Design Sensitivity Method for Sampling-Based RBDO With Varying Standard Deviation

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
David Lamb
Keyword(s):  
Standard Deviation ◽  
Design Variable ◽  
Score Function ◽  
Random Variable ◽  
Probability Of Failure ◽  
Design Sensitivity ◽  
Mean Value ◽  
Reliability Based Design ◽  
The Mean ◽  
Sensitivity Method

Conventional reliability-based design optimization (RBDO) uses the mean of input random variable as its design variable; and the standard deviation (STD) of the random variable is a fixed constant. However, the constant STD may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is present as a percentage of the mean value. For this kind of design problem, the STD of the input random variable should vary as the corresponding design variable changes. In this paper, a method to calculate the design sensitivity of the probability of failure for RBDO with varying STD is developed. For sampling-based RBDO, which uses Monte Carlo simulation (MCS) for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STD in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with varying STD. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed design sensitivity method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

Design Sensitivity Method for Sampling-Based RBDO With Fixed COV

2015 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
David Lamb
Keyword(s):  
Random Variables ◽  
Score Function ◽  
Random Variable ◽  
Probability Of Failure ◽  
Design Sensitivity ◽  
Mean Value ◽  
Reliability Based Design ◽  
Design Variables ◽  
Change In The Mean ◽  
The Mean

Conventional reliability-based design optimization (RBDO) uses the means of input random variables as its design variables; and the standard deviations (STDEVs) of the random variables are fixed constants. However, the fixed STDEVs may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is presented as a percentage of the mean value. For this kind of design problem, the coefficients of variations (COVs) of the input random variables should be fixed, which means STDEVs are not fixed. In this paper, a method to calculate the design sensitivity of probability of failure for RBDO with fixed COV is developed. For sampling-based RBDO, which uses Monte Carlo simulation for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STDEV in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with fixed COV. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

scholarly journals Sensitivity Developments for RBDO With Dependent Input Variable and Varying Input Standard Deviation

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
David Lamb
Keyword(s):  
Standard Deviation ◽  
Random Variable ◽  
Design Sensitivity ◽  
Statistical Correlation ◽  
Mean Value ◽  
Distribution Model ◽  
Target Point ◽  
Probabilistic Constraint ◽  
Reliability Based Design ◽  
Standard Normal

In reliability-based design optimization (RBDO), dependent input random variables and varying standard deviation (STD) should be considered to correctly describe input distribution model. The input dependency and varying STD significantly affect sensitivity for the most probable target point (MPTP) search and design sensitivity of probabilistic constraint in sensitivity-based RBDO. Hence, accurate sensitivities are necessary for efficient and effective process of MPTP search and RBDO. In this paper, it is assumed that dependency of input random variable is limited to the bivariate statistical correlation, and the correlation is considered using bivariate copulas. In addition, the varying STD is considered as a function of input mean value. The transformation between physical X-space and independent standard normal U-space for correlated input variable is presented using bivariate copula and marginal probability distribution. Using the transformation and the varying STD function, the sensitivity for the MPTP search and design sensitivity of probabilistic constraint are derived analytically. Using a mathematical example, the accuracy and efficiency of the developed sensitivities are verified. The RBDO result for the mathematical example indicates that the developed methods provide accurate sensitivities in the optimization process. In addition, a 14D engineering example is tested to verify the practicality and scalability of the developed sensitivity methods.

scholarly journals Blood Oxygenation Level Dependent Magnetic Resonance Imaging (MRI), Dynamic Contrast Enhanced MRI and Diffusion Weighted MRI for Benign and Malignant Breast Cancer Discrimination: A Preliminary Experience

Cancers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 2421
Author(s):  
Roberta Fusco ◽  
Vincenza Granata ◽  
Mauro Mattace Raso ◽  
Paolo Vallone ◽  
Alessandro Pasquale De Rosa ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Univariate Analysis ◽  
Mean Value ◽  
Blood Oxygenation ◽  
Breast Lesions ◽  
Dce Mri ◽  
Malignant Lesions ◽  
The Mean ◽  
And Diffusion ◽  
Skewness And Kurtosis

