Stochastic Behavior Research Articles

Immersion in Complex Dynamical Systems with Ergodicity

This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.

Modelling and evaluating different multi-carrier energy system configurations for a Dutch house

The urge to reduce the dependence on natural gas for heating at the residential level has led to the deployment of different fossil fuel-free alternatives. In the Netherlands, two technologies are leading the transition: heat pumps, due to their high COP, and photovoltaic–thermal systems, due to their dual electric-thermal output. However, both represent a challenge for users and grid operators, aside from their stochastic behavior. Heat pumps alone can surpass a typical Dutch house’s total energy and power consumption. Photovoltaic–thermal systems, as their only electric homologs, usually have a mismatch between generation and demand, causing energy injections to the grid. From the electric perspective, storage systems are a proven solution to reduce the energy exchange with the distribution network. This paper proposes four multi-carrier energy system configurations for a Dutch household, comprising different combinations of a photovoltaic–thermal system, a battery energy storage, a heat pump, and an underground water tank thermal energy system, providing analytical models for every component (including the thermal losses from the thermal storage to the ground), and the space heating and electrical demands. We determined the components’ compatibility and evaluated the combinations considering their thermal performance, electrical performance, and equivalent CO2 emissions. The results suggest that using a heat pump combined with a photovoltaic system and a battery provides the best trade-off. The photovoltaic–thermal system alone could not supply the thermal demand required for comfortable space heating nor reach temperatures high enough to charge the thermal storage. Combining the thermal storage with the heat pump allows a certain degree of flexibility for the heat pump activation at the cost of COPs between 0.8 and 1.38 when used to charge the thermal storage, thus increasing energy consumption and equivalent emissions considerably.

Scaling of stochastic growth and division dynamics: A comparative study of individual rod-shaped cells in the Mother Machine and SChemostat platforms.

Microfluidic platforms enable long-term quantification of stochastic behaviors of individual bacterial cells under precisely controlled growth conditions. Yet, quantitative comparisons of physiological parameters and cell behaviors of different microorganisms in different experimental and device modalities is not available due to experiment-specific details affecting cell physiology. To rigorously assess the effects of mechanical confinement, we designed, engineered, and performed side-by-side experiments under otherwise identical conditions in the Mother Machine (with confinement) and the SChemostat (without confinement), using the latter as the ideal comparator. We established a protocol to cultivate a suitably engineered rod-shaped mutant of Caulobacter crescentus in the Mother Machine and benchmarked the differences in stochastic growth and division dynamics with respect to the SChemostat. While the single-cell growth rate distributions are remarkably similar, the mechanically confined cells in the Mother Machine experience a substantial increase in interdivision times. However, we find that the division ratio distribution precisely compensates for this increase, which in turn reflects identical emergent simplicities governing stochastic intergenerational homeostasis of cell sizes across device and experimental configurations, provided the cell sizes are appropriately mean-rescaled in each condition. Our results provide insights into the nature of the robustness of the bacterial growth and division machinery.

Manufacturing-induced stochastic constitutive behaviors of additive manufactured specimens: testing, data-driven modeling, and optimization

PurposeFused deposition modeling (FDM) is an extensively used additive manufacturing method with the capacity to build complex functional components. Due to the machinery and environmental factors during manufacturing, the FDM parts inevitably demonstrated uncertainty in properties and performance. This study aims to identify the stochastic constitutive behaviors of FDM-fabricated polylactic acid (PLA) tensile specimens induced by the manufacturing process.Design/methodology/approachBy conducting the tensile test, the effects of the printing machine selection and three major manufacturing parameters (i.e., printing speed S, nozzle temperature T and layer thickness t) on the stochastic constitutive behaviors were investigated. The influence of the loading rate was also explained. In addition, the data-driven models were established to quantify and optimize the uncertain mechanical behaviors of FDM-based tensile specimens under various printing parameters.FindingsAs indicated by the results, the uncertain behaviors of the stiffness and strength of the PLA tensile specimens were dominated by the printing speed and nozzle temperature, respectively. The manufacturing-induced stochastic constitutive behaviors could be accurately captured by the developed data-driven model with the R2 over 0.98 on the testing dataset. The optimal parameters obtained from the data-driven framework were T = 231.3595 °C, S = 40.3179 mm/min and t = 0.2343 mm, which were in good agreement with the experiments.Practical implicationsThe developed data-driven models can also be integrated into the design and characterization of parts fabricated by extrusion and other additive manufacturing technologies.Originality/valueStochastic behaviors of additively manufactured products were revealed by considering extensive manufacturing factors. The data-driven models were proposed to facilitate the description and optimization of the FDM products and control their quality.

