Monte Carlo Simulation-based Method Research Articles

Capturing impacts of travel preference on connected autonomous vehicle adoption of risk-averse travellers in multi-modal transportation networks

ABSTRACT This paper proposes a reliability-based combined modal split and traffic assignment model for the multi-modal transportation network with uncertainties in which the travellers' travel preferences, vehicle ownership, and the characteristics of connected autonomous vehicles (CAVs) are considered. Travellers are classified into captive travellers and choice travellers according to their preference for travel modes and vehicle ownership. The choice travellers need to make a tradeoff among the out-of-pocket cost, comfort, and travel time reliability and make decisions between continuing to commute by subway or purchasing a human-driven vehicle (HV) or CAV. The dogit-nested-logit model is adopted to characterise the effect of travel preference on the adoption of CAVs of the choice travellers, and the multinomial logit model is adopted to capture the effect of the differences between HV and CAV on information quality and value of travel time reliability on the path choice behaviour of travellers. The problem is formulated as an equivalent variational inequality model based on the properties of the equilibrium state, and its equivalency and solution existence are discussed. A path-based algorithm is employed for solving the problem, which combines the Monte Carlo simulation-based method and the column generation method. Numerical experiments are presented to illustrate the properties of the proposed models and validate the algorithm.

On the long-term fatigue analysis of marine structures

This paper investigates the performance of several procedures available in literature used to evaluate the multi-dimensional integral associated with long-term fatigue assessment of marine structures. Direct integration methods, Monte Carlo-based approaches and Dimension-Reduction methods are investigated. The focus is on solving the four-dimensional integral for wave-induced fatigue cases when wind-sea and swell waves are simultaneously considered in the analysis. Although the procedures investigated can be used either for time-domain or frequency-domain fatigue approaches, all fatigue analyses performed in this work are restricted to the frequency-domain and are based on idealized stress transfer functions that attempt to mimic the complex behavior of some marine structures. To evaluate the performance of these methodologies, different transfer functions of unimodal and bimodal types are studied. The long-term fatigue damages are calculated using all the investigated methods, and their accuracies and efficiencies are compared. It is found that the efficiency of Monte Carlo Simulation-based methods is problem-dependent and may require many numerical simulations to achieve good accuracy for some cases. Additionally, the Dimension-Reduction methods can lead to highly suitable results with a very low number of integration points and, among all methods investigated, the BDRM (Bivariate Dimension-Reduction Method) stands out due to its excellent performance.

Extension of K-nearest neighbors and introduction of an applicable prediction criterion for a novel Monte Carlo simulation-based method in structural reliability

Efficiency is an important issue in structural reliability analysis. In this paper, a novel method is proposed to increase the efficiency of Monte Carlo Simulation by means of a machine learning algorithm. Using K-nearest neighbors method, the safe or failure region of many generated samples can be predicted without evaluating the limit state function. The proposed method represents three novel parts as its main core. In the first part of the proposed method, the classical K-nearest neighbors algorithm has been extended to a new fuzzy level such that the proposed method could predict even if all K neighbors are not in the same region. In previous similar methods, there is a prerequisite that K neighbors must be all in the failure region or all in the safe region. This extension to the fuzzy level is carried out by assigning a specific failure weight to each neighbor. In the second part of the proposed method, an innovative diagnostic criterion has been defined to check whether the region of a sample could be predicted or the sample has to be evaluated in the limit state function. The criterion describes the relative position of the newly generated sample with respect to the neighbors. This newly defined criterion is an effective alternative for the laborious action of drawing the convex hull around K neighbors, which is done as a time-consuming part in previous similar methods. Promotion of the accuracy or efficiency in the proposed method could be set using the adjusting parameter of the represented criterion. Since the implementation of the algorithm for each individual sample needs much time, in the third part, the proposed method introduces a technique to perform function evaluations or predictions in clusters. This part effectively reduces the computational burden, i.e. the number of function evaluations and run time. The performance of the proposed method, applying three novel and newly represented parts, has been verified using a number of mathematical and structural examples.

Cofitness network connectivity determines a fuzzy essential zone in open bacterial pangenome.

