Deterministic Part Research Articles

Distinguishing the Plateau and Valley Components of Profiles From Various Types of Two-Process Textures

Abstract This paper presents methods of separating the plateau part for various types of two-process profiles, having the traces of two processes. The traditional method based on the plateau-valley threshold, according to the ISO 13565-3 standard, is not always sufficient, since the valley portion can include plateau roughness. Starting and finishing points of each plateau in the measured profiles should be determined. The procedure found in the technical literature depends on setting not only the plateau-valley threshold but also a lower threshold. This approach was a little modified for profiles that contain both random and deterministic topography components. A new procedure of determination of the lower threshold was proposed for stratified profiles containing two deterministic parts. The valleys can be characterized by their widths and the distance between them. In addition, a description of the material probability curve is proposed.

Robust stabilization of hybrid uncertain stochastic systems by discrete‐time feedback control

SummaryThis paper aims to stabilize hybrid stochastic differential equations with norm‐bounded uncertainties by feedback controls based on the discrete‐time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of a stochastic differential equations, and the controlled system will be robustly exponentially stable in mean square. Our stabilization criteria are in terms of linear matrix inequalities whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.

Diagnostics of calibration methods: model adequacy of UV‐based determinations

Models such as ordinary least squares, independent component analysis, principle component analysis, partial least squares, and artificial neural networks can be found in the calibration literature. Linear or nonlinear methods can be used to explain the structure of the same phenomenon. Each type of model has its own advantages with respect to the other. These methods are usually grouped taxonomically, but different models can sometimes be applied to the same data set. Taxonomically, ordinary least square and artificial neural network use completely different analytical procedures but are occasionally applied to the same data set. The aim of the study of methodological superiority is to compare the residuals of models because the model with the minimum error is preferred in real analyses. Calibration models, in general, are based on deterministic and stochastic parts; in other words, the data are equal to the model + the error. Explaining a model solely using statistics such as the coefficient of determination or its related significance values is sometimes inadequate. The errors of a model, also called its residuals, must have minimum variance compared to its alternatives. Additionally, the residuals must be unpredictable, uncorrelated, and symmetric. Under these conditions, the model can be considered adequate. In this study, calibration methods were applied to the raw materials, hydrochlorothiazide and amiloride hydrochloride, of a drug, as well as a sample of the drug tablet. The applied chemical procedure was fast, simple, and reproducible. The various linear and nonlinear calibration methods mentioned above were applied, and the adequacy of the calibration methods was compared according to their residuals.

Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation.

Brownian particles interacting via repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We study this phenomenon in low-dimensional situations (one and two dimensions) at two levels of description: by performing numerical simulations of the discrete particle dynamics and by linear and nonlinear analysis of the corresponding Dean-Kawasaki equation for the macroscopic particle density. Restricting to low dimensions and neglecting fluctuation effects, we gain analytical insight into the mechanisms of the instability leading to clustering which turn out to be the interplay among diffusion, the intracluster forces, and the forces between neighboring clusters. We show that the deterministic part of the Dean-Kawasaki equation provides a good description of the particle dynamics, including width and shape of the clusters and over a wide range of parameters, and analyze with weakly nonlinear techniques the nature of the pattern-forming bifurcation in one and two dimensions. Finally, we briefly discuss the case of attractive forces.

PC expansion for material parameters using artificial data and statistical methods

AbstractThis paper investigates the uncertainty of a hyper‐elastic model by random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data in combination with artificial data for elastomers the distribution of the force‐displacement curves are known. In the numerical example the PC‐based stochastic and the deterministic parameter identification are used for generation of the distribution of Ogden's material parameters. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Regularity of stochastic Volterra equations by functional calculus methods

We establish pathwise continuity properties of solutions to a stochastic Volterra equation with an additive noise term given by a local martingale. The deterministic part is governed by an operator with an {H^infty}-calculus and a scalar kernel. The proof relies on the dilation theorem for positive definite operator families on a Hilbert space.

The Foraging Brain: Evidence of Lévy Dynamics in Brain Networks.

