Stochastic Parameters Research Articles

A Cost-Benefit Analysis Simulation for the Digitalisation of Cold Supply Chains.

This paper investigates using simulation to predict the benefits and costs of digitalising cold distribution chains. The study focuses on the distribution of refrigerated beef in the UK, where digitalisation was implemented to re-route cargo carriers. By comparing simulations of both digitalised and non-digitalised supply chains, the study found that digitalisation can reduce beef waste and decrease the number of miles driven per successful delivery, leading to potential cost savings. Note that this work is not attempting to prove that digitalisation is appropriate for the chosen scenario, only to justify a simulation approach as a decision making tool. The proposed modelling approach provides decision-makers with more accurate predictions of the cost-benefit of increased sensorisation in supply chains. By accounting for stochastic and variable parameters, such as weather and demand fluctuations, simulation can be used to identify potential challenges and estimate the economic benefits of digitalisation. Moreover, qualitative assessments of the impact on customer satisfaction and product quality can help decision-makers consider the broader impacts of digitalisation. Overall, the study suggests that simulation can play a crucial role in facilitating informed decisions about the implementation of digital technologies in the food supply chain. By providing a better understanding of the potential costs and benefits of digitalisation, simulation can help organisations make more strategic and effective decisions.

An Event-Based Stochastic Parametric Rainfall Simulator (ESPRS) for Urban Stormwater Simulation and Performance in a Sponge City

The temporal heterogeneity of rainfall is substantial in urban catchments, and it often has huge impacts on stormwater simulation and management. Using a design storm with a fixed pattern may cause uncertainties in hydrological modeling. Here, we propose an event-based stochastic parametric rainfall simulator (ESPRS) for stormwater simulation in a sponge city with green roofs, permeable pavements, and bioretention cells. In the ESPRS, we used five distributions to fit the measured rainfall events and evaluated their performance using Akaike’s Information Criterion, Anderson—Darling goodness-of-fit test, and p-values. The vast rainfall time series data generated using the ESPRS were used to run the storm water management model for outflow simulations in the catchment, thus revealing the influence of temporal rainfall characteristics on the hydrological responses. The results showed the following: (1) The ESPRS outperforms the Chicago method in predicting extreme precipitation events, and its control factors are the rainfall peak period, rainfall peak fraction, and cumulative rainfall fraction at the peak period. (2) The best-fit functions for the rainfall depth in each period have different distributions, mostly being in lognormal, gamma, and generalized extreme value distributions. (3) Rear-type precipitation events with high peak fractions are the most negative pattern for outflow control. The developed ESPRS can suitably reproduce rainfall time series for urban stormwater management.

On the value of shipment consolidation and machine learning techniques for the optimal design of a multimodal logistics network

We study a multimodal logistics network for a multi-echelon supply chain (SC) with multiple products, considering economic and environmental sustainability and shipment consolidation (ShC). The SC logistics network is modelled as a Mixed Integer Linear Program (MILP) and then tested on randomly generated but realistic test instances. The effects of ShC in SC network design on economic and environmental costs are analyzed, showing that consolidation decreases the SC cost, especially when the distance between the shipper and receiver is significant. Moreover, machine learning (ML) approaches for predicting stochastic parameters using historical data are evaluated compared to the more traditional stochastic programming approaches over multiple prediction periods. The three ML models utilized; namely, Attention CNN-LSTM, Attention ConvLSTM and an ensemble of both models using Support Vector Regression, performed significantly better than the stochastic programming approaches considered (simple recourse and chance-constrained) in all scenarios. The numerical examples show that the MILP models using the predictions from the ML algorithms provide the highest value of the stochastic solution and the lowest expected value of perfect information. This study makes a case for the continued integration of ML prediction methodologies into stochastic optimization modelling in the setting of sustainable SC logistics design problems.

A causality-based learning approach for discovering the underlying dynamics of complex systems from partial observations with stochastic parameterization

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to stochastic noise. A practical algorithm is designed to facilitate causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure. This mitigates the curse of dimensionality and prevents the finite time blow-up issue. Numerical experiments show that the new algorithm identifies the model structure and provides suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events.

Lévy noise influences basin stability in a delayed vegetation-water dynamical system.