Most in silico evolutionary studies commonly assumed that core genes are essential for cellular function, while accessory genes are dispensable, particularly in nutrient-rich environments. However, this assumption is seldom tested genetically within the pangenome context. In this study, we conducted a robust pangenomic Tn-seq analysis of fitness genes in a nutrient-rich medium for Sinorhizobium strains with a canonical open pangenome. To evaluate the robustness of fitness category assignment, Tn-seq data for three independent mutant libraries per strain were analyzed by three methods, which indicates that the Hidden Markov Model (HMM)-based method is most robust to variations between mutant libraries and not sensitive to data size, outperforming the Bayesian and Monte Carlo simulation-based methods. Consequently, the HMM method was used to classify the fitness category. Fitness genes, categorized as essential (ES), advantage (GA), and disadvantage (GD) genes for growth, are enriched in core genes, while nonessential genes (NE) are over-represented in accessory genes. Accessory ES/GA genes showed a lower fitness effect than core ES/GA genes. Connectivity degrees in the cofitness network decrease in the order of ES, GD, and GA/NE. In addition to accessory genes, 1599 out of 3284 core genes display differential essentiality across test strains. Within the pangenome core, both shared quasi-essential (ES and GA) and strain-dependent fitness genes are enriched in similar functional categories. Our analysis demonstrates a considerable fuzzy essential zone determined by cofitness connectivity degrees in Sinorhizobium pangenome and highlights the power of the cofitness network in understanding the genetic basis of ever-increasing prokaryotic pangenome data.

Optimal Mechanism in a Dynamic Stochastic Knapsack Environment

This study introduces an optimal mechanism in a dynamic stochastic knapsack environment. The model features a single seller who has a fixed quantity of a perfectly divisible item. Impatient buyers with a piece-wise linear utility function arrive randomly and they report the two-dimensional private information: marginal value and demanded quantity. We derive a revenue-maximizing dynamic mechanism in a finite discrete time framework that satisfies incentive compatibility, individual rationality, and feasibility conditions. This is achieved by characterizing buyers' utility and utilizing the Bellman equation. Moreover, we establish the essential penalty scheme for incentive compatibility, as well as the allocation and payment policies. Lastly, we propose algorithms to approximate the optimal policy, based on the Monte Carlo simulation-based regression method and reinforcement learning.

Reliability Assessment of Integrated Power and Road System for Decarbonizing Heavy-Duty Vehicles

With the continual expansion of urban road networks and global commitments to net zero, electric vehicles (EVs) have been considered to be the most viable solution to decarbonize the transportation sector. In recent years, the electric road system (ERS) has been introduced and piloted in a few countries and regions to decarbonize heavy-duty vehicles. However, little research has been carried out on its reliability. This paper fills the gap and investigates the reliability of electric truck power supply systems for electric road (ETPSS–ER), which considers both the power system and truck traffic networks. First, a brief introduction of electric roads illustrates the working principle of EV charging on roads. Then, an optimized electric truck (ET) travel pattern model is built, based on which the corresponding ET charging load demand, including both static charging and dynamic charging, is conducted. Then, based on the new ET travel pattern model, a daily travel-pattern-driven Monte Carlo simulation-based reliability assessment method for ETPSS–ER system is presented. Case studies based on the IEEE RBTS system shows that ETs driving on ERS systems can meet the daily travel demands. The case studies also examine the impacts of increasing number of ETs, extra wind power, and battery energy storage systems (BESS) on the reliability of ERS power systems.

A Comparison of Statistical Methods to Construct Confidence Intervals and Fiducial Intervals for Measures of Health Disparities.

Health disparities are differences in health status across different socioeconomic groups. Classical methods, e.g., the Delta method, have been used to estimate the standard errors of estimated measures of health disparities and to construct confidence intervals for these measures. However, the confidence intervals constructed using the classical methods do not have good coverage properties for situations involving sparse data. In this article, we introduce three new methods to construct fiducial intervals for measures of health disparities based on approximate fiducial quantities. Through a comprehensive simulation study, We compare the empirical coverage properties of the proposed fiducial intervals against two Monte Carlo simulation-based methods-utilizing either a truncated Normal distribution or the Gamma distribution-as well as the classical method. The findings of the simulation study advocate for the adoption of the Monte Carlo simulation-based method with the Gamma distribution when a unified approach is sought for all health disparity measures.

Monte Carlo simulation-based patient-specific QA using machine log files for line-scanning proton radiation therapy.

