Random Process Model Research Articles

Developing an algorithm for planning the periodicity of controls for a random process model

The problem of forecasting the beginning of the repair effects of equipment under the action of degradation processes was considered. The possibility of using the theory of emissions that form a non-stationary Poisson flow to establish the inspection interval was studied. It was found that when using the theory of emissions while assigning inter-control periods, it is necessary to compare paired correlation coefficients, one of which is r1,δ>>0.9 and tends to unity.

Построение моделей и статистическая оценка параметров надежности судовых технических средств

A method is proposed to solve the problems that arise when analyzing information obtained from various sources, it is necessary to combine it in a complex of coordinated stochastic models. For most processes of mechanical destruction of machine parts, such as wear, fatigue volumetric or surface destruction, corrosion, etc., the monotony of the implementation of degradation processes leading to failures is characteristic. The scheme of resource allocation formation is given, which corresponds to the main types of mechanical failures occurring in the elements of ship mechanisms. The diagram illustrates a fairly general case when, with an increase in the operating time of an element, its resistance to destruction decreases monotonously, and the damage parameter also increases monotonously. Based on the use of generalized distributions, it is possible to obtain several variants of complexes of mechanical reliability models in which the resource allocation has a fairly simple analytical form. When modeling degradation processes, the DM distribution can be obtained as a special case of distributions and without using the Markov model of random processes. Only the mixing condition of the process implementations is essential. Obtaining various types of operating time distributions before the parameter reaches a fixed level using the obtained dependencies is not associated with any assumptions about the nature of individual implementations of the degradation process, except for their monotony. From the point of view of practical application, the distribution under consideration, obtained on the basis of Weibull’s law, has the advantage of universality, since, unlike the normal law, it can also be used for values of the coefficient of variation significantly exceeding 0.3.

Synthesis of Itˆo Equations for a Shaping Filter with a Given Spectrum

The analytical method for the synthesis of a generator of a random process with a given spectrum in the form of a linear system of Ito’s equations is proposed. The stationarity of a random process is assumed, the spectral and corresponding transfer functions of which are defined in the form of rational fractions. The coefficients of the system of Ito’s equations of the generator are found from recurrent algebraic relations. The method is focused on working with mathematical models of nature random processes, such as the Dryden’s wind model. The transformation of the spectra of the wind gust model in three directions is presented in detail and the corresponding stochastic equations are given.

Machine learning predictive model for dynamic response of rising bubbles impacting on a horizontal wall

The integrated behavior of the fluid flow, encompassing variation of some specific response, has received more attention than mere examination of velocity and pressure distributions. A machine learning framework is introduced for the first time to elucidate and predict the complex fluid dynamic responses across varying time scales. For the same class of fluid processes, the dynamic response curves with varying time durations can be defined in terms of time scales and curve shapes. The former is predicted by a single-objective regression model, and the curves are normalized and recovered using time scaling and uniform interpolation. The latter are downscaled by Principal Component Analysis (PCA) and then predicted by a multi-objective regression model. As a novel application, this framework is employed to analyze small bubbles in a Newtonian fluid as they impact a horizontal wall, predicting the velocity, aspect ratio, and position dynamic response of the bubbles. Both Random Forest and Gaussian Process models, based on PCA-driven data processing, exhibit remarkable accuracy in describing and predicting complex dynamics of rising bubbles. Notably, PCA's principal components demonstrate independence and are set through rigorous cross-validation of the training set, rather than dependence on the Cumulative Variance Explained (CVE) values. Furthermore, our framework adeptly extends to predict the complex behavior of multiple bubble bounces by concatenating individual bounce predictions with high efficiency and precision. The proposed framework proves to be a catalyst for comprehending the dynamic response of fluids.

Model-data hybrid driven approach for remaining useful life prediction of cutting tool based on improved inverse Gaussian process

In the cutting process, reasonable evaluation of tool remaining useful life (RUL) is essential to ensure machining stability and safety. However, traditional data-driven methods rely on datasets with complete degradation data and prior knowledge, which are usually difficult to obtain in real scenarios. For these problems, this paper proposed a model-data hybrid driven approach for RUL prediction of cutting tool based on improved inverse Gaussian process. The tool wear degradation is considered as a random process, the cutting physical model and the data-driven stochastic process model are fused, so that the prior knowledge from the physical model and the statistical law of measured data are fully utilized to improve the accuracy of tool RUL prediction. The cutting physical model is established, and the prior knowledge of tool wear degradation is obtained based on physical simulation method. A data-driven random effects inverse Gaussian process model is constructed for tool RUL modeling and prediction. According to Bayesian method, the unknown parameters are estimated and updated integrating physical simulated and measured wear data, so as to obtain the probability density function for specific tool RUL, and quantify the prediction uncertainty. Finally, comparative experiments are conducted to validate the performance of the proposed method. The results suggest that the hybrid approach has the best performance in different tool RUL prediction.