The stochastic stability for the irregular attraction basin in a time-delayed vegetation-water ecosystem disturbed by Lévy noise is explored. We first discuss that average delay time does not change the attractors of the deterministic model but affects the corresponding attraction basins, and we present the generation of Lévy noise. Then, we investigate the influence of stochastic parameters and delay time on the ecosystem by two statistical indicators, the first escape probability (FEP) and the mean first exit time (MFET). The numerical algorithm for calculating the FEP and the MFET in the irregular attraction basin is implemented, which is effectively verified by Monte Carlo simulations. Furthermore, the metastable basin is defined by the FEP and the MFET and confirms the consistency of the two indicators reflecting results. The result shows that the stochastic stability parameter, especially the noise intensity, decreases the basin stability of the vegetation biomass. In this environment, the time delay effect can validly alleviate its instability.

Ensemble Learning Simulation Method for Hydraulic Characteristic Parameters of Emitters Driven by Limited Data

The emitter is one of the most critical components in drip irrigation. The flow path geometry parameters have a significant effect on the emitter’s hydraulic performance and have a direct impact on the emitter’s irrigation uniformity and lifetime. The hydraulic characteristics of the emitter are the key indicators of its performance. However, obtaining the hydraulic characteristics of the emitter is complex. Typically, only a small number of calibrations are performed for specific equipment models, making it difficult to obtain the parameter. Therefore, limited data corresponding to the morphological parameters and the flow rate were simulated using the FLUENT software, and the influence of the characteristics was analyzeanalyzed, based on which a flow rate prediction model was constructed using the ensemble learning (CatBoost) model. The extended data set was generated by stochastic simulation and parameter fitting. The flow index and flow coefficient prediction model were built and evaluated using the CatBoost model again with the augmented data set as a benchmark. The results show that the significant correlation between the geometric structure and the flow index and flow coefficient provides the basis for the correlation model. CatBoost can fit the complex nonlinear relationships between the parameters well, achieving excellent simulation accuracy for the flow rate (R2 = 0.9987), flow index (R2 = 0.9961), and flow coefficient (R2 = 0.9946), where the path width has the highest importance score in the model construction for the flow index (score = 55.97) and flow coefficient (score = 45.2). Furthermore, the CatBoost models used in this study achieved the best prediction results compared to seven typical models (XGBoost, Bagging, Random Forest, Tree, Adaboost, and KNN).

A new regularized stochastic approximation framework for stochastic inverse problems

We study the nonlinear inverse problem of estimating stochastic parameters in the fourth-order partial differential equation with random data. The primary focus is on developing a novel stochastic approximation framework for inverse problems consisting of three key components. As a first step, we reformulate the inverse problem into a stochastic convex optimization problem. The second step includes developing a new regularized stochastic extragradient framework for a nonlinear variational inequality, which subsumes the optimality conditions for the optimization formulation of the inverse problem. The third step involves modeling random variables by a Karhunen–Loève type finite-dimensional noise representation, allowing the direct and the inverse problems to be conveniently discretized. We show that the regularized extragradient methods are strongly convergent in a Hilbert space setting, and we also provide several auxiliary results for the inverse problem, including Lipschitz continuity and a derivative characterization of the solution map. We provide the outcome of computational experiments to estimate stochastic and deterministic parameters. The numerical results demonstrate the feasibility and effectiveness of the developed framework and validate stochastic approximation as an effective method for stochastic inverse problems.

Ocean Model Response to Stochastically Perturbed Momentum Fluxes

Abstract Recent studies of various stochastic forcing and subgrid-scale parameterization schemes applied to climate and atmospheric models have revealed a diversity of model responses. These responses include degeneracy in the response to different forcings and compensating model errors. While stochastic parameterization of the ocean eddies is an active area, this has mainly involved idealized models with fewer studies employing ocean general circulation models. Here we examine the sensitivity of a low-resolution climate model to stochastic forcing of the momentum fluxes restricted to regions of the three-dimensional ocean where an eddy-resolving ocean model configuration has high variability. We consider the changes in the modeled energetics of low-resolution simulations in response to increased stochastic forcing. We find that as forcing amplitudes are increased there is enhanced conversion of transient to seasonal potential energy. Additionally, there is a systematic redistribution from seasonal to small-scale transient kinetic energy. Our approach has zero mean noise such that the total kinetic energy spectra remain largely unchanged even as small-scale eddy kinetic energy is increased in the targeted regions. However, we also show that strong stochastic forcing, particularly when applied in the tropics, can induce substantial changes to the ocean steady state that are undesirable. These changes include overly strong vertical mixing leading to unrealistic increases in ocean heat content and latitudinally dependent changes to sea level. We show that judicious selection of the magnitude and spatial extent of the stochastic forcing is required for desirable results. Our results point to the importance of a comprehensive evaluation of ocean model responses to stochastic parameterizations.

