Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

172
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
172
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

35
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
35
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.1K
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...
1.1K
Uncertainty: Overview00:59

Uncertainty: Overview

1.2K
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.
1.2K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

140
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
140
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.3K
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...
1.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reformulated predictive torque and flux control with a full-order adaptive observer and accurate discrete-time models for sensorless induction machine drives.

Scientific reports·2026
Same author

An Optimal Integral Controller for Adaptive Optics Systems.

Sensors (Basel, Switzerland)·2023
Same author

Estimation of Soluble Solids for Stone Fruit Varieties Based on Near-Infrared Spectra Using Machine Learning Techniques.

Sensors (Basel, Switzerland)·2022
Same author

LoRa Based IoT Platform for Remote Monitoring of Large-Scale Agriculture Farms in Chile.

Sensors (Basel, Switzerland)·2022
Same author

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data.

Sensors (Basel, Switzerland)·2021
Same author

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data.

Sensors (Basel, Switzerland)·2021
Same journal

RETRACTED: Zhang et al. A Novel Framework for Reconstruction and Imaging of Target Scattering Centers via Wide-Angle Incidence in Radar Networks. <i>Sensors</i> 2025, <i>25</i>, 6802.

Sensors (Basel, Switzerland)·2026
Same journal

Enhancing Unsupervised Multi-Source Domain Adaptation for Person Re-Identification via Mixture of Experts and Graph-Based Relation.

Sensors (Basel, Switzerland)·2026
Same journal

Development of an Instrumented Glove for Palmar Pressure Assessment in Kayakers.

Sensors (Basel, Switzerland)·2026
Same journal

Development and Experimental Validation of an Autonomous IoT-Based Monitoring System for Real-Time Water Quality Assessment in the Amazon River.

Sensors (Basel, Switzerland)·2026
Same journal

Semi-Supervised Adversarial Learning Framework for Controller Area Network Bus Intrusion Detection.

Sensors (Basel, Switzerland)·2026
Same journal

Smart Optimization Method for Safety Signs in Innovative Manufacturing Environments Integrating Industrial Field IoT Sensors and Knowledge Graphs.

Sensors (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Oct 30, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
08:27

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines

Published on: January 5, 2024

1.4K

On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian

Rafael Orellana1,2,3, Rodrigo Carvajal1, Pedro Escárate4

  • 1Departamento Electrónica, Universidad Técnica Federico Santa María (UTFSM), Av. España 1680, Valparaíso 2390123, Chile.

Sensors (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for modeling uncertainty in linear dynamic systems using a stochastic embedding approach. It improves process control and fault diagnosis by accurately estimating system dynamics and error models.

Keywords:
expectation-maximizationgaussian mixture modelmaximum likelihoodstochastic embeddinguncertainty modeling

More Related Videos

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.3K

Related Experiment Videos

Last Updated: Oct 30, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
08:27

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines

Published on: January 5, 2024

1.4K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.3K

Area of Science:

  • Engineering
  • Control Systems
  • System Identification

Background:

  • Manufacturing process control requires understanding model uncertainty for consistency and quality.
  • Deterministic models are insufficient for complex systems, necessitating stochastic approaches to represent disturbances and wear.
  • Model uncertainties impact fault diagnosis, safety, and reliability in real-world applications.

Purpose of the Study:

  • To develop a maximum likelihood estimation algorithm for uncertainty modeling in linear dynamic systems.
  • To incorporate system uncertainties as stochastic error terms within a transfer function framework.
  • To enhance process control and fault detection/diagnosis methodologies through accurate dynamic system modeling.

Main Methods:

  • Utilized a stochastic embedding approach to represent system uncertainties.
  • Modeled the error-model probability density function as a finite Gaussian mixture model.
  • Developed an iterative Expectation-Maximization algorithm for estimating the nominal model and error-model parameters from independent experimental data.

Main Results:

  • Successfully developed a maximum likelihood estimation algorithm for uncertainty modeling.
  • Demonstrated the effectiveness of the stochastic embedding approach in handling system uncertainties.
  • Validated the proposed method's benefits through numerical simulations.

Conclusions:

  • The proposed method provides a robust way to model uncertainty in linear dynamic systems.
  • Accurate uncertainty modeling is crucial for effective process control and fault diagnosis.
  • The Expectation-Maximization algorithm offers an efficient approach for parameter and probability density function estimation.