Temporal-spatial cross-correlation analysis of non-stationary near-surface wind speed time series

Temporal-spatial cross-correlation analysis of non-stationary wind speed time series plays a crucial role in wind field reconstruction as well as in wind pattern recognition.Firstly,the near-surface wind speed time series recorded at different locations are studied using the detrended fluctuation analysis(DFA),and the corresponding scaling exponents are larger than 1.This indicates that all these wind speed time series have non-stationary characteristics.Secondly,concerning this special feature( i.e.,non-stationarity)of wind signals,a cross-correlation analysis method,namely detrended cross-correlation analysis(DCCA) coefficient,is employed to evaluate the temporal-spatial cross-correlations between non-stationary time series of different anemometer pairs.Finally,experiments on ten wind speed data synchronously collected by the ten anemometers with equidistant arrangement illustrate that the method of DCCA cross-correlation coefficient can accurately analyze full-scale temporal-spatial cross-correlation between non-stationary time series and also can easily identify the seasonal component,while three traditional cross-correlation techniques(i.e.,Pearson coefficient,cross-correlation function,and DCCA method) cannot give us these information directly.

Detrended cross-correlation analysis of electroencephalogram

In the paper we use detrended cross-correlation analysis （DCCA） to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject＇s brain function is healthy or not.

Cross-correlation analysis of crude oil and new energy markets: A new perspective based on carbon emission market

Taking the return series of the EU carbon allowance price, WTI crude oil price, the European renewable energy index and Shenzhen carbon emission price, Daqing crude oil price, the China securities new energy index as sample data, the multifractal detrend cross-correlation analysis method(MF-DCCA)is used to research the dynamic cross-correlation relationships among the carbon emission market, crude oil market and the new energy market in Europe and China and the source of the multifractality. The empirical analysis shows that the cross-correlations among the carbon emission market, crude oil market and new energy market in Europe and China have all significant multifractal characteristics. Moreover, the multifractal strength of cross-correlation between the carbon emission market and crude oil market is less than that between the carbon emission market and new energy market in Europe. The Chinese market is the opposite. In addition, the multifractal strength of cross-correlation between the crude oil market and new energy market in Europe is more than that between the crude oil market and new energy market in China. It is also found that the long-range correlation of the sequences themselves and the fat-tailed distribution in fluctuations are the common causes of the multifractality, and the fat-tailed in fluctuations distribution contributes more to the multifractals of the series.

Asymptotic Analysis of Estimated Cyclic Cross-Correlation Function Between Stationary and Cyclostationary Processes

The cyclic cross-correlation between a stationary process and a cyclostationary process at cycle frequency α(≠ 0)is identically zero under an ideal condition, which indicates that a cyclic cross-correlation method performs much better than the conventional cross-correlation method in suppressing the stationary noise or interference. But unfortunately, the cyclic cross-correlation will not really approach zero due to the limited data length in some real conditions. In this paper, the quantitative relation between the data length and the estimated cyclic cross-correlation is deduced, and some useful conclusions are drawn, which are proven by some computer simulations. The conclusion in this paper is really useful for the practical application of cyclostationary signal processing.

Feedback iterative learning control for time-delay systems based on 2D analysis approach

This paper deals with the iterative learning control （ILC） design for multiple-input multiple-output （MIMO）,time-delay systems （TDS）.Two feedback ILC schemes are considered using the so-called two-dimensional （2D） analysis approach.It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes,based on which necessary and sufficient conditions for their stability can be provided.A numerical example is included to validate the theoretical analysis.

Stability analysis and controller design of T-S fuzzy systems with time-delay under imperfect premise matching

The issue of the stability and controller design of Takagi-Sugeno（T-S） fuzzy control systems with time-delay is investigated under imperfect premise matching when the T-S fuzzy time-delay model and fuzzy controller do not share the same membership functions.A new stability criterion which contains the information of membership functions is derived.The new stability criterion is less conservative,and enhances the design flexibility.Two numerical examples are presented to illustrate the conservativeness and effectiveness of the proposed method.

