonlinear AC power flow equations are linearized using Taylor series expansions and piecewise linear (PWL) approximation techniques. The efficacy of the proposed DSCED-FSC model in supporting system frequency is investigated using the IEEE 118-bus test system.

A Semianalytical Gradient Model for Characterization of Conductors With Surface Roughness

In this paper, a novel semianalytical gradient model (SAGM) for characterizing conductors with surface roughness is presented. Based on the linear function of conductivity, the governing equation of the magnetic field is reduced to the modified Bessel equation, which has an analytical solution. With the piecewise linear approximation technique, the SAGM is derived to deal with arbitrary functions of conductivity. Three typical distributions, including the uniform, normal, and Rayleigh distributions, are investigated. The proposed SAGM is employed to evaluate the propagation properties of typical transmission line structures with different surface roughness profiles. The simulation results agree well with those from measurements, which confirm the validity and accuracy of the proposed method.

Time and Memory Efficient Online Piecewise Linear Approximation of Sensor Signals.

Piecewise linear approximation of sensor signals is a well-known technique in the fields of Data Mining and Activity Recognition. In this context, several algorithms have been developed, some of them with the purpose to be performed on resource constrained microcontroller architectures of wireless sensor nodes. While microcontrollers are usually constrained in computational power and memory resources, all state-of-the-art piecewise linear approximation techniques either need to buffer sensor data or have an execution time depending on the segment’s length. In the paper at hand, we propose a novel piecewise linear approximation algorithm, with a constant computational complexity as well as a constant memory complexity. Our proposed algorithm’s worst-case execution time is one to three orders of magnitude smaller and its average execution time is three to seventy times smaller compared to the state-of-the-art Piecewise Linear Approximation (PLA) algorithms in our experiments. In our evaluations, we show that our algorithm is time and memory efficient without sacrificing the approximation quality compared to other state-of-the-art piecewise linear approximation techniques, while providing a maximum error guarantee per segment, a small parameter space of only one parameter, and a maximum latency of one sample period plus its worst-case execution time.

Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion

Motivated by the strategic importance of congestion management, in this paper we present a model to design hub-and-spoke networks under stochastic demand and congestion. The proposed model determines the location and capacity of the hub nodes and allocate non-hub nodes to these hubs while minimizing the sum of the fixed cost, transportation cost and the congestion cost. In our approach, hubs are modelled as spatially distributed M/G/1 queues and congestion is captured using the expected queue lengths at hub facilities. A simple transformation and a piecewise linear approximation technique are used to linearize the resulting nonlinear model. We present two solution approaches: an exact method that uses a cutting plane approach and a novel genetic algorithm based heuristic. The numerical experiments are conducted using CAB and TR datasets. Analysing the results obtained from a number of problem instances, we illustrate the impact of congestion cost on the network topology and show that substantial reduction in congestion can be achieved with a small increase in total cost if congestion at hub facilities is considered at the design stage. The computational results further confirm the stability and efficiency of both exact and heuristic approaches.

Modeling the AgInSbTe Memristor

The AgInSbTe memristor shows gradual resistance tuning characteristics, which makes it a potential candidate to emulate biological plastic synapses. The working mechanism of the device is complex, and both intrinsic charge-trapping mechanism and extrinsic electrochemical metallization effect are confirmed in the AgInSbTe memristor. Mathematical model of the AgInSbTe memristor has not been given before. We propose the flux-voltage controlled memristor model. With piecewise linear approximation technique, we deliver the flux-voltage controlled memristor model of the AgInSbTe memristor based on the experiment data. Our model fits the data well. The flux-voltage controlled memristor model and the piecewise linear approximation method are also suitable for modeling other kinds of memristor devices based on experiment data.

An Automatic Selection of Segment Width for the Single Sensor Differential Thermal Analysis (SS-DTA) Based on Piecewise Linear Approximation Technique

