Stationary Random Noise Research Articles

Closed form expressions for H2 optimal control of negative stiffness and inerter-based dampers for damped structures

This study presents the H2 optimal control of negative stiffness and inerter-based dampers as supplemental dampers to a damped single degree of freedom system (SDOF). In total, five different negative stiffness and inerter combinations have been studied, viz., a negative stiffness damper (NSD), three negative stiffness inerter dampers (NSIDs) and a tuned inerter damper (TID). NSIDs are novel energy dissipation devices consisting of negative stiffness dampers (NSD) and inerter mechanisms. H2 optimal control minimises the root mean square (RMS) of structural response under random/stochastic excitations. The ground acceleration excitation is modelled as a stationary random white noise process. The equations of motion for the SDOF system with different supplemental dampers are written in a state space form, and corresponding closed-form expressions for the optimal parameters are arrived at. The closed-form expressions for NSD, NSIDs and TID are arrived at by a two-stage process: First, by using the numerical search technique for calculating the minima of the H2 norm. Second, using the results of the corresponding numerical search, a sequence of fitting curve schemes is employed to arrive at various closed-form expressions. The closed-form expressions are more straightforward to use. Finally, the comparative seismic performance of the base-isolated (BI) structure with the proposed optimal dampers is obtained under the set near fault (NF) and far-field (FF) ground motions. The time history analysis shows that the H2 optimal control is very efficient in response control of the base-isolated structures. In particular, optimally designed NSIDs outperform the NSD and TID as a control device to a base-isolated structure. Hence, the performance of both NSD and TID as the supplemental damper is enhanced by adding the inerter mechanism.

Main electromagnetic jammer sources with impact on the railroad automation systems

The article presents some results of research to improve the stability of rail circuits and automatic cab signaling on the Railways. Signals of automatic locomotive signaling under the influence of stationary harmonic and random impulse noise are considered, the sources of which can be power lines, power devices, radio frequency electromagnetic fields, electrostatic discharges, lightning discharges, traction power supply and rail networks, as well as adjacent rail circuits. Particular attention is paid to the negative effects of reverse traction current and the uneven magnetization of the rails. It is shown that the practical implementation and application of the developed methods to increase the reliability of automatic locomotive signaling systems should suppress powerful interference from reverse traction currents that occur on locomotive receiving coils during heavy train traffic. Also, this should provide suppression of interference from the uneven magnetic field of the rails laid in the path or in the rut and at the ends of the sleepers. This will lead to a decrease in the intensity of failures in the operation of automatic locomotive signaling and to an increase in the level of safety and uninterrupted movement of trains. The results are successfully used on the railways of Russia and abroad.

Reproducibility of dynamic cerebral autoregulation parameters: a multi-centre, multi-method study

Objective: Different methods to calculate dynamic cerebral autoregulation (dCA) parameters are available. However, most of these methods demonstrate poor reproducibility that limit their reliability for clinical use. Inter-centre differences in study protocols, modelling approaches and default parameter settings have all led to a lack of standardisation and comparability between studies. We evaluated reproducibility of dCA parameters by assessing systematic errors in surrogate data resulting from different modelling techniques. Approach: Fourteen centres analysed 22 datasets consisting of two repeated physiological blood pressure measurements with surrogate cerebral blood flow velocity signals, generated using Tiecks curves (autoregulation index, ARI 0–9) and added noise. For reproducibility, dCA methods were grouped in three broad categories: 1. Transfer function analysis (TFA)-like output; 2. ARI-like output; 3. Correlation coefficient-like output. For all methods, reproducibility was determined by one-way intraclass correlation coefficient analysis (ICC). Main results: For TFA-like methods the mean (SD; [range]) ICC gain was 0.71 (0.10; [0.49–0.86]) and 0.80 (0.17; [0.36–0.94]) for VLF and LF (p = 0.003) respectively. For phase, ICC values were 0.53 (0.21; [0.09–0.80]) for VLF, and 0.92 (0.13; [0.44–1.00]) for LF (p < 0.001). Finally, ICC for ARI-like methods was equal to 0.84 (0.19; [0.41–0.94]), and for correlation-like methods, ICC was 0.21 (0.21; [0.056–0.35]). Significance: When applied to realistic surrogate data, free from the additional exogenous influences of physiological variability on cerebral blood flow, most methods of dCA modelling showed ICC values considerably higher than what has been reported for physiological data. This finding suggests that the poor reproducibility reported by previous studies may be mainly due to the inherent physiological variability of cerebral blood flow regulatory mechanisms rather than related to (stationary) random noise and the signal analysis methods.

