Low-Carbon Dispatch of an Integrated Energy System Considering Confidence Intervals for Renewable Energy Generation

Addressing the insufficiency in down-regulation leeway within integrated energy systems stemming from the erratic and volatile nature of wind and solar renewable energy generation,this study focuses on formulating a coordinated strategy involving the carbon capture unit of the integrated energy system and the resources on the load storage side.A scheduling model is devised that takes into account the confidence interval associated with renewable energy generation,with the overarching goal of optimizing the system for low-carbon operation.To begin with,an in-depth analysis is conducted on the temporal energy-shifting attributes and the low-carbon modulation mechanisms exhibited by the source-side carbon capture power plant within the context of integrated and adaptable operational paradigms.Drawing from this analysis,a model is devised to represent the adjustable resources on the charge-storage side,predicated on the principles of electro-thermal coupling within the energy system.Subsequently,the dissimilarities in the confidence intervals of renewable energy generation are considered,leading to the proposition of a flexible upper threshold for the confidence interval.Building on this,a low-carbon dispatch model is established for the integrated energy system,factoring in the margin allowed by the adjustable resources.In the final phase,a simulation is performed on a regional electric heating integrated energy system.This simulation seeks to assess the impact of source-load-storage coordination on the system’s low-carbon operation across various scenarios of reduction margin reserves.The findings underscore that the proactive scheduling model incorporating confidence interval considerations for reduction margin reserves effectively mitigates the uncertainties tied to renewable energy generation.Through harmonized orchestration of source,load,and storage elements,it expands the utilization scope for renewable energy,safeguards the economic efficiency of system operations under low-carbon emission conditions,and empirically validates the soundness and efficacy of the proposed approach.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

Deep learning-based evaluation of factor of safety with confidence interval for tunnel deformation in spatially variable soil

The random finite difference method(RFDM) is a popular approach to quantitatively evaluate the influence of inherent spatial variability of soil on the deformation of embedded tunnels.However,the high computational cost is an ongoing challenge for its application in complex scenarios.To address this limitation,a deep learning-based method for efficient prediction of tunnel deformation in spatially variable soil is proposed.The proposed method uses one-dimensional convolutional neural network(CNN) to identify the pattern between random field input and factor of safety of tunnel deformation output.The mean squared error and correlation coefficient of the CNN model applied to the newly untrained dataset was less than 0.02 and larger than 0.96,respectively.It means that the trained CNN model can replace RFDM analysis for Monte Carlo simulations with a small but sufficient number of random field samples(about 40 samples for each case in this study).It is well known that the machine learning or deep learning model has a common limitation that the confidence of predicted result is unknown and only a deterministic outcome is given.This calls for an approach to gauge the model’s confidence interval.It is achieved by applying dropout to all layers of the original model to retrain the model and using the dropout technique when performing inference.The excellent agreement between the CNN model prediction and the RFDM calculated results demonstrated that the proposed deep learning-based method has potential for tunnel performance analysis in spatially variable soils.

Statistical damage detection method for frame structures using a confidence interval

A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, and exponentially weighted moving average （EWMA） are applied to detect damage information according to statistical process control （SPC） theory. It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution. On the other hand, the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter. A suitable moderate confidence level is explored for more significant damage location and quantification detection, and the impact of noise is investigated to illustrate the robustness of the method.

Confidence Intervals for Relative Intensity of Collaboration(RIC)Indicators

Purpose:We aim to extend our investigations related to the Relative Intensity of Collaboration(RIC)indicator,by constructing a confidence interval for the obtained values.Design/methodology/approach:We use Mantel-Haenszel statistics as applied recently by Smolinsky,Klingenberg,and Marx.Findings:We obtain confidence intervals for the RIC indicatorResearch limitations:It is not obvious that data obtained from the Web of Science(or any other database)can be considered a random sample.Practical implications:We explain how to calculate confidence intervals.Bibliometric indicators are more often than not presented as precise values instead of an approximation depending on the database and the time of measurement.Our approach presents a suggestion to solve this problem.Originality/value:Our approach combines the statistics of binary categorical data and bibliometric studies of collaboration.

Semi-empiricial Likelihood Confidence Intervals for the Differences of Two Populations Based on Fractional Imputation

Suppose that there are two populations x and y with missing data on both of them, where x has a distribution function F（·） which is unknown and y has a distribution function Gθ（·） with a probability density function gθ（·） with known form depending on some unknown parameter θ. Fractional imputation is used to fill in missing data. The asymptotic distributions of the semi-empirical likelihood ration statistic are obtained under some mild conditions. Then, empirical likelihood confidence intervals on the differences of x and y are constructed.

Confidence Interval Estimation of the Correlation in the Presence of Non-Detects

This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extreme imbalance in censoring proportions, and non-bivariate normal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. Confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. Intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.

Computing Confidence Intervals for the Postal Service’s Cost-Elasticity Estimates

This paper provides methods for assessing the precision of cost elasticity estimates when the underlying regression function is assumed to be polynomial. Specifically, the paper adapts two well-known methods for computing confidential intervals for ratios: the delta-method and the Fieller method. We show that performing the estimation with mean-centered explanatory variables provides a straightforward way to estimate the elasticity and compute a confidence interval for it. A theoretical discussion of the proposed methods is provided, as well as an empirical example based on publicly available postal data. Possible areas of application include postal service providers worldwide, transportation and electricity.