Forest fire spreading: A nonlinear stochastic model continuous in space and time

AbstractForest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that has the potentiality to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a kernel function that can take into account wind conditions, land slope, spotting phenomena, and so on, bringing to a system of integrodifferential equations whose solutions provide the evolution in time of the subprobability densities. That makes the model complementary to models based on cellular automata that furnish single instantiations of the stochastic phenomenon. Moreover, stochastic models based on cellular automata can be derived from the present model by space and time discretization. Existence and uniqueness of the solutions is proved by using Banach's fixed‐point theorem. The asymptotic behavior of the model is analyzed as well. By specifying a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving toward a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. The kernel could be slightly modified to include firefighters interventions and weather changes.

Persistence in the Realized Betas: Some Evidence from the Stock Market

This paper examines the stochastic behaviour of the realized betas in the CAPM model for the ten largest companies in terms of market capitalisation included in the U.S. Dow Jones stock market index. Fractional integration methods are applied to estimate their degree of persistence at daily, weekly, and monthly frequencies over the period July 2000–July 2020 over time spans of 1, 3, and 5 years. On the whole, the results indicate that the realized betas are highly persistent and do not exhibit weak mean-reverting behaviour at the weekly and daily frequencies, whilst there is some evidence of weak mean reversion at the monthly frequency. Our findings confirm the sensitivity of beta calculations to the choice of frequency and time span (the number of observations).

Enjoy the silence: Analysis of stochastic Petri nets with silent transitions

Capturing stochastic behaviour in business and work processes is essential to quantitatively understand how nondeterminism is resolved when taking decisions within the process. This is of special interest in process mining, where event data tracking the actual execution of the process are related to process models, and can then provide insights on frequencies and probabilities. Variants of stochastic Petri nets provide a natural formal basis to represent stochastic behaviour and support different data-driven and model-driven analysis tasks in this spectrum. However, when capturing business processes, such nets inherently need a labelling that maps between transitions and activities. In many state of the art process mining techniques, this labelling is not 1-on-1, leading to unlabelled transitions and activities represented by multiple transitions. At the same time, they have to be analysed in a finite-trace semantics, matching the fact that each process execution consists of finitely many steps. These two aspects impede the direct application of existing techniques for stochastic Petri nets, calling for a novel characterisation that incorporates labels and silent transitions in a finite-trace semantics. In this article, we provide such a characterisation starting from generalised stochastic Petri nets and obtaining the framework of labelled stochastic processes (LSPs). On top of this framework, we introduce different key analysis tasks on the traces of LSPs and their probabilities. We show that all such analysis tasks can be solved analytically, in particular reducing them to a single method that combines automata-based techniques to single out the behaviour of interest within an LSP, with techniques based on absorbing Markov chains to reason on their probabilities. Finally, we demonstrate the significance of how our approach in the context of stochastic conformance checking, illustrating practical feasibility through a proof-of-concept implementation and its application to different datasets.

Bayesian and empirical-Bayesian evaluations of the Topp–Leone lifetime model using lower record statistics

Record statistics are generally used to measure a process’ stochastic behavior at previously unheard-of values, either upper or lower. It can be obtained or calculated using order statistics from a sample whose size is dictated by the values and order of occurrence of observations. Due to its finite support and bathtub-shaped hazard function, the Topp–Leone (TL) distribution is appealing for reliability investigations. In today’s practical applications, estimating unknown parameters and predicting upcoming records is an essential issue. Thus, in this work, the TL distribution’s lower record values are taken into account. Against the symmetric squared-error loss, both Bayes and empirical-Bayes approaches are used to estimate the TL’s parameter and calculate prediction limits for upcoming lower record values. A Monte Carlo simulation experiment is performed to assess the accuracy of the estimation methodologies provided. To demonstrate the operability and usefulness of the various approaches, two useful applications are studied. The numerical evaluations show that the suggested approaches perform effectively and that the provided estimations are adequate in practice.

