To rate uncertainties within anomaly detection course for large span cable-supported bridges, a probabilistic approach is developed based on confidence interval estimation of extreme value analytics. First, raw signals from structural health monitoring system are pre-processed, including missing data imputation using moving time window mean imputation approach and thermal response separation through multi-resolution wavelet-based method. Then, an energy index is extracted from time domain signals to enhance robust of detection performance. A resampling-based method, namely the bootstrap, is adopted herein for confidence interval estimation. Four confidence levels are defined for the anomaly trend detection in this study, namely 95%, 80%, 50%, and 20%. Finally, the effectiveness of the proposed anomaly trend detection methodology is validated by using in-situ cable force measurements from the Nanjing Dashengguan Yangtze River Bridge. As a result, the four-level anomaly detection triggers are determined by using the confidence interval estimation based on cable force measurements in 2007, which are 58,671, 48,862, 42,499 and 39,035, respectively. Subsequently, three cases are presented, which are spike detection, overloading vehicle detection and snow disaster detection. Through the spike detection, it is verified that energy index is capable to tolerate signal spikes. Three overloading events are simulated to conduct overloading vehicle detections. As a result, the three overloading events are detected successfully associated with different confidences. Snow disaster is detected with a more than 80% confidence based on the field measurements during the snow storm time window.
Interval estimation is an important topic, especially in drawing conclusions on an event. Mathematics education students must possess the skill to formulate and use interval estimation. The errors of mathematics education students in formulating wrong interval estimates indicate a low understanding of interval estimation. This study explores the errors of mathematics education students in interpreting the variance in the questions regarding selecting the proper test statistic to formulate the interval estimation of mean accurately. Respondents in this study involved 36 students of mathematics education (N = 9 males, N = 27 females). This research is qualitative research with a qualitative descriptive approach. Data collection was carried out using the respondents’ ability test and interviews. The respondents’ ability test instrument was tested on 36 students and declared valid where r-count r-table with r-table of 0.3291, and declared reliable with a Cronbach Alpha value of 0.876 0.6. Through an exploratory approach, data were analyzed by categorizing, reducing, and interpreting to conclude students' abilities and thinking methods in formulating interval estimation of the mean based on the variance in questions. The results showed that mathematics education students neglected the variance, so they could not determine the test statistics correctly, resulting in error interval estimates. This study provides insight into the thinking methods of mathematics education students on variance in interval estimation problems in the hope of anticipating errors in formulating interval estimation problems.
The problem of statistical inference under joint censoring samples has received considerable attention in the past few years. In this paper, we adopted this problem when units under the test fail with different causes of failure which is known by the competing risks model. The model is formulated under consideration that only two independent causes of failure and the unit are collected from two lines of production and its life distributed with Burr XII lifetime distribution. So, under Type-I joint competing risks samples, we obtained the maximum likelihood (ML) and Bayes estimators. Interval estimation is discussed through asymptotic confidence interval, bootstrap confidence intervals, and Bayes credible interval. The numerical computations which described the quality of theoretical results are discussed in the forms of real data analyzed and Monte Carlo simulation study. Finally, numerical results are discussed and listed through some points as a brief comment.
Estimating the contact angle of a virus infected saliva droplet is seen to be an important area of research as it presents an idea about the drying time of the respective droplet and in turn of the growth of the underlying pandemic. In this paper we extend the data presented by Balusamy, Banerjee and Sahu [“Lifetime of sessile saliva droplets in the context of SARS-CoV-2,” Int. J. Heat Mass Transf. 123, 105178 (2021)], where the contact angles are fitted using a newly proposed half-circular wrapped-exponential model, and a sequential confidence interval estimation approach is established which largely reduces both time and cost with regards to data collection.
Range prediction is a standard feature in most modern road vehicles, allowing drivers to make informed decisions about when to refuel. Most vehicles make range predictions through data- or model-driven means, monitoring the average fuel consumption rate or using a tuned vehicle model to predict fuel consumption. The uncertainty of future driving conditions makes the range prediction problem challenging, particularly for less pervasive battery electric vehicles (BEV). Most contemporary machine learning-based methods attempt to forecast the battery SOC discharge profile to predict vehicle range. In this work, we propose a novel approach using two recurrent neural networks (RNNs) to predict the remaining range of BEVs and the minimum charge required to safely complete a trip. Each RNN has two outputs which can be used for statistical analysis to account for uncertainties; the first loss function leads to mean and variance estimation (MVE), while the second results in bounded interval estimation (BIE). These outputs of the proposed RNNs are then used to predict the probability of a vehicle completing a given trip without charging, or if charging is needed, the remaining range and minimum charging required to finish the trip with high probability. Training data was generated using a low-order physics model to estimate vehicle energy consumption from historical drive cycle data collected from medium-duty last-mile delivery vehicles. The proposed method demonstrated high accuracy in the presence of day-to-day route variability, with the root-mean-square error (RMSE) below 6% for both RNN models.
This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.
Quantifying the uncertainty of non-stationary flood frequency analysis is very crucial and beneficial for planning and design of water engineering projects, which is fundamentally challenging especially in the presence of high climate variability and reservoir regulation. This study proposed an integrated approach that combined the Generalized Additive Model for Location, Scale and Shape parameters (GAMLSS) method, the Copula function and the Bayesian Uncertainty Processor (BUP) technique to make reliable probabilistic interval estimations of design floods. The reliability and applicability of the proposed approach were assessed by flood datasets collected from two hydrological monitoring stations located in the Hanjiang River of China. The precipitation and the reservoir index were selected as the explanatory variables for modeling the time-varying parameters of marginal and joint distributions using long-term (1954–2018) observed datasets. First, the GAMLSS method was employed to model and fit the time-varying characteristics of parameters in marginal and joint distributions. Second, the Copula function was employed to execute the point estimations of non-stationary design floods. Finally, the BUP technique was employed to perform the interval estimations of design floods based on the point estimations obtained from the Copula function. The results demonstrated that the proposed approach can provide reliable probabilistic interval estimations of design floods meanwhile reducing the uncertainty of non-stationary flood frequency analysis. Consequently, the integrated approach is a promising way to offer an indication on how design values can be estimated in a high-dimensional problem.