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.

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

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.

scholarly journals New Hybrid Approach for Developing Automated Machine Learning Workflows: A Real Case Application in Evaluation of Marcellus Shale Gas Production

Fuels ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 286-303
Author(s):  
Vuong Van Pham ◽  
Ebrahim Fathi ◽  
Fatemeh Belyadi
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Shale Gas ◽  
Field Data ◽  
Marcellus Shale ◽  
Hybrid Approach ◽  
Gas Production ◽  
Bayesian Optimization ◽  
Real Field ◽  
Engineering Problems

The success of machine learning (ML) techniques implemented in different industries heavily rely on operator expertise and domain knowledge, which is used in manually choosing an algorithm and setting up the specific algorithm parameters for a problem. Due to the manual nature of model selection and parameter tuning, it is impossible to quantify or evaluate the quality of this manual process, which in turn limits the ability to perform comparison studies between different algorithms. In this study, we propose a new hybrid approach for developing machine learning workflows to help automated algorithm selection and hyperparameter optimization. The proposed approach provides a robust, reproducible, and unbiased workflow that can be quantified and validated using different scoring metrics. We have used the most common workflows implemented in the application of artificial intelligence (AI) and ML in engineering problems including grid/random search, Bayesian search and optimization, genetic programming, and compared that with our new hybrid approach that includes the integration of Tree-based Pipeline Optimization Tool (TPOT) and Bayesian optimization. The performance of each workflow is quantified using different scoring metrics such as Pearson correlation (i.e., R2 correlation) and Mean Square Error (i.e., MSE). For this purpose, actual field data obtained from 1567 gas wells in Marcellus Shale, with 121 features from reservoir, drilling, completion, stimulation, and operation is tested using different proposed workflows. A proposed new hybrid workflow is then used to evaluate the type well used for evaluation of Marcellus shale gas production. In conclusion, our automated hybrid approach showed significant improvement in comparison to other proposed workflows using both scoring matrices. The new hybrid approach provides a practical tool that supports the automated model and hyperparameter selection, which is tested using real field data that can be implemented in solving different engineering problems using artificial intelligence and machine learning. The new hybrid model is tested in a real field and compared with conventional type wells developed by field engineers. It is found that the type well of the field is very close to P50 predictions of the field, which shows great success in the completion design of the field performed by field engineers. It also shows that the field average production could have been improved by 8% if shorter cluster spacing and higher proppant loading per cluster were used during the frac jobs.

Surface wave attenuation of seismic records with the co-core trace transform filter

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. V115-V128 ◽  
Author(s):  
Ning Wu ◽  
Yue Li ◽  
Baojun Yang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Field Data ◽  
Wave Attenuation ◽  
Seismic Events ◽  
Data Sets ◽  
Transform Domain ◽  
Recent Developments ◽  
Seismic Records ◽  
Trace Transform

To remove surface waves from seismic records while preserving other seismic events of interest, we introduced a transform and a filter based on recent developments in image processing. The transform can be seen as a weighted Radon transform, in particular along linear trajectories. The weights in the transform are data dependent and designed to introduce large amplitude differences between surface waves and other events such that surface waves could be separated by a simple amplitude threshold. This is a key property of the filter and distinguishes this approach from others, such as conventional ones that use information on moveout ranges to apply a mask in the transform domain. Initial experiments with synthetic records and field data have demonstrated that, with the appropriate parameters, the proposed trace transform filter performs better both in terms of surface wave attenuation and reflected signal preservation than the conventional methods. Further experiments on larger data sets are needed to fully assess the method.

Developing an Empirical Yield-Prediction Model Based on Wheat and Wild Oat (Avena fatua) Density, Nitrogen and Herbicide Rate, and Growing-Season Precipitation

Weed Science ◽  
2007 ◽  
Vol 55 (6) ◽  
pp. 652-664 ◽  
Author(s):  
N. C. Wagner ◽  
B. D. Maxwell ◽  
M. L. Taper ◽  
L. J. Rew
Keyword(s):  
Field Data ◽  
Wheat Yield ◽  
Growing Season ◽  
Predictor Variables ◽  
Data Sets ◽  
Wild Oat ◽  
Best Fitting ◽  
Weed Infestation ◽  
Growing Season Precipitation ◽  
Better Than

To develop a more complete understanding of the ecological factors that regulate crop productivity, we tested the relative predictive power of yield models driven by five predictor variables: wheat and wild oat density, nitrogen and herbicide rate, and growing-season precipitation. Existing data sets were collected and used in a meta-analysis of the ability of at least two predictor variables to explain variations in wheat yield. Yield responses were asymptotic with increasing crop and weed density; however, asymptotic trends were lacking as herbicide and fertilizer levels were increased. Based on the independent field data, the three best-fitting models (in order) from the candidate set of models were a multiple regression equation that included all five predictor variables (R2= 0.71), a double-hyperbolic equation including three input predictor variables (R2= 0.63), and a nonlinear model including all five predictor variables (R2= 0.56). The double-hyperbolic, three-predictor model, which did not include herbicide and fertilizer influence on yield, performed slightly better than the five-variable nonlinear model including these predictors, illustrating the large amount of variation in wheat yield and the lack of concrete knowledge upon which farmers base their fertilizer and herbicide management decisions, especially when weed infestation causes competition for limited nitrogen and water. It was difficult to elucidate the ecological first principles in the noisy field data and to build effective models based on disjointed data sets, where none of the studies measured all five variables. To address this disparity, we conducted a five-variable full-factorial greenhouse experiment. Based on our five-variable greenhouse experiment, the best-fitting model was a new nonlinear equation including all five predictor variables and was shown to fit the greenhouse data better than four previously developed agronomic models with anR2of 0.66. Development of this mathematical model, through model selection and parameterization with field and greenhouse data, represents the initial step in building a decision support system for site-specific and variable-rate management of herbicide, fertilizer, and crop seeding rate that considers varying levels of available water and weed infestation.

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