Stochastic Input Research Articles

Smart Grid Forecasting with MIMO Models: A Comparative Study of Machine Learning Techniques for Day-Ahead Residual Load Prediction

With the fast expansion of intermittent renewable energy sources in the upcoming smart grids, simple and accurate day-ahead systems for residual load forecasts are urgently needed. Machine learning strategies can facilitate towards drastic cost minimizations in terms of operating-reserves avoidance to compensate the mismatches between the actual and forecasted values. In this study, a multi-input/multi-output model is developed based on artificial neural networks to map the relationship between different predictor inputs, including time indices, weather variables, human activity parameters, and energy price indicators, and target outputs such as wind and photovoltaic generation. While the information flows in only one direction (from the predictor nodes through the hidden layers to the target node), benchmark training algorithms are employed and assessed under different case studies. The model is evaluated under both parametric and non-parametric formulations, namely neural networks and Gaussian process regression. Essential improvements are achieved by enhancing the number of embedded predictors, while superior performance is observed by using Bayesian regularization mechanisms. In terms of mean-error indices and determination coefficient, this opens the pathway towards minimization via Bayesian inference-based approaches in the presence of increased and highly stochastic renewable inputs.

Access to credit and scale efficiency: Evidence from family farms in East China

Productivity improvement is an important driving force for developing countries to accelerate the development of agricultural sectors and promote the transformation of economic structures. However, few studies have focused on the impact of credit access on family farms’ scale efficiency, a contributor to productivity changes. We address this gap by using data collected from a survey of 565 family farms in East China. The stochastic frontier input distance function (SFIDF) is utilized to measure the scale efficiency, and the endogenous switching regression model (ESRM) is employed to estimate average treatment effect (ATT) and address the selection bias. The empirical results show that the average scale efficiency is 0.768, with credit users and non-users averaging 0.802 and 0.737, respectively. Most family farms operate below their optimal production scale, and only about 14.5% of family farms exceed this optimal scale. Access to credit has significantly improved the scale efficiency of family farms and has not contributed to the excessive pursuit of scale expansion for financial subsidies. These findings are validated by robustness checks. The conclusions of our study have important implications for developing countries seeking to increase financial support for agricultural development.

The Vestfold Hills are alive: characterising microbial and environmental dynamics in Old Wallow, eastern Antarctica.

Old Wallow is an underexplored, hyper-arid coastal desert in Antarctica's Vestfold Hills. Situated near an elephant seal wallow, we examined how stochastic nutrient inputs from the seal wallow affect soil communities amid environmental changes along a spatially explicit sampling transect. We hypothesized that nutrient levels would be elevated due to proximity to the seal wallow, influencing community distributions. While the soil bacterial and eukaryotic communities at the phylum level were similar to other terrestrial environments, analysis at class and family levels revealed a dominance of unclassified taxa that are often linked to marine environments. Elevated nutrient concentrations (NO3 -, SO4 2-, SO3) were found at Old Wallow, with conductivity and Cl- levels up to 10-fold higher at the lowest elevation soils, correlating with significantly (p < 0.05) higher abundances of halophilic (Halomonadaceace) and uncultivated lineages (Ca Actinomarinales, unclassified Bacillariophyta and unclassified Opisthonkonta). An improved Gradient Forest model was used to quantify microbial responses to 26 soil gradients at OW, revealing variable responses to environmental predictors and identifying critical environmental thresholds or drivers of community turnover. Major tipping points were projected for eukaryotes with SO4 2-, pH, and SO3, and for bacteria with moisture, Na2O, and Cl-. Thus, the Old Wallow ecosystem is primarily shaped by salt, sulphate, and moisture and is dominated by uncultivated taxa, which may be sensitive to environmental changes once critical tipping points are reached. This study provides critical baseline data for future regional monitoring under threats of environmental change.

Logistics of Medical Waste Management: A Systematic Review of Quantitative Models

Background: Medical waste poses various risks to public health, with heightened importance post-COVID-19. The pandemic escalated the ever-growing generation of medical waste, which demands meticulous handling to mitigate potential risks to the healthcare system and the public. Medical waste management relies heavily on logistics, ensuring the safe and proper disposal of medical waste. Objective: Quantitative models play an integral part in establishing effective, flexible, and costefficient logistics in medical waste management. They enable precise planning, optimizing routes, and determining the most efficient disposal methods. This paper provides a systematic review of quantitative models for the logistics of medical waste management. Methods: Through comprehensive search, filtering, and screening, we identify 96 documents for detail review. Results: We present a structural review covering key aspects of modeling: entities involved, objectives, constraints, solution methods, uncertainties and stochastic input, multi-criteria decision analysis, and post-optimality analysis. Conclusion: This state-of-the-art review provides a general guideline for the current approaches to modeling and quantitatively analyzing the logistics of wase management. Our paper also serves as a starting point for practitioners aiming to learn the basics of running logistics of medical waste management.

