Sampling Time Step Research Articles

Economic model predictive control based on a periodicity constraint

This paper addresses a novel economic model predictive control (MPC) formulation based on a periodicity constraint to achieve an optimal periodic operation for discrete-time linear systems. The proposed control strategy does not rely on forcing the terminal state by means of a terminal equality constraint and hence it does not require a priori knowledge of a periodic steady trajectory. Instead, at each sampling time step the economic cost function is optimized based on a periodicity constraint over all the periodic trajectories that include the current state. The recursive feasibility and the closed-loop convergence to a periodic steady trajectory are discussed. Moreover, an optimality certificate of this steady trajectory is provided based on the Karush–Kuhn–Tucker (KKT) optimality conditions. Finally, an application to a well-known water distribution network benchmark is presented to demonstrate the proposed economic MPC in which the closed-loop simulation results obtained with a linear model and a virtual–reality simulator are both provided.

Analysis and prediction of chilled water plant performance based on multivariate statistical methods and large historical data

The large datasets resulting from operating HVAC&R systems are currently scrutinized to find ways to exploit the useful information that they might contain. In this work, historical data of a centrifugal water chiller over the course of more than 1.5 years of operation is used to learn about the system and to suggest modifications to its operation scheme. The results show that principal component analysis (PCA) captures well the variance in the historical data. The first two principal components explained between 62 and 80% of the variance, depending on the cases considered. The main factors responsible for the variation of the chiller operation are found to be the weather and the cold water temperature setpoint. The effect of the sampling time step on the results is also studied. Moreover, this work demonstrates that partial least squares (PLS) regression can adequately predict an important indicator of the chiller performance, namely the coefficient of performance (COP), one time step ahead with an R² of 77.49% and root-mean square error of estimation (RMSEE) of 0.463 using a separate validation set of data. The PLS model was also able to predict future COP values up to 2 time steps (∼3 h) in advance.

Robust $H_{\infty }$ Control of Discrete-Time Nonhomogenous Markovian Jump Systems via Multistep Lyapunov Function Approach

This paper investigates the problems of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a class of discrete-time nonhomogenous Markovian jump linear systems (NMJLSs) by a multistep Lyapunov function (LF) approach. The proposed multistep LF is allowed to increase during the period of several sampling time step ahead of the current time within the Jump mode. First, a less conservative stability criterion is derived based on this multistep LF approach. Second, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is analyzed under the multistep case by properly dealing with the knowledge of future states and exogenous noises. These two results are then employed to facilitate a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control design for NMJLSs, which yields a better disturbance attenuation performance as compared with the existing results. Numerical examples are included to elucidate the effectiveness of the developed results.

Estimation of the water quality of a large urbanized river as defined by the European WFD: what is the optimal sampling frequency?

Assessment of the quality of freshwater bodies is essential to determine the impact of human activities on water resources. The water quality status is estimated by comparing indicators with standard thresholds. Indicators are usually statistical criteria that are calculated on discrete measurements of water quality variables. If the time step of the measured time series is not sufficient to fully capture the variable’s variability, the deduced indicator may not reflect the system’s functioning. The goal of the present work is to assess, through a hydro-biogeochemical modeling approach, the optimal sampling frequency for an accurate estimation of 6 water quality indicators defined by the European Water Framework Directive (WFD) in a large human-impacted river, which receives large urban effluents (the Seine River across the Paris urban area). The optimal frequency depends on the sampling location and on the monitored variable. For fast varying compounds that originate from urban effluents, such as PO_{4}^{3-}, NH_{4}^{+} and NO_{2}^{-}, a sampling time step of one week or less is necessary. To be able to reflect the highly transient character of bloom events, chl a concentrations also require a short monitoring time step. On the contrary, for variables that exert high seasonal variability, as NO_{3}^{-} and O 2, monthly sampling can be sufficient for an accurate estimation of WFD indicators in locations far enough from major effluents. Integrative water quality variables, such as O 2, can be highly sensitive to hydrological conditions. It would therefore be relevant to assess the quality of water bodies at a seasonal scale rather than at annual or pluri-annual scales. This study points out the possibility to develop smarter monitoring systems by coupling both time adaptative automated monitoring networks and modeling tools used as spatio-temporal interpolators.

Frequency-Domain Simulation of Electromagnetic Transients Using Variable Sampling Time-Step

This letter presents the extension of a previously proposed frequency-domain (FD) approach for the analysis of electromagnetic transients (EMTs), primarily due to a set of discrete switching events, in an electric power network. The method is based on dividing the analysis time window into a set of subwindows with equal or unequal time lengths and solving each in the FD. The sampling time step is also independently selected for each subwindow. The extended method, formerly proposed for a single transmission line, can readily use the concept of network equivalents, achieving efficient EMT solutions of large systems, and can simultaneously accommodate slow and fast dynamics.