Confidence Intervals for the Binomial Proportion: A Comparison of Four Methods

This paper presents four methods of constructing the confidence interval for the proportion p of the binomial distribution. Evidence in the literature indicates the standard Wald confidence interval for the binomial proportion is inaccurate, especially for extreme values of p. Even for moderately large sample sizes, the coverage probabilities of the Wald confidence interval prove to be erratic for extreme values of p. Three alternative confidence intervals, namely, Wilson confidence interval, Clopper-Pearson interval, and likelihood interval, are compared to the Wald confidence interval on the basis of coverage probability and expected length by means of simulation.

DEA Scores’ Confidence Intervals with Past-Present and Past-Present-Future Based Resampling

In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency scores need to be examined by considering these factors. In this paper, we propose new resampling models based on these variations for gauging the confidence intervals of DEA scores. The first model utilizes past-present data for estimating data variations imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second model deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to a dataset composed of Japanese municipal hospitals.

CONSTRUCTION AND COMPARISONS OF SIMULTANEOUS CONFIDENCE INTERVALS FOR THE MEAN DIFFERENCE OF MULTIVARIATE NORMAL DISTRIBUTIONS

In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that when there are only two populations,Bonferroni bounds and Simplified Scheffébounds are the same and they are shorter than Scheffé bounds for p10.In the case for 3k10and 2p10,there exists n(p,k)such that Bonferroni method is better than Simplified Schefféprocedure for nn(p,k),otherwise Simplified Scheffé procedure is better.Finally,the authors findout that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger thananother through numerical calculation.

GENERALIZED p-VALUES AND GENERALIZED CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN GENERAL RANDOM EFFECT MODEL WITH BALANCED DATA

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.

Constructing confidence intervals of extreme rainfall quantiles using Bayesian,bootstrap,and profile likelihood approaches

Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.

Scatter factor confidence interval estimate of least square maximum entropy quantile function for small samples

Classic maximum entropy quantile function method （CMEQFM） based on the probability weighted moments （PWMs） can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method （LSMEQFM） and that with constraint condition （LSMEQFMCC） are proposed. To improve the confidence level of quantile function estimation, scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples （10 samples）; LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples; with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples （10 samples）.

Semi-empirical Likelihood Confidence Intervals for the Differences of Quantiles with Missing Data

Detecting population （group） differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed.

CONFIDENCE INTERVALS FOR NONPARAMETRIC REGRESSION FUNCTIONS WITH MISSING DATA： MULTIPLE DESIGN CASE

This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x） ＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.

Coverage Accuracy of Confidence Intervals in Nonparametric Regression

Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable.

Confidence interval of intrinsic optimum temperature estimated using thermodynamic SSI model

The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecolog- ical and evolutional processes. The Sharpe-Schoolfield-Ikemoto （SSI） model succeeded in defining the temperature that can thermodynamically meet the condition that at a par- ticular temperature the probability of an active enzyme reaching its maximum activity is realized. Previously, an algorithm was developed by Ikemoto （Tropical malaria does not mean hot environments. Journal of Medical Entomology, 45, 963-969） to estimate model parameters, but that program was computationally very time consuming. Now, investi- gators can use the SSI model more easily because a full automatic computer program was designed by Shi et al. （A modified program for estimating the parameters of the SSI model. Environmental Entomology, 40, 462-469）. However, the statistical significance of the point estimate of the intrinsic optimum temperature for each ectotherm has not yet been determined. Here, we provided a new method for calculating the confidence interval of the estimated intrinsic optimum temperature by modifying the approximate bootstrap confidence intervals method. For this purpose, it was necessary to develop a new program for a faster estimation of the parameters in the SSI model, which we have also done.

Empirical Likelihood Ratio Confidence Interval for Positively Associated Series

Empirical likelihood is discussed by using the blockwise technique for strongly stationary, positively associated random variables. Our results show that the statistics is asymptotically chi-square distributed and the corresponding confidence interval can be constructed.

Using Confidence Interval to Summarize the EvaluatingResults of DSM Systems

Distributed Shared Memory (DSM) systems have gained popularacceptance by combining the scalability and low cost of distributed system with theease of use of single address space. Many new hardware DSM and software DSMsystems have been proposed in recent years. In general, benchmarking is widely usedto demonstrate the performance advantages of new systems. However, the commonmethod used to summarize the measured results is the arithmetic mean of ratios,which is incorrect in some cases. Furthermore, many published papers list a lot ofdata only, and do not summarize them effectively, which confuse users greatly. Infact, many users want to get a single number as conclusion, which is not providedin old summarizing techniques. Therefore, a new data-summarizing technique basedon confidence interval is proposed in this paper. The new technique includes twodata-summarizing methods: (1) paired confidence interval method; (2) unpairedconfidence interval method. With this new technique, it is concluded that at someconfidence one system is better than others. Four examples are shown to demonstratethe advantages of this new technique. Furthermore, with the help of confidence level,it is proposed to standardize the benchmarks used for evaluating DSM systems sothat a convincing result can be got. In addition, the new summarizing technique fitsnot only for evaluating DSM systems, but also for evaluating other systems, such asmemory system and communication systems.