Stochastic Process Model Research Articles

Enhancing Response Predictions with a Joint Gaussian Process Model for Stochastic Simulation Models

The stochastic Gaussian process model has been widely used in stochastic simulation metamodeling. In practice, the performance of this model can be largely affected by the noise in the observations. In this article, we propose an approach to mitigate the impact of the noisy observations by jointly modeling the response of interest with a correlated but less-noisy auxiliary response. The main idea is to leverage on and learn from the correlated and more accurate response to improve the prediction. To achieve this, we extend the existing deterministic multi-response model for stochastic simulation to jointly model the two responses, use some simplified examples to show the benefit of the proposed model, and investigate the input estimation of this model. Quantile prediction is used to illustrate the efficiency of the proposed approach by jointly modeling it with the expectation, which typically has a less noisy estimator compared with that of the quantile. Several numerical examples are then conducted, and the results show that the joint model can provide better performance. These promising results illustrate the potential of this joint model especially in situations where the response of interest is much noisier or when observations are scarce. We further propose a two-stage design approach based on the multi-response model to more efficiently utilize limited computing budget to improve predictions. We also see from these designs the benefits of the joint model, where the more accurate auxiliary response observations can be used to improve the response of interest.

Generating Stochastic Processes Through Convolutional Neural Networks

The present work establishes the use of convolutional neural networks as a generative model for stochastic processes that are widely present in industrial automation and system modelling such as fault detection, computer vision and sensor data analysis. This enables researchers from a broad range of fields—as in medical imaging, robotics and control engineering—to develop a general tool for artificial data generation and simulation without the need to identify or assume a specific system structure or estimate its parameters. We demonstrate the approach as a generative model on top of data retrieved from a wide set of classic, simplest to the most complex, deterministic and stochastic data generation processes of technological importance—from damped oscillators to autoregressive conditional heteroskedastic and jump-diffusion models. Also, a nonparametric estimation and forecast was carried out for the traditional benchmark “Fisher River” time-series dataset, yielding the superior mean absolute prediction error results compared to a standard ARIMA model. This approach can have potential applications as an alternative to simulation tools such as Gibbs sampling and Monte Carlo-based methods, in the enhancement of the understanding of generative adversarial networks (GANs) and in data simulation for training Reinforcement Learning algorithms.

Ensemble learning for predicting degradation under time‐varying environment

AbstractProduct lifetime prediction is challenging when the product is subject to a time‐varying operational environment. Most of the existing studies use some functions to explicitly specify the relationship between degradation parameters and environmental conditions so as to reveal how the degradation process evolves over time. However, in many applications, the assumptions needed for establishing these functions cannot be validated in engineering practice or they cannot accurately model the entire underlying degradation mechanism. In contrast to previous work, the focus of our study is placed on product degradation prognosis by implementing an ensemble learning method. This method combines the stochastic process modeling approach and the machine learning approach, taking advantage of these approaches to gain a more accurate and stable degradation prediction. The proposed method is demonstrated by some simulation examples and by a case study of lithium‐ion battery accelerated degradation test. Both the simulation study and the real case verify the superiority of the proposed method. The case study indicates that the ensemble learning method can further help to effectively manage the energy storage and energy distribution of battery packs.

Resilience planning in hazards-humans-infrastructure nexus: A multi-agent simulation for exploratory assessment of coastal water supply infrastructure adaptation to sea-level rise

Coastal water supply infrastructure systems are exposed to saltwater intrusion exacerbated by sea-level rise stressors. To enable assessing the long-term resilience of these systems to the impact of sea-level rise, this study developed a novel hazards-humans-infrastructure nexus framework that enables the integrated modeling of stochastic processes of hazard scenarios, decision-theoretic elements of adaptation planning processes of utility agencies, and dynamic processes of water supply infrastructure performance. Using the proposed framework and data collected from South Miami-Dade service area, a multi-agent simulation model was created to conduct exploratory assessments of the long-term resilience of water supply infrastructure under various sea-level rise scenarios and adaptation approaches. The results showed the capability of the proposed model for scenario landscape generation to discover robust adaptation pathways for enhanced infrastructure resilience under uncertainty. The analysis results could provide actionable scientific information to water infrastructure managers to improve their adaptation planning and investment decision-making processes.