In this research we have analyzed functional magnetic resonance imaging (fMRI) signals of different networks in the brain under resting state condition. To such end, the dynamics of signal variation, have been conceived as a stochastic motion, namely it has been modelled through a generalized Langevin stochastic differential equation, which combines a deterministic drift component with a stochastic component where the Gaussian noise source has been replaced with α-stable noise. The parameters of the deterministic and stochastic parts of the model have been fitted from fluctuating data. Results show that the deterministic part is characterized by a simple, linear decreasing trend, and, most important, the α-stable noise, at varying characteristic index α, is the source of a spectrum of activity modes across the networks, from those originated by classic Gaussian noise (α = 2), to longer tailed behaviors generated by the more general Lévy noise (1 ≤ α < 2). Lévy motion is a specific instance of scale-free behavior, it is a source of anomalous diffusion and it has been related to many aspects of human cognition, such as information foraging through memory retrieval or visual exploration. Finally, some conclusions have been drawn on the functional significance of the dynamics corresponding to different α values.

The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

The article extends the previous Hylleberg, Engle, Granger, and Yoo seasonal unit-root test commands (Baum and Sperling, 2001, https://ideas.repec.org/c/boc/bocode/s416502.html ; Depalo, 2009, Stata Journal 9: 422–438), which allow for the use of both quarterly and monthly data. It is also possible to choose between ordinary least-squares and generalized least-squares detrending (Rodrigues and Taylor, 2007, Journal of Econometrics 141: 548–573) procedures to deal with the deterministic part of the process. The command allows for the use of the sequential method proposed by Hall (1994, Journal of Business and Economic Statistics 12: 461–470) and Ng and Perron (1995, Journal of the American Statistical Association 90: 268–281), the adaptation of the modified Akaike information criteria to the case of seasonal unit-root tests (del Barrio Castro, Osborn, and Taylor, 2016, Econometric Reviews 35: 122–168) as well as the inclusion of Akaike information and Bayesian information criteria to determine the order of augmentation of the serial correlation in the augmented Hylleberg, Engle, Granger, and Yoo regression. Finally, the use of the command is illustrated with an empirical application to the case of monthly passenger airport arrivals to Palma de Mallorca.

Improving condition indicators for helicopter health and usage monitoring systems

Purpose – The purpose of this paper is to suggest new method for improving the condition indicators (CIs) used in health and usage monitoring system based on signal separation of gears. Design/methodology/approach – The research method is based on employing signal separation techniques to improve gears signal and fault signature. The signal separation is based on adaptive filters concept. Findings – CIs estimated for the deterministic part of vibration signal show higher sensitivity to gears faults in comparison to indicators estimated based on the original signal. This method proposed could enhance early fault detection in gears, particularly for those applications where strong background noise from other sources in the machine masks the characteristics fault components. Originality/value – The contribution of this research is improving the CIs currently used for helicopter gearboxes. As consequence the safe operation and availability will be improved.

Envelope analysis of rotating machine vibrations in variable speed conditions: A comprehensive treatment

Nowadays, the vibration analysis of rotating machine signals is a well-established methodology, rooted on powerful tools offered, in particular, by the theory of cyclostationary (CS) processes. Among them, the squared envelope spectrum (SES) is probably the most popular to detect random CS components which are typical symptoms, for instance, of rolling element bearing faults. Recent researches are shifted towards the extension of existing CS tools – originally devised in constant speed conditions – to the case of variable speed conditions. Many of these works combine the SES with computed order tracking after some preprocessing steps. The principal object of this paper is to organize these dispersed researches into a structured comprehensive framework. Three original features are furnished. First, a model of rotating machine signals is introduced which sheds light on the various components to be expected in the SES. Second, a critical comparison is made of three sophisticated methods, namely, the improved synchronous average, the cepstrum prewhitening, and the generalized synchronous average, used for suppressing the deterministic part. Also, a general envelope enhancement methodology which combines the latter two techniques with a time-domain filtering operation is revisited. All theoretical findings are experimentally validated on simulated and real-world vibration signals.

Fluctuation analysis of high frequency electric power load in the Czech Republic

We analyze the electric power load in the Czech Republic (CR) which exhibits a seasonality as well as other oscillations typical for European countries. Moreover, we detect 1/f noise property of electrical power load with extra additional peaks that allows to separate it into a deterministic and stochastic part. We then focus on the analysis of the stochastic part using improved Multi-fractal Detrended Fluctuation Analysis method (MFDFA) to investigate power load datasets with a minute resolution. Extracting the noise part of the signal by using Fourier transform allows us to apply this method to obtain the fluctuation function and to estimate the generalized Hurst exponent together with the correlated Hurst exponent, its improvement for the non-Gaussian datasets. The results exhibit a strong presence of persistent behaviour and the dataset is characterized by a non-Gaussian skewed distribution. There are also indications for the presence of the probability distribution that has heavier tail than the Gaussian distribution.

