Random Field Characterization Considering Statistical Dependence for Probability Analysis and Design

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn ◽  
Chao Hu
Keyword(s):  
Random Field ◽  
Goodness Of Fit ◽  
Probability Analysis ◽  
Statistical Dependence ◽  
System Response ◽  
Goodness Of Fit Test ◽  
Optimal Sequence ◽  
Engineering Product ◽  
Analysis And Design ◽  
Rosenblatt Transformation

The proper orthogonal decomposition method has been employed to extract the important field signatures of random field observed in an engineering product or process. Our preliminary study found that the coefficients of the signatures are statistically uncorrelated but may be dependent. To this point, the statistical dependence of the coefficients has been ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective random field characterization method that can account for the statistical dependence among the coefficients for probability analysis and design. The proposed approach has two technical contributions. The first contribution is the development of a natural approximation scheme of random field while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables, and their statistical properties are identified using the chi-square goodness-of-fit test. Then, as the paper’s second technical contribution, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. The number of the transformation sequences exponentially increases as the number of random field variables becomes large. It was found that improper selection of a transformation sequence among many may introduce high nonlinearity into system responses, which may result in inaccuracy in probability analysis and design. Hence, this paper proposes a novel procedure of determining an optimal sequence of the Rosenblatt transformation that introduces the least degree of nonlinearity into the system response. The proposed random field characterization can be integrated with any advanced probability analysis method, such as the eigenvector dimension reduction method or polynomial chaos expansion method. Three structural examples, including a microelectromechanical system bistable mechanism, are used to demonstrate the effectiveness of the proposed approach. The results show that the statistical dependence in the random field characterization cannot be neglected during probability analysis and design. Moreover, it is shown that the proposed random field approach is very accurate and efficient.

Effective Random Field Characterization Considering Statistical Dependence for Probability Analysis and Design

2010 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn ◽  
Chao Hu
Keyword(s):  
Random Field ◽  
Goodness Of Fit ◽  
Probability Analysis ◽  
Statistical Dependence ◽  
System Response ◽  
Goodness Of Fit Test ◽  
Engineering Product ◽  
Analysis And Design ◽  
Transformation Sequence ◽  
Rosenblatt Transformation

The Proper Orthogonal Decomposition (POD) method has been employed to extract the important signatures of the random field presented in an engineering product or process. Our preliminary study found that coefficients of the signatures are statistically uncorrelated but may be dependent. In general, the statistical dependence of the coefficients is ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective approach to characterize the random field for probability analysis and design while accounting for the statistical dependence among the coefficients. The proposed approach is composed of two technical contributions. The first contribution is to develop a generic approximation scheme of random field as a function of the most important field signatures while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables and their statistical properties are identified using the Chi-Square goodness-of-fit test. Second, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. There exist so many transformation sequences when the number of random field variables becomes large. It was found that an improper selection of a transformation sequence may introduce high nonlinearity into system responses, which causes inaccuracy in probability analysis and design. Hence, a novel procedure is proposed for determining an optimal transformation sequence that introduces the least degree of nonlinearity to the system response after the Rosenblatt transformation. The proposed random field characterization can be integrated with one of the advanced probability analysis methods, such as the Eigenvector Dimension Reduction (EDR) method, Polynomial Chaos Expansion (PCE) method, etc. Three structural examples including a Micro-Electro-Mechanical Systems (MEMS) bistable mechanism are used to demonstrate the effectiveness of the proposed approach. The results show that the statistical dependence in random field characterization cannot be neglected for probability analysis and design. Moreover, it is shown that the proposed random field approach is very accurate and efficient.