A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum and its performance evaluation against the Kurtogram

Envelope analysis is a widely used method for rolling element bearing fault detection. To obtain high detection accuracy, it is critical to determine an optimal frequency narrowband for the envelope demodulation. However, many of the schemes which are used for the narrowband selection, such as the Kurtogram, can produce poor detection results because they are sensitive to random noise and aperiodic impulses which normally occur in practical applications. To achieve the purposes of denoising and frequency band optimisation, this paper proposes a novel modulation signal bispectrum (MSB) based robust detector for bearing fault detection. Because of its inherent noise suppression capability, the MSB allows effective suppression of both stationary random noise and discrete aperiodic noise. The high magnitude features that result from the use of the MSB also enhance the modulation effects of a bearing fault and can be used to provide optimal frequency bands for fault detection. The Kurtogram is generally accepted as a powerful means of selecting the most appropriate frequency band for envelope analysis, and as such it has been used as the benchmark comparator for performance evaluation in this paper. Both simulated and experimental data analysis results show that the proposed method produces more accurate and robust detection results than Kurtogram based approaches for common bearing faults under a range of representative scenarios.

Statistical considerations on stationary-random noise propagating through a solid medium

In this paper the noise propagation through a solid medium is considered to study how the parameters of the statistical model change. In particular the external and internal sound fields of a box are taken into account. It is experimentally shown that the variance of the real and the imaginary parts of the external stationary random noise change differently while going through the box walls. The generalized Rayleigh distribution is shown to be more suitable to model the noise inside the cavity instead of the classical Rayleigh distribution. Starting from this outcome it has been studied how this noise affects a signal. It is known that a signal modulus affected by stationary random noise can be described by using the Rice distribution if the real and imaginary parts of the noise are statistically independent and identically distributed with zero mean and equal variances. Otherwise the less popular generalized Rice distribution must be used. The main differences of using the Rice or the generalized Rice distributions are shown by considering phasors both with constant and variable phases. In this paper it is shown that the bias estimation depends on the phase of the phasor if the variances of the real and imaginary parts are different and a numerical quantification is given. The attained results are useful when performing measurements of the sound pressure field due to a sound source inside a cavity affected by external noise.

Seismic random noise attenuation based on adaptive time–frequency peak filtering

Time–frequency peak filtering (TFPF) method uses a specific window with fixed length to recover band-limited signal in stationary random noise. However, the derivatives of signal such as seismic wavelets may change rapidly in some short time intervals. In this case, TFPF equipped with fixed window length will not provide an optimal solution. In this letter, we present an adaptive version of TFPF for seismic random noise attenuation. In our version, the improved intersection of confidence intervals combined with short-time energy criterion is used to preprocess the noisy signal. And then, we choose an appropriate threshold to divide the noisy signal into signal, buffer and noise. Different optimal window lengths are used in each type of segments. We test the proposed method on both synthetic and field seismic data. The experimental results illustrate that the proposed method makes the degree of amplitude preservation raise more than 10% and signal-to-noise (SNR) improve 2–4dB compared with the original algorithm.

Operational modal identification of offshore wind turbine structure based on modified stochastic subspace identification method considering harmonic interference

The structural modal parameter information can be generally obtained from different vibration responses triggered by unknown excitations using the classic modal identification methods which are based on the assumption that the input to the structure is exactly the same or close to the stationary random white noise. For the actual projects such as the offshore wind turbine structure, however, the imposed loads cannot be considered as the pure white noise excitation because the harmonic components emerge obviously in vibration responses due to periodic rotation excitations of the rotor. When the created harmonic components have greater energy and their frequencies are close to any natural modal frequency of the structure, the classic methods can no longer separate harmonic modes from actual structural operational modes under this strong harmonic disturbance, thus false modes may be generated and the identification accuracy may be badly affected. To identify the actual structural operational modes accurately under strong harmonic excitation, a modified stochastic subspace identification (SSI) method considering harmonic interference called the harmonic modification SSI (HM-SSI) method was proposed in this paper assuming the input harmonic frequencies are known and time-invariant. Then the effectiveness and accuracy of the HM-SSI method were verified through a simple numerical model of cantilever beam excited by various harmonic inputs superimposed on random loads. Besides, the superior robustness and better accuracy of identification results affected by the level of noise and the proportion of harmonic energy were reflected. Finally, the modal parameter information under different operational conditions was obtained and the safety assessment of an operational wind turbine was made based on the measured data from one offshore wind turbine test prototype at high running speed.

