Piecewise Linear Method Research Articles

A novel digital sensor-less synchronous rectification method for CLLLC resonant converters

With the rapid development of the renewable energy vehicles, pursuing the power converters with high efficiency and high reliability has caught more attention recently. In order to solve those problem with low cost, this paper proposes a sensor-less synchronous rectification method for the CLLLC resonant converters. The precise conduction time of the synchronous switches is obtained based on the analysis of the working principle of CLLLC resonant converter, and the relationship between the SRs switching time and the inverter switching time can be derived as well. To achieve the wide output voltage range, the converter requires wide working frequency. And the correct turn-on and turn-off time for the synchronous switches can be obtained respectively by calculation and piecewise linear function fitting methods within full working frequency range. Compared with traditional synchronous rectification control for CLLLC, which require additional high bandwidth voltage sensors or current sensors, the method proposed in this paper is realized by only one low-cost output voltage sensor. And the proposed method is suitable for high-power applications with a wide voltage and load variation. Moreover, because of the symmetrical topology, this method is valid in bidirectional power transfer. Additionally, the exist analog synchronous rectification control chips suffer from losing accuracy with wide bus voltage variation, however, this method can overcome this shortcoming. Thus, the proposed synchronous rectification method is a low-cost and suitable for high-power, high power density, high efficiency application which benefit from its simple algorithm. Finally, the proposed sensor-less synchronous rectification method is validated by the simulation results and experimental results. The results of simulation and experimental have shown the proposed method offers significant benefits which increases the efficiency of the whole CLLLC system by about 3%, and the reliability of the converter are greatly increased, due to the cooler SRs.

Tapping into the potential CO2 emission reduction of a crude oil transportation system from carbon footprint perspective

With more countries adopting a net-zero carbon emission goal, low carbon has become the focus of the transformation of the petroleum industry. Improper operations of the crude oil transportation system, one of the primary energy consumers of oilfields, usually cause severe environmental problems. Following the life cycle assessment method and considering the special process characteristics of the crude oil transportation system, a detailed carbon footprint analysis was conducted from the design to the recycling phase to identify the key phase for carbon emission control. Combined with process modifications, a multi-objective operation optimization model constrained by thermal constraints and insertion oil was developed to reach economic and environmental goals. Then, the multi-objective mixed integer nonlinear programming model was turned into a mixed integer linear programming model by the piecewise linearization method and augmented ε-constraint method. The models were validated using a typical case. The carbon footprint analysis showed that the average CO2e emissions were 2.68 t CO2e/(104 km m3•a) over the lifecycle, and the CO2e emissions during the operation phase were the highest (74.04%) among all phases. Moreover, the optimization model reduced the total cost and CO2e emissions by up to 18.72% and 16.97%. Additionally, sensitivity analysis revealed that the optimal operation scheme was highly sensitive to the crude oil price and transportation volume. The total CO2e emissions per unit volume exhibited a concave trend as the transportation volume increased, indicating the existence of an optimal transportation volume that achieved the lowest emissions. The study captured the weak points of carbon emissions over the lifecycle and tapped into potential CO2 emission reduction, providing a reference for the design and operation of the future pipeline system.

Implementation of Pipelined Multi_Precision (1, 2 and 4) Floating-point Arithmetic Operations

Abstract: The implementation of pipelined multi-precision-based arithmetic operations are carried out. In the existing system, the floating-point operation is based on single precision and is implemented on a divider. The proposed design has been implemented using single, double and quad precision using the universal piece-wise linear (PWL) approximation method and a modified Goldschmidt algorithm. The proposed design performs addition, subtraction, multiplication, and division using the universal PWL method to reduce maximum error. Small multipliers are used in the modified Goldschmidt algorithm. The pipelining process has been used in order to improve the speed of execution and accuracy. This pipelined architecture is described in Verilog and timing performance is measured with Xilinx timing analyser.