Research on modal combination coefficients considering the spectral characteristics of strong ground motion

To address the limitations of traditional complete quadratic combination (CQC) modal combination coefficients in calculating ground motions with narrow bandwidth and long periods, a revised methodology is proposed. The new CQC modal combination coefficients are formulated by considering the spectral characteristics of strong ground motion, taking the modified Kanai-Tajimi spectrum model as a prerequisite, and applying random vibration theory. Simultaneously, a random phase simple harmonic process model for a single harmonic component is established, and corresponding combination coefficients are provided. The necessity and rationality of considering the spectral characteristics of strong ground motion are demonstrated from three perspectives: differences in power spectral models, variations in combination coefficients, and the inherent combination mechanism. As an illustrative example, the layer shear model is analyzed and compared with the results of the structure's modal combination taking different combination coefficients. This comparison is conducted under the influence of long-period simple harmonic waves, four natural seismic waves in the basin, and the 50 natural ground motions suggested by ATC-63, respectively. The results indicate that the modal combination coefficients developed by considering the spectral characteristics of strong ground motions are more reasonable and can serve as a viable replacement for traditional CQC combination rules. This is especially advantageous when dealing with ground motion inputs characterized by narrow bandwidth and long periods, providing significant benefits in such scenarios.

Probabilistic models applied to concrete corrosion depth prediction under sulfuric acid environment

Accurate prediction of corrosion depth degradation law can provide a basis for the determination of the sacrificial layer thickness and the cover thickness of the concrete structural members in a corrosive environment. This study aims to explore a more accurate and safe method to predict corrosion depth. Six sets of concrete cylinder concrete specimens were adopted to perform an accelerated corrosion test in sulfuric acid solution with pH ≈ 0.95 for six different scheduled durations. 3D coordinates of a large number of points on the corroded cylindrical surface were obtained with the help of the 3D laser scanning technology. Then, a comparative study was carried out for the corrosion depth measured with the laser scanning method and vernier caliper method. The results prove that concrete corrosion depth predicted by the Gaussian random process model established by the laser scanning method was considered to possess higher credibility and better security.

Improved data quality and statistical power of trial-level event-related potentials with Bayesian random-shift Gaussian processes

Studies of cognitive processes via electroencephalogram (EEG) recordings often analyze group-level event-related potentials (ERPs) averaged over multiple subjects and trials. This averaging procedure can obscure scientifically relevant variability across subjects and trials, but has been necessary due to the difficulties posed by inference of trial-level ERPs. We introduce the Bayesian Random Phase-Amplitude Gaussian Process (RPAGP) model, for inference of trial-level amplitude, latency, and ERP waveforms. We apply RPAGP to data from a study of ERP responses to emotionally arousing images. The model estimates of trial-specific signals are shown to greatly improve statistical power in detecting significant differences in experimental conditions compared to existing methods. Our results suggest that replacing the observed data with the de-noised RPAGP predictions can potentially improve the sensitivity and accuracy of many of the existing ERP analysis pipelines.

Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.

Developing the health effect assessment of landscape (HEAL) Tool: Assessing the health effects of community greenspace morphology design on non-communicable diseases

Neighborhood greenspace benefits health, yet few tools are available for estimating the health consequences of community greenspace design alternatives, especially prior to the implementation of a landscape design plan. Herein we present a machine learning based tool for predicting the prevalence of non-communicable diseases based on landscape design maps at the community scale. We achieve this based on data collected in five major metropolises in the United States. By using high-resolution satellite imagery and remote sensing technologies, landscape spatial design characteristics were extracted through spatial pattern analysis, allowing the measurement of verdancy, fragmentation, connectedness, aggregation, and shape of greenspaces. We established a model to estimate the prevalence of poor mental health, coronary heart disease, stroke, diabetes, chronic obstructive pulmonary disease, and physical inactivity at the census tract level by adopting a combination of random forest decision tree algorithm and spatial Gaussian process models. Model accuracy was found to be significantly higher than ordinary regression models. The model accounted for very high levels of variance in the specified morbidities; viz., poor mental health (97%), heart disease (93%), stroke (93%), diabetes (95%), COPD (94%), and physical inactivity (98%). This tool is implemented using a freely available programming language (R), and we offer the model accessible to the public. This tool enables urban planners and landscape designers to assess and compare the health effects of different greenspace design plans prior to implementation, thus providing policymakers and designers with evidence-rich alternatives during the health-promoting greenspace planning process.