Purpose. To combine blood oxygenation level dependent magnetic resonance imaging (BOLD-MRI), dynamic contrast enhanced MRI (DCE-MRI), and diffusion weighted MRI (DW-MRI) in differentiation of benign and malignant breast lesions. Methods. Thirty-seven breast lesions (11 benign and 21 malignant lesions) pathologically proven were included in this retrospective preliminary study. Pharmaco-kinetic parameters including Ktrans, kep, ve, and vp were extracted by DCE-MRI; BOLD parameters were estimated by basal signal S0 and the relaxation rate R2*; and diffusion and perfusion parameters were derived by DW-MRI (pseudo-diffusion coefficient (Dp), perfusion fraction (fp), and tissue diffusivity (Dt)). The correlation coefficient, Wilcoxon-Mann-Whitney U-test, and receiver operating characteristic (ROC) analysis were calculated and area under the ROC curve (AUC) was obtained. Moreover, pattern recognition approaches (linear discrimination analysis and decision tree) with balancing technique and leave one out cross validation approach were considered. Results. R2* and D had a significant negative correlation (−0.57). The mean value, standard deviation, Skewness and Kurtosis values of R2* did not show a statistical significance between benign and malignant lesions (p > 0.05) confirmed by the ‘poor’ diagnostic value of ROC analysis. For DW-MRI derived parameters, the univariate analysis, standard deviation of D, Skewness and Kurtosis values of D* had a significant result to discriminate benign and malignant lesions and the best result at the univariate analysis in the discrimination of benign and malignant lesions was obtained by the Skewness of D* with an AUC of 82.9% (p-value = 0.02). Significant results for the mean value of Ktrans, mean value, standard deviation value and Skewness of kep, mean value, Skewness and Kurtosis of ve were obtained and the best AUC among DCE-MRI extracted parameters was reached by the mean value of kep and was equal to 80.0%. The best diagnostic performance in the discrimination of benign and malignant lesions was obtained at the multivariate analysis considering the DCE-MRI parameters alone with an AUC = 0.91 when the balancing technique was considered. Conclusions. Our results suggest that the combined use of DCE-MRI, DW-MRI and/or BOLD-MRI does not provide a dramatic improvement compared to the use of DCE-MRI features alone, in the classification of breast lesions. However, an interesting result was the negative correlation between R2* and D.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

scholarly journals Evaluation of Bearing Capacity of Strip Footing Using Random Layers Concept

2015 ◽  
Vol 37 (3) ◽  
pp. 31-39 ◽  
Author(s):  
Marek Kawa ◽  
Dariusz Łydżba
Keyword(s):  
Monte Carlo ◽  
Bearing Capacity ◽  
Failure Mechanism ◽  
Design Theory ◽  
Cohesive Soil ◽  
Probability Of Failure ◽  
Mean Value ◽  
Strip Footing ◽  
Random Field Theory ◽  
The Mean

Abstract The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

Synchronous Issue of IR-Based Large Scale Volume Localization System

2014 ◽  
Vol 496-500 ◽  
pp. 1643-1647
Author(s):  
Ying Feng Wu ◽  
Gang Yan Li
Keyword(s):  
Standard Deviation ◽  
Mobile Robot ◽  
Large Volume ◽  
Large Scale ◽  
Image Acquisition ◽  
Mean Value ◽  
Network Synchronization ◽  
Localization System ◽  
Localization Performance ◽  
The Mean

IR-based large scale volume localization system (LSVLS) can localize the mobile robot working in large volume, which is constituted referring to the MSCMS-II. Hundreds cameras in LSVLS must be connected to the control station (PC) through network. Synchronization of cameras which are mounted on different control stations is significant, because the image acquisition of the target must be synchronous to ensure that the target is localized precisely. Software synchronization method is adopted to ensure the synchronization of camera. The mean value of standard deviation of eight cameras mounted on two workstations is 12.53ms, the localization performance of LSVLS is enhanced.

Precise computation of the direct and indirect topographic effects of Helmert's 2nd method of condensation using SRTM30 digital elevation model

2011 ◽  
Vol 1 (4) ◽  
pp. 305-312 ◽  
Author(s):  
Y. Wang
Keyword(s):  
Standard Deviation ◽  
Digital Elevation Model ◽  
Outer Zone ◽  
Mean Value ◽  
Constant Density ◽  
Topographic Effects ◽  
Topographic Effect ◽  
Digital Elevation ◽  
The Mean ◽  
Elevation Model

Precise computation of the direct and indirect topographic effects of Helmert's 2nd method of condensation using SRTM30 digital elevation modelThe direct topographic effect (DTE) and indirect topographic effect (ITE) of Helmert's 2nd method of condensation are computed using the digital elevation model (DEM) SRTM30 in 30 arc-seconds globally. The computations assume a constant density of the topographic masses. Closed formulas are used in the inner zone of half degree, and Nagy's formulas are used in the innermost column to treat the singularity of integrals. To speed up the computations, 1-dimensional fast Fourier transform (1D FFT) is applied in outer zone computations. The computation accuracy is limited to 0.1 mGal and 0.1cm for the direct and indirect effect, respectively.The mean value and standard deviation of the DTE are -0.8 and ±7.6 mGal over land areas. The extreme value -274.3 mGal is located at latitude -13.579° and longitude 289.496°, at the height of 1426 meter in the Andes Mountains. The ITE is negative everywhere and has its minimum of -235.9 cm at the peak of Himalayas (8685 meter). The standard deviation and mean value over land areas are ±15.6 cm and -6.4 cm, respectively. Because the Stokes kernel does not contain the zero and first degree spherical harmonics, the mean value of the ITE can't be compensated through the remove-restore procedure under the Stokes-Helmert scheme, and careful treatment of the mean value in the ITE is required.

scholarly journals Time-to-Boundary Function to Study the Development of Upright Stance Control in Children

