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

Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.2K
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
1.2K
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

9.7K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
9.7K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

372
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...
372
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

1.3K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
1.3K
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

3.4K
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
3.4K
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

121
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
121

You might also read

Related Articles

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

Sort by
Same author

Superior Conductivity of Transparent ZnO/MoS<sub>2</sub> Composite Films for Optoelectronic and Solar Cell Applications.

Gels (Basel, Switzerland)·2023
Same author

Exploring non-linear relationships between perceived interactivity or interface design and acceptance of collaborative web-based learning.

Education and information technologies·2023
See all related articles

Related Experiment Video

Updated: Feb 28, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K

Robust HMM-Based Remaining Useful Life Estimation Using a Ridge-Regularized EM Algorithm.

Halime Beyza Küçükdağ1, Gokhan Kirkil1, Mustafa Hekimoğlu2

  • 1Department of Computational Applied Science and Engineering, Kadir Has University, Istanbul 34083, Turkey.

Sensors (Basel, Switzerland)
|February 27, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a robust framework for predicting the remaining useful life (RUL) of engineering systems using a hidden Markov model (HMM). The novel approach enhances accuracy and reliability in prognostics for critical machinery.

Keywords:
EM algorithmHuber losscondition monitoringhidden Markov modelsremaining useful liferidge regressionrobust statistics

More Related Videos

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

11.2K
Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.7K

Related Experiment Videos

Last Updated: Feb 28, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

11.2K
Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.7K

Area of Science:

  • Engineering
  • Statistics
  • Machine Learning

Background:

  • Estimating remaining useful life (RUL) is vital for maintenance planning and ensuring the reliability of complex mechanical systems.
  • Accurate RUL predictions are essential for preventing unexpected failures and enabling timely interventions.

Purpose of the Study:

  • To develop a statistically robust framework for modeling system degradation and predicting RUL.
  • To enhance the accuracy and reliability of RUL estimation in engineering systems.

Main Methods:

  • Utilized a hidden Markov model (HMM) with a simple-failure structure and an absorbing terminal state.
  • Employed a ridge-regularized expectation-maximization (EM) algorithm for parameter estimation, incorporating a Huber-based scale estimator.
  • Computed RUL as a weighted expected time to absorption using the forward-backward algorithm for smoothed posterior-state probabilities.

Main Results:

  • The proposed ridge-regularized EM algorithm demonstrated significantly reduced parameter variance compared to baseline WLS-EM.
  • Achieved improved predictive accuracy and smoother, more reliable RUL prediction trajectories in simulation and real-data analyses.
  • The framework provides a low-variance, state-aware RUL estimator that preserves the HMM's probabilistic structure.

Conclusions:

  • The developed framework offers a robust and interpretable approach for practical prognostics applications.
  • The method effectively models degradation signals and enhances RUL estimation accuracy.
  • This statistically sound method is suitable for maintaining complex engineering systems.