Dependable Control for Wireless Distributed Control Systems

The use of wireless communications for real-time control applications poses several problems related to the comparatively low reliability of the communication channels. This paper is concerned with adaptive and predictive application-level strategies for ameliorating the effects of packet losses and burst errors in industrial sampled-data Distributed Control Systems (DCSs), which are implemented via one or more wireless and/or wired links, possibly spanning multiple hops. The paper describes an adaptive compensator that reconstructs the best estimates (in a least squares sense) of a sequence of one or more missing sensor node data packets in the controller node. At each sample time, the controller node calculates the current control, and a prediction of future controls to apply over a short time horizon; these controls are forwarded to the actuator node every sample time step. A simple design method for a digital Proportional Integral Derivative (PID)-like adaptive controller is also described for use in the controller node. Together these mechanisms give robustness to packet losses around the control loop; in addition, the majority of the computational overhead resides in the controller node. An implementation of the proposed techniques is applied to a case study using a Hardware in the Loop (HIL) test facility, and favorable results (in terms of both performance and computational overheads) are found when compared to an existing robust control method for a DCS experiencing artificially induced burst errors.

Elastic full-waveform inversion using the second-generation wavelet and an adaptive-operator-length scheme

Elastic full-waveform inversion (FWI) can generally yield subsurface model parameters of high spatial resolution. However, the computational and storage burden is tremendous. To mitigate this problem, we developed the following three strategies: First, we derived a time-space-domain adaptive staggered-grid finite-difference method. The size of the calculation was reduced by using smaller operator lengths for high S-wave velocities. Second, we evaluated a multiscale elastic FWI scheme based on the second-generation wavelet, by which scale decompositions of data and model space were implemented. With the scale increasing, spatial sampling intervals and time steps became larger. Therefore, the minimum computational cost could be achieved by combining the variable-operator-length scheme with the multiscale scheme. Third, to economize the memory consumption, we extended the efficient boundary storage and checkpointing schemes into elastic FWI. Only wavefields of several parts in the boundary area between two adjacent checkpoints were stored and used to reconstruct source wavefields of the inner area. Furthermore, the optimal number of checkpoints could be automatically determined by minimizing the amount of storage. We validated these new strategies for the SEG/EAGE overthrust model. The synthetic example suggested the feasibility and robustness of the new elastic FWI method in terms of improving computational efficiency and alleviating large amounts of data storage. We also analyzed the accuracy of our FWI method. The inversion results revealed that our wavelet-based method had better reconstructed structures and higher convergence rate than the conventional filtering-based multiscale FWI method.

Variability of mineral dust concentrations over West Africa monitored by the Sahelian Dust Transect

The “Sahelian belt” is known as a region where mineral dust content is among the highest in the world. In the framework of the AMMA international Program, a transect of three ground based stations, the “Sahelian Dust Transect” (SDT), has been deployed in order to obtain quantitative information on the mineral dust content over the Sahel. These three stations: Banizoumbou (Niger), Cinzana (Mali) and M'Bour (Senegal) are aligned at 13°N along the east–west main pathway of the Saharan and Sahelian dust toward the Atlantic Ocean. The SDT provides a set of aerosol measurements and local meteorological parameters to describe and understand the mechanisms that control the temporal and regional variability of mineral dust content in these regions.In this work we analyze the seasonal and diurnal variability of the dust concentrations over the period 2006–2010. The analysis of the dust concentrations measured between 2006 and 2010 confirmed a regional seasonal cycle characterized by a maximum in the dry season, with median concentration ranging from 205μgm−3 at Banizoumbou to 144μgm−3 at M'Bour, and a minimum (11–32μgm−3) in the wet season. The five year data set allowed the quantification of the variability of the monthly concentrations. The range between the percentiles 75 and 25 varies linearly with the median concentration: it is of the same order than the median value in M'Bour, 17% slightly higher in Cinzana and 50% higher in Banizoumbou. The range between the accepted maximum and minimum is also correlated with the median value, with slopes ranging from 14 in Banizoumbou to 7 in M'Bour. Part of the variability of the concentration at the monthly scale is due to interannual variability. Extremely high or low monthly concentration can be recorded that significantly impacts the five year median concentration and its range. Compared to the 3-year data set analyzed by Marticorena et al. (2010), the two additional years used in this work appear as the less dusty year (2009) and one of the dustier years (2010).The sampling time step and the high recovery rates of the measurement stations allowed to investigate the diurnal cycle of the dust concentration for the first time. During the dry season, the hourly median concentrations range from 80 to 100μgm−3 during the night to 100–160μgm−3 during the day-time maximum. The diurnal cycle of the PM10 concentrations is phased with the diurnal cycle of the surface wind speed and thus modulated by the interactions between the nocturnal lower level jet (NLLJ) and the surface boundary layer. The NLLJ appears as a major agent to transport Saharan dust toward the Sahel. During the wet season, the median PM10 concentrations are maximum at night-time (<50μgm−3). The night-time concentrations are associated with a large range of variability and coincide with the periods of higher occurrence of meso-scale convective systems. The amplitude of the diurnal cycle is of the order of 60μgm−3 in the dry season and 20μgm−3 in the wet season. Both in the dry and in the wet season, despite a month to month variability of the daily dust concentration, a typical diurnal pattern has been established suggesting that this temporal pattern is mainly driven by local meteorological conditions.