Single Sensor Differential Thermal Analysis (SS-DTA) is a novel non-destructive testing technique for studying and detecting the phase transformations and structural changes in materials. It uses only one temperature sensor to measure the temperature in a particular point of interest in the material during actual and simulated thermal processing of the material. SS-DTA compares the temperature recorded in a tested specimen against a reference thermal profile which can be generated either by analytical formulae or piecewise linear approximation. The main advantage of piecewise linear approximation over the analytical formulae is that it does not need the knowledge of tested material and processing conditions to optimally estimate the parameters of reference thermal history. On the other hand, in order to apply the piecewise linear approximation technique we must specify the segment width which is normally fixed at a nominal value of 1.5 seconds. We have recently found that this nominal value might not be an optimal choice for the segment width as it does not guarantee to give the best detectability of phase transformation. Therefore, in this research work we proposed a technique to automatically select an appropriate value of the segment width. The performance of proposed method has been evaluated by investigating the phase transformations of welded stainless steel SUS 321and SUS 304. It was found that the appropriate segment width could be ranging from 1.25-1.75 seconds and by using this selection technique, we could detect the differential temperature more accurately than when using the nominal value.

Making Sensor Networks Immortal: An Energy-Renewal Approach With Wireless Power Transfer

Wireless sensor networks are constrained by limited battery energy. Thus, finite network lifetime is widely regarded as a fundamental performance bottleneck. Recent breakthrough in the area of wireless power transfer offers the potential of removing this performance bottleneck, i.e., allowing a sensor network to remain operational forever. In this paper, we investigate the operation of a sensor network under this new enabling energy transfer technology. We consider the scenario of a mobile charging vehicle periodically traveling inside the sensor network and charging each sensor node's battery wirelessly. We introduce the concept of renewable energy cycle and offer both necessary and sufficient conditions. We study an optimization problem, with the objective of maximizing the ratio of the wireless charging vehicle (WCV)'s vacation time over the cycle time. For this problem, we prove that the optimal traveling path for the WCV is the shortest Hamiltonian cycle and provide a number of important properties. Subsequently, we develop a near-optimal solution by a piecewise linear approximation technique and prove its performance guarantee.

Synthesis of Bias-Scalable CMOS Analog Computational Circuits Using Margin Propagation

Approximation techniques are useful for implementing pattern recognizers, communication decoders and sensory processing algorithms where computational precision is not critical to achieve the desired system level performance. In our previous work, we had proposed margin propagation (MP) as an efficient piecewise linear (PWL) approximation technique to a log-sum-exp function and had demonstrated its advantages for implementing probabilistic decoders. In this paper, we present a systematic and a generalized approach for synthesizing analog piecewise-linear (PWL) computing circuits using the MP principle. MP circuits use only addition, subtraction and threshold operations and hence can be implemented using universal conservation principles like the Kirchoff's current law. Thus, unlike the conventional translinear CMOS current-mode circuits, the operation of the MP circuits are functionally similar in weak, moderate, and strong inversion regimes of the MOS transistor making the design approach bias-scalable. This paper presents measured results from MP circuits prototyped in a 0.5 μm standard CMOS process verifying the bias-scalable property. As an example, we apply the synthesis approach towards designing linear classifiers and we verify its performance using measured results.

Piecewise-linear approximation of the Hindmarsh-Rose neuron model

This paper is concerned with the approximation of the Hindmarsh and Rose neuron model, which is able to reproduce the main neuronal behaviours, in view of its circuit implementation. The method is based on two main tools: a piecewise-linear approximation technique and bifurcation analysis. The piecewise-linear approximation of the Hindmarsh and Rose model is obtained by solving a mixed-integer optimization problem by a genetic algorithm. The result obtained exhibits a good degree of similarity to the original model, both from a qualitative and a quantitative standpoint.

Modified piecewise linear current density recursive convolution finite-difference time-domain method for anisotropic magnetised plasmas

A modified piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) for anisotropic magnetised plasma is proposed. The method is derived using two recursive conclusion. The electric field is time-shifted in the first convolution and the current density is time-shifted in the second convolution. The computation of the current density and the electric field employ the piecewise linear approximation technique. Like PLCDRC FDTD, the method has more accuracy over CDRC FDTD. Moreover, it is faster in computation velocity than PLCDRC FDTD. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetised plasma layer, with the direction of propagation parallel to the direction of the biasing field. The bistatic radar cross-section of conducting sphere covered with magnetised plasma is also calculated. Then, the numerical dispersion relation of the new PLCDRC FDTD scheme is derived. The numerical dispersion error and dissipation error caused by the new PLCDRC-FDTD method are investigated by comparing the real and imaginary parts of the numerical wave number with those of the analytical wave number. Finally, the stability of the new PLCDRC-FDTD method is discussed. This method can also be used in other frequency dispersion electromagnetic problem if it is modified slightly.