Quality assurance (QA) is a prerequisite for safe and accurate pencil-beam proton therapy. Conventional measurement-based patient-specific QA (pQA) can only verify limited aspects of patient treatment and is labor-intensive. Thus, a better method is needed to ensure the integrity of the treatment plan. Line scanning, which involves continuous and rapid delivery of pencil beams, is a state-of-the-art proton therapy technique. Machine performance in delivering scanning protons is dependent on the complexity of the beam modulations. Moreover, it contributes to patient treatment accuracy. A Monte Carlo (MC) simulation-based QA method that reflects the uncertainty related to the machine during scanning beam delivery was developed and verified for clinical applications to pQA. Herein, a tool for particle simulation (TOPAS) for nozzle modeling was used, and the code was commissioned against the measurements. To acquire the beam delivery uncertainty for each plan, patient plans were delivered. Furthermore, log files recorded every 60 μs by the monitors downstream of the nozzle were exported from the treatment control system. The spot positions and monitor unit (MU) counts in the log files were converted to dipole magnet strengths and number of particles, respectively, and entered into the TOPAS. For the 68 clinical cases, MC simulations were performed in a solid water phantom, and two-dimensional (2D) absolute dose distributions at 20-mm depth were measured using an ionization chamber array (Octavius 1500, PTW, Freiburg, Germany). Consequently, the MC-simulated 2D dose distributions were compared with the measured data, and the dose distributions in the pre-treatment QA plan created with RayStation (RaySearch Laboratories, Stockholm, Sweden). Absolute dose comparisons were made using gamma analysis with 3%/3mm and 2%/2mm criteria for 47 clinical cases without considering daily machine output variation in the MC simulation and 21 cases with daily output variation, respectively. All cases were analyzed with 90% or 95% of passing rate thresholds. For 47 clinical cases not considering daily output variations, the absolute gamma passing rates compared with the pre-treatment QA plan were 99.71% and 96.97%, and the standard deviations (SD) were 0.70% and 3.78% with the 3%/3mm or 2%/2mm criteria, respectively. Compared with the measurements, the passing rate of 2%/2mm gamma criterion was 96.76% with 3.99% of SD. For the 21 clinical cases compared with pre-treatment QA plan data and measurements considering daily output variations, the 2%/2mm absolute gamma analysis result was 98.52% with 1.43% of SD and 97.67% with 2.72% of SD, respectively. With a 95% passing rate threshold of 2%/2mm criterion, the false-positive and false-negative were 21.8% and 8.3% for without and with considering output variation, respectively. With a 90% threshold, the false-positive and false-negative reduced to 11.4% and 0% for without and with considering output variation, respectively. A log-file-based MC simulation method for patient QA of line-scanning proton therapy was successfully developed. The proposed method exhibited clinically acceptable accuracy, thereby exhibiting a potential to replace the measurement-based dosimetry QA method with a 90% gamma passing rate threshold when applying the 2%/2mm criterion.

Analysis of UTM Tracking Performance for Conformance Monitoring via Hybrid SITL Monte Carlo Methods

Conformance monitoring supports UTM safety by observing if unmanned aircraft (UA) are adhering to declared operational intent. As a supporting system, robust cooperative tracking is critical. Nevertheless, tracking systems for UAS traffic management (UTM) are in an early stage and under-standardized, and existing literature hardly addresses the problem. To bridge this gap, this study aims to probabilistically evaluate the impact of the change in tracking performances on the effectiveness of conformance monitoring. We propose a Monte Carlo simulation-based method. To ensure a realistic simulation environment, we use a hybrid software-in-the-loop (SITL) scheme. The major uncertainties contributing to the stochastic evaluation are measured separately and are integrated into the final Monte Carlo simulation. Latency tests were conducted to assess the performance of different communication technologies for cooperative tracking. Flight technical error generation via SITL simulations and navigational system error generation based on flight experiments were employed to model UA trajectory uncertainty. Based on these tests, further Monte Carlo simulations were used to study the overall impacts of various tracking key performance indicators in UTM conformance monitoring. Results suggest that the extrapolation of UA position enables quicker non-conformance detection, but introduces greater variability in detection delay, and exacerbates the incidence of nuisance alerts and missed detections, particularly when latencies are high and velocity errors are severe. Recommendations for UA position update rates of ≥1 Hz remain consistent with previous studies, as investments in increasing the update rate do not lead to corresponding improvements in conformance monitoring performance according to simulation results.