Algorithms for Control Criteria for the Participation of Thermal Power Plant Generating Units in Standardized Primary Frequency Control1

A mathematical description, methods, and algorithms are given for evaluating the participation of power generating units at thermal power plants in standardized primary frequency control in accordance with the following criteria: absence of adequate/required reaction to frequency changes, inconsistency of the steady state of primary control with the specified state, nonconformity of the magnitude of the dead band with specifications, mismatch of measurement resolution with specifications, and mismatch of the sampling time step for transmitted parameters with specifications.

Robust MPC controller design: Infinite prediction horizon

We present a new technique for the synthesis of a robust model predictive controller with infinite prediction horizon. The proposed controller design approach ensures a parameter-dependent quadratic stability and guaranteed cost for linear polytopic uncertain systems. The proposed design procedure based on BMI or LMI reduces to off-line output feedback controller gain calculation minimizing an upper bound on the “worst case” an objective function. For the case of our approach and input (output) constraints at each sample time step for each input (output) scalar parameter is calculated, which radically decreases the computational load. The controller design is illustrated by examples.

Analysis of delay compensation in real-time dynamic hybrid testing with large integration time-step

With the sub-stepping technique, the numerical analysis in real-time dynamic hybrid testing is split into the response analysis and signal generation tasks. Two target computers that operate in real-time may be assigned to implement these two tasks, respectively, for fully extending the simulation scale of the numerical substructure. In this case, the integration time-step of solving the dynamic response of the numerical substructure can be dozens of times bigger than the sampling time-step of the controller. The time delay between the real and desired feedback forces becomes more striking, which challenges the well-developed delay compensation methods in real-time dynamic hybrid testing. This paper focuses on displacement prediction and force correction for delay compensation in the real-time dynamic hybrid testing with a large integration time-step. A new displacement prediction scheme is proposed based on recently-developed explicit integration algorithms and compared with several commonly-used prediction procedures. The evaluation of its prediction accuracy is carried out theoretically, numerically and experimentally. Results indicate that the accuracy and effectiveness of the proposed prediction method are of significance.

Dynamic analysis and numerical simulation of a discrete model of a bistable system

Numerical simulation is the generally used method for studying stochastic resonance (SR), which is a kind of non-linear phenomenon that usually occurs in non-linear bistable systems. It has been found that the input signal needs to be over-sampled during the numerical simulation of SR. In this paper we provide an explanation of this phenomenon based on a stability analysis of the bistable system. We begin by studying the stability of a discrete model of a bistable system in numerical simulations. We then give a theoretical derivation of the stability conditions for the simulation model with different parameters, and carry out numerical experiments to show that the results coincide with the predictions of the theory. We explain why the input signal needs to be over-sampled in the simulation and provides guidelines for the choice of system parameters for the bistable system and the sampling time step in the numerical simulation of SR. Finally, we present the results of simulations showing an example of SR occurring in a bistable system and an example of weak periodic signal detection when it is processed by a bistable system.