An Effective Random Field Characterization for Probability Analysis and Design

2008 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn
Keyword(s):  
Spatial Variability ◽  
Random Field ◽  
Goodness Of Fit ◽  
Random Parameter ◽  
Probability Analysis ◽  
Field Variation ◽  
Random Parameters ◽  
Goodness Of Fit Test ◽  
Analysis And Design ◽  
Engineering Design Problems

So far manufacturing tolerance variability over samples has been widely considered in many engineering design problems. Traditionally the tolerance variability is modeled as a spatially independent random parameter although the variability is a function of spatial variables (x, y, and z) in many engineering applications. Little attention has been paid to spatial variability (or random field) in manufacturing and operational conditions, which may dominantly affect system performances in smaller scale applications. This paper presents an effective approach to characterize a random field for probability analysis and design. The Proper Orthogonal Decomposition (POD) method is employed to extract the important signatures of the random field over product samples. A normalized posteriori error is defined to automatically decide the minimal number of the important signatures while preserving a prescribed accuracy in approximating the random field. The random projected values of the spatial variability over the samples onto each important signature are modeled as a random parameter. The signatures and corresponding random parameters are thus used for modeling the random field. A Chi-Squae goodness-of-fit test is used for determining statistical models of random parameters. This proposed approach can facilitate to characterize the random field for probability analysis and design. By modeling the random field with the most significant random signatures, the Eigenvector Dimension Reduction (EDR) method can be employed for probability analysis because of its relatively high efficiency and accuracy. Two examples (one beam and Micro-Electro-Mechanical Systems (MEMS) bistable mechanism) are used to illustrate the effectiveness of the proposed approach while considering only a geometric random field. Compared to Monte Carlo Simulation (MCS), the proposed random field approach is appeared to be very accurate and efficient. Moreover, the results show that the random field variation cannot be neglected for probability analysis and design practices.

Random Field Characterization With Insufficient Data Sets for Probability Analysis and Design

2011 ◽  
Author(s):  
Zhimin Xi ◽  
Byung C. Jung ◽  
Byeng D. Youn
Keyword(s):  
Random Field ◽  
Field Data ◽  
Lithium Ion ◽  
Probability Analysis ◽  
Statistical Dependence ◽  
Data Sets ◽  
Insufficient Data ◽  
Analysis And Design ◽  
Field Modeling ◽  
Engineering Problems

Random field is a generalization of a stochastic field, of which randomness can be characterized as a function of spatial variables. Examples of the random field can often be found as a geometry, material, and process variation in engineering products and processes. It has been widely acknowledged that consideration of the random field is quite significant to accurately predict variability in system performances. However, current approaches for characterizing the random field can only be applied to the situation with sufficient random field data sets and are not suitable to most engineering problems where the data sets are insufficient. The contribution of this paper is to model the random field based on the insufficient data sets such that sufficient data sets can be simulated or generated according to the random field modeling. Therefore, available random field characterization approaches and probability analysis methods can be used for probability analysis and design of many engineering problems with the lack of random field data sets. The proposed random field modeling is composed of two technical components including: 1) a Bayesian updating approach using the Markov Chain Monte Carlo (MCMC) method for modeling the random field based on available random field data sets; and 2) a Bayesian Copula dependence modeling approach for modeling statistical dependence of random field realizations at different measurement locations. Three examples including a mathematical problem, a heat generation problem of the Lithium-ion battery, and a refrigerator assembly problem are used to demonstrate the effectiveness of the proposed approach.

scholarly journals Probabilistic Modelling of Variation in FGMOSFET

2017 ◽  
Vol 11 (1) ◽  
pp. 50-62
Author(s):  
Rawid Banchuin ◽  
Roungsan Chaisricharoen
Keyword(s):  
Goodness Of Fit ◽  
Drain Current ◽  
Probabilistic Modelling ◽  
Goodness Of Fit Test ◽  
Analysis And Design ◽  
Trade Offs ◽  
Saturation Region ◽  
Current Variation ◽  
The Impact ◽  
Statistical Variability

