Uncorrelated Processes Research Articles

Analogies between spectral methods and multiaxial criteria in fatigue damage evaluation

This work aims to emphasize some analogies existing between multiaxial fatigue criteria and spectral methods in the context of fatigue damage assessment for uniaxial stochastic loadings in the frequency domain. Among multiaxial criteria available in literature, attention is focused on the so-called “Projection-by-Projection” (PbP) approach, in which fatigue damage of a multiaxial process is computed by using a non-linear summation rule of single damage contributions of uncorrelated projected loadings. In this work the theoretical framework of PbP method will be used to provide a possible mathematical interpretation of the so-called “single moment” (SM) approach, a spectral method for estimating fatigue damage in uniaxial stochastic loadings that was elaborated in 1990 on a purely “empirical” basis. The idea here formalized is to split the spectrum of a uniaxial process into an infinite set of narrow-band spectral contributions, so to define a set of mutually uncorrelated uniaxial narrow-band stochastic processes. The analogy between the damage of a multiaxial process and that of a uniaxial process split into infinitesimal spectral components is shown. Once the formal analogy between uniaxial and multiaxial spectral methods is established, numerical simulations are used to evaluate the accuracy of SM method with reference to different types of stochastic processes with bimodal spectral density.

Spatial propagation of coherency matrix in polarization optics

In this work, the question of the coherency matrix propagation of a light beam is addressed by means of the analysis of interpolation processes between two physical situations. These physical situations are defined according to the second order statistical properties of the underlying process. Two states of a light beam or the path in a medium to go from a physical situation at distance z(1) to another one at distance z(2) is related to the correlation between both these physical situations. Equivalence classes are derived from the definition of a group action on the set of coherency matrices. The geodesic curves on each equivalence class define the process of interpolation. The general solution is derived as a symbolic equation, and the solution is explicitly developed for the situation of uncorrelated statistical processes. Interpolating coherency matrix in this particular case describes the propagation of a light beam into a uniform nondepolarizing medium characterized by a differential Jones matrix determined by the far points of the interpolation curve up to a unitary matrix.

Total and inelastic cross sections at LHC ats=7 TeVand beyond

We discuss expectations for the total and inelastic cross-sections at LHC CM energies $\sqrt{s}\ =\ 7\ TeV$ {and $ 14\ TeV$} obtained in an eikonal minijet model augmented by soft gluon $k_t$-resummation, which we describe in some detail. We present a band of predictions which encompass recent LHC data and suggest that the inelastic cross-section described by two channel eikonal models include only uncorrelated processes. We show that this interpretation of the model is supported by the LHC data.

Supporting Design and Control of a Reversed‐Phase Chromatography Step by Mechanistic Modeling

AbstractThere is a need to design and understand control strategies for biopharmaceutical processes. The control strategy will influence the design space and process performance and should be chosen together with the operating point and design space. Mechanistic modeling is used to design and evaluate control strategies for product pooling in preparative chromatography. A kinetic dispersive model was calibrated to reversed‐phase chromatography experiments. Uncorrelated process disturbances were introduced to optimized operating points, and the effects of disturbances were evaluated and reduced by control strategies. Pooling control was implemented at a fixed UV absorbance or as a function of retention volume and UV peak height. The higher flexibility of the second control strategy decreased the loss of yield and productivity caused by the disturbances.

Non-Gaussian spatiotemporal modelling through scale mixing

We construct non-Gaussian processes that vary continuously in space and time with nonseparable covariance functions. Starting from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable covariance functions, the resulting models are generalized by allowing for outliers as well as regions with larger variances. We induce this through scale mixing with separate positive-valued processes. Smooth mixing processes are applied to the underlying correlated processes in space and in time, thus leading to regions in space and time of increased spread. An uncorrelated mixing process on the nugget effect accommodates outliers. Posterior and predictive Bayesian inference with these models is implemented through a Markov chain Monte Carlo sampler. An application to temperature data in the Basque country illustrates the potential of this model in the identification of outliers and regions with inflated variance, and shows that this improves the predictive performance.

Reconstruction of Moving Target's HRRP Using Sparse Frequency-Stepped Chirp Signal

This paper introduces a novel reconstruction method of high-resolution range profile (HRRP) using sparse frequency-stepped chirp signal (FSCS). In the method, Compressed Sensing (CS) theory is utilized to reconstruct the moving target's HRRP. With this method even if the subpulses number of FSCS is incomplete, the HRRP can still be reconstructed successfully, and the final reconstructed ISAR image is clear enough for identification and classification of the target. Furthermore, the effect of noise is also analyzed by corrupting the data via an uncorrelated additive white Gaussian process.

Description of stochastic and chaotic series using visibility graphs

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution P(k)∼exp(-λk), where the value of λ characterizes the specific process. The frontier between chaotic and correlated stochastic processes, λ=ln(3/2) , can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series.

