Stochastic Parameters Research Articles

A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems

In this paper, a new deterministic method is proposed. This method depends on presenting (suggesting) some modifications to existing parameters of some conjugate gradient methods. The parameters of our suggested method contain a mix of deterministic and stochastic parameters. The proposed method is added to a line search algorithm to make it a globally convergent method. The convergence analysis of the method is established. The gradient vector is estimated by a finite difference approximation approach, and a new step-size h of this approach is generated randomly. In addition, a set of stochastic parameter formulas is constructed from which some solutions are generated randomly for an unconstrained problem. This stochastic technique is hybridized with the new deterministic method to obtain a new hybrid algorithm that finds an approximate solution for the global minimization problem. The performance of the suggested hybrid algorithm is tested in two sets of benchmark optimization test problems containing convex and non-convex functions. Comprehensive comparisons versus four other hybrid algorithms are listed in this study. The performance profiles are utilized to evaluate and compare the performance of the five hybrid algorithms. The numerical results show that our proposed hybrid algorithm is promising and competitive for finding the global optimum point. The comparison results between the performance of our suggested hybrid algorithm and the other four hybrid algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions.

A probabilistic combined high and low cycle fatigue life prediction framework for the turbine shaft with random geometric parameters

Combined high and low cycle fatigue (CCF) is a common failure mode of turbine shaft. This study presents a generic procedure for probabilistic CCF life prediction, and combined with the modified highly stressed volume (HSV) method to improve a prediction framework, which considers the effect of random geometric parameters on fatigue life and establishes the dynamic relationship between key geometric parameters and life distribution. The probabilistic CCF life modeling of turbine shafts with stochastic geometric parameters is presented, whose predicted result is consistent with practical engineering. This research is of great significance for life estimation and prolongation of turbine shaft.

Improved teleconnection between Arctic sea ice and the North Atlantic Oscillation through stochastic process representation

Abstract. The extent to which interannual variability in Arctic sea ice influences the mid-latitude circulation has been extensively debated. While observational data support the existence of a teleconnection between November sea ice in the Barents–Kara region and the subsequent winter North Atlantic Oscillation, climate models do not consistently reproduce such a link, with only very weak inter-model consensus. We show, using the EC-Earth3 climate model, that while an ensemble of coupled EC-Earth3 simulations shows no evidence of such a teleconnection, the inclusion of stochastic parameterizations to the ocean and sea ice component results in the emergence of a robust teleconnection comparable in magnitude to that observed. While the exact mechanisms causing this remain unclear, we argue that it can be accounted for by an improved ice–ocean–atmosphere coupling due to the stochastic perturbations, which aim to represent the effect of unresolved ice and ocean variability. In particular, the weak inter-model consensus may to a large extent be due to model biases in surface coupling, with stochastic parameterizations being one possible remedy.

Experimental data-driven uncertainty quantification for the dynamic fracture toughness of particulate polymer composites

This paper presents an experimental investigation supported by data-driven approaches concerning the influence of critical stochastic effects on the dynamic fracture toughness of glass-filled epoxy composites using a computationally efficient framework of uncertainty quantification. Three different shapes of glass particles are considered including rod, spherical and flaky shapes with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction. An artificial neural network based surrogate assisted Monte Carlo simulation is carried out here in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy to quantify the uncertainty and sensitivity associated with the dynamic fracture toughness of composites in terms of stress intensity factor under dynamic impact. The study reveals that the pre-crack initiation time regime shows the most prominent effect of uncertainty. Additionally, rod shape and the aspect ratio are the most sensitive filler type and input parameter respectively for characterizing dynamic fracture toughness. Here the quantitative results based on large-scale data-driven approaches convincingly demonstrate using a computational mapping between the stochastic input and output parameter spaces that the effect of uncertainty gets pronounced significantly while propagating from the compound source level to the impact responses. Such outcomes based on experimental data essentially bring us to the realization that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive analysis and design framework for the dynamic fracture of particulate composites. With limited literature available on the determination of fracture toughness considering inertial effects, the present work demonstrates a novel and insightful experimental approach for uncertainty quantification and sensitivity analysis of dynamic fracture toughness of particulate polymer composites based on surrogate modeling.

