Robust Design Concept in Possibility Theory and Optimization for System With Both Random and Fuzzy Input Variables

2007 ◽  
Author(s):  
Liu Du ◽  
Kyung K. Choi ◽  
Ikjin Lee
Keyword(s):  
Robust Design ◽  
Fuzzy Variable ◽  
Possibility Theory ◽  
Random Variable ◽  
Search Method ◽  
Design Concept ◽  
Output Performance ◽  
Robustness Measure ◽  
Fuzzy Input ◽  
Input Variables

Whereas the robust design concept has been well established in the probability theory, it has not been developed in the possibility theory. For problems where accurate statistical information for input data is not available, a possibility-based (or fuzzy set) robust design concept is proposed in this paper by investigating the similarity between the membership function of the fuzzy variable and the cumulative distribution function of the random variable. Based on the probability-possibility consistency principle, a random variable that corresponds to the fuzzy variable is introduced in this paper in order to define the robust design concept for the fuzzy variable. For the system with input fuzzy variables, the robustness measure of the output performance is computed using the performance measure integration (PMI) method, while the integration points are obtained from the inverse possibility analysis by using the maximal possibility search method with interpolation (MPS). For the system with mixed random and fuzzy input variables, the robustness measure of the output performance is computed using PMI method, with the integration points obtained from the inverse mixed analysis by using the maximal failure search method (MFS). A new mixed (random and fuzzy) variable robust design optimization (MVRDO) method is proposed and several numerical examples are used to verify the robust design concept in the possibility theory and the MVRDO formulation.

3 Power and sample size for ABE in the 2× 2 design Here we give formulae for the calculation of the power of the TOST procedure assuming that there are in total n subjects in the 2× 2 trial. Suppose that the null hypotheses given below are to be tested using a 100(1 − α)% two-sided confidence interval and a power of (1 − β) is required to reject these hypotheses when they are false. H :µ ≤− ln 1.25 H :µ ≥ ln 1.25. Let us define x to be a random variable that has a noncentral t-distribution with df degrees of freedom and noncentrality parameter nc, i.e., x ∼ t(df,nc). The cumulative distribution function of x is defined as CDF(t,df,nc) = Pr(x≤ t). Assume that the power is to be calculated using log(AUC). If σ is the common within-subject variance for T and R for log(AUC), and n/2 subjects are allocated to each of the sequences RT and TR, then 1−β = CDF(t , df,nc )−CDF(t , df,nc ) (7.1) where √ n(log(µ )− log(0.8)) nc = 2σ √ n(log(µ )− log(1.25)) nc = 2σ √ (n− 2)(nc −nc = ) df 2t and t is the 100(1 − α)% point of the central t-distribution on n− 2 degrees of freedom. Some SAS code to calculate the power for an ABE 2 × 2 trial is given below, where the required input variables are α, σ value of the ratio µ and n, the total number of subjects in the trial.

2003 ◽  
pp. 361-361
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Degrees Of Freedom ◽  
Random Variable ◽  
Noncentrality Parameter ◽  
Cumulative Distribution ◽  
Total N ◽  
The Common ◽  
Input Variables ◽  
T Distribution

scholarly journals Klasifikasi Motif Batik Berbasis Kemiripan Ciri dengan Wavelet Transform dan Fuzzy Neural Network

2014 ◽  
Vol 5 (1) ◽  
pp. 361
Author(s):  
A Haris Rangkuti
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Fuzzy Neural Network ◽  
Classification Methods ◽  
Neural Network Classification ◽  
Fuzzy Input ◽  
Fuzzy Neural ◽  
Input Variables

 This paper introduces a classification of the image of the batik process, which is based on the similarity of the characteristics, by combining the method of wavelet transform Daubechies type 2 level 2, to process the characteristic texture consisting of standard deviation, mean and energy as input variables, using the method of Fuzzy Neural Network (FNN). Fuzzyfikasi process will be carried out all input values with five categories: Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH). The result will be a fuzzy input in the process of neural network classification methods. The result will be a fuzzy input in the process of neural network classification methods. For the image to be processed seven types of batik motif is ceplok, kawung, lereng, parang, megamendung, tambal and nitik. The results of the classification process with FNN is rule generation, so for the new image of batik can be immediately known motif types after treatment with FNN classification.  For the degree of precision of this method is 86-92%.