Moving Target Localization and Tracking Algorithms: A Particle Filter Based Method

提出一种基于粒子滤波的目标定位算法PFTL(particle filter based target localization)以及一种基于网络覆盖问题的节点组织策略SAC(sampling aware tracking cluster formation).PFTL 的基本思想是,采用一系列带权粒子(weighted particles)来预测移动物体位置的后验分布空间,每个新时刻根据传感器的测量数据来权衡和定位目标.PFTL 通过引入误差容忍(error tolerant)的方式来存储和发送目标位置数据,使汇聚点关于物体位置信息的数据误差在一个可控的范围内,进而极大地减少网络通信负荷.SAC基于传感器采样离散化的特点来制订数据融合策略,并以最大化覆盖物体运动轨的方式动态地选取节点和进行节点簇的有效组织.模拟实验结果表明,与现有的几种定位算法和追踪协议相比,结合PFTL 算法和SAC 策略能够以较小的代价取得更好的定位效果和网络负载均衡,进而延长网络寿命.;This paper proposes a particle filter based target localization (PFTL) algorithm, and a sampling aware tracking cluster formation (SAC) scheme for organizing the sensor nodes, which maximizes the coverage area of target's trajectory in each cluster. The key idea of PFTL is to represent the possible locations of mobile target with a number of weighted particles, and to estimate the particles for computing the position of the object when the range measurements are available at next sampling time step. The motivation behind PFTL is that if the sink is willing to tolerate a small error, regarding the position of the target, the in-network communication can be greatly decreased, as well as the consumed energy, which is the most precious resource in wireless sensor networks. To balance the computation and communication overhead of network, this study designed a node scheduling scheme SAC, which dynamically clusters the sensors aimed at minimizing the times of tracking data hand-offs, so as to save the energy expenditure. Extensive simulations are conducted to verify the proposed methodologies, and the results reveal that PFTL and SAC not only reduce the localization error, but also efficiently extend the network lifetime.

Selection of sampling numerical parameters for the DSMC method

In this work the problem of selection of a number of numerical parameters of the direct simulation Monte Carlo (DSMC) method (such as time step, cell size, and number of time steps) is addressed. We study the errors of the DSMC method relating to the quality and amount of information sampled during simulation for three main macroparameters of a gas flow (density, velocity, and temperature). The expressions for optimal selection of the sampling time step, the number of sampling cells, and the sample size which guarantee attaining a specified level of the error are proposed on the basis of the theory of functional Monte Carlo algorithms. Practical recommendations are given for evaluating the quantities involved in the expressions simultaneously with the calculation of the flow macroparameters. The proposed approaches are examined on the examples of the Fourier problem, the gas recondensation problem between two infinite parallel plates, and the supersonic plane-parallel rarefied gas flow around a flat plate.

Moving Low-Pass Gauss Filter with Automatically Defined Influence Region for Diffusive Studies

b = probe position, m C = heat capacity, kJ= kg C cn = conventional power spectra coefficient d = source parameter, s, Eq. (8b) f = frequency, Hz fc = cutoff frequency, Hz j = time data index, Eq. (5) jo = time data index, Eq. (6) k = thermal conductivity,W= m C kxx = thermal conductivity coefficient in x direction, W= m C kyx = thermal conductivity coefficient in x-y cross direction, kyx kxy, W= m C kyy = thermal conductivity coefficient in y direction, W= m C M = number of data points less one M = kernel function with arguments b; t=u in Eq. (4b) N = number of terms in influence region, Eq. (7d) N = first approximation to N, Eq. (7c) n = number of terms in power spectra nc = cutoff value in power spectra p = derivative order, Eq. (8c) q00 o = dimensional surface heat flux magnitude, W=m, Eq. (8b) q00 x = dimensional heat flux in x direction, W=m 2 rmsg = root-mean-square-error global filter, C, Eq. (10b) rmsl = root-mean-square-error local filter, C, Eq. (10c) rmso = root-mean-square-error original data, C, Eq. (10a) r = variable in Gauss function r1 = asymptotic infinity value T = temperature, C Ttc = thermocouple temperature, C Ttc;j = noisy thermocouple data at time t tj, C, Eq. (9) t = time, s tinfluence = influence time, s tj = discrete time, s tmax = maximum time for experiment, s u = dummy time variable, s x = spatial variable perpendicular to surface, m y = spatial variable parallel to surface, m yo = dummy spatial variable, m = thermal diffusivity, kxx= C or k= C , m=s t = sampling time width, s tmax -width = maximum time width of influence, s tsampling-time-step = sampling time step, s

Natural and artificial recharge investigation in the Zéroud Basin, Central Tunisia: impact of Sidi Saad Dam storage

Hydrochemical and isotopic data of waters from the Zeroud aquifer have been used to potentially provide a means for locating occurrences and to trace movements of a variety of natural and anthropogenic recharge waters in the Zeroud Basin, Central Tunisia. Geochemical data have been measured during the dam water release, from May to September 2005, with a sampling time step of 15 days. An implication of dam water has been demonstrated that is noticeable up along the main flow path to a distance of 10 km far from the injection site. Environmental isotopes 2H, 18O and 3H of water molecule were studied to investigate the effect of dam water on the hydrological system, and an isotope balance was established to compute the contribution of water storage component in groundwater. Based on isotopic mass balance, we assess that an average of 13% of total groundwater in the upper aquifer came from dam water storage. Three distinctive recharge waters in the aquifer can be determined. Water from local rainfall (pre-dam Zeroud River) that infiltrated into the boundaries of the Draa Affane Mountain was easily distinguished from the water influenced by anthropogenic recharge located in the Zeroud right rivulet. Distinguishable isotopic signatures of native wadi Zeroud recharge due to “recent lineal recharge” through the riverbed were also identified.