On the noise performances of fractal‐fractional electrical circuits

AbstractIn this work, the noise performances of the fractal‐fractional electrical circuits have been addressed. The nonlocal fractal calculus has been adopted as our mathematical basis. The fractal time component has also been included for the physical measurability of electrical quantities. The derivations of crucial stochastic parameters of circuit responses, which determine their noise performances, have been performed. Numerical simulations have also been conducted where the influences of Hausdorff dimension of the fractal set, orders of fractal‐fractional reactive components, and other parameters on the noise performances have been studied. Regardless to any specific circuit, we have found that the noise performances can be improved by increasing the orders of fractal‐fractional reactive components. The optimum Hausdorff dimensions, which the best noise performances can be achieved given the orders of fractal‐fractional reactive components, have also been calculated. The results proposed in this work serve as the foundation for understanding noise in fractal‐fractional electrical circuits and can be extensively applied to large‐scaled circuits, for example, the infinite circuit networks and so forth.

Managing quality and pricing during a product recall: An analysis of pre-crisis, crisis and post-crisis regimes

Product recalls are often consequences of quality failures. While such failures are related to a manufacturer’s or supplier’s design quality, the perceived quality of products may be severely damaged when a product harm crisis occurs. However, most often, such a crisis will not last forever, and a firm at fault eventually recovers. Considering an optimal control model, we investigate the optimal pricing decisions, advertising and quality efforts of a firm while it anticipates a product recall and a subsequent recovery. We show that the decisions and profits of the manufacturer vary widely with the stochastic parameters: crisis likelihood, recovery likelihood, crisis impact and recovery intensity. We illustrate that myopic firms are more severely affected by a product recall than farsighted firms when the impact of recall is high. However, it might not be so detrimental to take myopic decisions for low impact recalls. In the absence of recovery, a product recall can lead to bankruptcy. High initial perceived quality may not insulate a firm against bankruptcy.

Optimal configuration of low impact development practices for the management of urban runoff pollution under uncertainty

The urbanization process has seen an accelerated increase in recent decades, leading to urban runoff pollution becoming more prominent. However, uncertainty of the pollution output and complexity of management systems have made controlling urban runoff pollution challenging. Therefore, it is necessary to propose advanced modeling methods for these challenges. This research presents an integrated urban runoff pollution management (IURPM) model for optimal configuration of low impact development (LID) practices under multiple uncertainties. The IURPM model combines the hybrid land-use prediction and improved pollution estimation models with interval parameter, stochastic parameter, and multi-objective programming. The proposed IURPM model can not only predict the output characteristics, but also provide optimal configuration schemes for the LID practices in the management of urban runoff pollution under multiple scenarios. In addition, uncertainties expressed as discrete intervals and probability density function in the management systems can be effectively addressed. A case study of the IURPM model was conducted in Dongguan City, South China. Results show that considerable amounts of urban runoff pollutants would export from Dongguan City by 2025. The export loads and pollution output flux per unit area would have significant spatial heterogeneity. The results further indicate that population size, gross domestic product, and regional area size are expected to play important roles in the pollution export, while impervious surface coverage and population density would likely have great influences on the output flux of urban runoff pollution. Based on the model findings, multiple LID practices should be adopted in Dongguan City to reduce the urban runoff pollution loads. Using the IURPM model, multiple LID implementation schemes can be obtained under different pollution reduction scenarios and significance levels, that can provide decision-making support for urban water environmental management, considering variations in the policymaker's decision-making preferences. This study demonstrates that the IURPM model can be applied to the optimal configuration of LID practices for the management of urban runoff pollution under uncertainty.

A new vaccine supply chain network under COVID-19 conditions considering system dynamic: Artificial intelligence algorithms

With the discovery of the COVID-19 vaccine, what has always been worrying the decision-makers is related to the distribution management, the vaccination centers' location, and the inventory control of all types of vaccines. As the COVID-19 vaccine is highly demanded, planning for its fair distribution is a must. University is one of the most densely populated areas in a city, so it is critical to vaccinate university students so that the spread of this virus is curbed. As a result, in the present study, a new stochastic multi-objective, multi-period, and multi-commodity simulation-optimization model has been developed for the COVID-19 vaccine's production, distribution, location, allocation, and inventory control decisions. In this study, the proposed supply chain network includes four echelons of manufacturers, hospitals, vaccination centers, and volunteer vaccine students. Vaccine manufacturers send the vaccines to the vaccination centers and hospitals after production. The students with a history of special diseases such as heart disease, corticosteroids, blood clots, etc. are vaccinated in hospitals because of accessing more medical care, and the rest of the students are vaccinated in the vaccination centers. Then, a system dynamic structure of the prevalence of COVID -19 in universities is developed and the vaccine demand is estimated using simulation, in which the demand enters the mathematical model as a given stochastic parameter. Thus, the model pursues some goals, namely, to minimize supply chain costs, maximize student desirability for vaccination, and maximize justice in vaccine distribution. To solve the proposed model, Variable Neighborhood Search (VNS) and Whale Optimization Algorithm (WOA) algorithms are used. In terms of novelties, the most important novelties in the simulation model are considering the virtual education and exerted quarantine effect on estimating the number of the vaccines. In terms of the mathematical model, one of the remarkable contributions is paying attention to social distancing while receiving the injection and the possibility of the injection during working and non-working hours, and regarding the novelties in the solution methodology, a new heuristic method based on a meta-heuristic algorithm called Modified WOA with VNS (MVWOA) is developed. In terms of the performance metrics and the CPU time, the MOWOA is discovered with a superior performance than other given algorithms. Moreover, regarding the data, a case study related to the COVID-19 pandemic period in Tehran/Iran is provided to validate the proposed algorithm. The outcomes indicate that with the demand increase, the costs increase sharply while the vaccination desirability for students decreases with a slight slope.