Robust Design Optimization of Ball Grid Array Packaging

2011 ◽  
Author(s):  
Jae Chang Kim ◽  
Joo-Ho Choi ◽  
Yeong K. Kim
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Strain Energy ◽  
Reduction Method ◽  
Ball Grid Array ◽  
Robust Design Optimization ◽  
Molding Compound ◽  
Materials Modeling ◽  
Solder Balls ◽  
Input Variables

In this paper, comparisons of the design optimization of ball grid array packaging geometry based on the elastic and viscoelastic material properties are made. Six geometric dimensions of the packaging are chosen as input variables. Molding compound and substrate are modeled as elastic and viscoelastic, respectively. Viscoplastic finite element analyses are performed to calculate the strain energy densities (SED) of the eutectic solder balls. Robust design optimizations to minimize SED are carried out, which accounts for the variance of the parameters via Kriging dimension reduction method. Optimum solutions are compared with those by the Taguchi method. It is found that the effects of the packaging geometry on the solder ball reliability are significant, and the optimization results are different depending on the materials modeling.

Application of the Robust Design Concept for Fuel Loading Pattern

2011 ◽  
Vol 48 (7) ◽  
pp. 1077-1086 ◽  
Author(s):  
Tomohiro ENDO ◽  
Kazuma OHORI ◽  
Akio YAMAMOTO
Keyword(s):  
Robust Design ◽  
Design Concept ◽  
Fuel Loading ◽  
Loading Pattern

Effect of Material and Manufacturing Variations on Membrane Electrode Assembly Pressure Distribution

2003 ◽  
Author(s):  
Andreas Vlahinos ◽  
Kenneth Kelly ◽  
Jim D’Aleo ◽  
Jim Stathopoulos
Keyword(s):  
Pressure Distribution ◽  
Robust Design ◽  
Proton Exchange Membrane ◽  
Research Effort ◽  
Plate Thickness ◽  
Membrane Electrode Assembly ◽  
Proton Exchange ◽  
Membrane Electrode ◽  
Input Variables ◽  
Stress Uniformity

A design is robust when it is not sensitive to variations in noise parameters such as manufacturing tolerances, material properties, environmental temperature, humidity, etc. In recent years several robust design concepts have been introduced in an effort to obtain optimum designs and minimize the variation in the product characteristics. Increasing the pressure on a PEM (Proton Exchange Membrane) fuel cell’s MEA (Membrane Electrode Assembly) leads to increasing the electric conductivity and reducing the permeability of the assembly. In this study, a probabilistic FEA analysis was performed on a simplified fuel cell stack in order to identify the effect of material and manufacturing variations on the MEA’s pressure distribution. The bi-polar flow plate thickness, the modulus of elasticity and the end plate bolt loading were considered as randomly varying parameters with given mean and standard deviation. The normal stress uniformity of the MEA was determined in terms of the probabilistic input variables. The methodology for implementing robust design used in this research effort is summarized in a reusable workflow diagram.

A FUZZY RELIABILITY ANALYSIS BASED ON THE TRANSFORMATION BETWEEN DISCRETE FUZZY VARIABLES AND DISCRETE RANDOM VARIABLES

2006 ◽  
Vol 13 (01) ◽  
pp. 25-35 ◽  
Author(s):  
YUGE DONG ◽  
AINAN WANG
Keyword(s):  
Reliability Analysis ◽  
Fuzzy Variable ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Information ◽  
Discrete Random Variable ◽  
Fuzzy Reliability ◽  
Fuzzy Variables ◽  
Discrete Random Variables ◽  
Fuzzy Random

When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended to continuous case, and can also be used in the fuzzy reliability analysis of repairable system.

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