Rapid Estimation of Sulfur Content in High-Ash Indian Coal Using Mid-Infrared FTIR Data

High-ash Indian coals are primarily used as thermal coal in power plants and industries. Due to the presence of sulfur in thermal coal, flue gas is a major environmental concern. Conventional methods (Ultimate Analysis of Coal) for sulfur content estimation are time-consuming, relatively costly, and destructive. In this study, Fourier-transform infrared (FTIR) spectroscopy has emerged as a promising alternative method for the rapid and nondestructive analysis of the sulfur content in coal. In the present study, the actual sulfur content in the coal samples was determined using Ultimate Analysis (CHNS analyzer). In contrast, mid-infrared FTIR spectroscopic data (4000–400 cm−1) were used to analyze the functional groups related to sulfur or its compounds in the coal samples to predict the sulfur content. A comparison of sulfur estimated using a CHNS analyzer and predicted using mid-infrared spectroscopy (FTIR) data shows that it can accurately predict sulfur content in high-ash Indian coals using the piecewise linear regression method (Quasi-Newton, QN). The proposed FTIR-based sulfur prediction model showed a coefficient of determination (R2) of up to 0.93, where the total no. of samples (Coal + KBr pellets, n) was 126 (using 17:1 split, K-fold cross validation). The root-mean-square error (RMSE, wt.%) is 0.0035, mean bias error (MBE, wt.%) is −0.0003, MBE (%) is 3.31% and mean absolute error (MAE, wt.%) is 0.0020. The two-tailed t-test and F-test for mean and variance indicated no significant difference between the pair of values of observed sulfur (SCHNS, wt.%) using CHNS data and the model predicted sulfur (SFTIR, wt.%) using FTIR data. The prediction model using mid-infrared FTIR spectroscopy data and the Quasi-Newton method with a breakpoint and loss function performs well for coal samples from the Johilla Coalfield, Umaria. Thus, it can be a valuable tool for analyzing sulfur in other ash-rich coals from various basins worldwide.

Joint chance-constrained multi-objective multi-commodity minimum cost network flow problem with copula theory

This study focuses on a specific problem in network optimization, namely the minimum cost multi-commodity network flow (MCNF) problem. The problem is complicated by the presence of uncertain parameters, including various types of costs associated with each arc in the network. The study presents a multi-objective approach to solving this problem, where the coefficients of the capacity constraints are modelled as random variables with a normal distribution, and the dependence between them is modelled using an Archimedean copula. The capacity constraints are presented as joint chance constraints, and a multi-objective problem is formulated to deal with the uncertainty. This uncertain multi-objective problem is then converted into a certain multi-objective problem using fuzzy programming. The resulting certain multi-objective MCNF problem is converted to a certain single objective problem using second-order cone programming (SOCP), which is solved using either piecewise tangent approximation or piecewise linear approximation methods. The proposed approaches are tested using numerical examples and experimental tests to demonstrate their effectiveness in solving large-scale network problems efficiently. The results show that the proposed approaches are a useful tool for solving uncertain multi-objective MCNF problems in real-world applications.

Noninvasive measurement of temperature for simulated tissue based on piezoelectric micromachined ultrasonic transducers

This paper reports a noninvasive measurement of temperature for simulated tissue based on an AlN piezoelectric micromachined ultrasonic transducer array. Polydimethylsiloxane and a built-in heating plate are used to simulate the thermal therapy of human tissue. Based on time-of-flight (ToF) from the simulated tissue surface to the heating plate surface and corresponding temperature data, the piecewise linear fitting method is used to fit the ToF-temperature curve, and its sensitivity is (below 50 °C) and (from 50 °C to 65 °C). The average error of real-time temperature measurements is 0.58 °C for temperatures below 65 °C. The proposed method can provide a good solution for temperature detection during thermal therapy.