Bivariate q- generalized extreme value distribution: A comparative approach with applications to climate related data

The premise of extreme value theory focuses on the stochastic behaviour and occurrence of extreme observations in an event that is random. Traditionally for univariate case, the behaviour of the maxima is described either by the types-I, types-II or types-III extreme value distributions, primarily known as the Gumbel, Fréchet or reversed Weibull models. These are all particular cases of the generalized extreme value (GEV) model. However, in real-world scenario, these incidents take place as a consequence of concurrent dependent random events, where the relationship between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the q− generalized extreme value (q−GEV) distribution, as well as the q− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bi-variate (EV) data, arising naturally from independent q−GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model interdependent bivariate observations consisting of extreme values in terms of q−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate q−GEV. Additionally, conventional method to propose the newly defined bivariate (q−GEV) distribution with bivariate q− Gumbel distribution (a special case for ξ→0) has also been established with related inferences and application to climate data.

Nonlinear stochastic behavior of soft-core sandwich panels

The nonlinear stochastic behavior of soft-core sandwich panels and the evolution of uncertainty along the nonlinear path are investigated. The paper focuses on the way the geometrically nonlinear and unstable behavior is affected by uncertainty and considers, for the first time, the evolution of uncertainty along the unstable structural response. The structural modeling relies on the EHSAPT and its integration into the geometrically nonlinear stochastic regime. A tailored nonlinear FE model that is based on a variational formulation and an arc-length solution scheme are developed. The stochastic analysis adopts the Perturbation-based SFEM and its generalization for the evolution of uncertainty along the process axis. A numerical study demonstrates the stochastic methodology and explores the impact of uncertainty on the nonlinear structural behavior. The evolution of the stochastic stress resultants at the displaced end is studied along the two axes of evolution. The differences between the two representations and their physical and engineering significance are highlighted revealing significant changes to the uncertainty evolution pattern with the shift from global buckling to localized wrinkling instabilities. The representation of the stochastic results along the process axis also quantifies the level of uncertainty near critical and singular points where conventional analyses diverge.

Stochastic bifurcation and chaos study for nonlinear ship rolling motion with random excitation and delayed feedback controls

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The Itoˆ-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. We also analyze the properties and shape changes of the system’s probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P-bifurcation and D-bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series.

Renewable microgeneration cooperation with base station sleeping-mode strategy for energy-efficient operation of 5G infrastructures

The energy consumption of the mobile network is becoming a growing concern for mobile network operators and it is expected to rise further with operational costs and carbon footprints due to the massive deployment of small cell base stations in 5G and beyond 5G networks. Renewable energy harvesting has proved its extraordinary potential in green mobile communication to reduce energy costs and carbon footprints. However, the stochastic behavior of renewable energy generation and traffic load makes the reliable operation of mobile networks challenging. Therefore, this paper proposes an energy-sustainable framework of cooperative microgeneration energy power supplies for nearby clusters of small cells to maximize the utilization of sustainable energy by intra-microgrid and inter-microgrid energy cooperation. In addition, a resource-on-demand approach of small cells based on advanced sleep modes is integrated with energy cooperation to optimize energy saving and the techno-economic feasibility of microgrids. The proposed solution of microgeneration energy cooperation framework with a resource-on-demand strategy optimally shares surplus energy between microgrids via physically deployed resistive transmission lines under a practical energy loss model and restrains the mismatch between traffic arrival and energy production. Exhaustive simulation is performed to examine the optimal system performance, carbon emissions performance, energy savings, and cost assessment. Results suggest that the proposed solution performs effectively in terms of cost, emissions, and energy savings.

