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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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.
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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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
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Related Experiment Video

Updated: Jul 2, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Two-stage maximum likelihood weighted recursive least squares algorithm for nonlinear systems and an application in

Dachuan Yu1, Yan Ji1

  • 1College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China.

ISA Transactions
|June 30, 2026
PubMed
Summary

This study introduces new algorithms for identifying Hammerstein systems with dead-zone nonlinearity under colored noise. The proposed two-stage method enhances accuracy and efficiency in parameter estimation.

Keywords:
Dead-zoneMaximum likelihoodTwo-stage methodWeighted recursive least squares

Related Experiment Videos

Last Updated: Jul 2, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Control Systems Engineering
  • Nonlinear System Identification
  • Signal Processing

Background:

  • Hammerstein systems are widely used in modeling complex nonlinear dynamics.
  • Identifying parameters in systems with dead-zone nonlinearity and colored noise presents significant challenges.
  • Existing methods may suffer from computational complexity or suboptimal performance.

Purpose of the Study:

  • To develop robust parameter identification algorithms for Hammerstein systems with dead-zone nonlinearity.
  • To address the challenge of colored noise interference in system identification.
  • To improve estimation accuracy and computational efficiency compared to existing methods.

Main Methods:

  • Introduction of a switching function to obtain a linear parameter expression for the piecewise nonlinear subsystem.
  • Construction of a maximum likelihood weighted recursive least squares (ML-WRLS) identification algorithm based on the maximum likelihood principle.
  • Proposal of a two-stage recursive least squares algorithm to enhance estimation accuracy and reduce computational load.

Main Results:

  • The proposed two-stage ML-WRLS algorithm demonstrates improved steady-state performance over the standard ML-WRLS algorithm.
  • The developed algorithms effectively identify parameters in Hammerstein systems with dead-zone nonlinearity and colored noise.
  • Simulation examples validate the effectiveness and superiority of the proposed identification methods.

Conclusions:

  • The novel two-stage recursive least squares algorithm offers a significant improvement for identifying Hammerstein systems with dead-zone nonlinearity.
  • The proposed methods provide accurate and computationally efficient solutions for complex nonlinear system identification problems.
  • This work contributes to the advancement of robust parameter estimation techniques in the presence of noise and nonlinearities.