Theoretical analysis on stationary Gaussian random noise in narrowband Fourier transform spectrometer

The spectral resolution can be increased by detecting the optical signal in a narrowband spectrum for the Fourier transform spectrometer based on spatial modulated in our study. In this paper, to study the effect of the radiant source on the interference system, we regard the radiant noise as a narrowband stationary Gaussian random process. Using the linear system analysis method and the statistical theory, we deduce the input signal-to-noise ratio (SNR) and the output SNR after the optical signal and the radiant noise have passed through the interference system. Then we simulate the system and compare the obained result with a narrowband rectangle spectrum, and obtain the SNR gains along the optical path difference (OPD) in different autocorrelation degree and cross-correlation degree values. The simulation result indicates that the SNR gains at different OPDs in the correlation degree space each are a monotonic smooth surface. The SNR gain maximum moves along the radius and the contour of the correlation degree circle, and it returns to the initial position. after an OPD According to the analysis of the SNR gain, the autocorrelation degree and cross-correlation degree values can be controlled in a certain area, which can serve as a criterion for the design and the test of the radiant source.

Problem of invariance for discrete stabilization systems operating in conditions of regular chaos

New models of maps oriented to the solution of invariance problems in discrete dynamic systems that operate in conditions of deterministic chaos are proposed. The idea of K(E) transformation for quasi-stochastic sequences is developed based on these maps. The result is a method for the synthesis of discrete stabilization systems; this method, in combination with the principles of the classical theory of random processes, provides compensation for deterministic chaos and optimal filtering of stationary random noise.

Approximate Stochastic Self-Similarity of Envelopes of High-Frequency Teleseismic P-Waves from Large Earthquakes

A wavetrain of high-frequency (HF) P waves from a large earthquake, when recorded at a distant station, looks like a segment of modulated noise, with its duration close to the duration of rupture. These wavetrains, with their bursts and fadings, look much more intermittent than a segment of common stationary random noise. We try to describe quantitatively this bursty behavior. To this end, variogram and spectral analyses are applied to time histories of P-wave envelopes (squared-amplitude or instant-power signals) in six HF bands of 1-Hz width. Nine M w = 7.6–9.2 earthquakes were examined, using, in total, 232 records and 992 single-band traces. Variograms of integrated instant power are approximately linear on a log–log scale, indicating that the correlation structure of the instant-power signal is approximately self-similar. Also, estimates of the power spectrum of the instant-power signal look approximately linear on a log–log scale. Log–log slopes of the variograms and spectra deliver estimates of the Hurst exponent H that are mostly in the range 0.6–0.9, markedly above the value H = 0.5 of uncorrelated (white-noise) signals. The preferred estimate over the entire data set is H = 0.83, still, this estimate may include some bias, and must be treated as preliminary. The inter-event scatter of H estimates is about 0.04, reflecting individual event-to-event variations of H. Many of the average log–log spectral plots show slight concavity that perturbs the approximately linear slope; this is a secondary effect that seems to be mostly related to the limited bandwidth of the data. Evidence is given in support of the idea that the observed approximately self-similar correlation structure of the P-wave envelope originates in a similar structure of the body wave instant-power signal radiated by the source, so that the propagation-related distortions can be regarded as limited. The facts presented suggest that the space–time organization of the earthquake rupture process is multiscaled and bears significant fractal features; it deviates from the brittle-crack model with its two well-separated characteristic scales. Phenomenologically, the high-frequency body-wave radiation from an earthquake source can be thought of as a product of stationary noise and the square root of a positive random envelope function with a power-law spectrum. From the viewpoint of applications, the self-similarity of body wave envelopes provides a useful constraint for earthquake source models used to simulate strong ground motions.