Correlation analysis between the Aral Sea shrinkage and the Amu Darya River

The shrinkage of the Aral Sea,which is closely related to the Amu Darya River,strongly affects the sustainability of the local natural ecosystem,agricultural production,and human well-being.In this study,we used the Bayesian Estimator of Abrupt change,Seasonal change,and Trend(BEAST)model to detect the historical change points in the variation of the Aral Sea and the Amu Darya River and analyse the causes of the Aral Sea shrinkage during the 1950–2016 period.Further,we applied multifractal detrend cross-correlation analysis(MF-DCCA)and quantitative analysis to investigate the responses of the Aral Sea to the runoff in the Amu Darya River,which is the main source of recharge to the Aral Sea.Our results showed that two significant trend change points in the water volume change of the Aral Sea occurred,in 1961 and 1974.Before 1961,the water volume in the Aral Sea was stable,after which it began to shrink,with a shrinkage rate fluctuating around 15.21 km3/a.After 1974,the water volume of the Aral Sea decreased substantially at a rate of up to 48.97 km3/a,which was the highest value recorded in this study.In addition,although the response of the Aral Sea's water volume to its recharge runoff demonstrated a complex non-linear relationship,the replenishment of the Aral Sea by the runoff in the lower reaches of the Amu Darya River was identified as the dominant factor affecting the Aral Sea shrinkage.Based on the scenario analyses,we concluded that it is possible to slow down the retreat of the Aral Sea and restore its ecosystem by increasing the efficiency of agricultural water use,decreasing agricultural water use in the middle and lower reaches,reducing ineffective evaporation from reservoirs and wetlands,and increasing the water coming from the lower reaches of the Amu Darya River to the 1961–1973 level.These measures would maintain and stabilise the water area and water volume of the Aral Sea in a state of ecological restoration.Therefore,this study focuses on how human consumption of recharge runoff affects the Aral Sea and provides scientific perspective on its ecological conservation and sustainable development.

OPERATIONAL MODAL ANALYSIS SCHEMES USING CORRELATION TECHNIQUE

For some large-scale engineering structures in operating conditions, modal param- eters estimation must base itself on response-only data. This problem has received a considerable amount of attention in the past few years. It is well known that the cross-correlation function between the measured responses is a sum of complex exponential functions of the same form as the impulse response function of the original system. So this paper presents a time-domain operating modal identifcation global scheme and a frequency-domain scheme from output-only by cou- pling the cross-correlation function with conventional modal parameter estimation. The outlined techniques are applied to an airplane model to estimate modal parameters from response-only data.

Analysis on observational results of Pi2 geomagnetic pulsation in Henan region

A measurement profile consisted of 5 sites from Xinyang to Tangyin in Henan Province was set up in September of 1996 to carry out simultaneous observation of Pi2 geomagnetic pulsations. Simultaneity of Pi2 geomagnetic pulsation occurrence along the N-S profile was investigated. Results of analysis pointed out that Pi2 gcomagnetic pulsations appeared at first at the site of Xinyang at the southern end of the profile, the later the same Pi2 geomag netic pulsation appeared, the more north the site was at. Apparent propagation speed of Pi2 in N-S direction in the region is about 140 kin/s. Because Pi2 geomagnetic pulsation varying with time is of instability, and based on characteristics that basic wavelet can be dilated and localized, we selected proper basic wavelat form and by means of wavelet transform to analyze the changes of periods and amplitudes of main periodic components included in Pi2 pulsations with time. The results show that there existed complex form in periods and amplitudes of wavelet varying with time.

Stability analysis of a time-delayed Van der Pol–Helmholtz–Duffing oscillator in fractal space with a non-perturbative approach

The time-delayed fractal Van der Pol–Helmholtz–Duffing(VPHD)oscillator is the subject of this paper,which explores its mechanisms and highlights its stability analysis.While time-delayed technologies are currently garnering significant attention,the focus of this research remains crucially relevant.A non-perturbative approach is employed to refine and set the stage for the system under scrutiny.The innovative methodologies introduced yield an equivalent linear differential equation,mirroring the inherent nonlinearities of the system.Notably,the incorporation of quadratic nonlinearity into the frequency formula represents a cutting-edge advancement.The analytical solution's validity is corroborated using a numerical approach.Stability conditions are ascertained through the residual Galerkin method.Intriguingly,it is observed that the delay parameter,in the context of the fractal system,reverses its stabilizing influence,impacting both the amplitude of delayed velocity and the position.The analytical solution's precision is underscored by its close alignment with numerical results.Furthermore,the study reveals that fractal characteristics emulate damping behaviors.Given its applicability across diverse nonlinear dynamical systems,this non-perturbative approach emerges as a promising avenue for future research.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.

RMT-Based Urban Traffic Cross-Correlation Analysis and Its Application on Traffic Incident Impact Analyses

Cross-correlating traffic flow data at different intersections in an urban transportation network is important for understanding the collective behavior of constituents in a complex system and for predicting the risk of network-wide congestion. In this work, a Random Matrix Theory （RMT） based method is used to describe the collective behavior from massive traffic data sets. Nonrandom correlations between traffic flow series recorded in the Beijing road network occur both with and without detrending. The effect of the traffic load on the correlation patterns of network-wide traffic flows is analyzed using the RMT analysis of a simulated data set collected from Paramics. The RMT analysis is also used to evaluate the impact of incidents on the network-wide traffic status. Cluster analysis is used to find the largest cluster in the network which indicates the critical congestion caused by the incident. All the results show that RMT analyses are an effective method for investigating systematic interactions in urban transportation systems.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