Calculation of reliability index for in-plane shear failure of unreinforced masonry walls based on Gaussian process model

The current methods for reliability index calculation are less effective for in-plane shear failure of unreinforced masonry (URM) walls because there is significant uncertainty in the walls’ mechanical parameters and resistance model. To address this issue, the authors propose a new method based on stochastic Gaussian process (GP) model. They conducted in-plane shear resistance experiments on six URM walls and converted the walls’ deterministic shear resistance models to prior GP models, which they updated to posterior models using the experimental results. The posterior GP models specified normal probability density functions (PDFs) for shear resistance of the walls, and the PDFs linearized the walls’ performance functions to the simplest form. With the linearized performance functions, the walls’ failure probability was calculated by direct integration and their reliability indices were determined accordingly. The reliability indices are in good agreement with those given by the Monte Carlo simulation (MCS) using a large number of samples. The proposed method does not deal with high dimensional limit state surfaces, it relieves the influence of uncertainty of the shear resistance model, and it is time-efficient. With these features, the proposed method can facilitate the reliability index calculation for in-plane shear failure of the URM walls.

Long-term resilience and loss assessment of highway bridges under multiple natural hazards

Highway bridges play a significant role in maintaining safety and functionality of the society. The immediate damage of highway bridges caused by natural hazards can disrupt transportation systems, impede rescue and recovery activities. This disruption may result in tremendous financial and societal losses. Therefore, assessing vulnerability, recovery capability, and potential losses of bridges under natural hazards becomes a primary concern to decision-makers to facilitate the emergency response and recovery efforts. Under these concerns, resilience is a paramount performance indicator to evaluate and recover the functionality of structural systems under extreme events. In this article, an integrated framework for long-term resilience and loss assessment of highway bridges under multiple independent natural hazards is presented. The impacts of extreme events such as earthquakes, hurricanes and floods on the life-cycle performance of bridges are illustrated. A stochastic renewal process model of the random occurrence of hazard events is used to compute the expected long-term resilience and damage loss by considering both time-independent and time varying occurrence characteristics. The proposed approach is applied to a bridge by considering the impacts of earthquake and hurricane hazards. The proposed framework can be implemented to the design, maintenance and retrofit optimisation of infrastructure systems under multiple extreme events.

МОДЕЛЮВАННЯ НЕСИМЕТРИЧНО РОЗПОДІЛЕНИХ ПРОЦЕСІВ

The article deals with the problems of modeling asymmetrically distributed stochastic processes and assessing the quality of the modeling process based on the use of the Pearson chi-square criterion. The problems that arise in each individual case of modeling are identified. As a method of generating an output stream of random numbers distributed according to a given law of probability distribution, the method of inverse functions is proposed, and as a generator of the input stream, it is proposed to use a stream generated by the Mersenne generator. The analysis of research methods and evaluation of computer models of stochastic processes is given and the choice of a nonparametric research method based on histograms is substantiated. Suggestions on the choice of their main parameters are provided: the size of the interval for separating the statistical set of values of the output stream of the model and the number of such intervals, calculated on the basis of the size of the statistical sample. It is shown that the quality of statistical material significantly affects the success of modeling. In the case of an asymmetric nature of the distribution of the model's output stream, the accuracy of calculating the chi-square exponent is significantly affected by those values that fall into the extreme intervals of the histogram. It is shown that the reason for this is the incommensurability of their values with the values in the central part of the histogram and this is a separate modeling problem, as a solution to which there can be filtering of the statistical set, preceding the determination of the quality indicator. The sequence of procedures for forming a model of a stochastic process and processing the results of calculating the parameters of the histogram is determined.