2017 ◽  
Vol 11 (1) ◽  
pp. 49-58
Author(s):  
Carmen D'Anna ◽  
Maurizio Schmid ◽  
Andrea Scorza ◽  
Salvatore A. Sciuto ◽  
Luisa Lopez ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Postural Control ◽  
Postural Stability ◽  
Age Groups ◽  
Boundary Function ◽  
Mean Value ◽  
Upright Stance ◽  
Eyes Closed ◽  
The Mean ◽  
Spatio Temporal

Background: The development of postural control across the primary school time horizon is a complex process, which entails biomechanics modifications, the maturation of cognitive ability and sensorimotor organization, and the emergence of anticipatory behaviour. Postural stability in upright stance has been thus object of a multiplicity of studies to better characterize postural control in this age span, with a variety of methodological approaches. The analysis of the Time-to-Boundary function (TtB), which specifies the spatiotemporal proximity of the Centre of Pressure (CoP) to the stability boundaries in the regulation of posture in upright stance, is among the techniques used to better characterize postural stability in adults, but, as of now, it has not yet been introduced in developmental studies. The aim of this study was thus to apply this technique to evaluate the development of postural control in a sample population of primary school children. Methods: In this cross-sectional study, upright stance trials under eyes open and eyes closed were administered to 107 healthy children, divided into three age groups (41 for Seven Years' Group, Y7; 38 for Nine Years' Group, Y9; 28 for Eleven Years' Group, Y11). CoP data were recorded to calculate the Time-to-Boundary function (TtB), from which four spatio-temporal parameters were extracted: the mean value and the standard deviation of TtB minima (Mmin, Stdmin), and the mean value and the standard deviation of the temporal distance between two successive minima (Mdist, Stddist). Results: With eyes closed, Mmin and Stdmin significantly decreased and Mdist and Stddist increased for the Y7 group, at Y9 Mmin significantly decreased and Stddist increased, while no effect of vision resulted for Y11. Regarding age groups, Mmin was significantly higher for Y9 than Y7, and Stdmin for Y9 was higher than both Y7 and Y11; Mdist and Stddist resulted higher for Y11 than for Y9. Conclusion: From the combined results from the spatio-temporal TtB parameters, it is suggested that, at 9 years, children look more efficient in terms of exploring their limits of stability than at 7, and at 11 the observed TtB behaviour hints at the possibility that, at that age, they have almost completed the maturation of postural control in upright stance, also in terms of integration of the spatio-temporal information.

The Content of IMF Staff Reports for Euro Area Countries

2014 ◽  
pp. 272-292
Author(s):  
Lena Golubovskaja
Keyword(s):  
Standard Deviation ◽  
Euro Area ◽  
Mean Value ◽  
Systematic Bias ◽  
Executive Board ◽  
Sample Mean ◽  
Warning Tone ◽  
The Mean ◽  
Run Up ◽  
The Imf

This chapter analyzes the tone and information content of the two external policy reports of the Internal Monetary Fund (IMF), the IMF Article IV Staff Reports, and Executive Board Assessments for Euro area countries. In particular, the researchers create a tone measure denoted WARNING based on the existing DICTION 5.0 Hardship dictionary. This study finds that in the run-up to the current credit crises, average WARNING tone levels of Staff Reports for Slovenia, Luxembourg, Greece, and Malta are one standard deviation above the EMU sample mean; and for Spain and Belgium, they are one standard deviation below the mean value. Furthermore, on average for Staff Reports over the period 2005-2007, there are insignificant differences between the EMU sample mean and Staff Reports’ yearly averages. Researchers find the presence of a significantly increased level of WARNING tone in 2006 (compared to the previous year) for the IMF Article IV Staff Reports. There is also a systematic bias of WARNING scores for Executive Board Assessments versus WARNING scores for the Staff Reports.

A model for the effect of bias for cholesterol on the population at risk.

1988 ◽  
Vol 34 (11) ◽  
pp. 2256-2259 ◽  
Author(s):  
M H Kroll ◽  
M Ruddel ◽  
R J Elin
Keyword(s):  
At Risk ◽  
Standard Deviation ◽  
Reference Values ◽  
Gaussian Distribution ◽  
Population Distribution ◽  
Reference Value ◽  
Mean Value ◽  
The Body ◽  
Methodological Bias ◽  
The Mean

Abstract The location of the Reference Value for an analyte within the population distribution affects the magnitude of error due to methodological bias. Using the gaussian distribution, we evaluated the effects of systematic and proportional biases of the method (positive and negative), mean value, and standard deviation on the magnitude of error. We chose four Reference Values for cholesterol as a model. For a population with a mean of 2.0 and SD of 0.36 g of cholesterol per liter, a 3% positive proportional bias causes sixfold more error at the 50th percentile than at the 97.5th. In general, the error for a given bias (proportional or systematic) is greater for a Reference Value within the body than at the tails of the distribution. Further, the magnitude of the error varies as a function of the mean and standard deviation of the population.

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