A note on the Gamma test

Stefánsson, Adalbjörn; Končar, Nenad; Jones, A.

doi:10.1007/bf01413858

Cited by 231 publications

(75 citation statements)

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“…5, No. 4; The Reconstruction Parameters Calculation dialog box, implements a lot of known methods used for the estimation of the optimum values for the reconstruction parameters, such as the False Nearest Neighbors (FNN method) (Kennel, Brown, & Abarbanel, 1992), the Singular System Approach (SSA method) (Broomhead & King, 1986) and the Γ-test method (Stefansson, Concar, & Jones, 1997) for the estimation of the embedding dimension d, as well as the autocorrelation method (Albano, Muench, Schwartz, Mees, & Rapp, 1988) for the estimation of the time delay τ. In Figure 2, the FNN method is used to calculate the optimum dimension of the embedding space for a time series emerged from the Henon attractor.…”

Section: Phase Space Reconstructionmentioning

confidence: 99%

Simulation and Visualization of Chaotic Systems

Margaris¹

2012

CIS

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The objective of this paper is to present a suite of applications that allow the simulation and study of chaotic systems, as well as the estimation of the most important properties associated with them. These applications implement fundamental algorithms from the field of chaotic system dynamics, such as the reconstruction of the system trajectory in the appropriate embedding space, and the estimation of the Lyapunov exponents and the fractal dimension. Furthermore, they provide additional features such as the study of bifurcation diagrams and the detection of chaotic regions in the parameter space. The current version of the applications has been developed in the programming framework of Visual C++ 6.0 and they can be used under the operating system of Microsoft Windows.

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Section: Phase Space Reconstructionmentioning

confidence: 99%

Simulation and Visualization of Chaotic Systems

Margaris¹

2012

CIS

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“…The Gamma test is an algorithm developed by [10], [21], [4] as a tool to aid in the construction of data-driven models of smooth systems. It is a technique aimed at estimating the level of noise (its variance) present in a dataset.…”

Section: B Gamma Test (Residual Variance) Analysismentioning

confidence: 99%

Computational intelligence methods for helicopter loads estimation

Valdés

Cheung

Wang

2011

The 2011 International Joint Conference on Neural Networks

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Abstract-Accurately determining component loads on a helicopter is an important goal in the helicopter structural integrity field. While measuring dynamic component loads directly is possible, these measurement methods are not reliable and are difficult to maintain. This paper explores the potential of using computational intelligence methods to estimate some of these helicopter dynamic loads. Thirty standard timedependent flight state and control system parameters were used to construct a set of 180 input variables to estimate the main rotor blade normal bending during forward level flight at full speed. Unsupervised nonlinear mapping was used to study the structure of the multidimensional time series from the predictor and target variables. Based on these criteria, black and white box modeling techniques (including ensemble models) for main rotor blade normal bending prediction were applied. They include neural networks, local linear regression and model trees, in combination with genetic algorithms based on residual variance (gamma test) for predictor variables selection. The results from this initial work demonstrate that accurate models for predicting component loads can be obtained using the entire set of predictor variables, as well as with smaller subsets found by computational intelligence based approaches.

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“…The Gamma test is an algorithm developed by [11], [21], [5] as a tool to aid in the construction of data-driven models of smooth systems. It is a technique aimed at estimating the level of noise (its variance) present in a dataset.…”

Section: A Gamma Test (Residual Variance) Analysismentioning

confidence: 99%

Evolutionary computation methods for helicopter loads estimation

Valdés

Cheung

Wang

2011

2011 IEEE Congress of Evolutionary Computation (CEC)

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Abstract-The accurate estimation of component loads in a helicopter is an important goal for life cycle management and life extension efforts. This paper explores the use of evolutionary computational methods to help estimate some of these helicopter dynamic loads. Thirty standard time-dependent flight state and control system parameters were used to construct a set of 180 input variables to estimate the main rotor blade normal bending during forward level flight at full speed. Evolutionary computation methods (single and multi-objective genetic algorithms) optimizing residual variance, gradient, and number of predictor variables were employed to find subsets of the input variables with modeling potential. Clustering was used for composing a statistically representative training set. Machine learning techniques were applied for prediction of the main rotor blade normal bending involving neural networks, model trees (black and white box techniques) and their ensemble models. The results from this work demonstrate that reasonably accurate models for predicting component loads can be obtained using smaller subsets of predictor variables found by evolutionarycomputation based approaches.

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A note on the Gamma test

Cited by 231 publications

References 1 publication

Simulation and Visualization of Chaotic Systems

Simulation and Visualization of Chaotic Systems

Computational intelligence methods for helicopter loads estimation

Evolutionary computation methods for helicopter loads estimation

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