Remaining Useful Life Prediction for Complex Systems With Multiple Indicators Based on Particle Filter and Parameter Correlation

In practical applications, the failure of large-scale complex equipment is often caused by the simultaneous degradation of multiple components. It is necessary to predict the remaining useful life (RUL) of the equipment with multiple degradation indicators. This article proposes a new joint-RUL-prediction method in the presence of multiple degradation indicators based on parameter correlation. The stochastic process model is established for each degradation indicator, and the model parameters are estimated by kernel smoothing particle filter (KS-PF) and maximum likelihood estimation (MLE). Meanwhile, to facilitate the dependencies between multiple degradation indicators, correlations of the degradation model parameter between multiple degradation indicators are established in KS-PF. In addition, optimal tuning (OT) is introduced to choose the best kernel parameter. A case study on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset is applied to verify the proposed method, the experiment shows that the proposed joint-RUL-prediction method based on parameter correlation possesses a superior prediction performance compared with that by using a single degradation indicator.

A Stochastic Control Approach to Defined Contribution Plan Decumulation: 'The Nastiest, Hardest Problem in Finance'

We pose the decumulation strategy for a Defined Contribution (DC) pension plan as a problem in optimal stochastic control. The controls are the withdrawal amounts and the asset allocation strategy. We impose maximum and minimum constraints on the withdrawal amounts, and impose no-shorting no-leverage constraints on the asset allocation strategy. Our objective function measures reward as the expected total withdrawals over the decumulation horizon, and risk is measured by Expected Shortfall (ES) at the end of the decumulation period. We solve the stochastic control problem numerically, based on a parametric model of market stochastic processes. We find that, compared to a fixed constant withdrawal strategy, with minimum withdrawal set to the constant withdrawal amount, the optimal strategy has a significantly higher expected average withdrawal, at the cost of a very small increase in ES risk. Tests on bootstrapped resampled historical market data indicate that this strategy is robust to parametric model mis-specification.

Generalised cepstral models for the spectrum of vector time series

The paper treats the modeling of stationary multivariate stochastic processes via a frequency domain model expressed in terms of cepstrum theory. The proposed model nests the vector exponential model of [20] as a special case, and extends the generalised cepstral model of [36] to the multivariate setting, answering a question raised by the last authors in their paper. Contemporarily, we extend the notion of generalised autocovariance function of [35] to vector time series. Then we derive explicit matrix formulas connecting generalised cepstral and autocovariance matrices of the process, and prove the consistency and asymptotic properties of the Whittle likelihood estimators of model parameters. Asymptotic theory for the special case of the vector exponential model is a significant addition to the paper of [20]. We also provide a mathematical machinery, based on matrix differentiation, and computational methods to derive our results, which differ significantly from those employed in the univariate case. The utility of the proposed model is illustrated through Monte Carlo simulation from a bivariate process characterized by a high dynamic range, and an empirical application on time varying minimum variance hedge ratios through the second moments of future and spot prices in the corn commodity market.

Математическое моделирование стохастических процессов распространения вирусов в среде обитания людей

Математическое моделирование стохастических процессов распространения вирусов в среде обитания людей

Calculating Infinitesimal Generators

Ito’s lemma is a standard approach for calculating infinitesimal generators for stochastic process models. We present alternate ad-hoc methods based on elementary calculations for many commonly considered stochastic models. The only tools that we employ are binomial expansion, Taylor series expansion and solution methods for elementary differential equations. Our alternate approaches are especially useful for processes which cannot be expressed as stochastic differential equations, for which Ito’s lemma cannot be applied.

Modelling Covid-19 Deaths in Ghana as a Discrete State Process in Continuous Time