Channel Coordination in a Multi-Period Newsvendor Model with Dynamic, Price-Dependent Stochastic Demand

In this study, we extend the single-period newsvendor problem with stochastic demand into a multi-period and time-dependent one and find a solution for it. We analyze the multi-period newsvendor problem with stochastic demand in a Stackelberg framework where the wholesaler is the leader and the retailer (newsvendor) is the follower. We use an additive-multiplicative structure for the demand so that both its mean and variance are considered as functions of the current retail price. Moreover, in our model, the demand mean and variance can be either time-dependent or autonomous with respect to time. A price-dependent memory function is also embedded in this representation of demand that carries the effect of demand level at present over to the demand in future. This leads to a strategic game in which the players must balance immediate high profits with reduced future earnings. We propose a complete solution to this stochastic multi-period Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using Cobb-Douglas demand functions as the deterministic part, while a random variable brings in stochasticity into the model. Because our theory is very flexible with respect to the assumptions made about the demand, market memory, and the behavior of the two agents, it is applicable to a wide variety of functional forms and capable to model many different economic contexts.

Discriminating between the UV-A, UV-B and UV-C regions by novel Biologically Inspired Photochromic Fuzzy Logic (BIPFUL) systems: A detailed comparative study

This work presents the analysis of the deterministic part of human colour perception at the computational, algorithmic and implementation levels. At the computational and algorithmic levels, we invoke the theory of Fuzzy sets. At the implementation level, we present Biologically Inspired Photochromic Fuzzy Logic (BIPFUL) systems that are useful to discriminate between the three regions of the UV spectrum (UV-A, UV-B and UV-C). Such BIPFUL systems have been devised by imitation of the human photosensitive system on retina. After transforming the absorption spectra, originated by the BIPFUL systems under UV-A, UV-B and UV-C, in chromaticity coordinates and vectors in CIE L*a*b* spaces, we have compared their performances through the determination of two parameters: The Colourability and the Eucledian distance. Finally, the guiding principles for the design of new BIPFUL systems are outlined.

Modeling of the Trajectory of the Level Fluctuations in Lake Naroch

Abstract As a result of the conducted investigations of the level fluctuations in lake naroch the initial data are divided into 3 components: a polynomial regression that makes it possible to find out an independent on time law of trajectory, a periodic component of sinusoidal type and a residual sequence of independent random quantities. Modeling of the trajectory fluctuations is based on the deterministic part, consisting of the regression of the 8th order and periodic component, and also the random part, consisting of independent equally distributed quantities. Using this model it can be modeled the trajectory of the level fluctuations in lake naroch. The modeled trajectory by 200 years long demonstrated the probability of exceeding of maximum annual level, equal 1 per cent.

An extension of the asymmetric causality tests for dealing with deterministic trend components

ABSTRACTThis article extends the asymmetric causality tests, as developed by Hatemi-J (2012), for dealing with deterministic trend parts. It is shown how integrated variables up to three degrees with deterministic trend parts can be transformed into positive and negative cumulative partial components. These cumulative components can be used for implementing the asymmetric causality tests based on a Wald test statistic that is shown to follow a chi-square distribution asymptotically. Each solution is expressed as a proposition and a mathematic proof is provided for each underlying proposition. This issue is important because most economic or financial variables seem to be characterized by both stochastic as well as deterministic trend parts. An empirical application is provided in order to show how the oil prices and the exchange rates as integrated variables with drift and trend can be transformed into cumulative partial sums of positive and negative components. The conducted causality tests reveal that allowing for asymmetry has important repercussions for the underlying causal inference between these two variables.