The analytical probabilistic modelling of random variation in the drain current of a Floating-Gate MOSFET (FGMOSFET) induced by manufacturing process variations has been performed. Both triode and saturation region operated FGMOSFETs have been considered. The results have been found to be very efficient since they can accurately fit the probabilistic distributions of normalized random drain current variations of the candidate triode and saturation FGMOSFETs obtained using the 0.25μm level BSIM3v3 based Monte-Carlo SPICE simulations, where the variation of the saturation FGMOSFET has been found to be more severe. These results also satisfy the goodness of fit test at a very high level of confidence and more accurately than the results of the previous probabilistic modelling attempts. Using our results, many statistical parameters, probabilities and the objective functions, which are useful in statistical/variability aware analysis and design involving FGMOSFETs can be formulated. The impact of drain current variation upon the design trade-offs can be studied. It has been found that the occurrence of the drain current variation is absolutely certain. Moreover, the analytical probabilistic modelling and computationally efficient statistical/ variability aware simulation of FGMOSFET based circuits can also be performed. 

Random field modeling with insufficient field data for probability analysis and design

2014 ◽  
Vol 51 (3) ◽  
pp. 599-611 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn ◽  
Byung C. Jung ◽  
Joung Taek Yoon
Keyword(s):  
Random Field ◽  
Field Data ◽  
Probability Analysis ◽  
Analysis And Design ◽  
Field Modeling

Validation of the CASUS score in Tunisian patients: a quality management tool in intensive care units

2020 ◽  
Vol 30 (Supplement_5) ◽  
Author(s):  
T Besbes ◽  
S Mleyhi ◽  
J Sahli ◽  
M Messai ◽  
J Ziadi ◽  
...  
Keyword(s):  
Cardiac Surgery ◽  
Roc Curve ◽  
Goodness Of Fit ◽  
Cardiovascular Surgery ◽  
Management Tool ◽  
Medical Decision ◽  
Tunisian Population ◽  
Correct Classification ◽  
Goodness Of Fit Test ◽  
A Value

Abstract Background Early prediction of patients at highest risk of a poor outcome after cardiovascular surgery, including death can aid medical decision making, and adapt health care management in order to improve prognosis. In this context, we conducted this study to validate the CASUS severity score after cardiac surgery in the Tunisian population. Methods This is a retrospective cohort study conducted among patients who underwent cardiac surgery under extracorporeal circulation during the year 2018 at the Cardiovascular Surgery Department of La Rabta University Hospital in Tunisia. Data were collected from the patients hospitalization records. The discrimination of the score was assessed using the ROC curve and the calibration using the Hosmer-Lemeshow goodness of fit test and then by constructing the calibration curve. Overall correct classification was also obtained. Results In our study, the observed mortality rate was 10.52% among the 95 included patients. The discriminating power of the CASUS score was estimated by the area under the ROC curve (AUC), this scoring system had a good discrimination with AUC greater than 0.9 from postoperative Day 0 to Day 5.From postoperative day 0 to day 5, the Hosmer-Lemeshow's test gave a value of chi square test statistic ranging from 1.474 to 8.42 and a value of level of significance ranging from 0.39 to 0.99 indicating a good calibration. The overall correct classification rate from postoperative day 0 to day 5 ranged from 84.4% to 92.4%. Conclusions Despite the differences in the profile of the risk factors between the Tunisian population and the population constituting the database used to develop the CASUS score, we can say that this risk model presents acceptable performances in our population, attested by adequate discrimination and calibration. Prospective and especially multicentre studies on larger samples are needed before definitively conclude on the performance of this model in our country. Key messages The casus score seems to be valid to predict mortality among patients undergoing cardiac surgery. Multicenter study on larger sample is needed to derive and validate models able to predict in-hospitals mortality.

Goodness-of-fit test with a robustness feature

Test ◽  
2021 ◽  
Author(s):  
Jiming Jiang ◽  
Mahmoud Torabi
Keyword(s):  
Goodness Of Fit ◽  
Goodness Of Fit Test
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