Cross-Correlation Analysis of the Stability of Heterogeneous Slopes

Geologic material properties of hillslopes are inherently heterogeneous, with complex layering structures due to geological deposition processes. Lacking detailed sampling of the properties’ spatial distribution has led to the stochastic representation of the properties to address uncertainty in the hillslope stability evaluation. This study treats the spatial distributions of the shear strength parameters, the cohesion (c), and the internal friction angle (φ), in a synthetic two-dimensional slope as stochastic random fields characterized by their means, variances, and correlation scales. This study then evaluates the cross-correlation between these parameters and the factor of safety (FS) using unconditional Monte Carlo simulation (MCS). Different from classical sensitivity analyses, the cross-correlation analysis of FS and the stochastic parameter fields stresses the importance of the orientation of the large-scale geological layering, the correlation between the geological media’s cohesion, and the internal friction angle at the local scale on the probability and uncertainty of failure of the heterogeneous hillslope. The analysis further guides the field sampling strategy to reduce uncertainty in the slope stability analysis due to unknown heterogeneity. More importantly, it suggests the location of stability reinforcement measures. The results of this study provide cost-effective tools for geoengineers to deal with field slope stability analysis under uncertainty.

Nonlinear dynamic analysis of a stochastic delay wheelset system

Considering not only the stochastic track irregularity and the possible effect of stochastic parameter excitation, but also the time delay of spring, that is, its response is in place, but the force generated is not in place, a stochastic delay wheelset system is established. The infinite dimensional system is reduced to the finite dimensional stochastic differential equation by using the center manifold, and further reduced to a one-dimensional diffusion process by using the stochastic averaging method. The stability of the wheelset system is obtained by analyzing the singular boundary theory and calculating the maximum Lyapunov exponent. The conditions and types of stochastic bifurcation in wheelset system are obtained by combining probability density function. The numerical simulation verifies the correctness of the theoretical analysis and shows that the time delay affects the critical hunting instability speed of wheelset. The stochastic term affects the lateral displacement of the stochastic delay wheelset system.

Temporally Local Maximum Likelihood with Application to SIS Model.

The parametric estimators applied by rolling are commonly used for the analysis of time series with nonlinear patterns, including time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of temporally local maximum likelihood (TLML) estimators. We consider the TLML estimators of (a) constant parameters, (b) stochastic, stationary parameters and (c) parameters with the ultra-long run (ULR) dynamics bridging the gap between the constant and stochastic parameters. We show that the weights used in the TLML estimators have a strong impact on the inference. For illustration, we provide a simulation study of the epidemiological susceptible-infected-susceptible (SIS) model, which explores the finite sample performance of TLML estimators of a time varying contagion parameter.

Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan.

Since the start of the COVID-19 pandemic, scientists have begun to actively use models to determine the epidemiological characteristics of the pathogen. The transmission rate, recovery rate and loss of immunity to the COVID-19 virus change over time and depend on many factors, such as the seasonality of pneumonia, mobility, testing frequency, the use of masks, the weather, social behavior, stress, public health measures, etc. Therefore, the aim of our study was to predict COVID-19 using a stochastic model based on the system dynamics approach. We developed a modified SIR model in AnyLogic software. The key stochastic component of the model is the transmission rate, which we consider as an implementation of Gaussian random walks with unknown variance, which was learned from real data. The real data of total cases turned out to be outside the predicted minimum-maximum interval. The minimum predicted values of total cases were closest to the real data. Thus, the stochastic model we propose gives satisfactory results for predicting COVID-19 from 25 to 100 days. The information we currently have about this infection does not allow us to make predictions with high accuracy in the medium and long term. In our opinion, the problem of the long-term forecasting of COVID-19 is associated with the absence of any educated guess regarding the dynamics of β(t) in the future. The proposed model requires improvement with the elimination of limitations and the inclusion of more stochastic parameters.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes.