Analytical Model of Inverter-Interfaced Renewable Energy Sources for Power System Protection

The accurate analytical fault analysis model of the emerging inverter-interfaced renewable energy sources (IIRESs) is an important basis for protection of power system with RESs. However, factors of dynamic characteristics of the control system (DCCS) such as the controller saturation and phase-locked loop (PLL) dynamics have rarely been simultaneously studied in the existing analytical models of IIRESs. As a result, the accurate analytical models can hardly be guaranteed. To address this issue, this paper proposes an analytical model for IIRESs taking DCCS into account to characterize the complex fault responses of IIRESs. Both the controller saturation and PLL dynamics are considered in the transient and steady-state phases to investigate the fault current characteristics. On this basis, the analytical fault current formulations under the influences of DCCS are yielded using the piecewise linearization method. Field short-circuit and simulation tests indicate that the proposed model is applicable to various fault conditions and its calculation accuracy can be improved by at most 55% in comparison with the existing IIRESs' analytical models.

Real-Time Power Market Clearing Model With Improved Network Constraints Considering PTDF Correction and Fast-Calculated Dynamic Line Rating

The increasing penetration of renewables in power systems reconfigures the generation mix and geography distribution, resulting in more frequent power flow congestion. Conventionally, a relatively conservative dispatch margin for transmission congestion in network constraints was reserved to ensure safe operation due to potential deviations introduced by DC power flow modeling and conservative line rating. This article proposes a real-time power market clearing model with improved network constraints considering power transfer distribution factor (PTDF) correction and fast-calculated dynamic line rating. The clearing model based on PTDF correction is proposed first employing the Taylor expansion with the voltage and phase angle approximation. An improved dynamic line rating model is further applied into the clearing model based on the piecewise linear approximation method, which calculates real-time conductor temperature faster with sufficient precision. We test and verify the validity of the proposed model based on three independent systems including the IEEE 39-bus system, the IEEE 2383-bus system, and the real power grid system in Yunnan province of China, respectively. The results show that the improved clearing model reduces the calculated power flow deviation between the clearing results and real conditions compared with traditional security constraints, where the efficiency of power grid operation is also increased.

Potential changes in cooling degree day under different global warming levels and shared socioeconomic pathways in West Africa

Increasing levels of climatic warming are expected to affect the global development of energy consumption. The cooling degree day (CDD) is one of the climate-driven indices that captures the impact of climate on energy demand. However, little is known about the spatiotemporal trends of CDD in relation to a changing climate and economy in West Africa and its main implications. Hence, in order to analyze how energy demand could evolve, this study aims to assess the changes in CDD under 1.5, 2.0, 2.5, and 3.0 °C global warming levels (GWLs), with and without population exposure and trends under the two representative concentration pathways (RCPs) of RCP4.5 and RCP8.5 for West Africa. A climate-reflective base temperature (T-base) is used and was determined using a piecewise linear regression method. Seasonal electricity consumption was derived using a decomposition feature. An ensemble of seven Global Climate Models (GCMs) were used for the future temperature projections. The future population was based on shared socioeconomic pathway outputs. Based on the analysis, the reported average T-base for the West African region is 24 °C. An increasing CDD trend was identified in all of the RCP scenarios, but is more pronounced in RCP8.5. RCP8.5 departs from the mean historical period of approximately 20% by 2100 with the standardized value. The same trend is observed under different GWLs as the warming level increased and was most striking in the Sahelian zone. Population exposure to CDD (labelled CDDP) increases with warming levels, but is more pronounced in highly agglomerated areas. The CDDP index best captures the spatial representation of areas with high cooling demand potential with respect to the demographic distribution. This study can serve to inform better energy demand assessment scenarios and supply planning against the backdrop of changing climate conditions in West Africa.

