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Uncertainty: Overview

Uncertainty: Overview

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.

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

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...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

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...

Design Example: Maintaining Level of an Embankment

Design Example: Maintaining Level of an Embankment

Constructing a roadway embankment over uneven terrain requires precise leveling to ensure stability and proper drainage. Surveyors use a leveling instrument and staff to calculate ground elevations and determine the required fill material at each point along the embankment alignment.The process begins by positioning a leveling instrument near a benchmark with a known elevation. A backsight reading establishes the instrument height, which serves as a reference for subsequent measurements. A...

Avoidance Learning and Learned Helplessness

Avoidance Learning and Learned Helplessness

Avoidance learning and learned helplessness are critical concepts in understanding behavioral responses to negative stimuli.
Avoidance learning occurs when an organism learns that a specific behavior can prevent an unpleasant outcome. For example, a student who receives a bad grade may start studying harder to avoid future poor grades. This behavior persists even when the negative outcome is no longer present. Avoidance learning is powerful because it maintains behavior in the absence of the...

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Updated: Jan 15, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Bayesian deep reinforcement learning for uncertainty quantification and adaptive support optimization in deep

¹Architectural Engineering Institute, Yancheng Polytechnic College, Yancheng, 224005, Jiangsu, China. gwming0228@126.com.

Scientific Reports

|October 9, 2025

Summary

This summary is machine-generated.

This study introduces an intelligent framework for deep foundation pit support, combining Bayesian inference and deep reinforcement learning. The system enhances safety and efficiency in geotechnical engineering by optimizing support and reducing costs.

Keywords:

Adaptive optimization Bayesian inference Deep foundation pit Deep reinforcement learning Multi-physics coupling Uncertainty quantification

Related Experiment Videos

Last Updated: Jan 15, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Area of Science:

Geotechnical Engineering
Computational Mechanics
Artificial Intelligence

Background:

Deep foundation pits require robust support systems to manage complex multi-physics interactions.
Traditional methods often lack adaptability and precise uncertainty quantification.

Purpose of the Study:

To develop an integrated framework for uncertainty quantification and adaptive support optimization in deep foundation pit systems.
To enhance the safety, efficiency, and cost-effectiveness of geotechnical construction through intelligent automation.

Main Methods:

Integration of Bayesian inference (Markov Chain Monte Carlo) with deep reinforcement learning.
Development of a multi-physics coupled numerical model (mechanical-hydraulic-thermal).
Real-time monitoring data incorporation for adaptive support adjustments.

Main Results:

Achieved high prediction accuracy (R²=0.91) and reliability (coverage probability=96.8%).
Demonstrated significant reductions in wall displacement (35%) and surface settlement (42%).
Reported 18% cost savings, 12% construction duration reduction, and zero safety incidents.

Conclusions:

The novel framework provides superior performance over conventional deterministic approaches.
Intelligent adaptive support optimization enhances deformation control and construction efficiency.
The research offers practical tools for advanced urban geotechnical engineering.