Stepped Function Research Articles

Vulnerability-based seismic resilience and post-earthquake recovery assessment for substation systems

The function of substation systems is significantly influenced by earthquakes. To assess the seismic resistance of substation systems and improve post-earthquake recovery efficiency, this study constructs a multi-module framework for seismic vulnerability assessment of substations. Based on the equipment functional status analysis module, a functional network model was established considering the structural function and electrical load of substation systems. The system functional state matrix was obtained through Monte Carlo simulation, and the seismic vulnerability was assessed from the aspects of electrical transmission reliability and the importance of power users. Subsequently, a substation functional index was established based on seismic vulnerability parameters. Post-earthquake functional recovery strategy analysis frameworks were constructed to quantitatively evaluate the recovery process. A stepped functional time-varying function was proposed through iterative analysis, thereby converting the probability parameters of functional status into seismic resilience deterministic indices. Through seismic resilience analysis of a typical 220 kV step-down substation, seismic vulnerability curves for both electrical transmission and power users were obtained. Furthermore, the seismic sensitive intervals of the substation and key equipment for post-earthquake recovery were clarified. Notably, the seismic resilience level and optimal recovery strategy of the typical 220 kV step-down substation were determined.

Profiling of weathered argillaceous limestone rock with MWD data from advanced drilling for tunnelling along Wu-Kai expressway in Chongqing, China

Advanced drilling was employed for the ongoing excavation of a tunnel on Wu-Kai Expressway in Chongqing, aiming to characterize the ground condition ahead of the tunnel face and avoid potential geohazards. Measurement While Drilling (MWD) system and the hydraulic rotary crawler drilling machine are used for the advanced drillhole in the weathered argillaceous limestone rock mass. However, the MWD data exhibits random variations in penetration rate and cannot be correlated with ground conditions. In addition, there is little MWD data on the weathered argillaceous limestone with time-series algorithm in relevant open literature. This paper presents further analysis of the MWD data, resolves the random variation issue in penetration rate, and re-interprets the MWD data along three advanced drillholes in this tunnel project. The re-calculated penetration rate with the time-series algorithm for each drillhole is a stepped function of the drillhole depth. The constant penetration rates for the different homogeneous zones can be further correlated with the weathering degrees of the rock and compared with those from other five ground sites with different ground conditions in China and London. The findings of the paper can enhance the general applicability of MWD data for accurate profiling of weathered argillaceous limestone rock mass for safe tunnelling.

A multi-strategy framework to evaluate seismic resilience improvement of substations

Electrical substations suffer significant functionality and economic damage during earthquakes. To improve the seismic reliability and safety of substation systems, this study proposes a seismic resilience evaluation methodology based on the characteristics of the substation's functionality. A probability-based substation functionality network model was built using Bayesian network algorithms, and a stepped functional recovery function was established to quantitatively assess the resilience of substations. Moreover, a network seismic resilience improvement framework was constructed based on the seismic reliability and function recovery of substations. The approach develops network learning algorithms to determine the importance of substation equipment. Based on the proposed multi-strategy seismic resilience optimization algorithm, the post-earthquake repair path and combination strategies for substations were optimized through iterative simulation. Taking a typical 220 kV substation as a case study for seismic resilience analysis, the key equipment was obtained, and post-earthquake resource constraints on system functionality were identified. Notably, multi-dimensional seismic resilience improvement strategies were obtained. The analysis results provide references for post-earthquake resource allocation and economic benefit evaluation in practical engineering.

A three phase 3-level inverter with reduced THD factor

The paper presents an mathematical analysis of a stepped function denoted as fN=6 . This function describes precisely an output voltage waveform of a 3-level inverter. The analysis proves that cascaded inverters give a very good performance of the output voltage according to a criterion of minimal THD. Optimal parameters are indicated in the paper. They permit to diminish the THD factor to a level below 21% while in standard NPC inverters such a result requires special treatment.

Generation a solution to the equations of elasticity theory for a layered strip basing on the principle of compressed mappings

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained.

An approach for optimum performance-based seismic design of 3D steel moment frames

An optimal performance-based design (PBD) of a three-dimensional (3D) structure requires repeated evaluation; thus, proposed approaches should attempt to significantly reduce the number of evaluations required during optimization. The current study proposes a multi-step approach for optimal PBD of a 3D steel moment frame in which the structure is examined at each step for one performance level in a specific direction. To advance to the next step, the acceptance criteria for linear static analysis of the steel moment frame from ASCE 41-17 should have been satisfied in the previous step. An objective function has been formulated using the proposed stepped penalty function to achieve a feasible space, the value of which can be determined based on the number of unexamined steps. Finally, the optimal PBDs for 3D three-story and nine-story steel moment frames were evaluated using EVPS and WSA metaheuristic algorithms to evaluate the proposed process. The final optimal designs were assessed using the acceptance criteria of nonlinear static analysis. The number of performance level evaluations in each direction during optimization showed approximately 60 % and 70 % reductions during analysis by the proposed method for the WSA and EVPS algorithms, respectively.