Time-Reduced Model for Multilayer Spiking Neural Networks

Spiking neural networks (SNNs) is a type of biological neural network model, which is more biologically plausible and computationally powerful than traditional artificial neural networks (ANNs). SNNs can achieve the same goals as ANNs, and can build a large-scale network structure (i.e. deep spiking neural network) to accomplish complex tasks. However, training deep spiking neural network is difficult due to the non-differentiable nature of spike events, and it requires much computation time during the training period. In this paper, a time-reduced model adopting two methods is presented for reducing the computation time of a deep spiking neural network (i.e. approximating the spike response function by the piecewise linear method, and choosing the suitable number of sub-synapses). The experimental results show that the methods of piecewise linear approximation and choosing the suitable number of sub-synapses is effective. This method can not only reduce the training time but also simplify the network structure. With the piecewise linear approximation method, the half of computation time of the original model can be reduced by at least. With the rule of choosing the number of sub-synapses, the computation time of less than one-tenth of the original model can be reduced for XOR and Iris tasks.

Real‐time emission and cost estimation based on unit‐level dynamic carbon emission factor

AbstractThe real‐time carbon emission estimation of generators helps quantify the carbon emission costs and reduce power system emissions of power generation. Accurate estimation relies on the accuracy of the carbon emission factors (EFs) and power generation measurements. The dynamic carbon emission factor (DEF) of generators was proposed recently as a linear function of the output power. However, there is a significant deviation between the modelled DEFs and the actual measurement EFs, especially when the output power is low. This paper first presents the general definition of the DEF to characterize the emissions and focuses on the unit‐level DEF (UDEF). The piecewise non‐linear UDEF (P‐UDEF) model is then proposed, which can better represent the unit emission characteristics. Then an accurate piecewise linear cost approximation method is proposed considering the segment points and extreme points of both P‐UDEF and generation costs function. Last, the system carbon emissions and costs estimation are estimated by combined economic emission dispatch (CEED), and the reduction potential is evaluated. Case studies on an IEEE 30‐bus system with piecewise linear cost functions show that the proposed P‐UDEF can realize real‐time emission and cost estimation as well as reduce the total system emissions by considering the incomplete combustion cost of generating units.

Quality Evaluation Method of Anchor Chain Flash Butt Welding Based on Deep Learning

Flash butt welding, a mainstream welding method employed in producing anchor chains, is a critical manufacturing process affecting the quality of anchor chains. Ultrasonic and load testing are used to evaluate the welding quality of anchor chains, but the cost of checking and replacing unqualified chain links is high. A deep learning-based quality evaluation method for flash butt welding is proposed to reduce the cost of detecting and replacing substandard chain links. First, displacement and current sensors collect electrode position and current signals during welding. Second, since the number of qualified anchor links is much larger than that of unqualified ones, a new data synthesis method is proposed: nearest-neighbor splicing sampling, which achieves the enhancement of minority samples by segmenting and combining existing data samples according to the features of anchor chain welding. Then, a piecewise linear interpolation method is used to handle the varying data length problem, thus satisfying the input requirements of the convolutional neural network (CNN). Finally, a CNN model is established, and dropout is used to reduce the over-fitting phenomenon. The experimental results show that the accuracy of the under-sampling method, over-sampling method, and nearest-neighbor splicing sampling method are 93.8%, 95.9%, and 96.3%, respectively, and the sensitivity, specificity, and accuracy of the CNN model are 95.7%, 93%, and 94.3%, respectively, which are better than those of the support vector machine (SVM).

Strong convergence rates for the approximation of a stochastic time-fractional Allen–Cahn equation

The paper is concerned with the strong approximation of a stochastic time-fractional Allen-Cahn equation driven by an additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time; namely, a Caputo fractional derivative of order α∈(0,1), and a Riemann–Liouville fractional integral operator of order γ∈[0,1] applied to a Gaussian noise. We approximate the model by a standard piecewise linear finite element method (FEM) in space and the classical Grünwald–Letnikov method in time (for both time-fractional operators), and the noise by the L2-projection. Spatially semidiscrete and fully discrete schemes are analyzed and strong convergence rates are obtained by exploiting the temporal Hölder continuity property of the solution. Numerical experiments are presented to illustrate the theoretical results.