Probabilistic Performance-Pattern Decomposition (PPPD): Analysis framework and applications to stochastic mechanical systems

Numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as “solved” when a complete or partial probabilistic description on quantities of interest (QoIs) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond computing probabilities. In fact, to gain a better understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoIs, especially when the QoIs are computed in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: (1) an illustrative example with hypothetical stochastic processes input and output; (2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and (3) a simplified shear-building model subjected to a stochastic ground motion excitation.

Sensory choices as logistic classification

Logistic classification is a simple way to make choices based on a set of factors: give each factor a weight, sum the results, and use the sum to set the log odds of a random draw. This operation is known to describe human and animal choices based on value (economic decisions). There is increasing evidence that it also describes choices based on sensory inputs (perceptual decisions), presented across sensory modalities (multisensory integration) and combined with non-sensory factors such as prior probability, expected value, overall motivation, and recent actions. Logistic classification can also capture the effects of brain manipulations such as local inactivations. The brain may implement it by thresholding stochastic inputs (as in signal detection theory) acquired over time (as in the drift diffusion model). It is the optimal strategy under certain conditions, and the brain appears to use it as a heuristic in a wider set of conditions.

Slope displacement reliability analysis considering rock parameters spatial variability subjected to stochastic mainshock-aftershock earthquake

A new and efficient framework for analyzing the stochastic dynamic response and reliability of the rock slope was constructed based on the generalized probability density evolution method (GPDEM). The left bank slope of Jinping dam was taken as an illustrative example and the effects of mainshock-aftershock sequence randomness, spatial variability of geotechnical materials and coupled uncertainties on the slope dynamic response and reliability were compared and analyzed for the first time. Firstly, a series of mainshock-aftershock sequences and parameter random fields were generated as stochastic factors inputs. Then, the effectiveness of GPDEM was validated by comparing with Monte Carlo Simulation (MCS). The Newmark slip displacement method was combined with GPDEM to analyze the slope dynamic response and reliability subjected to single and coupled uncertainties from a probabilistic viewpoint. Finally, the fragility curves of three risk levels were established based on the reliabilities with different seismic intensities. The result suggests that parameter spatial variability affects the dynamic response and reliability of the slope to some extent, but this effect will be overshadowed by the uncertainty of mainshock-aftershock sequences when it is considered simultaneously. Besides, aftershocks will cause the decrease of slope reliability and the impact of aftershock cannot be overlooked.

Sensory choices as logistic classification.

Logistic classification is a simple way to make choices based on a set of factors: give each factor a weight, sum the results, and use the sum to set the log odds of a random draw. This operation is known to describe human and animal choices based on value (economic decisions). There is increasing evidence that it also describes choices based on sensory inputs (perceptual decisions), presented across sensory modalities (multisensory integration) and combined with non-sensory factors such as prior probability, expected value, overall motivation, and recent actions. Logistic classification can also capture the effects of brain manipulations such as local inactivations. The brain may implement by thresholding stochastic inputs (as in signal detection theory) acquired over time (as in the drift diffusion model). It is the optimal strategy under certain conditions, and the brain appears to use it as a heuristic in a wider set of conditions.

Trajectory-based global sensitivity analysis in multiscale models

This research introduces a novel global sensitivity analysis (GSA) framework for agent-based models (ABMs) that explicitly handles their distinctive features, such as multi-level structure and temporal dynamics. The framework uses Grassmannian diffusion maps to reduce output data dimensionality and sparse polynomial chaos expansion (PCE) to compute sensitivity indices for stochastic input parameters. To demonstrate the versatility of the proposed GSA method, we applied it to a non-linear system dynamics model and epidemiological and economic ABMs, depicting different dynamics. Unlike traditional GSA approaches, the proposed method enables a more general estimation of parametric sensitivities spanning from the micro level (individual agents) to the macro level (entire population). The new framework encourages the use of manifold-based techniques in uncertainty quantification, enhances understanding of complex spatio-temporal processes, and equips ABM practitioners with robust tools for detailed model analysis. This empowers them to make more informed decisions when developing, fine-tuning, and verifying models, thereby advancing the field and improving routine practice for GSA in ABMs.

Robustness of reaction–diffusion PDEs predictor-feedback to stochastic delay perturbations

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r+1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant’s state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C0-semigroup theory for well-posedness. Our stability result refers to the L2-norm of the plant state and the H2-norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficientand the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study.