An uncertainty quantification framework for logistic regression based geospatial natural hazard modeling

There is a class of data-driven global natural hazard predictive models that take advantage of broadly available geospatial proxies. These data-driven geospatial models have been commonly used for landslides and are becoming more available in recent years for liquefaction. Logistic regression is the most common method for predicting these ground failure occurrences. These models do not often include robust quantification of uncertainties although they are widely used in the pre-disaster planning and post-disaster response around the world. Taking the logistic regression based global geospatial liquefaction model (GGLM) (Zhu et al., 2017) as an example, we propose an uncertainty quantification (UQ) framework that consists of characterization of different sources of uncertainty, model sensitivity analysis, and forward uncertainty propagation. In this study, we have identified the main sources of uncertainty in such predictive models as parameter estimation uncertainty, modeling error, and geospatial input uncertainty. A Bayesian inference algorithm is used to quantify the posterior distribution of model parameters and quantify model parameter estimation uncertainties which are found to be negligible when a large amount of data is used in the parameter estimation process. Modeling errors are characterized based on the observed residuals between model predictions and measurements and by fitting a Gaussian distribution to the liquefaction probability residuals. The geospatial input uncertainties are characterized using the literature and expert judgment and propagated into model output. Second, we investigate the sensitivity of model output to different uncertain inputs and find that the variance of model output is largely controlled by the geospatial input uncertainties and model errors. Last, we propose an approximate forward uncertainty propagation method, which provides comparable results to a Monte Carlo simulation-based method with better computational efficiency. The proposed UQ framework provides a measure of uncertainty on model predictions and can be applied to any logistic-regression models and other geospatial modeling problems.

An Overview of Multilevel Inverters Lifetime Assessment for Grid-Connected Solar Photovoltaic Applications

Nowadays, due to advancements in power electronic devices as well as the rise in consumer awareness of the need to protect the environment on a global scale, many people are turning to the use of solar photovoltaic (PV) technology in the distributed power generation side. In the field of power electronics, manufacturers need to develop products that have high lifespans. Power electronic device reliability is important for the maintenance of the device and may be scheduled under that information. Rather than preventing failures, reliability can be improved by predicting them. Even though some research has been conducted over the past few years to investigate the reliability of power electronic devices, the reliability is many common circuits has not been investigated and this leads to a big challenge for researchers. In this review paper, an overview of the grid-connected multilevel inverters for PV systems with motivational factors, features, assessment parameters, topologies, modulation schemes of the multilevel inverter, and the selection process for specific applications are presented. In this paper, the findings of a comprehensive reliability analysis of fundamental multilevel inverters are studied. To evaluate the reliability of three basic multilevel inverters, a calculation is made using each component’s mean time before its failure. Two techniques of computation approximate and exact were used to arrive at the final result. To calculate power losses in temperature-sensitive components such as diodes and switches, MATLAB Simulink is employed. In addition, the concept of oversizing photovoltaic (PV) arrays is presented in this study. This concept proposes that energy output may be increased by increasing the size of the PV array under conditions of poor solar irradiation. Finally, the mission-profile-based and Monte Carlo simulation-based methods process flows are discussed for the accurate lifetime prediction and reliability assessments of PV inverters in a real-time scenario, followed by a conclusion with future work.

Probabilistic method for the size design of energy piles considering the uncertainty in soil parameters

Energy piles have attracted increasing attention as profitable solutions for the utilization of shallow geothermal energy. Although various complex geotechnical design models of energy piles have been proposed, a simplified sizing method that considers the uncertainty propagation in the soil is required. In this study, a Monte Carlo Simulation-based method was proposed for the size design of energy piles considering the uncertainty of parameters in the soil, such as thermal conductivity and friction angle. The small-sample analysis method of Markov chain Monte Carlo simulation combined with the Bayesian theoretical framework was developed to generate equivalent samples. Subsequently, the thermal response function and thermomechanical load transfer methods were employed to address the failure probability of the energy pile in the serviceability limit state and ultimate limit state. In addition, a case study was presented to illustrate the implementation of the proposed probabilistic sizing method. The analysis results of the case study confirm the necessity of modeling the soil uncertainty in the energy pile size design.

Development of an In Vitro System To Emulate an In Vivo Subcutaneous Environment: Small Molecule Drug Assessment.