We propose a stochastic process modelling of covid-19 deaths in Ghana. The objective is to accurately capture the death processes resulting from the pandemic and to predict future deaths resulting from Covid-19 infections in Ghana. The mathematical derivation is based strictly on the compound Poisson process, a class of a Levy process. The model is verified by using empirical data of deaths resulting from Covid-19 from the onset of the pandemic up to the time of writing this report. That is, Covid-19 deaths in Ghana from March to August 2020. The method departs slightly from the usual differential equations used in modeling pandemics due to the unique occurrence of deaths from the disease in Ghana. As the methods are basically compound Poisson process, we delve into Levy processes as it allows us to effectively simulate the future behaviour of the death process. To test the effectiveness of the model, we compared the simulated results to the actual reported number of deaths from Covid-19 cases in Ghana from March to August 2020. The results show that at a 95% confidence interval there is no significant difference between the actual deaths and the simulated results. The results of the simulation, when extended to February 2021 (one year after the advent of the pandemic) shows that if the current conditions remain same, that is, if there is no immediate intervention by the discovery of an effective drug or a vaccine, then the number of deaths could reach four hundred and forty six (446) by February 28, 2020.We propose a stochastic process modelling of covid-19 deaths in Ghana. The objective is to accurately capture the death processes resulting from the pandemic and to predict future deaths resulting from Covid-19 infections in Ghana. The mathematical derivation is based strictly on the compound Poisson process, a class of a Levy process. The model is verified by using empirical data of deaths resulting from Covid-19 from the onset of the pandemic up to the time of writing this report. That is, Covid-19 deaths in Ghana from March to August 2020. The method departs slightly from the usual differential equations used in modeling pandemics due to the unique occurrence of deaths from the disease in Ghana. As the methods are basically compound Poisson process, we delve into Levy processes as it allows us to effectively simulate the future behaviour of the death process. To test the effectiveness of the model, we compared the simulated results to the actual reported number of deaths from Covid-19 cases in Ghana from March to August 2020. The results show that at a 95% confidence interval there is no significant difference between the actual deaths and the simulated results. The results of the simulation, when extended to February 2021 (one year after the advent of the pandemic) shows that if the current conditions remain same, that is, if there is no immediate intervention by the discovery of an effective drug or a vaccine, then the number of deaths could reach four hundred and forty six (446) by February 28, 2020.

Mixed Stochastic Process Modelling for Accelerated Degradation Testing

Accelerated degradation testing (ADT) is used to efficiently assess the reliability and lifetime of a high reliable products under normal stress. In general, it is common in practice to build stochastic models of degradation under a single failure mechanism based on the ADT data. However, in real applications, multi-failure mechanisms may influence the degradation process. Motivated by this, a mixed stochastic process model for ADT is proposed in this paper. The mixed stochastic process combines two single-stochastic processes with weights determined by a quantitative method that establishes the relationship with accelerated stress. After the unknown parameter estimation, the proposed model under normal stress level can be obtained. The results show that the proposed model can be used for ADT modeling under multi-failure mechanisms.

Predicting and Analysis of Phishing Attacks and Breaches In E-Commerce Websites

Analyzing cyber incident data sets is an important method for deepening our understanding of the evolution of the threat situation. This is a relatively new research topic, and many studies remain to be done. In this paper, I reported a statistical analysis of a breach incident data set corresponding to 12 years (2005–2017) of cyber hacking activities that include malware attacks. I shown that, in contrast to the findings reported in the literature, both hacking breach incident inter-arrival times and breach sizes should be modeled by stochastic processes, rather than by distributions because they exhibit autocorrelations. Then, I proposed a particular stochastic process models to, respectively, fit the inter-arrival times and the breach sizes. I also shown that these models can predict the inter-arrival times and the breach sizes. In order to get deeper insights into the evolution of hacking breach incidents, we conduct both qualitative and quantitative trend analyses on the data set. I drew a set of cyber security insights, including that the threat of cyber hacks is indeed getting worse in terms of their frequency, but not in terms of the magnitude of their damage.

Degradation Modeling Using Stochastic Processes With Random Initial Degradation

In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to the traditional stochastic process models, which presumes that the product has experienced some degradation at the beginning of the test. Such a modeling technique can also capture the correlation between the initial degradation and the degradation rate, when the degradation rate of each path does vary from unit to unit. We apply this technique to the three popular stochastic process models, i.e., the Wiener process, the gamma process, and the inverse Gaussian process, and develop the corresponding parameter inference procedures. Monte Carlo simulations are implemented to validate the proposed models and the estimation procedures. Applications to the degradation analysis of block error rates data and GaAs laser data reveal good performance of the proposed models.