Polynomial chaos expansion of SAR and temperature increase variability in 3 T MRI due to stochastic input data

Objective. Numerical simulations are largely adopted to estimate dosimetric quantities, e.g. specific absorption rate (SAR) and temperature increase, in tissues to assess the patient exposure to the radiofrequency (RF) field generated during magnetic resonance imaging (MRI). Simulations rely on reference anatomical human models and tabulated data of electromagnetic and thermal properties of biological tissues. However, concerns may arise about the applicability of the computed results to any phenotype, introducing a significant degree of freedom in the simulation input data. In addition, simulation input data can be affected by uncertainty in relative positioning of the anatomical model with respect to the RF coil. The objective of this work is the to estimate the variability of SAR and temperature increase at 3 T head MRI due to different sources of variability in input data, with the final aim to associate a global uncertainty to the dosimetric outcomes. Approach. A stochastic approach based on arbitrary Polynomial Chaos Expansion is used to evaluate the effects of several input variability’s (anatomy, tissue properties, body position) on dosimetric outputs, referring to head imaging with a 3 T MRI scanner. Main results. It is found that head anatomy is the prevailing source of variability for the considered dosimetric quantities, rather than the variability due to tissue properties and head positioning. From knowledge of the variability of the dosimetric quantities, an uncertainty can be attributed to the results obtained using a generic anatomical head model when SAR and temperature increase values are compared with safety exposure limits. Significance. This work associates a global uncertainty to SAR and temperature increase predictions, to be considered when comparing the numerically evaluated dosimetric quantities with reference exposure limits. The adopted methodology can be extended to other exposure scenarios for MRI safety purposes.

METHOD FOR GENERATING A DATA SET FOR TRAINING A NEURAL NETWORK IN A TRANSPORT CONVEYOR MODEL

The object of research is a stochastic input flow of material coming in the input of a conveyor-type transport system. Subject of research is the development of a method for generating values of the stochastic input material flow of transport conveyor to form a training data set for neural network models of the transport conveyor. The goal of the research is to develop a method for generating random values to construct implementations of the input material flow of a transport conveyor that have specified statistical characteristics calculated based on the results of previously performed experimental measurements. The article proposes a method for generating a data set for training a neural network for a model of a branched, extended transport conveyor. A method has been developed for constructing implementations of the stochastic input flow of material of a transport conveyor. Dimensionless parameters are introduced to determine similarity criteria for input material flows. The stochastic input material flow is presented as a series expansion in coordinate functions. To form statistical characteristics, a material flow implementation based on the results of experimental measurements is used. As a zero approximation for expansion coefficients, that are random variables, the normal distribution law of a random variable is used. Conclusion. It is shown that with an increase in the time interval for the implementation of the input material flow, the correlation function of the generated implementation steadily tends to the theoretically determined correlation function. The length of the time interval for the generated implementation of the input material flow was estimated.

Three-dimensional stochastic dynamical modeling for wind farm flow estimation

Modifying turbine blade pitch, generator torque, and nacelle direction (yaw) are conventional approaches for enhancing energy output and alleviating structural loads. However, the efficacy of such methods is challenged by the lag in adjusting such settings after atmospheric variations are detected. Without reliable short-term wind forecasting tools, current practice, which mostly relies on data collected at or just behind turbines, can result in sub-optimal performance. Data-assimilation strategies can achieve real-time wind forecasting capabilities by correcting model-based predictions of the incoming wind using various field measurements. In this paper, we revisit the development of a class of prior models for real-time estimation via Kalman filtering algorithms that track atmospheric variations using ground-level pressure sensors. This class of models is given by the stochastically forced linearized Navier-Stokes equations around the three-dimensional waked velocity profile defined by a curled wake model. The stochastic input to these models is devised using convex optimization to achieve statistical consistency with high-fidelity large-eddy simulations. We demonstrate the ability of such models in reproducing the second-order statistical signatures of the turbulent velocity field. In support of assimilating ground-level pressure measurements with the predictions of said models, we also highlight the significance of the wall-normal dimension in enhancing two-point correlations of the pressure field between the ground and the computational domain.

Exact Distribution of the Quantal Content in Synaptic Transmission.

During electrochemical signal transmission through synapses, triggered by an action potential (AP), a stochastic number of synaptic vesicles (SVs), called the "quantal content," release neurotransmitters in the synaptic cleft. It is widely accepted that the quantal content probability distribution is a binomial based on the number of ready-release SVs in the presynaptic terminal. But the latter number itself fluctuates due to its stochastic replenishment, hence the actual distribution of quantal content is unknown. We show that exact distribution of quantal content can be derived for general stochastic AP inputs in the steady state. For fixed interval AP train, we prove that the distribution is a binomial, and corroborate our predictions by comparison with electrophysiological recordings from MNTB-LSO synapses of juvenile mice. For a Poisson train, we show that the distribution is nonbinomial. Moreover, we find exact moments of the quantal content in the Poisson and other general cases, which may be used to obtain the model parameters from experiments.