A multi-model probabilistic framework to evaluate seismic resilience of UHV converter stations

Ultra-high voltage converter stations are significant electric power infrastructures with a high electric energy load. To quantitatively evaluate the seismic and recovery capability of a UHV converter station, this paper proposes a multi-model probabilistic resilience assessment framework divided into four analysis modules for hierarchical evaluation. The conditional probability set of the functional state between network nodes is determined using a matrix-based approach. Taking connectivity and power transmission capacity into account, the functional reliability model was built through the improved Bayesian network. A multi-parameter quantification of the post-earthquake recovery process was carried out by constructing the stepped functional recovery function as well as the time-varying seismic resilience function. The economic loss assessment model was built from multiple aspects. Taking a typical ± 800 kV UHV converter station as a case study for seismic resilience analysis, the probabilistic resilience assessment was realized, and variation trends of the multi-parameter expected value were obtained by mathematical expectation. This article shows that taking measures to postpone the sensitive interval of the system helps to avoid the seismic active area. This avoidance of seismic activity is the objective of optimization. The proposed framework can serve as a reference for the operation and optimization of power systems.

Post-earthquake recover strategy for substations based on seismic resilience evaluation

Electrical substations need a sufficient amount of time to repair damaged equipment and restore power after an earthquake. Yet, the devastation and danger inherent in an earthquake requires fastest return to power possible; thus, finding better methods to improve the efficiency of post-earthquake emergency recover is an urgent issue. This paper presents a rapid seismic resilience assessment framework which combines a network model and functional time-varying feature. The authors developed a dual-dimensional functional network model of a typical 220 kV substation built with an emphasis on its connectivity capabilities and the power transmission capacity of its equipment. The model’s rapid function status was evaluated based on its network dependence on Bayesian network nodes. The authors’ post-earthquake iterative analysis focuses on resource constraint and power user importance. This article shows how the authors obtained the stepped functional time-varying function as a basis for quantification in the post-earthquake recovery process and provides a seismic resilience analysis of the electrical substation. The multi-objective heuristic optimization algorithm was developed to determine an optimal post-earthquake multi-level repair strategy for substation post-earthquake recovery and to determine substation’s seismic resilience levels.

Underwater sound absorption performance of exponential gradient anechoic coating

In this paper, the gradient anechoic coating whose density changes exponentially along direction of thickness is investigated. A numerical model is established by finite element method (FEM) to analyze the underwater sound absorption performance under different density distribution. The calculation results show that the exponential anechoic coating has better sound absorption performance compared with the homogeneous medium and linear anechoic coating. In addition, a discrete layered method is proposed to achieve gradient characteristics. In order to change the equivalent density of each layer, periodically distributed semi-cylindrical steel scatterers with different diameters are embedded in each layer. Therefore, the density function of the whole coating changes in exponential gradient with stepped function. Based on the sound absorption mechanism of multiple scattering and waveform conversion, the sound absorption is improved in low-frequency band from 0 Hz to 1000 Hz. The exponential gradient anechoic coating has potential applications in underwater sound absorption and vibration control.

3SHACC: Three stages hybrid agglomerative constrained clustering

Traditionally within the unsupervised learning paradigm, hierarchical and partitional clustering techniques have been shown to produce better results when provided with partial information, leading to a renewed attention towards this topic. Constrained clustering is a semi-supervised learning problem that combines classic clustering techniques with background knowledge given in the form of a set of constraints. In this paper, we propose to incorporate constraints into the clustering process in three phases: the first phase is devoted to quantify constraint relevance and to learn a metric matrix according to such relevance, a second phase computing similarities between instances by means of the reconstruction coefficient and pairwise distances, and a third stage performing agglomerative hierarchical clustering with a reward-style stepped affinity function favoring merges satisfying the higher possible number of constraints. Experimental results, supported by Bayesian statistical testing, show a consistent improvement in favor of our proposal over previous approaches to the constrained clustering problem.

Simulated Annealing Particle Swarm Optimization for High-Efficiency Power Amplifier Design

In this article, a method for design automation high-efficiency power amplifiers (PAs) based on an optimization-oriented is proposed. The advantages of using particle swarm optimization to design PAs in electronic design automatic tools are analyzed, and then, simulated annealing is combined to form simulated annealing particle swarm optimization (SA-PSO). In this article, the perfectly inelastic collision used in conventional PSO is replaced by the perfectly elastic collision to improve the searching ability through reducing kinetic energy consumption. A stepped fitness function is defined to avoid the performance pit at a single-frequency point, and the concept “missing and returning” is introduced to solve the nonconvergence problem in simulation. Based on the improved SA-PSO algorithm, a broadband 10 W and a triband 6-W PA are designed. The broadband 10-W PA achieves an average drain efficiency (DE) of 62.5% and an output power of 41.2 dBm in the 0.8-3-GHz frequency band, respectively; the triband 6-W PA achieves an average of 57.4%/47.9%/47.3% DE and 37.7-/38.3-/37.4 dBm output power in 3.35-3.55-/5.75-5.95-/7.65-7.95-GHz frequency bands, respectively, while the gains of most stopbands reach less than 0 dB. With digital predistortion technology, the adjacent channel power ratio (ACPR) can reach less than -45 dBc.