Some approaches to error analysis and optimization of the DSMC method

Some new approaches to error analysis and optimization of the Direct Simulation Monte Carlo (DSMC) method are presented. It is demonstrated that the interdependence of the estimates at adjacent time steps has a significant effect on the statistical error value. In this context the ‘sparse samples’ method for computational cost reduction is suggested. It means that different time steps have to be used for collision simulation (collision time step) and information sampling (sampling time step). The error of the DSMC method related to the quality and size of information sampled during the process simulation (the ‘external’ error) is investigated. The optimal relations between the sampling time step, the number of sampling cells, and the sample size, which guarantee the prescribed level of the ‘external’ error, are suggested on the basis of the theory of functional Monte Carlo algorithms. These optimal relations are examined using the Fourier and Couette problems as examples.

Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes

The zero-mean process \(\{X(t){:}\ t\in\mathbb{R} \}\) is said to be almost periodically correlated whenever its shifted covariance kernel \({(t,\tau) {\mapsto} {\rm cov}[X(t),X(t+\tau)]}\) is almost periodic in t uniformly with respect to \(\tau\in\mathbb{R}\). Then it admits a Fourier–Bohr decomposition: \({\rm cov}[X(t),X(t+\tau)] \sim \sum_{\lambda}a(\lambda,\tau) e^{{i}{\lambda}{t}}\). This paper deals with the estimation of the spectral covariance a(λ,τ) from a discrete time observation of the process \(\{X(t){:}\ t\in\mathbb{R} \}\), when jitter and delay phenomena are present in conjunction with periodic sampling. Under mixing conditions, we establish the consistency and the asymptotic normality of empirical estimators as the sampling time step tends to 0 and the sampling period tends to infinity.

Determination of upward/downward groundwater fluxes using transient variations of soil profile temperature: test of the method with Voyons (Aube, France) experimental data

AbstractThe temperature variations recorded at several points of a vertical shallow‐depth profile are governed both by conductive and convective heat transfers and can be used to calculate the vertical component of the Darcy velocity and thermal diffusivity in the soil. This paper describes such calculations when transient variations over tens of days are considered and tests them using data collected at Voyons (Aube, France). The temperature was recorded during a year and a half period with a 1 h sampling time step at three different depths: 0·2, 0·4 and 0·75 m. By processing the annual variation of temperature, we obtained a value of the Darcy velocity in good agreement with the value of actual/potential evapotranspiration ratio. By processing transient variations, despite the limitation of the calculations due to the lack of sensitivity of the sensors, results obtained at Voyons were in good correlation with tensiometric data. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Aggregation and sampling in deterministic chaos: implications for chaos identification in hydrological processes

Abstract. A review of the literature reveals conflicting results regarding the existence and inherent nature of chaos in hydrological processes such as precipitation and streamflow, i.e. whether they are low dimensional chaotic or stochastic. This issue is examined further in this paper, particularly the effect that certain types of transformations, such as aggregation and sampling, may have on the identification of the dynamics of the underlying system. First, we investigate the dynamics of daily streamflows for two rivers in Florida, one with strong surface and groundwater storage contributions and the other with a lesser basin storage contribution. Based on estimates of the delay time, the delay time window, and the correlation integral, our results suggest that the river with the stronger basin storage contribution departs significantly from the behavior of a chaotic system, while the departure is less significant for the river with the smaller basin storage contribution. We pose the hypothesis that the chaotic behavior depicted on continuous precipitation fields or small time-step precipitation series becomes less identifiable as the aggregation (or sampling) time step increases. Similarly, because streamflows result from a complex transformation of precipitation that involves accumulating and routing excess rainfall throughout the basin and adding surface and groundwater flows, the end result may be that streamflows at the outlet of the basin depart from low dimensional chaotic behavior. We also investigate the effect of aggregation and sampling using series derived from the Lorenz equations and show that, as the aggregation and sampling scales increase, the chaotic behavior deteriorates and eventually ceases to show evidence of low dimensional determinism.