АСИМПТОТИЧНІ ВЛАСТИВОСТІ ВИПАДКОВИХ МАТРИЦЬ

The work explores the asymptotic properties of large-dimensional stochastic matrices N under the condition of independence of matrix elements or rows (columns). An analysis of the main properties of eigenvalues of stochastic matrices is conducted. The work is dedicated to investigating the asymptotic characteristics of random matrices under the absence of the second moment and also considers the presence of "heavy tails" in the corresponding transitions in the adjacency matrices of the respective graph. The main result of the work is formulated in terms of the transition matrix of a discrete Markov chain and its eigenvalues. In proving the theorem, a non-degenerate Markov chain is considered, describing a mathematical model of random processes that do not change over time with known transition probabilities between states and a corresponding stochastic matrix P, one of whose eigenvalues is unity, and all eigenvalues of the stochastic matrix do not exceed it in absolute value. The proof of this fact follows from the Perron–Frobenius theorem, which concerns the properties of positive matrices and their eigenvalues. Thus, the theorem considered manages to expand the class of random matrices A for which convergence of eigenvalues of the matrix can be applied under the conditions imposed on the elements of the adjacency matrix. Moreover, the imposed conditions are relaxed compared to classical results, where the existence of a finite second moment for the elements of the adjacency matrix is required. This result generalizes both classical results for the normal distribution and similar results of other authors. The obtained result can be used in graph clustering problems to choose the optimal number of clusters, namely, they can be applied to determine the optimal number of clusters in a Grid system, complex networks, in investigations of the structure of the web space, etc.

ОБНАРУЖЕНИЕ РАЗЛАДОК В НЕСТАЦИОНАРНЫХ РЯДАХ НАБЛЮДЕНИЙ: ОБЗОР ТЕХНОЛОГИЙ И КРИТИЧЕСКИЙ АНАЛИЗ

A critical analysis of modern mathematical technologies used to solve the problem of nonstationary time series change point, taking into account the chaotic nature of the observed processes, is considered. The known methods of the quickest change point detection in nonstationary time series described by traditional models of random processes are considered as initial assumptions. The discrepancy between the known time series observation models and the real processes occurring in unstable immersion environments described by the concept of stochastic chaos is shown. Time series segmentation technologies based on a posteriori analysis of changes in the properties of observation sites of chaotic processes are presented. Options for building online algorithms for the quickest change point detection based on methods of multiregressive data analysis and metric machine learning technologies are considered.

Scale-dependent power law properties in hashtag usage time series of Weibo

We analyze the time series of hashtag numbers of social media data. We observe that the usage distribution of hashtags is characterized by a fat-tailed distribution with a size-dependent power law exponent and we find that there is a clear dependency between the growth rate distributions of hashtags and size of hashtags usage. We propose a generalized random multiplicative process model with a theory that explains the size dependency of the fat-tailed distribution. Numerical simulations show that our model reproduces these size-dependent properties nicely. We expect that our model is useful for understanding the mechanism of fat-tailed distributions in various fields of science and technology.

Advantages of periodic non-stationary random process model in vibration signal processing

The use of two different techniques for the analysis of vibration signals, whose carrier harmo¬nics are modulated by high-frequency narrow-band random processes is discussed. Periodically non-stationary random processes (PNRP) are suitable models for description of vibration signals of damaged mechanism. A proposed processing technique can be considered as an alternative to squared envelope analysis, kurtosis techniques, squared envelope spectrum (SES) and its use in the analysis of a vibration signal is discussed. It is shown that the spectral estimates obtained by the envelope square method are biased and inconsistent. The possibility of obtaining of the unbiased estimates by the PNVP method even for a signal/noise ratio equal to 0.07 has been demonstrated.

A Reliability Evaluation Method for Gamma Processes with Multiple Random Effects

The multi-random-effects gamma process has a better characterization effect for degraded data with individual differences. In this paper, a reliability evaluation method for gamma stochastic processes with multiple random effects is studied. The mathematical model of multiple random effects gamma process was established. The model parameters estimation method was established based on the Bayesian approach. The prior distribution acquisition method was discussed, and the parameters of the multiple randomeffects gamma process were estimated by the MCMC-Gibbs method. The correctness of the model and method was verified by numerical simulation, the influence of algorithm parameters on the algorithm solving process was studied. In the fourth part, the reliability of aviation hydraulic rotary joints was studied by using multiple random effects gamma processes.