INFORMATION FUSION STEADY-STATE WHITE NOISE DECONVOLUTION ESTIMATORS WITH TIME-DELAYED MEASUREMENTS AND COLORED MEASUREMENT NOISES

White noise deconvolution or input white noise estimation problem has important appli-cation backgrounds in oil seismic exploration,communication and signal processing.By the modern time series analysis method,based on the Auto-Regressive Moving Average(ARMA) innovation model,under the linear minimum variance optimal fusion rules,three optimal weighted fusion white noise deconvolution estimators are presented for the multisensor systems with time-delayed measurements and colored measurement noises.They can handle the input white noise fused filtering,prediction and smoothing problems.The accuracy of the fusers is higher than that of each local white noise estimator.In order to compute the optimal weights,the formula of computing the local estimation error cross-covariances is given.A Monte Carlo simulation example for the system with 3 sensors and the Bernoulli-Gaussian input white noise shows their effectiveness and performances.

Drought Forecasting in a Semi-arid Watershed Using Climate Signals:a Neuro-fuzzy Modeling Approach

Large-scale annual climate indices were used to forecast annual drought conditions in the Maharlu-Bakhtegan watershed,located in Iran,using a neuro-fuzzy model.The Standardized Precipitation Index(SPI) was used as a proxy for drought conditions.Among the 45 climate indices considered,eight identified as most relevant were the Atlantic Multidecadal Oscillation(AMO),Atlantic Meridional Mode(AMM),the Bivariate ENSO Time series(BEST),the East Central Tropical Pacific Surface Temperature(NINO 3.4),the Central Tropical Pacific Surface Temperature(NINO 4),the North Tropical Atlantic Index(NTA),the Southern Oscillation Index(SOI),and the Tropical Northern Atlantic Index(TNA).These indices accounted for 81% of the variance in the Principal Components Analysis(PCA) method.The Atlantic surface temperature(SST:Atlantic) had an inverse relationship with SPI,and the AMM index had the highest correlation.Drought forecasts of neuro-fuzzy model demonstrate better prediction at a two-year lag compared to a stepwise regression model.

New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay

This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay.A new delay-product-type augmented Lyapunov-Krasovskii functional(LKF)is constructed.Based on the LKF and by employing a generalized free-matrix-based integral inequality,less conservative delay-dependent stability criteria are obtained.Finally,two well-known numerical examples are used to confirm the effectiveness and the superiority of the presented stability criteria.

Effects of heterogeneity distribution on hillslope stability during rainfalls

The objective of this study was to investigate the spatial relationship between the most likely distribution of saturated hydraulic conductivity(Ks) and the observed pressure head(P) distribution within a hillslope. The cross-correlation analysis method was used to investigate the effects of the variance of ln Ks, spatial structure anisotropy of ln Ks, and vertical infiltration flux(q) on P at some selected locations within the hillslope. The cross-correlation analysis shows that, in the unsaturated region with a uniform flux boundary, the dominant correlation between P and Ksis negative and mainly occurs around the observation location of P. A relatively high P value is located in a relatively low Kszone, while a relatively low P value is located in a relatively high Kszone. Generally speaking, P is positively correlated with q/Ksat the same location in the unsaturated region. In the saturated region, the spatial distribution of Kscan significantly affect the position and shape of the phreatic surface. We therefore conclude that heterogeneity can cause some parts of the hillslope to be sensitive to external hydraulic stimuli(e.g., rainfall and reservoir level change), and other parts of the hillslope to be insensitive. This is crucial to explaining why slopes with similar geometries would show different responses to the same hydraulic stimuli, which is significant to hillslope stability analysis.

Variation of Hyporheic Temperature Profiles in a Low Gradient Third-Order Agricultural Stream—A Statistical Approach

Sediment size governs advection, controlling the hydraulic conductivity of the stratum, and conduction, influencing the amount of surface area in contact between the sediment particles. To understand the role of sediment particle size on thermal profiles within the hyporheic zone, a statistical approach, involving general summary statistics and time series cross-correlation, was employed. Data were collected along two riffles: Site 1: gravel (d50 = 3.9 mm) and Site 2: sand (d50 =0.94 mm).Temperature probe grids collected 15-minute temperature data at 30, 60, 90, and140cm below the streambed surface over a 6 month period. Surface water and air temperature were recorded. Diel temperature signal penetration depth was limited to the upper 30cm of the streambed and was driven by advection. Surface seasonal trends were detected at greater depths, indicating that thermal pulses are transmitted initially by advection and by conduction to areas deeper in the hyporheic zone. Site 1 showed a high degree of thermal heterogeneity via a localized downwelling zone within a gaining stream environment. Site 2 exhibited a vertically and horizontally homogenized thermal environment attributed to an increased amount of sand sediments that limited advection and significant groundwater discharge that mediated the effects of downwelling surface water.

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.