Dynamical Symmetry Breaking of Infinite-Dimensional Stochastic System

The mapping relationship between the symmetry and the conserved quantity inspired researchers to seek the conserved quantity from the viewpoint of the symmetry for the dynamic systems. However, the symmetry breaking in the dynamic systems is more common than the symmetry in the engineering. Thus, as the supplement of our previous work on the symmetry breaking of infinite-dimensional deterministic dynamic systems, the dynamical symmetry breaking of infinite-dimensional stochastic systems is discussed in this paper. Following a brief review of the stochastic (multi-)symplectic for the dynamic system excited by stochastic white noise, two types of stochastic symmetry breaking factors, including the general stochastic excitation and the general stochastic parameters of the infinite-dimensional dynamic systems, are investigated in detail. We find that both the general stochastic excitation and the general stochastic parameters will not break the local multi-symplectic structure of the dynamic systems. However, the local energy conservation law will be broken by the general stochastic excitation, as well as by the stochastic parameters, which are given by the local energy dissipation in this paper. To illustrate the validity of the analytical results, the stochastic vibration of a clamped single-walled carbon nanotube is investigated and the critical condition of the appearance of chaos is obtained. The theoretical results obtained can be used to guide us to construct the structure-preserving method for the stochastic dynamic systems.

Lagrangian Particle Dispersion Models in the Grey Zone of Turbulence: Adaptations to FLEXPART-COSMO for Simulations at 1 km Grid Resolution

Lagrangian particle dispersion models (LPDMs) are frequently used for regional-scale inversions of greenhouse gas emissions. However, the turbulence parameterizations used in these models were developed for coarse resolution grids, hence, when moving to the kilometre-scale the validity of these descriptions should be questioned. Here, we analyze the influence of the turbulence parameterization employed in the LPDM FLEXPART-COSMO model. Comparisons of the turbulence kinetic energy between the turbulence schemes of FLEXPART-COSMO and the underlying Eulerian model COSMO suggest that the dispersion in FLEXPART-COSMO suffers from a double-counting of turbulent elements when run at a high resolution of 1 times 1 ,hbox {km}^2. Such turbulent elements are represented in both COSMO, by the resolved grid-scale winds, and FLEXPART, by its stochastic parameterizations. Therefore, we developed a new parametrization for the variations of the winds and the Lagrangian time scales in FLEXPART in order to harmonize the amount of turbulence present in both models. In a case study for a power plant plume, the new scheme results in improved plume representation when compared with in situ flight observations and with a tracer transported in COSMO. Further in-depth validation of the LPDM against methane observations at a tall tower site in Switzerland shows that the model’s ability to predict the observed tracer variability and concentration at different heights above ground is considerably enhanced using the updated turbulence description. The high-resolution simulations result in a more realistic and pronounced diurnal cycle of the tracer concentration peaks and overall improved correlation with observations when compared to previously used coarser resolution simulations (at 7 km times 7 km). Our results indicate that the stochastic turbulence schemes of LPDMs, developed in the past for coarse resolution models, should be revisited to include a resolution dependency and resolve only the part of the turbulence spectrum that is a subgrid process at each different mesh size. Although our new scheme is specific to COSMO simulations at 1 times 1 ,hbox {km}^2 resolution, the methodology for deriving the scheme can easily be applied to different resolutions and other regional models.