A Novel Degradation Modeling and Prognostic Framework for Closed-Loop Systems With Degrading Actuator

This article presents a novel degradation modeling and prognostic method for a class of closed-loop feedback systems with degrading actuators. Toward this end, we first present a degradation modeling framework by integrating the stochastic degradation process model of the actuator and the state transition model of the system. This takes into consideration the mutual effects between the component-level degradation and system-level state. Then, the particle filter algorithm is utilized to jointly estimate the hidden degradation state of the actuator and the system state through indirect observations. Further, a time-varying nonlinear diffusion process equipped with two-stage parameters updating procedure is used to learn the evolving progression of the hidden degradation state. As such, a residual-threshold-based remaining useful life (RUL) prediction method is presented by simulating future system states and degradation trajectories based on the learned degradation process. As the application of the predicted RUL, a fault tolerant control method is presented by adjusting the controller parameter so as to extend the life of the system. Finally, a simulation study is conducted using a closed-loop control system in an inertial platform to verify the proposed method. The results indicate that the proposed method can reduce prognosis error, improve robustness, and extend the lifetime of the system.

Optimal degradation-based burn-in policy using Tweedie exponential-dispersion process model with measurement errors

In this paper, degradation-based burn-in for highly-reliable products subject to degradation is studied. Since the common degradation models for burn-in are usually established on the basis of a specific stochastic process, such as Wiener process and gamma process, it greatly restricts the scope of application. Moreover, measurement errors are often inevitable due to the imperfect inspection and environment disturbance. Hence, a Tweedie exponential-dispersion process with measurement errors (TEDPE) model is developed to describe the degradation paths of the population which includes weak units and normal units. The TEDPE model contains the common stochastic process models as special case by setting different forms of variance function. Then, a joint saddle-point approximation and expectation maximization algorithm is proposed for parameter estimation. To identity and eliminate weak units, the linear discriminant analysis method, which can make full use of the degradation sequence of observations, is used to develop classification criterion. The optimal burn-in policy involving the duration and cutoff point can be obtained by minimizing the total per-unit cost. Furthermore, considering the failure costs in field operation, a joint policy of burn-in and preventive maintenance is optimized. Finally, a case study based on an IRLED dataset is implemented to illustrate the proposed methods.

Speaker Verification Using Autoregressive Spectrum of Speech Signal in Composite Vector Stochastic Processes Model Representation

Speaker Verification Using Autoregressive Spectrum of Speech Signal in Composite Vector Stochastic Processes Model Representation

LEVERAGING ANALYTIC METHODS TO EXPAND OPPORTUNITIES IN AGING-RELATED HEALTH DISPARITIES RESEARCH

The objective of the Symposium is to improve the understanding of how existing analytic methods and data can be leveraged to make progress in understanding the causes and mechanisms of health-related disparities in Alzheimer’s disease, related dementias and other prominent age-related diseases. Topics will cover a range of academic and administrative topics including: i) advanced analytic methods and modeling of health disparities with application to racial and geographic disparities in AD/ADRD; ii) the role of repeated anesthetic and surgical exposure in generation of disparities in AD/ADRD risk; iii) the nature of health disparities in cognitive aging as parallel to or distinct from health disparities in patterns of aging in other systems in the body; iv) recent advances in machine learning applied to large claims databases involving medical disparities; and v) geographic-related disparities in life expectancy across the U.S. A focus will be made on demonstrating how studies using established administrative data resources such as Medicare claims databases combined with innovative analytic approaches such as partitioning analyses, time-series based methods of projection and forecasting, and stochastic process models can be used to uncover previously overlooked or understudied aspects in this area of research. Analyses of such increasingly available large health datasets provides an opportunity to obtain nationally representative multiethnic results based on individual-level measures that reflect the real care-related and epidemiological processes ongoing in the U.S. healthcare system and allows the targetting of relatively rare diseases in relatively small population subgroups.