A Method for Calculating the Derivative of Activation Functions Based on Piecewise Linear Approximation

Nonlinear functions are widely used as activation functions in artificial neural networks, which have a great impact on the fitting ability of artificial neural networks. Due to the complexity of the activation function, the computation of the activation function and its derivative requires a lot of computing resources and time during training. In order to improve the computational efficiency of the derivatives of the activation function in the back-propagation of artificial neural networks, this paper proposes a method based on piecewise linear approximation method to calculate the derivative of the activation function. This method is hardware-friendly and universal, it can efficiently compute various nonlinear activation functions in the field of neural network hardware accelerators. In this paper, we use least squares to improve a piecewise linear approximation calculation method that can control the absolute error and get less number of segments or smaller average error, which means fewer hardware resources are required. We use this method to perform a segmented linear approximation to the original or derivative function of the activation function. Both types of activation functions are substituted into a multilayer perceptron for binary classification experiments to verify the effectiveness of the proposed method. Experimental results show that the same or even slightly higher classification accuracy can be achieved by using this method, and the computation time of the back-propagation is reduced by 4–6% compared to the direct calculation of the derivative directly from the function expression using the operator encapsulated in PyTorch. This shows that the proposed method provides an efficient solution of nonlinear activation functions for hardware acceleration of neural networks.

A real-time data acquisition method of industrial production line based on OPC technology

In view of the low timeliness and accuracy of traditional production line data acquisition methods, this study proposed a real-time data acquisition method of industrial production line based on OPC technology. Considering the heterogeneity of industrial production line data sources, a data transmission scheme is generated based on OPC technology and multi-point communication with Modbus protocol after data preprocessing by piecewise linear interpolation method. Then, the improved decision tree algorithm is used to design the data processing mode. Finally, the current state of industrial production line data is judged by comparing the threshold value, and the real-time data collection of industrial production line is completed after the collection interval is determined. Experimental results show that the acquisition accuracy of this method is up to 96.8%, the maximum acquisition time is only 12.5 s, and the highest packet loss rate is only 1.89%, indicating that this method improves the acquisition quality.

Enkripsi Nilai Piksel Pada Citra Digital Dengan Algoritma Piecewise Linear Chaotic Map

The process of recording, storing and sharing digital images is very easy to do nowadays. To protect the information in the image, the image can be encrypted by scrambling the image into an unintelligible image form. The Piecewise Linear Chaotic Map algorithm is used in research to encrypt images. The trick is that the Piecewise Linear Chaotic Map algorithm generates random numbers, and these random numbers are used to randomize image pixel values using the XOR function. The application implements the Piecewise Linear Chaotic Map method to encrypt pixel values in digital images, so that only certain parties who know the key can access digital images.

Algebraic flux correction finite element method with semi-implicit time stepping for solute transport in fractured porous media

This work is concerned with the numerical modeling of the Darcy flow and solute transport in fractured porous media for which the fractures are modeled as interfaces of codimension one. The hybrid-dimensional flow and transport problems are discretizaed by a lumped piece-wise linear finite element method, combined with the algebraic correction of the convective fluxes. The resulting transport discretization can be interpreted as a conservative finite volume scheme that satisfies the discrete maximum principle, while introducing a very limited amount of numerical diffusion. In the context of fractured porous media flow the CFL number may vary by several order of magnitude, which makes explicit time stepping unfeasible. To cope with this difficulty we propose an adaptive semi-implicit time stepping strategy that reduces to the low order linear implicit discretization in the high CFL regions that include, but may not be limited to the fracture network. The performance of the fully explicit and semi-implicit variants of the method are investigated through the numerical experiment.