A reliable in vitro system can support and guide the development of subcutaneous (SC) drug products. Although several in vitro systems have been developed, they have some limitations, which may hinder them from getting more engaged in SC drug product development. This study sought to develop a novel in vitro system, namely, Emulator of SubCutaneous Absorption and Release (ESCAR), to better emulate the in vivo SC environment and predict the fate of drugs in SC delivery. ESCAR was designed using computer-aided design (CAD) software and fabricated using the three-dimensional (3D) printing technique. ESCAR has a design of two acceptor chambers representing the blood uptake pathway and the lymphatic uptake pathway, respectively, although only the blood uptake pathway was investigated for small molecules in this study. Via conducting a DoE factor screening study using acetaminophen solution, the relationship of the output (drug release from the "SC" chamber to the "blood circulation" chamber) and the input parameters could be modeled using a variety of methods, including polynomial equations, machine learning methods, and Monte Carlo simulation-based methods. The results suggested that the hyaluronic acid (HA) concentration was a critical parameter, whereas the influence of the injection volume and injection position was not substantial. An in vitro-in vivo correlation (IVIVC) study was developed using griseofulvin suspension to explore the feasibility of applying ESCAR in formulation development and bioequivalence studies. The developed LEVEL A IVIVC model demonstrated that the in vivo PK profile could be correlated with the in vitro release profile. Therefore, using this model, for new formulations, only in vitro studies need to be conducted in ESCAR, and in vivo studies might be waived. In conclusion, ESCAR had important implications for research and development and quality control of SC drug products. Future work would be focused on further optimizing ESCAR and expanding its applications via assessing more types of molecules and formulations.

Reliability analysis-based investigation of the historical Széchenyi Chain Bridge deck system

Before the recent reconstruction, significant corrosion damages were observed on the deck system of the ∼170-year-old Széchenyi Chain Bridge. Therefore, an advanced reliability analysis-based study is executed to assess the risk of failure of the structure in its situation until the refurbishment starts. The current paper has the aim to introduce the applied assessment method for the risk analysis and damage grade determination of the historical structure. The novel method combines the following techniques: (i) input data coming from on-site measurements implemented into state-of-the-art corrosion models, (ii) advanced finite element model-based resistance calculation (GMNI analysis) implemented into (iii) Monte Carlo simulation-based stochastic reliability assessment method to determine the risk of the bridge deck system failure. It is concluded that the introduced method is a powerful tool for risk assessment of existing aging structures.

Monte-Carlo Simulation-Based Accessibility Analysis of Temporal Systems

Temporal networks and network-structured systems are gaining ground in daily life. Such net-works are Vehicular Ad-hoc NETworks (VANET) and Mobile Ad-hoc NETworks (MANET), in fact, Industry 4.0 requires similar local networks. During mathematical model-based analysis of real temporal systems, it is vital to determine the existence and frequency of accessibility between components. Graph theory is a well-known mathematical tool used for studying accessibility of network components. In previous publications, the author proposed an easy-usable algorithm for determining the existence of interconnection between system-components. The Monte-Carlo Simulation can model the temporality of systems. The aim of this paper is to propose a Monte-Carlo Simulation-based method that estimates symmetry or asymmetry and the frequency of accessibilities between the components of temporal network-structured systems.

An Ultralow-Power 65-nm Standard Cell Library for Near/Subthreshold Digital Circuits

In this brief, a standard cell library targeting ultra-low voltages (ULVs) is designed in a 65-nm low-power CMOS technology to enable digital integrated circuits (ICs) to achieve good tradeoff among speed, power consumption, area, and reliability in the near/subthreshold region. The transistor sizes in the standard cells are optimized by threshold voltage tuning and technology feature exploration to enhance the switching and area efficiency of transistors. To balance the pull-up and pull-down networks, a Monte Carlo (MC) simulation-based balancing method is proposed. An AES-128 test circuit is fabricated by using the proposed library, achieving a minimum voltage of 0.338 V. Compared to the state of the art, our test circuit reduces the minimum energy delay product (EDP) by at least <inline-formula> <tex-math notation="LaTeX">$3.55\times $ </tex-math></inline-formula>.