A cumulative-summation-based stochastic knock controller

In this paper, an analysis of knock signals suggests that the knock intensity is a cyclically uncorrelated random process, and that it is therefore not possible to control individual cycles to a specified knock intensity in a deterministic manner. A new knock control algorithm is therefore developed on the basis of a stochastic interpretation of the knock signal, and on the basis of a control objective specified as a certain percentage of knocking cycles. Unlike traditional controllers, the new algorithm does not respond to knock events provided that these are occurring within a specified tolerance of the target knock rate. The new controller uses the cumulative summation of knock events to make this determination, thereby avoiding the slow transient response times sometimes associated with ‘stochastic’ knock controllers. When a spark adjustment is deemed necessary, the magnitude of the control action is scaled according to the likelihood ratio of the observed events since the last spark adjustment was made. A theoretical analysis of the new controller is presented and a simulation tool which is closely based on experimental data is used to assess its performance. The results show that the new controller is able to achieve the same target knock rate as a traditional controller while operating at a more advanced mean spark angle. There is also less cyclic variance about this mean and the regulatory response is significantly improved. The transient response to overly advanced or retarded conditions is similar to the traditional controller. These results suggest that the new controller will deliver increased torque and engine efficiency under knock-limited conditions without increasing the risk of engine damage.

Identifying the time of step change in the mean of autocorrelated processes

Control charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process analysts. Change-point methods for the uncorrelated process have been studied extensively in the literature; however, less attention has been given to change-point methods for autocorrelated processes. Autocorrelation is common in practice and is often modeled via the class of autoregressive moving average (ARMA) models. In this article, a maximum likelihood estimator for the time of step change in the mean of covariance-stationary processes that fall within the general ARMA framework is developed. The estimator is intended to be used as an “add-on” following a signal from a phase II control chart. Considering first-order pure and mixed ARMA processes, Monte Carlo simulation is used to evaluate the performance of the proposed change-point estimator across a range of step change magnitudes following a genuine signal from a control chart. Results indicate that the estimator provides process analysts with an accurate and useful estimate of the last sample obtained from the unchanged process. Additionally, results indicate that if a change-point estimator designed for the uncorrelated process is applied to an autocorrelated process, the performance of the estimator can suffer dramatically.

Calculation of delay characteristics for multiserver queues with constant service times

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.

A THEORETICAL ANALYSIS OF MULTISCALE ENTROPY UNDER THE INVERSE GAUSSIAN DISTRIBUTION

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

Influence of tire damping on mixed [formula omitted] synthesis of half-car active suspensions

In this paper, multi-objective control of a half-car suspension system using linear matrix inequalities is studied. It is observed that when tire damping is precisely known, road-holding quality of the suspension system can be improved to some extent by the design procedure while ride comfort and compactness of suspension rattling space are only slightly affected as tire damping coefficients are increased. In the absence of tire damping information, a robust controller is designed for a suspension system with polytopic tire damping uncertainties. In contrast to multi-objective control of quarter-car models with polytopic tire damping uncertainties, this robust design does not offer any advantage over an active suspension system designed by neglecting tire damping. The results, based on the assumption that the front and the rear road velocity inputs are uncorrelated white-noise processes, demonstrate that the body pitch significantly impacts the closed-loop performance of the active suspension system. This implies that decomposition of a half-car model into two independent quarter-car models by a linear transformation is not realistic for a study of the performance limitations and the trade-offs.

Imaging Small PEC Spheres by a Linear $\delta$ Approach

The problem of localizing small inhomogeneities from the knowledge of their scattered field is dealt with. In particular, the case of small perfect electric conducting spheres is of concern, with the scattered field data collected under multistatic/multifrequency/single-view or multistatic/single-frequency/multiview far zone configurations. The multiple scattering between the spheres is neglected, and their locations are represented as the supports of the Dirac delta functions. This allows one to cast the problem as the inversion of a linear integral operator, with the delta functions being the unknowns of the problem. The inversion of this linear integral operator is achieved by means of the truncated singular value decomposition. The performance of the linear inversion algorithm against the model error (i.e., for situations where the multiple scattering is not negligible) is investigated by numerical simulations. Furthermore, the effect of noise is also analyzed by corrupting the data by an uncorrelated additive white Gaussian process.

Real-time recognition of control chart patterns in autocorrelated processes using a learning vector quantization network-based approach

Researchers have been investigating the use of artificial neural networks (NNs) in the application of control chart pattern (CCP) recognition with encouraging results in recent years. Most of the NN models in this field are designed to be used in uncorrelated processes where the process data are independent. Unfortunately, the prerequisite of data independence is not even approximately satisfied in many manufacturing processes. To the best of the author's knowledge, no research results have been published to date on the application of NNs for CCP recognition in autocorrelated processes. This work first shows that autocorrelation in process data greatly affects the performance of NN-based CCP recognizers developed with independent data and then presents a learning vector quantization network-based system that can effectively recognize CCPs in real-time for processes with various levels of autocorrelation. The system performance is evaluated in terms of the classification rate and the average run length. An empirical comparison using simulation indicates that the proposed learning-based system performs better than the traditional control chart methods in detecting shifts when the process data are positively correlated, while it also offers pattern classification. A demonstration example is provided using real data.