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

A Robust Strategy to Account for Data Sampling Variability in the Development of Hydrological Models

AbstractIt is typical to use a single portion of the available data to calibrate hydrological models, and the remainder for model evaluation. To minimize model‐bias, this partitioning must be performed so as to ensure distributional representativeness and mutual consistency. However, failure to account for data sampling variability (DSV) in the underlying Data Generating Process can weaken the model's generalization performance. While “K‐fold cross‐validation” can mitigate this problem, it is computationally inefficient since the calibration/evaluation operations must be repeated numerous times. This paper develops a general strategy for stochastic evolutionary parameter optimization (SEPO) that explicitly accounts for DSV when calibrating a model using any population‐based evolutionary optimization algorithm (EOA), such as Shuffled Complex Evolution (SCE). Inspired in part by the machine‐learning strategy of stochastic gradient descent (SGD), we use various representative random sub‐samples to drive the EOA toward the distribution of the model parameters. Unlike in SGD, derivative information is not required and hence SEPO can be applied to any hydrological model where such information is not readily available. To demonstrate the effectiveness of the proposed strategy, we implement it within the well‐known SCE, to calibrate the GR4J conceptual rainfall‐runoff model to 163 hydro‐climatically diverse catchments. Using only a single optimization run, our Stochastic SCE method converges to population‐based estimates of model parameter distributions (and corresponding simulation uncertainties), without compromising model performance during either calibration or evaluation. Further, it effectively reduces the need to perform independent evaluation tests of model performance under conditions that are represented by the available data.

The deterministic excitation paradigm and the late Pleistocene glacial terminations.

A deterministic excitation (DE) paradigm is formulated, according to which the abrupt late Pleistocene glacial terminations correspond to the excitation, by the orbital forcing, of nonlinear relaxation oscillations (ROs) internal to the climate system in the absence of any stochastic parameterization. Specific rules are derived from the DE paradigm: they parameterize internal climate feedbacks, which, when activated by the crossing of certain tipping points, excite a RO. Such rules are then applied to the output of an energy-balance model simulating the fluctuations induced by realistic orbital forcing on the glacial state. The timing of the glacial terminations, thus, obtained in a reference simulation is found to be in good agreement with proxy records. A sensitivity analysis insures the robustness of the timing. The potential irrelevance of noise allowing DE to hold is discussed, and a possible explanation of the 100-kyr cycle problem based on DE is outlined. In conclusion, the DE paradigm provides the simplest possible dynamical systems characterization of the link between orbital forcing and glacial terminations implied by the Milankovitch hypothesis.

Synchronous Medical Image Augmentation framework for deep learning-based image segmentation.

Various deep learning (DL) models are widely applied in medical image analysis, and their performance depends on the scale and diversity of available training data. However, medical images often suffer from difficulty in data acquisition, imbalance in sample categories, and high cost of labeling. In addition, most image augmentation approaches mainly focus on image synthesis only for classification tasks, and rarely consider the synthetic image-label pairs for image segmentation tasks. In this paper, we focus on the medical image augmentation for DL-based image segmentation and the synchronization between augmented image samples and their labels. We design a Synchronous Medical Image Augmentation (SMIA) framework, which includes two modules based on stochastic transformation and synthesis, and provides diverse and annotated training sets for DL models. In the transform-based SMIA module, for each medical image sample and its tissue segments, a subset of SMIA factors with a random number of factors and stochastic parameter values are selected to simultaneously generate augmented samples and the paired tissue segments. In the synthesis-based SMIA module, we randomly replace the original tissues with the augmented tissues using an equivalent replacement method to synthesize new medical images, which can well maintain the original medical implications. DL-based image segmentation experiments on bone marrow smear and dermoscopic images demonstrate that the proposed SMIA framework can generate category-balanced and diverse training data, and have a positive impact on the performance of the models.

Stochastic Parameters of Flash Floods Formation in the North of the Black Sea Coast

Abstract—Flash floods are one of the most dangerous hydrometeorological events all over the World. In the current paper stochastic parameters of flash floods formation are studied on the basis of data on flash floods in 1990–2021 in the small river basins of the Caucasus and Crimea Black Sea Coast. The main factor of flash floods formation is heavy rain, but in some cases its occurrence could depend on critical combination of various factors. Flash floods are usually formed in summer-autumn period in the studied region with the maximum of observed events in August. They are characterised by very rapid water level rise of about 1.2–1.3 m/h. Sediment yield during one flash flood could be compared with mean annual values. Statistical analysis of precipitation long ranges demonstrates probability of more often flash floods occurrence in the region in comparison with observed events.