Diverse, Neural Trojan Resilient Ecosystem of Neural Network IP

Adversarial machine learning is a prominent research area aimed towards exposing and mitigating security vulnerabilities in AI/ML algorithms and their implementations. Data poisoning and neural Trojans enable an attacker to drastically change the behavior and performance of a Convolutional Neural Network (CNN) merely by altering some of the input data during training. Such attacks can be catastrophic in the field, e.g. for self-driving vehicles. In this paper, we propose deploying a CNN as an ecosystem of variants , rather than a singular model. The ecosystem is derived from the original trained model, and though every derived model is structurally different, they are all functionally equivalent to the original and each other. We propose two complementary techniques: stochastic parameter mutation , where the weights θ of the original are shifted by a small, random amount, and a delta-update procedure which functions by XOR’ing all of the parameters with an update file containing the Δ θ values. This technique is effective against transferability of a neural Trojan to the greater ecosystem by amplifying the Trojan’s malicious impact to easily detectable levels; thus, deploying a model as an ecosystem can render the ecosystem more resilient against a neural Trojan attack.

Machine-learning-assisted high-temperature reservoir thermal energy storage optimization

High-temperature reservoir thermal energy storage (HT-RTES) has the potential to become an indispensable component in achieving the goal of the net-zero carbon economy, given its capability to balance the intermittent nature of renewable energy generation. In this study, a machine-learning-assisted computational framework is presented to identify HT-RTES site with optimal performance metrics by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems.

Bearing Fault Diagnosis Based on Stochastic Resonance and Improved Whale Optimization Algorithm

In light of the problem of difficult model parameter selection and poor resonance effects in traditional bearing fault detection, this paper proposes a parameter-adaptive stochastic resonance algorithm based on an improved whale optimization algorithm (IWOA), which can effectively detect bearing fault signals of rotating machinery. First, the traditional WOA was improved with respect to initial solution distribution, global search ability and population diversity generalization, effectively improving the global convergence of the WOA. Then, the parameters of the bistable stochastic resonance model were optimized using the improved WOA, and adaptive adjustment of the stochastic resonance parameters was realized. Finally, the Case Western Reserve University bearing data set and the XJTU-SY bearing data set were used as fault data for the actual bearing to be tested for experimental verification. The signal-to-noise ratios of the detected fault frequencies for the above two data sets were −20.5727 and −21.1289, respectively. Among the algorithms compared, the IWOA proposed in this paper had the highest signal-to-noise ratio of the detected fault frequencies. The experimental results show that the proposed method can effectively detect a weak bearing fault signal in enhanced noise.

A deep learning based reduced order modeling for stochastic underground flow problems

In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate mapping from the stochastic parameter space that characterizes the possible highly heterogeneous media to the solution space of a stochastic flow problem. Offline preparation includes collecting a set of full-order solutions to form a global snapshot space and extracting dominating POD modes using a particular well-designed spectral problem to represent full-order solutions. Due to the small dimension of reduced-order solutions, the complexity of neural network is significantly lightened, which effectively relieves the burden of training. We adopt the generalized multiscale finite element method (GMsFEM), where a set of local multiscale basis functions that can capture the heterogeneity of the media and source information are constructed to efficiently generate globally defined snapshot space. In an online stage, one can rapidly obtain the reduced-order pressure and then corresponding full-order solution is recovered using a linear transformation. Due to the decoupling of offline and online procedures, the proposed reduced order method serves as a non-intrusive tool that can achieve fast simulations independent of input parameters. Rigorous theoretical analyses are provided and extensive numerical experiments for linear and nonlinear stochastic flows are provided to verify the superior performance of the proposed method.

Cellular Automata Model for Traffic Flow with Optimised Stochastic Noise Parameter

Based on the existing safe distance cellular automata model, an improved cellular automata model based on realistic human reactions is proposed in this paper, which aims to reproduce the characteristics of congested traffic flow. In the proposed model, the stochastic noise param-eter is optimised by considering driving behavioural dif-ference. The relative speed, gap and acceleration of the front vehicle are introduced into the optimised stochastic noise parameter oriented to describing the asymmetric acceleration behaviour of drivers in congestion. The sim-ulation results show that an uneven distribution of accel-eration trajectories of vehicles experiencing congestion exhibited on the spatial-temporal diagram of the pro-posed model is reproduced. Based on the analysis of the NGSIM, compared with the model with traditional sto-chastic noise parameter, the vehicles that move accord-ing to the proposed model can follow more easily and more realistically. Then the actual gap of vehicles can be better reflected by the proposed model and the change of vehicle speed is more stable. Additionally, the traffic efficiency from two aspects of flow and speed shows that the proposed model can significantly improve the traffic efficiency in the medium high density region.