Resilience-Based Repair Strategy for Gas Network System and Water Network System in Urban City

In resilience-based frameworks, optimizing the repair strategy and approaches is important for the recovery of the function of gas network systems (GNS) and water network systems (WNS). According to the resilience quantification results of GNS and WNS for a real example urban city in China, the potential impact of utilizing different repair sequences and repair/replacement approaches was investigated. First, a Monte Carlo simulation-based method was proposed to search for the optimal repair sequence according to the skew of the recovery trajectory (SRT). Under high seismic intensity conditions, the significant difference between the repair sequence corresponding to maximum SRT and minimum SRT indicates that choosing the optimal repair sequence is important in the enhancement of repair efficiency, especially when the pipelines have experienced serious damage. We also discussed the parallel repair strategy, which is more consistent with the practice, and can greatly improve the recovery efficiency compared with the single pipeline repair strategy under large damage conditions; however, under minor damage levels, the parallel repair strategy may result in a certain degree of redundancy. Next, three different repair approaches were thoroughly compared, including the point-by-point repair approach, whole pipeline replacement, and hybrid repair approach. At the condition of high seismic intensity (e.g., macroseismic intensity IX), the resilience curves for the hybrid repair approach and the pipeline replacement approach are overall similar and take less time and economic cost than the point-by-point repair approach. However, when the seismic intensity is low, the point-by-point repair approach is most efficient and has the shortest recovery time. Therefore, the choice of repair approach should be determined by stakeholders based on the specific pipeline’s damage situation. Finally, we calculated the joint resilience curves by allocating different weight factors to GNS and WNS, to represent the proportion of water and gas supply that contributes to community resilience.

An interval evidential reasoning-based dynamic performance evaluation method for complex systems

The performance of complex systems is closely related to its safety and reliability. Grasping the performance of complex systems accurately and timely can help avoid or reduce losses if performance drops. In engineering practice, the monitoring information in interval form can express uncertainty. The upper and lower bounds of monitoring information are easier to obtain than the probability distribution, which can reduce the requirements for information distribution. In this paper, the interval evidential reasoning approach is used to evaluate performance of complex systems. A Monte Carlo simulation-based method for calculating the reliability and weight of evidence is proposed. The initial performance evaluation results are obtained by constructing a nonlinear optimization model. Then the historical performance evaluation information is fully considered to obtain the optimal evaluation results dynamically using a linear weighted update method. An uncertainty quantification method is proposed to quantify the uncertainty of input information and evaluation results. Finally, a case study is carried out for a kind of diesel generator to validate the applicability of the proposed method, and shows that the proposed method can improve the evaluation accuracy.

Reliability Evaluation of Smart Microgrids Considering Cyber Failures and Disturbances under Various Cyber Network Topologies and Distributed Generation’s Scenarios

Smart microgrids (SMGs), as cyber–physical systems, are essential parts of smart grids. The SMGs’ cyber networks facilitate efficient system operation. However, cyber failures and interferences might adversely affect the SMGs. The available studies about SMGs have paid less attention to SMGs’ cyber–physical features compared to other subjects. Although a few current research works have studied the cyber impacts on SMGs’ reliability, there is a research gap about reliability evaluation simultaneously concerning all cyber failures and interferences under various cyber network topologies and renewable distributions scenarios. This article aims to fill such a gap by developing a new Monte Carlo simulation-based reliability assessment method considering cyber elements’ failures, data/information transmission errors, and routing errors under various cyber network topologies. Considering the microgrid control center (MGCC) faults in comparion to other failures and interferences is one of the major contributions of this study. The reliability evaluation of SMGs under various cyber network topologies, particularly based on an MGCC’s redundancy, highlights this research’s advantages. Moreover, studying the interactions of uncertainties for cyber systems and distributed generations (DGs) under various DG scenarios is another contribution. The proposed method is applied to a test system using actual historical data. The comparative test results illustrate the advantages of the proposed method.

Novel fast forecasting method for nodal voltage violations

With the increase penetration of new energy and electric vehicles (EVs), the nodal voltage violations (NVVs) problem is widely concerned. Voltage predictive regulation methods can prevent NVVs and improve the performance of traditional voltage control. A fast and reliable forecasting method for NVVs is a key requirement to support this application. However, it is time-consuming to forecast NVVs using a Monte Carlo simulation-based probabilistic load flow method and the traditional deterministic method based on load forecasting has low reliability due to it not considering the uncertainty of load forecasting errors. A novel fast forecasting method for NVVs with shorter computational time and higher reliability is proposed. In the proposed method, the uncertainty of the load forecasting is taken into account and the impact of active/reactive power change on NVVs can be quantified like the traditional deterministic method. Thus, this method can assist in correcting voltage regulation plans so that voltage constraints can be satisfied as much as possible. Finally, the IEEE 69-bus test system and real historical load series are used to validate the effectiveness of the proposed method.