Parameter influence analysis of stochastic resonance and stochastic P-bifurcation for the shape-memory alloy laminate

This paper investigates the transverse vibration of an axially moving shape-memory alloy (SMA) fiber hybrid laminations under the combined action of transverse harmonic excitation and stochastic disturbance. Considering the shape memory alloy (SMA) fiber volume fraction random field, the kinetic energy and strain potential energy of SMA laminates are solved, and the axial motion equation of SMA laminates is derived according to Hamilton principle, a non-dimensional differential equation of the transverse vibration of the axially moving SMA laminated plates is obtained by adopting the Galerkin integral method. Considering the volume-fraction stochastic field, the stochastic natural vibration of a SMA laminate is analyzed. Considering the stochastic resonance of the SMA laminate under the action of Gaussian white noise and harmonic excitation, the effects of geometric parameters, physical parameters of materials, and temperature on the stochastic resonance behavior of the SMA laminate is analyzed. Finally, the effect of the stochastic P-bifurcation phenomenon of the parameters on the steady-state response of the SMA laminate is analyzed.

Remote Low-Cost Web-Based Battery Monitoring System and Control Using LoRa Communication Technology

Batteries are a complex electrochemical device that exhibit non-linearity and stochastic behavior which rely upon the operational conditions and environmental factors, making battery monitoring a vital feature throughout its application. This paper introduces a novel web-based battery monitoring and control system that utilizes Long Range (LoRa) communication technology, an integral part of the Internet of Things (IoT). The system is implemented with the ESP32 microcontroller, with an emphasis on affordability in broader applications. The system provides comprehensive real-time online data by integrating a combination of multiple sensors. The proposed system seeks to address the limitations of existing communication technology by utilizing the benefits of LoRa, a technology that facilitates effective long-range, low-energy communication which makes it particularly well-suited for real-time monitoring applications. In addition, a control operation enables users to regulate crucial aspects of batteries, such as their charging and discharging. The research conducted a meticulous experimental evaluation of the proposed system at different operations, and the results successfully aligned with the main objective and aims of the research. The proposed system successfully enables real-time remote monitoring and user control, long-term data visualization through data logging, and assessment of battery conditions. Data logging was introduced to enhance the utilization of future battery evaluation, such as State-of-Charge (SOC), State-of-Health (SOH) and Remaining Useful Life (RUL). As a result, the developed system makes it suitable for many applications requiring effective energy storage solutions, such as renewable energy and Electric Vehicle (EV) applications.

Model of conversion of flow from confined to unconfined aquifers with stochastic approach

Abstract This work deals with the conversion of flow from confined to unconfined aquifers, a real-world problem that has attracted the attention of several authors. We have introduced a piecewise modified mathematical model where the first part deals with the flow within a confined system, and the second part deals with the flow within an unconfined system. In the unconfined part, we added the randomness to capture stochastic behaviours that could occur due to the geological formation. Moreover, we used a numerical method to solve the stochastic differential equations. The obtained model was evaluated numerically using some numerical scheme, and the stability analysis was performed using the von Neumann approach and the numerical simulations were presented.

Machine learning-powered compact modeling of stochastic electronic devices using mixture density networks

The relentless pursuit of miniaturization and performance enhancement in electronic devices has led to a fundamental challenge in the field of circuit design and simulation-how to accurately account for the inherent stochastic nature of certain devices. While conventional deterministic models have served as indispensable tools for circuit designers, they fall short when it comes to capturing the subtle yet critical variability exhibited by many electronic components. In this paper, we present an innovative approach that transcends the limitations of traditional modeling techniques by harnessing the power of machine learning, specifically Mixture Density Networks (MDNs), to faithfully represent and simulate the stochastic behavior of electronic devices. We demonstrate our approach to model heater cryotrons, where the model is able to capture the stochastic switching dynamics observed in the experiment. Our model shows 0.82% mean absolute error for switching probability. This paper marks a significant step forward in the quest for accurate and versatile compact models, poised to drive innovation in the realm of electronic circuits.