A parallel workflow framework using encoder-decoder LSTMs for uncertainty quantification in contaminant source identification in groundwater

Groundwater contamination is a major problem and it can be contaminated by natural or manmade activities. Contaminant sources cannot be identified promptly after a contamination event due to slow groundwater movement in aquifers. To limit the further spread of the plume and to take appropriate remedial measures, it is essential to determine the release rates associated with source locations as soon as a contaminant is detected in one of the observation wells in the aquifer. Conventional techniques for contaminant source identification such as the simulation–optimization (SO) uses a simulation model, which is based on estimated or, measured hydrogeological parameters, for replicating the aquifer response to contamination at source locations. However, the associated intrinsic uncertainty in the parameters can affect the estimated release histories at the source locations. To assess confidence in the results, it is important to consider stochasticity in the hydrogeological parameters for contaminant release history estimation requiring numerous runs of the SO model for corresponding breakthrough curves. The present study proposes a novel surrogate simulation optimization (SSO) framework which utilizes an Encoder-Decoder Long Short-Term Memory (ED-LSTM) based surrogate model along with Multiverse Optimization (MVO) for contaminant source identification. The comparison of ED-LSTM with other surrogate models shows its better accuracy and significantly low computational time requirement compared to the simulation model. To enhance the computational efficiency further, the SSO model is embedded in a parallel workflow for the quantification of uncertainty associated with the inverse modelling. The study shows that the proposed workflow can be efficiently used for uncertainty quantification in contaminant source identification due to stochastic parameters with a reduced computational cost.

Understanding the Drivers of Atlantic Multidecadal Variability Using a Stochastic Model Hierarchy

Abstract The relative importance of ocean and atmospheric dynamics in generating Atlantic multidecadal variability (AMV) remains an open question. Comparisons between climate models with a slab ocean (SLAB) and fully dynamic ocean components (FULL) are often used to explore this question, but cannot reveal how individual ocean processes generate these differences. We build a hierarchy of physically interpretable stochastic models to investigate the contribution of two upper-ocean processes to AMV: the role of seasonal variation and mixed-layer entrainment. This interpretability arises from the stochastic model’s simplified representation of sea surface temperature (SST), considering only the local upper-ocean response to white-noise atmospheric forcing and its impact on surface heat exchange. We focus on understanding differences between SLAB and FULL non-eddy-resolving preindustrial control simulations of the Community Earth System Model 1 (CESM), and estimate the stochastic model parameters from each respective simulation. Despite its simplicity, the stochastic model reproduces temporal characteristics of SST variability in the SPG, including reemergence, seasonal-to-interannual persistence, and power spectra. Furthermore, the unrealistically persistent SST of the CESM-SLAB ocean simulation is reproduced in the equivalent stochastic model configuration where the mixed-layer depth (MLD) is constant. The stochastic model also reveals that vertical entrainment primarily damps SST variability, thus explaining why SLAB exhibits larger SST variance than FULL. The stochastic model driven by temporally stochastic, spatially coherent forcing patterns reproduces the canonical AMV pattern. However, the amplitude of low-frequency variability remains underestimated, suggesting a role for ocean dynamics beyond entrainment.

A stochastic interior disturbance parameter model considering double uncertainty for probabilistic load calculation

The probabilistic method of calculating air-conditioning design load can effectively solve the oversizing problem in the deterministic method. However, the realization of the probabilistic method requires the quantification of the uncertain input parameters. Among them, the interior disturbance parameters are the key, whose uncertainties are caused by the unknown nature of interior configuration and the randomness of interior disturbance fluctuations. A stochastic interior disturbance parameter model considering double uncertainties (referred to simply as the DUSP model) was thus proposed. In this model, the uncertainty in the interior disturbance design parameters and interior disturbance time coefficients, which comes from two different sources, are described using probability distributions and occupant behavior models respectively. On this basis, the time series of interior disturbance parameters are generated by random sampling, to characterize the uncertainty of the interior disturbance parameters. Comparing the DUSP model with two models considering single-source uncertainty, the results showed that in the probabilistic load calculation, neglecting the uncertainty of the interior disturbance time coefficients may result in an overestimation of the design load by up to 9.2%; neglecting the uncertainty of the interior disturbance design parameters may result in an underestimation of the design load by up to 2.5%. Therefore, it is necessary to quantify the uncertainty in both sources simultaneously to ensure the reasonableness of the probabilistic load calculation.