Secrecy Analysis of DCSK-Based PLC Systems With Multiple Eavesdroppers

In the past two decades, chaotic modulation schemes have drawn much attention for their significant advantages over other traditional modulation techniques. One of the noticeable advantages is the capability of providing secure communication in the presence of an eavesdropper. In this article, we study the physical layer security (PLS) performance of low-frequency power line communication (PLC) systems against multiple eavesdroppers by employing differential chaos shift keying based modulation technique. A wiretap power line channel model is investigated by considering two different cases: 1) when all the channels are assumed to be independent and identically distributed (IID) following Log-normal distribution; and 2) the wiretap channels are considered to be identical but correlated Log-normally distributed and independent of the main channel. Contemporaneously, the Bernoulli-Gaussian random process models the PLC noise. Further, a comprehensive PLS study of the considered PLC system is characterized in terms of the average secrecy capacity, secure outage probability, and strictly positive secrecy capacity. We also propose an algorithm to maximize the secrecy throughput under security and reliability constraints. Moreover, to obtain essential insights, we reveal the impact of various crucial parameters onto the proposed system.

Modeling SARS-CoV-2 nucleotide mutations as a stochastic process.

This study analyzes the SARS-CoV-2 genome sequence mutations by modeling its nucleotide mutations as a stochastic process in both the time-series and spatial domain of the gene sequence. In the time-series model, a Markov Chain embedded Poisson random process characterizes the mutation rate matrix, while the spatial gene sequence model delineates the distribution of mutation inter-occurrence distances. Our experiment focuses on five key variants of concern that had become a global concern due to their high transmissibility and virulence. The time-series results reveal distinct asymmetries in mutation rate and propensities among different nucleotides and across different strains, with a mean mutation rate of approximately 2 mutations per month. In particular, our spatial gene sequence results reveal some novel biological insights on the characteristic distribution of mutation inter-occurrence distances, which display a notable pattern similar to other natural diseases. Our findings contribute interesting insights to the underlying biological mechanism of SARS-CoV-2 mutations, bringing us one step closer to improving the accuracy of existing mutation prediction models. This research could also potentially pave the way for future work in adopting similar spatial random process models and advanced spatial pattern recognition algorithms in order to characterize mutations on other different kinds of virus families.

Component Maintenance Strategies and Risk Analysis for Random Shock Effects Considering Maintenance Costs

Maintenance can improve a system’s reliability in a long operation period or when a component has failed. The reliability modeling method that uses the stochastic process degradation model to describe the system degradation process has been widely used. However, the existing reliability models established using stochastic processes only consider the internal degradation process, and do not fully consider the impact of external random shocks on their reliability modeling. Furthermore, the existing theory of importance does not consider the actual factors of maintenance cost. In this paper, based on the reliability modeling of random processes, the degradation rate under the influence of random shocks is introduced into the time scale function to solve the impact of random shocks on product reliability, and two cost importance measures are proposed to guide the maintenance selection of the components under limited resources in the system.Finally, a subsystem of an aircraft hydraulic system is analyzed to verify the proposed method’s performance.

Variance of the number of zeros of dependent Gaussian trigonometric polynomials

We compute the variance asymptotics for the number of real zeros of trigonometric polynomials with random dependent Gaussian coefficients and show that under mild conditions, the asymptotic behavior is the same as in the independent framework. In fact our proof goes beyond this framework and makes explicit the variance asymptotics of various models of random Gaussian processes. Our proof relies on intrinsic properties of the Kac–Rice density in order to give a short and concise proof of variance asymptotics.

Modeling a Hybrid Power System with Intermediate Energy Storage

The purpose of this work is to develop a model for balancing the processes of the generation and consumption of electricity, taking into account the random nature of these processes. The subject of the study is hybrid power systems that use traditional and renewable energy sources and have the properties of a local network. Such systems are sensitive to variable generation modes, and the presence of rapid changes in power requires short time intervals. The presence of wind and solar power plants makes it difficult to ensure a balance of power, which increases the need for intermediate energy storage. The research method is a mathematical modeling of random processes of energy consumption and generation, which allows for the analysis of the current power balancing and the obtaining of the integrated characteristics of the state of energy storage and reuse. The unique goal of the study is to take into account the power gradients and the state of charge of the batteries. The results of the study allow for the comparison of the different configurations of the power system in terms of balance, storage needs, and energy loss. It has been shown that the increase in battery capacity and speed limitations are nonlinearly related to the possibilities of energy conservation and the probability of the incomplete use of the capabilities of the energy storage system.