Weakened long-range correlation of renal sympathetic nerve activity in Wistar rats after anaesthesia

In this study we employed multiscale entropy (MSE) measurement to assess the long-range temporal correlation (LRTC) of multifibre renal sympathetic nerve activity (RSNA) signals in conscious and anaesthetized Wistar rats. It was found that both groups presented more complex MSE profiles than an uncorrelated process. Moreover, the results of MSE analysis of RSNA demonstrated that the entropy values, derived from the conscious group, increased on small time scales and then stabilized to a relatively constant value, however, the entropy measure, derived from animals with anaesthesia, almost monotonically decreased. The present study shows that while LRTC in the temporal dynamics of energy fluctuations of RSNA does not implicate a unique mechanism, the data for the first time provide evidence of much less temporal correlation in anaesthetized condition. This suggests the fractal properties of underlying dynamical system have been effectively eliminated by anaesthesia. These results demonstrate that apparently random fluctuations in multifibre RSNA are dictated by a complex deterministic process that imparts "long-term" memory to the dynamic system. However, this memory is significantly weakened by anaesthesia.

Statistical properties of short term price trends in high frequency stock market data

We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths were measured. We found that such a distribution does not fit to the results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives a qualitative agreement with the real data.

Reactor noise in accelerator driven systems – II

Reactor Noise in accelerator driven systems (ADS) is expected to show differences from critical or radioactive source driven sub-critical systems due to the periodically pulsed source and its non-Poisson character. A theory of ADS Reactor Noise, incorporating these features was worked out by us and has been published earlier. The present paper is a continuation of the earlier work and constitutes an extension and generalization of the theory. We present theoretical arguments as well as empirical evidence to elucidate the non-Poisson character of the ADS neutron source. We solve the delta-function pulse train problem by treating the source as an exponentially correlated process as against the uncorrelated non-Poisson process considered earlier. In yet another direction, the theory is extended to treat pulses having finite width by describing the source as a doubly stochastic Poisson point process. It is shown that the results of the extended theory reduce to those of our earlier formulation (or to other published results) under appropriate conditions. Evaluation of various descriptors gets simplified by going to the Laplace domain but results in infinite series. Calculations in the time domain are more difficult but yield closed form expressions. We describe both approaches in the course of this paper. We use the Rossi alpha and Feynman alpha formulae, which are evaluated for all the cases considered, for illustrating our approach. In addition to these, we also obtain the auto correlation function, cross-correlation function and the corresponding power spectral in one of the cases. A brief discussion on the various noise techniques vis-a-vis other methods for sub-critical monitoring is included.

Exponential Distribution of Long Heart Beat Intervals During Atrial Fibrillation and Their Relevance for White Noise Behaviour in Power Spectrum

The statistical properties of heart beat intervals of 130 long-term surface electrocardiogram recordings during atrial fibrillation (AF) are investigated. We find that the distribution of interbeat intervals exhibits a characteristic exponential tail, which is absent during sinus rhythm, as tested in a corresponding control study with 72 healthy persons. The rate gamma of the exponential decay lies in the range 3-12 Hz and shows diurnal variations. It equals, up to statistical uncertainties, the level of the previously uncovered white noise part of the power spectrum, which is also characteristic for AF. The overall statistical features can be described by decomposing the intervals into two statistically independent times, where the first one is associated with a correlated process with 1/f noise characteristics, while the second one belongs to an uncorrelated process and is responsible for the exponential tail. It is suggested to use gamma as a further parameter for a better classification of AF and for the medical diagnosis. The relevance of the findings with respect to a general understanding of AF is discussed.

Testing the martingale difference hypothesis using integrated regression functions

An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. A unified approach for dealing with all of these testing problems is proposed. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. In order to circumvent this problem pairwise integrated regression functions are introduced as measures of linear and nonlinear dependence. The proposed test does not require to chose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, the test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then, the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate are investigated.

Two-electron capture with emission of one photon in fast collisions between a highly charged ion and a light atom

We consider the electron capture process in fast non-relativistic ion–atom collisions in which the transfer of two electrons from the atom to the ion is accompanied by emission of one photon with the mean energy ω(2)k about two times larger than that ω(1)k characteristic for the radiative capture of one electron. Such a photon can appear both due to the uncorrelated capture process, in which two electrons are transferred to the ion independently via the non-radiative and radiative capture channels, and due to the correlated two-electron capture, where the electron–electron interaction plays the crucial role. The uncorrelated capture produces a photon spectrum which has a maximum at ω(1)k and gives the main contribution to the two-electron capture. The correlated capture mechanism leads to very small capture cross sections but produces a photon spectrum having a maximum at ∼ω(2)k which in principle enables separation of this process in an experiment.