An Enhanced Bayesian Based Model Validation Method for Dynamic Systems

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Zhenfei Zhan ◽  
Yan Fu ◽  
Ren-Jye Yang ◽  
Yinghong Peng
Keyword(s):  
Dynamic System ◽  
Hypothesis Testing ◽  
Model Validation ◽  
Dynamic Systems ◽  
Computational Models ◽  
Principal Component ◽  
Functional Responses ◽  
New Approach ◽  
Validation Method ◽  
Critical Issues

Validation of computational models with multiple correlated functional responses requires the consideration of multivariate data correlation, uncertainty quantification and propagation, and objective robust metrics. This paper presents an enhanced Bayesian based model validation method together with probabilistic principal component analysis (PPCA) to address these critical issues. The PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate functional responses. The Bayesian interval hypothesis testing is used to quantitatively assess the quality of a multivariate dynamic system. The differences between the test data and computer-aided engineering (CAE) results are extracted for dimension reduction through PPCA, and then Bayesian interval hypothesis testing is performed on the reduced difference data to assess the model validity. In addition, physics-based threshold is defined and transformed to the PPCA space for Bayesian interval hypothesis testing. This new approach resolves some critical drawbacks of the previous methods and adds some desirable properties of a model validation metric for dynamic systems, such as symmetry. Several sets of analytical examples and a dynamic system with multiple functional responses are used to demonstrate this new approach.

A Stochastic Multivariate Validation Method for Dynamic Systems

2016 ◽  
Author(s):  
Jun Lu ◽  
Zhenfei Zhan ◽  
Pan Wang ◽  
Yudong Fang ◽  
Junqi Yang
Keyword(s):  
Dynamic Model ◽  
Model Validation ◽  
Dynamic Systems ◽  
Probability Model ◽  
Principal Component ◽  
Kernel Principal Component Analysis ◽  
New Approach ◽  
Processing Ability ◽  
Highly Correlated

As computer models become more powerful and popular, the complexity of input and output data raises new computational challenges. One of the key difficulties for model validation is to evaluate the quality of a computer model with multivariate, highly correlated and non-normal data, the direct application of traditional validation approaches does not appear to be suitable. This paper proposes a stochastic method to validate the dynamic systems. Firstly, a dimension reduction utilizing kernel principal component analysis (KPCA) is used to improve the computational efficiency. A probability model is then established by non-parametric kernel density estimation (KDE) method, and differences between the test data and simulation results are finally extracted to further comparative validation. This new approach resolves some critical drawbacks of the previous methods and improves the processing ability to nonlinear problem to validation the dynamic model. The proposed method and process are successfully illustrated through a real-world vehicle dynamic system example. The results demonstrate that the method of incorporate with KPCA and KDE is an effective approach to solve the dynamic model validation problem.

scholarly journals Antisystem-Approach (ASA) for Engineering of Wide Range of Dynamic Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 52-66
Author(s):  
Serge Zacher
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Chemical Engineering ◽  
Original System ◽  
New Approach ◽  
Analysis And Design ◽  
Wide Range ◽  
Newton’S Laws ◽  
Definition Of

Following the famous third physical Newton’s laws, “for every action there is an equal and opposite re-action”, a new approach for analysis and design of dynamic systems was introduced by [Zacher, 1997] and called «Antisystem-Approach» (ASA). According to this approach, a single isolated dynamic system does not exist alone. For every dynamic system, which transfers its inputs into outputs with an operator A in one direction, there is an equal system with the same operator A, which transfers other inputs into outputs in opposite direction. The antisystem does not have to be a physical system; it can also be a mathematical model of the original system. The most important feature of ASA is the exact balance between a system and its antisystem, which is called “energy” or “intensity”. In the group theory the system and antisystem are denote as antisymmetric. They build duality, which is common in many branches of sciences as mathematics, physics, biology etc. In the twenty years since first publication of the ASA there were developed different methods and applications, which enable to simplify the engineering, analysing the antisystem instead of original system. In the proposed paper is given the definition of ASA und are shown its features. It is described, how the ASA was used in electrical and chemical engineering, automation, informatics. Only several applications will be discussed, although ASA-solutions are common and could be used for wide range of dynamic systems.