Importance Sampling for Nonlinear Oscillating Systems driven by Stationary Noise Using a Probability Measure Transformation

We develop an importance sampling simulation scheme for estimating extremely small probability of level exceedance with respect to a nonlinear oscillating systems driven by a stationary random noise, where we use a probability measure transformation technique for constructing a simulation scheme based upon the Maruyama-Girsanov theorem. First, a system of Ito random differential equations and the related level exceedance are formulated, where the system nonlinearity is incorporated in terms of a nonlinear restoring force based upon the Masing rule. Next, an importance sampling simulation scheme is constructed, in which the optimal selection of the importance sampling measure is newly proposed. Finally, we give some numerical examples to demonstrate the efficiency of the proposed scheme and quantitatively examine effects of model parameters as well as the nonlinearity.

TIME-SCALE APPROACH FOR CHIRP DETECTION II

A new approach for joint detection and estimation of signals embedded in stationary random noise is considered and compared to previously studied methods, for the subclass of amplitude and frequency modulated signals. The method is a "reassigned" version of the Hough-wavelet transform and it is compared to the matched filter approach and the Hough-wavelet transform itself. Extensions to previous results obtained with these two methods are also presented. As target application, the problem of gravitational waves at interferometric detectors is considered. Our main conclusion is that there is no gain in introducing the reassignment operation.

Importance sampling for stochastic systems under stationary noise having a specified power spectrum

We develop an importance sampling simulation scheme for estimating an extremely small probability of system failure with respect to a time-dependent stochastic system excited by stationary random noise having a specified power spectrum. First, we construct a system of random differential equations driven by a Wiener process, which can approximately give such a stationary random noise by the use of an extended version of the well-known Ornstein–Uhlenbeck process. Next, we suppose a stochastic response system driven by the constructed stationary random noise. Next, formulating the probability of system failure, we give an importance sampling scheme through the probability measure transformation based upon the Girsanov theorem, where multi design times are introduced to cope with stationary or almost stationary behavior of the system. Finally, we give numerical examples to demonstrate the efficiency of the proposed scheme.

Transfer Matrices and Statistical Analysis of Sampled-data Systems with Continuous Periodic Processes

The paper considers the statistical analysis problem for closed-loop sampled-data control systems. Hereby, a periodic non-stationary continuous-time process is fed back by a digital controller under the assumption that the sampling period coincides with the period of the continuous-time process. The analysis is based on the investigation of the parametric transfer matrix (PTM) for the whole system. A closed formula for constructing the parametric transfer matrix of the closed-loop system W (s,t) is provided, and its properties as functions of the variable s are investigated. On basis of these stated properties of the PTM W (s,t), a constructive method for calculating the variance of the quasi-stationary output d y (t) = d y (t+T) is derived. In practical applications, the mean variance of the output for excitation by stationary random white noise is of interest. An appropriate formula for this system characteristic is provided. The application of the statistical analysis method is demonstrated by an example.

Mode Superposition Method of Non Stationary Seismic Responses for Non Classically Damped Linear Systems

The real earthquake ground accelerations are usually non stationary vibration process. In order to estimate the influence of the non stationarity of ground motion on the accuracy of modal superposition rule of complex complete quadratic combination (CCQC), a new time-dependent CCQC(t) algorithm is derived by using a determinate envelope function to modulate a stationary random white noise process and remaining other assumptions same as normal CQC method. The proposed time-dependent CCQC(t) method needs to calculate the variances, covariance, and cross variances for different modes as time functions. For CCQC(t) method, the cross variances between a pair of two different modes are usually named cross correlation coefficients and play very important role in estimation of maximum responses just as for CQC method, but in this case the cross correlation coefficients are time dependent. Moreover, CCQC(t) and CQC(t) methods need to define envelop function and to calculate the corresponding non stationary seismic response rather than CCQC and CQC methods where only stationary steady-state responses are concerned. Hence, the analyses and computations related to envelop function in CCQC(t) and CQC(t) methods also play very a important role in this article. Several closed form formulas of time-dependent variances and cross variances are derived by using integration technique developed in time domain for four popularly used envelope functions. In order to verify these closed form formulas deduced in this article, we use four different envelope functions to fit identical envelope curve of real acceleration time history and then to carry out numerical analyses for certain examples. The numerical analysis based on proposed CCQC(t) algorithm shows that all the seismic responses of the examples computed from the adopted four different envelope functions which are used to depict same envelop curve of input acceleration are almost the same. The example analyses also show that for normal structure and ground motion input the discrepancy of the maximum seismic responses calculated from CCQC(t) and CCQC methods for non classically damped linear system and that from CQC(t) and CQC methods for classically damped linear system is of insignificance because the occurrence times of the variance responses and cross covariance responses usually concentrate within very narrowed time interval and close to the peak value location of the input motion at time axis. Further analyses show that the significance of the non stationarity mainly depends on how far the peak value arrival times of the modal responses shift each other and how sharper the shape of the envelop of input motion. Generally speaking, the larger the peak values arrival time shift and the sharper the shapes of the different modal response envelops, the greater the influence of non stationarity of ground motion on the results of mode superposition based on response spectra. These results are obtained on the basis of white noise input assumption. In addition, it is also shown that if using colorful spectrum such as Kanai power spectrum density function to replace white noise to simulate the power spectrum of the input acceleration records, the results coming from both CCQC(t) and CCQC methods may be improved to certain degree.