Investigation of long-range dependencies in the stochastic part of daily GPS solutions

The long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series we used more than 130 ASG-EUPOS (active geodetic network EUPOS) stations from an area of Poland with a 5-year span of the daily topocentric coordinate changes. The deterministic part of time series was removed by means of the least-squares (LS) method, median absolute deviation (MAD) criterion and the sequential t-test algorithm, respectively. Then the self-similarity of the residue was proved by the results of the Ljung–Box test, whose values close to zero showed the dependence of the stochastic part of the GPS time series. The residue was analysed by means of the rescaled range (R/S) method with the H (Hurst) parameter and the detrended fluctuation analysis (DFA) with the scaling exponent α. Both H and α values ranged within assumed LRD limits of 0.5 and 1. This analysis was followed by noise investigation with a maximum likelihood estimation (MLE). The white plus the power-law noise models were assumed a priori, which gave us a spectral indices κ between − 0.4 and − 1.2 for all of the time series. It proved that fractional white noise outweighs other types of noises in GPS time series. Authors found here, that the LRD methods by omitting the noise amplitude data led to an underestimation of H values and their misinterpretation. The larger the omitted amplitude is, the greater the difference between the noise characters estimated with R/S values in comparison to the reference values of κ are. Some of these differences exceed even the value of 0.6, which may result in the estimation of false noise character in GPS data thus eliciting wrong conclusions.

Stochastic simplified modelling of abrasive waterjet footprints.

Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling.

Estimation of insurance-related losses resulting from coastal flooding in France

Abstract. A model has been developed in order to estimate insurance-related losses caused by coastal flooding in France. The deterministic part of the model aims at identifying the potentially flood-impacted sectors and the subsequent insured losses a few days after the occurrence of a storm surge event on any part of the French coast. This deterministic component is a combination of three models: a hazard model, a vulnerability model, and a damage model. The first model uses the PREVIMER system to estimate the water level resulting from the simultaneous occurrence of a high tide and a surge caused by a meteorological event along the coast. A storage-cell flood model propagates these water levels over the land and thus determines the probable inundated areas. The vulnerability model, for its part, is derived from the insurance schedules and claims database, combining information such as risk type, class of business, and insured values. The outcome of the vulnerability and hazard models are then combined with the damage model to estimate the event damage and potential insured losses. This system shows satisfactory results in the estimation of the magnitude of the known losses related to the flood caused by the Xynthia storm. However, it also appears very sensitive to the water height estimated during the flood period, conditioned by the junction between seawater levels and coastal topography, the accuracy for which is still limited by the amount of information in the system.

Realistic Hodgkin–Huxley Axons Using Stochastic Behavior of Memristors

Ion-channel variability has critical effect on the spike initiation and propagation in nervous system. Noise can play a constructive role leading to increased reliability or regularity of neuronal firing and spike propagation in the nervous system. In this paper we show that memristors can be considered as an electronic analogous of the Hodgkin–Huxley ion channels not only in terms of threshold switching effect but also in terms of stochastic behavior. In other words, memristor can also implement stochastic version of Hodgkin–Huxley equation. Switching effect in memristive devices is thermodynamically driven, which is stochastic in nature. We show that if the intrinsic stochastic behavior of memristor is taken into account, memristor based neuristor can also implement stochastic version of Hodgkin–Huxley axon model in generation of action potential. Ion channel variability in neurons can be modeled by intrinsic stochastic behavior of memristor. We incorporate noise in the memristor model by adding white Gaussian noise to the deterministic part of dynamical state evolution function of the memristor. We study the reliability of spike timing for spike train generated by memristor based neuristor in which the noise included memristor model is used. Also, the reliability of spike propagation along thin axons is discussed. A series connection of neuristors can be used as an axon in which neuristor acts as a node of Ranvier on an axon. Probabilistic nature of spike propagation on thin axons can be modeled using neuristor in which the variability nature of memristor is included.

Two-Stage Explicit Stochastic Rational Runge-Kutta Method for Solving Stochastic Ordinary Differential Equations

This paper discussed the derivation of two-stage explicit St ochastic Rational Runge-Kutta (SRRK) methods for the solution of stochastic first order ordin ary differential equations. The derivation is based on the use of Taylor series expansion for the deterministic and stochastic parts of the stochastic differential equation. Efforts were made to analyse the stability of the methods and also applied the methods to test some numerical problems to solve Stochas tic Differential Equations (SDE). From the results obtained it is obvious that the methods derived performe d better than the ones with which we compared our results.