Improved step tracking algorithm based on gradient method

The basic principle of the satcom on the move antenna is to detect the error angle between the antenna beam pointing and the satellite direction according to the received satellite signal, and convert it into the corresponding error electrical signal. The controller uses the error electrical signal to control the antenna to make the antenna move in the direction where the error signal decreases. The tracking accuracy of traditional step tracking is not high, and the response speed is very slow, and the signal amplitude fluctuation affects the tracking accuracy. Since the gain graph of the antenna can be regarded as a non-linear stepped objective function, an improved step tracking algorithm based on the gradient method is proposed, which combines the step tracking with the optimization algorithm to achieve precise tracking. The algorithm optimizes the antenna gain pattern as the objective function to find the azimuth and elevation coordinates corresponding to the maximum point of the antenna gain function. The gain function maximization is transformed into the objective function minimization problem, and the minimum value of the objective function is found through the optimization algorithm, which corresponds to the direction of the antenna when the satellite is accurately aligned. The gradient method is selected for optimization, which is stable as a whole and simple iterative process. Theoretical analysis and simulation results show that the algorithm can obtain higher tracking accuracy while maintaining a lower program complexity.

Construction of a method for representing an approximation model of an object as a set of linear differential models

This paper has demonstrated the need to use models not only at the stage of theoretical research and design operations but also when studying existing objects. The techniques to build them on the basis of identification methods have been analyzed. The identification methods have been shown when determining the parameters of processes and objects. The difficulty of defining the models' structures has been emphasized.A method has been proposed to determine the structure of an arbitrary object's model as the approximating set of linear differential models. The data on the object's response to external impact have been used as source data. Demonstrating the method's feasibility employed a set of standard links and a standard external influence in the form of a stepped function as a model. This approach helps assess the adequacy of the obtained approximation results based on the precise solutions available. In a general case, there are no specific requirements for the form of an external influence and an object's reaction.The data that reflect the object's response should allow their approximation using a polynomial. That makes it possible to represent them following a Laplace transform in the form of a truncated power series in the image domain. The transfer function is written in a general form as a rational fraction. It underlies a Padé approximant of the truncated power series.The comparison of the available accurate calculation results and those derived on the basis of the built model has shown good agreement. In the cases under consideration, the computation error did not exceed the 5 % value permissible for engineering calculations. This is also the case when using the approximation of original data over a limited period.The response of the resulting model to the external influence that simulates a real pulse was investigated. The comparison with precise results showed a discrepancy not exceeding the value permissible for engineering calculations (<5 %)

Optimal Design of a Residential Photovoltaic Renewable System in South Korea

An optimal design model for residential photovoltaic (PV) systems in South Korea was proposed. In the optimization formulation, the objective function is composed of three costs, including the monthly electricity bill, the PV system construction cost (including the government’s subsidy), and the PV system maintenance cost. Here, because the monthly electricity bill is not differentiable (it is a stepped piecewise linear function), it cannot be solved by using traditional gradient-based approaches. For details considering the residential electric consumption in a typical Korean household, consumption was broken down into four types (year-round electric appliances, seasonal electric appliances, lighting appliances, and stand-by power). For details considering the degree of PV generation, a monthly generation dataset with different PV tilt angles was analyzed. The optimal design model was able to obtain a global design solution (PV tilt angle and PV size) without being trapped in local optima. We hope that this kind of practical approach will be more frequently applied to real-world designs in residential PV systems in South Korea and other countries.

Transport and the Fourth Industrial Revolution: The Emerging High-Growth Economies

This is a response case. The excitation is the fourth industrial revolution, and it is modelled as a stepped sinusoidal function. The object is transport in the lower-income (high-growth) countries, and particularly Africa. The paper retains the methodological variety of case study. Semiotic questions lead to textual analysis and the calculus of dynamical systems provides the analytical lens. The case allows us to examine possible holonomic controls in the dynamical space (state-society-market interaction). That way, the paper stays central in the epistemological object of case study – explication of reality. Except, here the reality is not a single capsule but two, and the interaction is inevitable: the region must face the revolution. It will need a development frame more robust than the developmental state of the past decades.