Optimal Investment, Consumption and Life Insurance Problem with Stochastic Environments

Optimal investment, consumption and life insurance problem with stochastic environments for a CRRA wage-earner is solved in this study.  The wage-earner invests in the financial market with one risk-free security, one risky security, receives labor income and has a life insurance policy in the insurance market. A life insurance policy is purchased to hedge the financial wealth for the beneficiary in case of wage earner premature death. The interest rate and the volatility are stochastic. The stochastic interest rate dynamics of risk-free security follow a Ho-Lee model and the risky security follow Heston’s model with stochastic volatility parameter dynamics following a Cox-Ingersoll-Ross (CIR) model. The objective of the wage-earner is to allocate wealth between risky security and risk-free security but also buy a life insurance policy during the investment period to maximize the expected discounted utilities derived from consumption, legacy and terminal wealth over an uncertain lifetime. By applying Bellman's optimality principle, the associated HJB PDE for the value function is established. The power utility function is employed for our analysis to obtain the value function and optimal policies. Finally, numerical examples and simulations are provided.

Sensitivity of Modeled Microphysics to Stochastically Perturbed Parameters

AbstractThis study examines the characteristics of several model parameter perturbation methodologies for ensemble simulations of cloud microphysical processes in convection. A simplified 1D model is used to focus the results on cloud microphysics without the complication of feedbacks to the dynamics and environment. Several parameter perturbation methods are tested, including non‐stochastic and stochastic with various distributions and parameter covariance. We find that an ensemble comprised of different time‐invariant parameters (non‐stochastic) exhibits little bias, but small spread. In addition, its behavior does not respect the time evolution of convection through its various phases. Stochastic parameter (SP) methods in which no inter‐parameter covariance is applied produce greater spread, but significant bias. The bias is particularly large for lognormal parameter perturbation distributions. The ensemble spread is retained and the bias reduced when time‐varying parameter covariance is applied. In this case, the SP scheme is able to adapt to the time and state‐dependent covariance structures and produce ensemble characteristics that are consistent with the specific microphysical processes operating at any given time. The results suggest that SP schemes would benefit from inclusion of parameter covariances, and specifically those that vary with the state of the system. It also suggests that a Normal or LogNormal SP scheme with no covariance may significantly impact the ensemble bias. Finally, the results indicate that high temporal and spatial resolution observations may be needed to characterize the variability in parameter values and covariance.

Stochastic Parameterizations for Improving the Estimation of Channelized Reservoirs in an Assisted History Matching Context

Stochastic Parameterizations for Improving the Estimation of Channelized Reservoirs in an Assisted History Matching Context

Reliability estimation of a Tibetan heritage timber structure with inclination in its Que-Ti joints

The reliability of a Tibetan timber frame in a heritage building in Lasha, China is studied. The frame is featured with stochastic Que-Ti joints with inclination. A new method integrating the relative entropy-based probabilistic sensitivity analysis and the Probabilistic Density Evolution Method with absorbing boundary condition is developed for this study. The contributions of stochastic parameters to the probabilistic bearing capacity of the joint can be clearly defined from the differences between the probability density functions of the bearing capacity with different parameter perturbation. Results are obtained via sensitivity analysis with engineering considerations of the heritage frame structure with a large number of uncertain parameters. The Que-Ti inclination angle, column inclination angle, the parallel-to-grain shear modulus and perpendicular-to-grain elastic modulus, which have greater influence on the performances of the heritage frame structure are identified with acceptable computation requirements. A reduced-dimensioned model of the structure with selected variables is then verified and used for the reliability estimation. The structural reliability is noted efficiently implemented with the random variables of the frame system reduced from 13 to 4. The frames in this heritage building with stochastic inclined Que-Ti joints are relatively safe comparing to the recommended reliability limit in the design code.

Polynomial neural network based probabilistic hydrodynamic analysis of two-lobe bearings with stochasticity in surface roughness

This paper investigates the probabilistic response of two-lobe bearings considering the uncertainty in eccentricity ratio, preload value, bearing clearance, supply pressure, oil viscosity and surface roughness. To simulate stochasticity in input variables, Monte Carlo simulation (MCS) is carried out in conjunction with the Reynolds equation using finite difference method. Polynomial neural network based machine learning model is used as a surrogate model to increase the efficiency of MCS. To assess the relative importance of the stochastic input parameters, a sensitivity analysis is carried out. The physically insightful new probabilistic results, presented here covering a wide spectrum of uncertainty sources including surface roughness, make it evident that different forms of source-uncertainties have a significant effect on the critical performance of bearings.