Smoothing in linear multicompartment biological processes subject to stochastic input.

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs. In this work, we study a simple analog of this problem through a linear multicompartment model subject to a stochastic input in the form of a mean-reverting Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the system as a multidimensional Gaussian process, we derive several closed-form analytical results relating to the covariances and autocorrelations of the system, quantifying the smoothing effect discrete compartments afford multicompartment systems. Semianalytical results demonstrate that feedback and feedforward loops can enhance system robustness, and simulation results probe the intractable problem of the first passage time distribution, which has specific relevance to eventual cell lysis in the viral replication cycle. Finally, we demonstrate that the smoothing seen in the process is a consequence of the discreteness of the system, and does not manifest in systems with continuous transport. While we make progress through analysis of a simple linear problem, many of our insights are applicable more generally, and our work enables future analysis into multicompartment processes subject to stochastic inputs.

Understanding and Quantifying Network Robustness to Stochastic Inputs.

A variety of biomedical systems are modeled by networks of deterministic differential equations with stochastic inputs. In some cases, the network output is remarkably constant despite a randomly fluctuating input. In the context of biochemistry and cell biology, chemical reaction networks and multistage processes with this property are called robust. Similarly, the notion of a forgiving drug in pharmacology is a medication that maintains therapeutic effect despite lapses in patient adherence to the prescribed regimen. What makes a network robust to stochastic noise? This question is challenging due to the many network parameters (size, topology, rate constants) and many types of noisy inputs. In this paper, we propose a summary statistic to describe the robustness of a network of linear differential equations (i.e. a first-order mass-action system). This statistic is the variance of a certain random walk passage time on the network. This statistic can be quickly computed on a modern computer, even for complex networks with thousands of nodes. Furthermore, we use this statistic to prove theorems about how certain network motifs increase robustness. Importantly, our analysis provides intuition for why a network is or is not robust to noise. We illustrate our results on thousands of randomly generated networks with a variety of stochastic inputs.

A Stochastic Methodology for EV Fast-Charging Load Curve Estimation Considering the Highway Traffic and User Behavior

The theoretical impact of the electric vehicle (EV) market share growth has been widely discussed with regards to technical and socioeconomic aspects in recent years. However, the prospection of EV scenarios is a challenge, and the difficulty increases with the granularity of the study and the set of variables affected by user behavior and regional aspects. Moreover, the lack of a robust database to estimate fast-charging stations’ load curves, for example, affects the quality of planning, allocation, or grid impact studies. When this problem is evaluated on highways, the challenge increases due to the reduced number of trips related to the reduced number of charger units installed and the limited EVs range, which influence user anxiety. This paper presents a methodology to estimate the highway fast-charging station operation condition, considering regional and EV user aspects. The process is based in a block of traffic simulation, considering the traffic information and highway patterns composing the matrix solution model. Also, the output block estimates charging stations’ operational conditions, considering infrastructure scenarios and simulated traffic. A Monte Carlo simulation is presented to model entrance rates and charging times, considering the PDF of stochastic inputs. The results are shown for the aspects of load curve and queue length for one case study, and a sensibility study was conducted to evaluate the impact of model inputs.

Formation Control of Second-Order Multiagent System via Stochastic Control Input

Formation Control of Second-Order Multiagent System via Stochastic Control Input

Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees

We study an online allocation problem with sequentially arriving items and adversarially chosen agent values, with the goal of balancing fairness and efficiency. Our goal is to study the performance of algorithms that achieve strong guarantees under other input models such as stochastic inputs, in order to achieve robust guarantees against a variety of inputs. To that end, we study the PACE (Pacing According to Current Estimated utility) algorithm, an existing algorithm designed for stochastic input. We show that in the equal-budgets case, PACE is equivalent to an integral greedy algorithm. We go on to show that with natural restrictions on the adversarial input model, both the greedy allocation and PACE have asymptotically bounded multiplicative envy as well as competitive ratio for Nash welfare, with the multiplicative factors either constant or with optimal order dependence on the number of agents. This completes a "best-of-many-worlds" guarantee for PACE, since past work showed that PACE achieves guarantees for stationary and stochastic-but-non-stationary input models.

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

The passivity‐based boundary control is considered for stochastic Korteweg–de Vries–Burgers (SKdVB) equations. Both the stochastic input strictly passive (SISP) and stochastic output strictly passive (SOSP) are studied. By introducing Lyapunov functionals and Wirtinger's inequality, sufficient criteria are derived to establish SISP and SOSP for SKdVB equations with boundary disturbances. Moreover, when parameter uncertainties arise in SKdVB equations, the robust stochastic passivity is also investigated and sufficient criteria are presented to achieve the robust SISP and SOSP. Two numerical simulations are employed to show the effectiveness and advantages of our theoretical results.