The development of face expertise: Evidence for a qualitative change in processing

There is conflicting evidence regarding the development of expert face recognition, as indexed by the face-inversion effect (FIE; de Heering, Rossion, & Maurer, 2011; Young and Bion, 1981) potentially due to the nature of the stimuli used in previous research. The developmental trajectory of the FIE was assessed in participants aged between 5- and 18-years using age-matched and adult stimuli. Four experiments demonstrated that upright face recognition abilities improved linearly with age (presumably due to improved memory storage capacities) and this was larger than for inverted faces. The FIE followed a stepped function, with no FIE for participants younger than 9-years of age. These results indicate maturation of expert face processing mechanisms that occur at the age of 10-years, similar to expertise in other domains.

Forecasting Tourist Arrivals and Supply and Demand Gap Analysis for Hotel Sector in Addis Ababa, Ethiopia

This paper aims to forecast the long term behavior of tourist arrivals and analyze the gap between supply and demand for the hotel/accommodation sector of the city of Addis Ababa. It also intends to provide vital information in regards to the sparse knowledge in the subject of forecasting tourist arrivals in Ethiopia. The research is largely conducted based on the secondary data obtained from the Ministry of Culture and Tourism (MOCT) in the tenth edition of the Policy, Planning, Evaluation and Monitoring Directorate’s bulletin publication on Tourism Statistics (2009-2012),(MOCT, 2013). Theoretical assessments of the requirement of a forecasting process and a critical analysis of available forecasting methods have been carried out to fit the profile of long term tourist arrivals. Based on the assessments and analysis, the Box-Jenkins process was selected. Furthermore, the gap analysis is done using the Funneling Technique. The method has also determined that the annual tourist arrivals for the country in the year 2015 will be 798,157 and for the year of 2020, it is expected to be 1,130,971 and finally in 2025, the annual tourist arrivals are expected to climb to 1,463,743. The use of the Funneling Technique in combination with the Stepped Function Intervention Model establishes a different case scenario (positive, negative and starched intervention) which has then been studied to foresee the relationship between supply and demand of the accommodation sector under different circumstances.Keywords: Forecasting, tourist arrival, X-12-ARIMA, Supply, demand.

Time-Domain Analysis of Sampling Effect in DPWM of DC–DC Converters

This paper investigates time-domain analysis of sampling effect in digital pulsewidth modulation (DPWM) of dc–dc converters. The relation between the sampling delay, duty ratio, and multisampling factor (sampling to carrier frequency ratio) has been characterized. The sampling delay of the digital controller used for DPWM of the dc–dc converter has close relation with the actual pulsewidth-modulation output. An increase in the multisampling factor can reduce the delay effect of the DPWM. The output voltage varies as a stepped function of the duty ratio instead of the linear function as observed in ideal modulation. It is shown in this paper that this delay is a periodic function of the duty ratio. The effect of variations in the sampling frequency, switching frequency, and modulation index has been analyzed. The proposed sampling effect has been verified analytically for the buck, boost, and buck–boost dc–dc converters. The experimental results for the buck and boost converters have been obtained with the control circuit realized through a field-programmable gate array-based digital controller.

Dynamic performance of vacuum membrane distillation system

The aim of this work was the development of a numerical methodology to simulate and study the dynamic behavior of vacuum membrane distillation (VMD) system. A time-dependent one-dimensional finite difference numerical model is developed to study the flow as well as thermal regimes and the dynamic operational performance of VMD under stepped flow disturbance function in the hot channel. The study simulates the process parameters including mass flow rates, temperatures, vapor pressures, and concentration distributions for the hot feed channels along the flat-plate membrane length with transmembrane flux. The developed dynamic tool predicts the hydrodynamic behaviors and thermal characteristics of the very thin channels of VMD module. A rectangular pulse disturbance function is applied to rise up the inlet hot mass flow rate from steady state (SS) value of 1 to 1.34 kg/s for 60 s. The model ran for 3 min, which included the 60 s of applied dynamic disturbance; it started at the 10th s and finished at the 70th s. The results show that the probability of the pressure rise and the salt precipitation (scaling problem) will appear on the second half of the membrane length more than on the first half. The hydrodynamic influence of the flow conditions on the permeate flux appears to be more significant at the feed side of the VMD module fillet.

Price Instability in Multi-Unit Auctions

We consider a procurement auction, where each supplier has private costs and submits a stepped supply function. We solve for a Bayesian Nash equilibrium and show that the equilibrium has a price instability in the sense that a minor change in a suppliers cost sometimes result in a major change in the market price. In wholesale electricity markets, we predict that the bid price of the most expensive production unit can change by 1-10% due to price instability. The price instability is reduced when suppliers have more steps in their supply functions for a given production technology. In the limit, as the number of steps increases and the cost uncertainty decreases, the Bayesian equilibrium converges to a pure-strategy NE without price instability, the Supply Function Equilibrium (SFE).