Abrupt increase of stochastic behavior in domain-wall motion near depinning field

The domain-wall motion in ferromagnetic films exhibits stochastic behavior due to thermal agitation with quenched disorders. The stochasticity is an obstacle in the sense of consistent repeatability of domain-wall position control in magnetic domain-wall devices. In general, the level of stochasticity is expected to decrease as driving force increases. This property suggests that the magnetic domain-wall devices are capable of simultaneously achieving both high operational speed and decrease in the level of stochasticity. However, we report here an observation of stochasticity anomaly, which involves a significant increase in relative speed dispersion near the depinning field. Domain-wall motion measurements were performed in ferromagnetic wires with perpendicular magnetic anisotropy over the same position to measure the relative speed dispersion. The stochasticity in domain-wall motion is intertwined with the number of pinning–depinning events throughout the domain-wall motion. The size of cluster events, which leads to the number of events, reflects the trend in the relative speed dispersion. The observed anomaly is provided by occurrence of large avalanches of cluster events. The anomaly occurs within the tech-relevant speed range of 1–100 m/s, signaling the necessity of material engineering to mitigate its effects.

Efficient resource allocation for 5G/6G cognitive radio networks using probabilistic interference models

The Cognitive Radio Network, incorporating Device-to-Device communication and a heterogeneous network, has garnered significant attention due to its ability to address spectrum shortage issues and optimize the efficient utilization of spectrum resources. However, resource allocation considering stochastic behavior has not been considered in existing studies. In this paper, our work aimed to maximize the throughput of the overall network considering multiple users under the umbrella of the Cognitive radio network assisted by amplify and forward relay. The constraints are treated as chance constraints with a probability of satisfaction in them, which leads to a non-convex mixed integer nonlinear problem which is an NP-Hard problem. To solve this problem an exhaustive search solution for optimal results is required. However, the computational burden always increases with the user equipment. Therefore, to obtain an optimal solution with having low computational burden, the Outer Approximation Algorithm is utilized in this research. To evaluate the desired results, extensive simulations have been carried out. The effectiveness of the proposed algorithm is verified by results in terms of throughput maximization under the impact of chance constraint formulation in the cognitive radio networks.

Approach of establishing a high-resolution shading occupant behavior model in the office building

Occupant behavior in buildings is becoming a critical factor in determining indoor comfort and energy consumption performance. The diversity and uncertainty of occupant behavior affect the implementation of occupant-centric building operations. However, existing shading behavior models do not account for various shading states (fully open, fully closed, or partially open, significantly deviating from real-world scenarios), accessibility of shading behavior (ASB), room configurations (single-person rooms and multi-person rooms), occupancy, and other factors, resulting in lower model accuracy. This study aims to address these limitations by proposing a high-resolution shading occupant behavior (HRSOB) model that integrates occupancy considerations, accessibility of shading behavior, and data mining techniques. This HRSOB model can classify various shading occupant behaviors and be integrated into the optimization controls of occupant-centric buildings. The utilization of Markov chain occupancy models significantly improves the accuracy of predicting stochastic shading behavior. The ASB classification method analyzes the features of the occupant shading adjustment behavior (hereafter referred to as shading behavior) and objectively reflects shading behavior patterns using spatial features, thereby enhancing the resolution of the shading occupant behavior model. Data-driven techniques, such as feature selection and soft voting, enable the analysis, training, and application of shading behavior data, and rigorous evaluation and validation of the HRSOB model are conducted. The results demonstrated a 10.92% improvement in the predictive performance of the HRSOB model compared with the typical shading occupant behavior (SOB) model.

State of Health Estimation for Lithium-Ion Batteries Under Arbitrary Usage Using Data-Driven Multimodel Fusion

Accurately estimating the state of health (SoH) of batteries is indispensable for the safety, reliability, and optimal energy and power management of electric vehicles. However, from a data-driven perspective, complications, such as dynamic vehicle operating conditions, stochastic user behaviors, and cell-to-cell variations, make the estimation task challenging. This work develops a data-driven multi-model fusion method for SoH estimation under arbitrary usage profiles. All possible operating conditions are categorized into six scenarios. For each scenario, an appropriate feature set is extracted to indicate the SoH. Based on the obtained features, four machine learning algorithms are applied individually to train SoH estimation models using time-series data. In addition to the estimates at the current time step, a histogram data-based and online adaptive model is taken from previous work for predicting the next-step SoH. Then, a Kalman filter is applied to systematically fuse the results of all the estimation and prediction models. Experimental data collected from different types of batteries operated under diverse profiles verify the effectiveness and practicability of the developed method, as well as its superiority over individual models.