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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Uncertainty: Overview00:59

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Design Example: Calculating Safe Diameter for Wind-Exposed Disc01:17

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Assessing safety in wind-exposed installations is crucial to preventing potential failures. This example explores the calculation and design adjustments needed to mount a circular disc on a building facade, where wind forces are a primary concern. A 4-meter diameter disc was initially designed as an aesthetic feature facing winds at a velocity of 25 meters per second, with an air density of 1.25 kilograms per cubic meter. Given these conditions, the drag force on the disc was determined using...
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Updated: Sep 9, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Probabilistic machine learning-based forecasting of wind speed uncertainty using adaptive kernel density estimation.

Rami Al-Hajj1

  • 1College of Engineering and Technology, American University of the Middle East, Kuwait.

Mathematical Biosciences and Engineering : MBE
|September 3, 2025
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Summary
This summary is machine-generated.

Accurate short-term wind speed forecasting is vital for renewable energy. This study introduces a hybrid Support Vector Regression with Adaptive Kernel Density Estimation (SVR-AKDE) model for precise prediction intervals, improving wind energy reliability.

Keywords:
AKDESVRadaptive kernel density estimatorprediction intervalsprobabilistic energy forecastingrenewable energysupport vector regressorswind speed forecasting

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Area of Science:

  • Renewable Energy Systems
  • Machine Learning Applications
  • Statistical Forecasting

Background:

  • Short-term wind speed forecasting is critical for efficient wind energy integration.
  • Conventional point predictions lack accuracy in capturing wind speed uncertainty.
  • Quantifying forecast uncertainty is essential for reliable wind energy operations.

Purpose of the Study:

  • To develop a hybrid forecasting methodology for short-term wind speed prediction intervals.
  • To quantify forecast uncertainty using Support Vector Regression (SVR) and Adaptive Kernel Density Estimation (AKDE).
  • To evaluate the proposed SVR-AKDE model against conventional methods for improved uncertainty estimation.

Main Methods:

  • A hybrid model combining Support Vector Regression (SVR) with Adaptive Kernel Density Estimation (AKDE) was developed.
  • Adaptive KDE was utilized to adjust bandwidth based on local forecast error distribution for precise uncertainty quantification.
  • The SVR-AKDE model was assessed for short-term horizons (10, 30, 60, 120 minutes).

Main Results:

  • The SVR-AKDE model demonstrated superior performance in estimating wind speed prediction intervals.
  • The proposed method consistently provided enhanced prediction interval coverage probability (PICP) and narrower prediction interval normalized average width (PINAW).
  • Simulation findings confirmed the efficacy of SVR-AKDE over traditional KDE-based interval estimation.

Conclusions:

  • The SVR-AKDE hybrid model offers a robust solution for short-term wind speed forecasting with quantifiable uncertainty.
  • This approach enhances the reliability and operational control of wind energy installations.
  • Accurate uncertainty quantification is key to maximizing the potential of wind power generation.