Optimal Scheduling of an Electric Propulsion Tugboat Considering Various Operating Conditions and Navigation Uncertainties

The operating conditions of all-electric tugboats are flexible and changeable. They are more complicated than conventional vessels in terms of joint voyages and power generation scheduling. To guarantee the reliable operation of the ship, a new coordinated optimization scheme that combines economy and operational reliability is proposed. It is based on the various operating conditions of the tugboat during its voyage, taking into account the random outages of equipment and load fluctuations due to speed and wave uncertainties. Due to the difficulty of implementing a stochastic sampling method with space-time coupling constraints (e.g., the voyage is related to propulsion load), an analytical approach is needed to transform the model into a readily solvable mixed-integer linear program (MINP) which attributes risk scenarios to load fluctuations under various conditional probabilities. In addition, this paper proposes an improved piecewise linearization method based on a differential evolutionary algorithm to speed up the solution process and improve computational accuracy. Meanwhile, the energy storage loss cost due to battery degradation is added to the optimization target. The battery’s cycle life is extended by rational scheduling of charging and discharging. Simulations validate this paper’s joint scheduling optimization scheme in multiple comparison experiments. The results show that it can effectively balance the economic and reliability levels under various risk scenarios and improve the environmental energy efficiency indicators.

Three-dimensional face stability analysis of rock tunnels excavated in Hoek-Brown media with a novel multi-cone mechanism

In order to give a more accurate prediction of the required face pressure, this work revisits the three-dimensional (3D) face stability problems of rock tunnels excavated in Hoek-Brown media. The Piecewise Linear Method (PLM) is introduced to account for the nonlinearity of the rock strength rather than the simple linear substitution for the strength envelope. A novel multi-cone rotational mechanism consisting of n truncated curvilinear cones is generated respecting the plastic normality flow rule. Two typical linearized measures: Generalized Tangential Technique (GTT) and Equivalent Mohr-Coulomb parameters Method (EMM) are also included in this study for comparison and analysis. In terms of the energy-work balance equation, the required face pressure is formulated as an optimization problem depending on 2n variables and is resolved by a recently-proposed Marine Predators Algorithm (MPA). Parametric study implies that the solution of two-dimensional (2D) analysis is very conservative, despite being safe in engineering, it is uneconomical compared with 3D analysis. In 3D analysis, the required face pressure predicted by PLM is significantly improved by 9 % compared with that of GTT, and the results calculated from EMM show a good consistency with PLM and GTT for heavily fractured rock mass, while for high-quality rock masses, the diversity between the results of EMM and other two methods is distinct. To further extend the application of such modified mechanism, design charts of the normalized face pressure are calculated for a quick assessment of face stability in rock masses with different quality.

Transactive charging management of electric vehicles in office buildings: A distributionally robust chance-constrained approach

In this paper, a new energy management model is proposed to determine the optimal scheduling of an office building which includes electric vehicle (EV) charging piles, batteries, and rooftop photovoltaic systems. To optimally manage the electricity procurement of the building and mitigate the rate of transformer aging, the building energy management system (BEMS) employs the flexibility of batteries and EV charging. In the proposed model, to incentivize EV owners to offer their flexibility, the BEMS organizes a transactive market among plugged-in EVs. To this end, EV owners submit their response curves and the target state-of-charge to the BEMS. Then, the transactive market is cleared to determine the market-clearing price for each EV, the optimal EV charging decisions, and accordingly, the scheduling of office building. Also, to model the correlated uncertainties of solar power generation and demand, the distributionally robust chance-constrained method is employed. Moreover, the “Big-M” technique and the piecewise linear approximation method are utilized to linearize the optimization problem. Finally, the case of a building with 100 charging piles is studied. The numerical results illustrate a decrease in the total operating cost of BEMS and the rate of transformer aging compared to uncontrolled charging and direct control approaches. • Developing a TE model to incentivize EVs’ participation in the energy management program. • Developing a new response curve model for EV owners. • Incorporating the transformer’s loss of life in the proposed TE model. • Developing a distributionally robust chance-constrained building energy management model. • Linearizing non-linear equations to mitigate the computational complexity.