Bayesian Based Multivariate Model Validation Method Under Uncertainty for Dynamic Systems

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Zhenfei Zhan ◽  
Yan Fu ◽  
Ren-Jye Yang ◽  
Yinghong Peng
Keyword(s):  
Data Analysis ◽  
Dynamic System ◽  
Hypothesis Testing ◽  
Uncertainty Quantification ◽  
Model Validation ◽  
Statistical Data ◽  
New Method ◽  
Statistical Data Analysis ◽  
Bayesian Hypothesis Testing ◽  
Repeated Test

Validation of computational models with multiple, repeated, and correlated functional responses for a dynamic system requires the consideration of uncertainty quantification and propagation, multivariate data correlation, and objective robust metrics. This paper presents a new method of model validation under uncertainty to address these critical issues. Three key technologies of this new method are uncertainty quantification and propagation using statistical data analysis, probabilistic principal component analysis (PPCA), and interval-based Bayesian hypothesis testing. Statistical data analysis is used to quantify the variabilities of the repeated tests and computer-aided engineering (CAE) model results. The differences between the mean values of test and CAE data are extracted as validation features, and the PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate difference curves. The variabilities of the repeated test and CAE data are propagated through the data transformation to the PPCA space. In addition, physics-based thresholds are defined and transformed to the PPCA space. Finally, interval-based Bayesian hypothesis testing is conducted on the reduced difference data to assess the model validity under uncertainty. A real-world dynamic system example which has one set of the repeated test data and two stochastic CAE models is used to demonstrate this new approach.

PERTURBATION PARAMETERS TUNING OF MULTI-OBJECTIVE OPTIMIZATION DIFFERENTIAL EVOLUTION AND ITS APPLICATION TO DYNAMIC SYSTEM MODELING

2015 ◽  
Vol 75 (11) ◽  
Author(s):  
Mohd Zakimi Zakaria ◽  
Hishamuddin Jamaluddin ◽  
Robiah Ahmad ◽  
Azmi Harun ◽  
Radhwan Hussin ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Dynamic System ◽  
Dynamic Systems ◽  
System Modeling ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Structure Selection ◽  
Dynamic System Modeling ◽  
Perturbation Parameters ◽  
Model Structure Selection

This paper presents perturbation parameters for tuning of multi-objective optimization differential evolution and its application to dynamic system modeling. The perturbation of the proposed algorithm was composed of crossover and mutation operators.  Initially, a set of parameter values was tuned vigorously by executing multiple runs of algorithm for each proposed parameter variation. A set of values for crossover and mutation rates were proposed in executing the algorithm for model structure selection in dynamic system modeling. The model structure selection was one of the procedures in the system identification technique. Most researchers focused on the problem in selecting the parsimony model as the best represented the dynamic systems. Therefore, this problem needed two objective functions to overcome it, i.e. minimum predictive error and model complexity.  One of the main problems in identification of dynamic systems is to select the minimal model from the huge possible models that need to be considered. Hence, the important concepts in selecting good and adequate model used in the proposed algorithm were elaborated, including the implementation of the algorithm for modeling dynamic systems. Besides, the results showed that multi-objective optimization differential evolution performed better with tuned perturbation parameters.

scholarly journals Modeling the Radial Stem Growth of the Pine (Pinus sylvestris L.) Forests Using the Satellite-Derived NDVI and LST (MODIS/AQUA) Data

Atmosphere ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 12
Author(s):  
Yulia Ivanova ◽  
Anton Kovalev ◽  
Vlad Soukhovolsky
Keyword(s):  
Land Surface ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Principal Component ◽  
Stem Growth ◽  
Forest Growth ◽  
Parabolic Approximation ◽  
New Approach ◽  
The Relationship ◽  
Tree Increment

The paper considers a new approach to modeling the relationship between the increase in woody phytomass in the pine forest and satellite-derived Normalized Difference Vegetation Index (NDVI) and Land Surface Temperature (LST) (MODIS/AQUA) data. The developed model combines the phenological and forest growth processes. For the analysis, NDVI and LST (MODIS) satellite data were used together with the measurements of tree-ring widths (TRW). NDVI data contain features of each growing season. The models include parameters of parabolic approximation of NDVI and LST time series transformed using principal component analysis. The study shows that the current rate of TRW is determined by the total values of principal components of the satellite indices over the season and the rate of tree increment in the preceding year.

Cox Survival Analysis of Microarray Gene Expression Data Using Correlation Principal Component Regression

2007 ◽  
Vol 6 (1) ◽  
Author(s):  
Qiang Zhao ◽  
Jianguo Sun
Keyword(s):  
Gene Expression ◽  
Gene Expression Data ◽  
Principal Component Regression ◽  
Predictive Ability ◽  
Principal Component ◽  
Microarray Gene Expression Data ◽  
Expression Data ◽  
Microarray Gene Expression ◽  
New Approach ◽  
Microarray Gene

Statistical analysis of microarray gene expression data has recently attracted a great deal of attention. One problem of interest is to relate genes to survival outcomes of patients with the purpose of building regression models for the prediction of future patients' survival based on their gene expression data. For this, several authors have discussed the use of the proportional hazards or Cox model after reducing the dimension of the gene expression data. This paper presents a new approach to conduct the Cox survival analysis of microarray gene expression data with the focus on models' predictive ability. The method modifies the correlation principal component regression (Sun, 1995) to handle the censoring problem of survival data. The results based on simulated data and a set of publicly available data on diffuse large B-cell lymphoma show that the proposed method works well in terms of models' robustness and predictive ability in comparison with some existing partial least squares approaches. Also, the new approach is simpler and easy to implement.

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document