Precise integration strategy for aseismic LQG control of structures

Although LQG regulators have been used in many engineering fields, the relevant control technique still requires further development, particularly when the disturbances are random and non-stationary. Therefore this paper presents a new method for non-stationary seismic random excitations in which LQG control is applied to adjacent tall buildings which are connected together by active hydraulic actuators. The ground motion is induced by non-stationary uniformly modulated white noise excitation of the bedrock which passes through a single layered soil which is regarded as a single-peak filter. This represents an advance on other papers in the literature, which use stationary random white noise or filtered white noise as the ground excitation. The method uses the pseudo excitation method in conjunction with two different precise integration schemes to analyse structural non-stationary seismic random responses via solution of the differential Riccati equations of this transient LQG control process. Unlike previous work in the literature, the performance index used has a finite time region, rather than an infinite one. Reasonable control effects are demonstrated via numerical simulation for two adjacent 20-storey buildings which are connected by hydraulic activators. Copyright © 2006 John Wiley & Sons, Ltd.

Consistency of the LSE in Linear regression with stationary noise

We obtain conditions for $L_2$ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure $L_2$-consistenc

Predictive self-organizing map for vector quantization of migratory signals and its application to mobile communications

This paper proposes a predictive self-organizing map (P-SOM) that performs an adaptive vector quantization of migratory time-sequential signals whose stochastic properties such as average values of signals in each cluster are varying continuously. The P-SOM possesses not only the weight corresponding to the signal values themselves but also those related to the time-derivative information. All the weights self-organize to predict appropriate future reference vectors. The prediction using the time-derivative weights enables the separation of continuously varying components form random noise components, resulting in a better performance of the adaptive vector quantization. That is to say, the stationary random noise components are captured by the ordinary weights, whereas the migrating components are captured by the first (and higher) order time-derivative ones. An application to a mobile communication receiver using quasi-coherent detection is presented. By utilizing both the ordinary and time-derivative weights consistently, the P-SOM generates a predictive reference vectors and quantizes the migratory signals adaptively. Simulation experiments on the bit-error rates (BERs) demonstrate that a P-SOM adaptive demodulator has a superior capability to track phase rotations caused by the Doppler effect. A theoretical noise analysis is also reported for the conventional SOM and the P-SOM. It is found that the calculation results are approximately in good agreement with the experimental ones.

TIME SCALE APPROACH FOR CHIRP DETECTION

Two different approaches for joint detection and estimation of signals embedded in stationary random noise are considered and compared, for the subclass of amplitude and frequency modulated signals. Matched filter approaches are compared to time-frequency and time scale based approaches. Particular attention is paid to the case of the so-called "power-law chirps", characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered.

Confidence intervals of Leq in the case of stationary random noise measurements.

A common practice in random noise measurements is to assume that the noise samples are normally distributed. Since the sound pressure level (Lp) is related with the sound energy by a non linear equation, the distribution of the two variables will be different. If one assumes that the probability density function (pdf) of Lp is normal, the pdf of noise energy is not and vice versa. A simple criterion based on statistical properties of sampled noise can be used for the determination of the kind of distribution of the measured noise. The case in which the noise energy emitted by the source, and the case in which the measured noise level is normally distributed are examined. For each case confidence intervals of the calculated equivalent level are calculated.