scholarly journals Using Modified Intelligent Experimental Design in Parameter Estimation of Chaotic Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Zahra Shourgashti ◽  
Hamid Keshvari ◽  
Shirin Panahi
Keyword(s):  
Parameter Estimation ◽  
System Identification ◽  
Dynamical Systems ◽  
Experimental Design ◽  
Chaotic Systems ◽  
Initial Condition ◽  
Sampled Data ◽  
One Dimensional ◽  
Using Data ◽  
Set Up

Computational modeling plays an important role in prediction and optimization of real systems and processes. Models usually have some parameters which should be set up to the proper value. Therefore, parameter estimation is known as an important part of the modeling and system identification. It usually refers to the process of using sampled data to estimate the optimum values of parameters. The accuracy of model can be increased by adjusting its parameters to the optimum value which need a richer dataset. One simple solution for having a richer dataset is increasing the amount of data, but that can be costly and time consuming. When using data from animals or people, it is especially important to have a proper plan. There are several available methods for parameter estimation in dynamical systems; however there are some basic differences in chaotic systems due to their sensitivity to initial condition (butterfly effect). Accordingly, in this paper, a new cost function which is proper for chaotic systems is applied to the chaotic one-dimensional map. Then the efficiency of a newly introduced intelligent method experimental design in extracting proper data is investigated. The results show the success of the proposed method.

Spectral Collocation-Based Optimization in Parameter Estimation for Nonlinear Time-Varying Dynamical Systems

2007 ◽  
Author(s):  
Venkatesh Deshmukh
Keyword(s):  
Parameter Estimation ◽  
Dynamical Systems ◽  
Dynamic System ◽  
Unique Solution ◽  
Time Varying ◽  
Unknown Parameters ◽  
Spectral Collocation ◽  
System Models ◽  
Chebyshev Spectral Collocation ◽  
Set Up

A constructive optimization algorithm using Chebyshev spectral collocation and quadratic programming is proposed for unknown parameter estimation in nonlinear time-varying dynamic system models to be constructed from available data. The parameters to be estimated are assumed to be identifiable from the data which also implies that the assumed system models with known parameter values have a unique solution corresponding to every initial condition and parameter set. The nonlinear terms in the dynamic system models are assumed to have a known form, and the models are assumed to be parameter affine. Using an equivalent algebraic description of dynamical systems by Chebyshev spectral collocation and data, a residual quadratic cost is set up which is a function of unknown parameters only. The minimization of this cost yields the unique solution for the unknown parameters since the models are assumed to have a unique solution for a particular parameter set. An efficient algorithm is presented step-wise and is illustrated using suitable examples.

Diffraction on a Barrier

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Organic Molecules ◽  
Tight Binding ◽  
Higher Dimensions ◽  
Initial Condition ◽  
Tight Binding Model ◽  
Binding Model ◽  
One Dimensional ◽  
Set Up ◽  
Planar Heterojunction ◽  
Function Matrix

The transport through a one-dimensional barrier is calculated within the tight-binding model. The surface Green’s functions are introduced as a method to invert the Green’s function matrix and to set-up convenient boundary conditions for simulations. The formalism is applied to calculate the transport properties of parallel stacked organic molecules. The extension to higher dimensions and multiband crystals is discussed. In this section we apply the GKB formalism to diffraction of electrons on a barrier. The system we study is a planar heterojunction of two ideal semi-infinite crystals or a surface of a crystal. As an initial condition we take a stream of electrons with a sharp momentum.

Respirometry for determination of the influents SS-concentration

1996 ◽  
Vol 33 (1) ◽  
pp. 311-323 ◽  
Author(s):  
A. Witteborg ◽  
A. van der Last ◽  
R. Hamming ◽  
I. Hemmers
Keyword(s):  
Experimental Design ◽  
Activated Sludge ◽  
Substrate Concentration ◽  
Full Scale ◽  
Activated Sludge Process ◽  
Respiration Rates ◽  
On Line ◽  
Large Measurement ◽  
Set Up

A method is presented for determining influent readily biodegradable substrate concentration (SS). The method is based on three different respiration rates, which can be measured with a continuous respiration meter which is operated in a cyclic way. Within the respiration meter nitrification is inhibited through the addition of ATU. Simulations were used to develop the respirometry set-up and decide upon the experimental design. The method was tested as part of a large measurement programme executed at a full-scale plant. The proposed respirometry set-up has been shown to be suitable for a semi-on-line determination of an influent SS which is fully based on the IAWQ #1 vision of the activated sludge process. The YH and the KS play a major role in the principle, and should be measured directly from the process.

scholarly journals Integration of various scales for measurement of insomnia

2021 ◽  
pp. 263208432110100
Author(s):  
Satyendra Nath Chakrabartty
Keyword(s):  
Test Scores ◽  
Data Driven ◽  
Weighted Sum ◽  
Future Studies ◽  
Normal Probability ◽  
Equivalent Test ◽  
Item Scores ◽  
Using Data ◽  
Set Up ◽  
Different Levels

Background Scales for evaluating insomnia differ in number of items, response format, and result in different scores distributions and score ranges and may not facilitate meaningful comparisons. Objectives Transform ordinal item-scores of three scales of insomnia to continuous, equidistant, monotonic, normally distributed scores, avoiding limitations of summative scoring of Likert scales. Methods Equidistant item-scores by weighted sum using data-driven weights to different levels of different items, considering cell frequencies of Item-Levels matrix, followed by normalization and conversion to [1, 10]. Equivalent test-scores (as sum of transformed item- scores) for a pair of scales were found by Normal Probability curves. Empirical illustration given. Results Transformed test-scores are continuous, monotonic and followed Normal distribution with no outliers and tied scores. Such test-scores facilitate ranking, better classification and meaningful comparison of scales of different lengths and formats and finding equivalent score combinations of two scales. For a given value of transformed test-score of a scale, easy alternate method avoiding integration proposed to find equivalent scores of another scales. Equivalent scores of scales help to relate various cut-off scores of different scales and uniformity in interpretations. Integration of various scales of insomnia is achieved by finding one-to-one correspondence among the equivalent score of various scales with correlation over 0.99 Conclusion Resultant test-scores facilitated undertaking analysis in parametric set up. Considering the theoretical advantages including meaningfulness of operations, better comparison, use of such method of transforming scores of Likert items/test is recommended test and items, Future studies were suggested.

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