scholarly journals Probabilistic and Nonprobabilistic Sensitivity Analyses of Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sheng-En Fang ◽  
Qiu-Hu Zhang ◽  
Bao Zhang ◽  
Xiao-Hua Zhang
Keyword(s):  
Probability Distributions ◽  
Probabilistic Method ◽  
Sensitivity Analyses ◽  
Uncertain Parameters ◽  
Stochastic Response ◽  
First Order ◽  
Simple Implementation ◽  
Probability Information ◽  
Main Effects ◽  
Mathematical Derivation

Parameter sensitivity analyses have been widely applied to industrial problems for evaluating parameter significance, effects on responses, uncertainty influence, and so forth. In the interest of simple implementation and computational efficiency, this study has developed two sensitivity analysis methods corresponding to the situations with or without sufficient probability information. The probabilistic method is established with the aid of the stochastic response surface and the mathematical derivation proves that the coefficients of first-order items embody the parameter main effects on the response. Simultaneously, a nonprobabilistic interval analysis based method is brought forward for the circumstance when the parameter probability distributions are unknown. The two methods have been verified against a numerical beam example with their accuracy compared to that of a traditional variance-based method. The analysis results have demonstrated the reliability and accuracy of the developed methods. And their suitability for different situations has also been discussed.

Effect of Uncertainty in the Balancing Weights on the Vibration Response of a High-Speed Rotor

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Janina Datz ◽  
Mahmoud Karimi ◽  
Steffen Marburg
Keyword(s):  
High Speed ◽  
Probability Distributions ◽  
Probabilistic Method ◽  
Turbine Rotor ◽  
Vibration Response ◽  
Galerkin Projection ◽  
System Response ◽  
Influence Coefficient ◽  
Uncertain Parameters ◽  
Influence Coefficient Method

Abstract This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

Differential Credibility of Climate Modes in CMIP6

2021 ◽  
pp. 1
Author(s):  
Jacob Coburn ◽  
S.C. Pryor
Keyword(s):  
Southern Oscillation ◽  
Probability Distributions ◽  
Critical Role ◽  
Regional Scale ◽  
Southern Annular Mode ◽  
Climate Projections ◽  
Annular Mode ◽  
Climate Modes ◽  
First Order ◽  
Skill Scores

AbstractThis work quantitatively evaluates the fidelity with which the Northern Annular Mode (NAM), Southern Annular Mode (SAM), Pacific-North American pattern (PNA), El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO) and the first-order mode interactions are represented in Earth System Model (ESM) output from the CMIP6 archive. Several skill metrics are used as part of a differential credibility assessment (DCA) of both spatial and temporal characteristics of the modes across ESMs, ESM families and specific ESM realizations relative to ERA5. The spatial patterns and probability distributions are generally well represented but skill scores that measure the degree to which the frequencies of maximum variance are captured are consistently lower for most ESMs and climate modes. Substantial variability in skill scores manifests across realizations from individual ESMs for the PNA and oceanic modes. Further, the ESMs consistently overestimate the strength of the NAM-PNA first-order interaction and underestimate the NAM-AMO connection. These results suggest that the choice of ESM and ESM realizations will continue to play a critical role in determining climate projections at the global and regional scale at least in the near-term.

Computer Aided Tolerance Analysis of Parts and Assemblies

1989 ◽  
Author(s):  
R. T. Scott ◽  
G. A. Gabriele
Keyword(s):  
Real World ◽  
Probability Distributions ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
The Real ◽  
Assembly Tolerance ◽  
Computer Aided ◽  
Probability Information ◽  
Exact Constraint

Abstract An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

On Stochastic Characterization of Temporal Storm Patterns

1984 ◽  
Vol 16 (8-9) ◽  
pp. 147-153 ◽  
Author(s):  
Van-Thanh-Van Nguyen
Keyword(s):  
Markov Chain ◽  
Probability Distributions ◽  
First Order ◽  
Stochastic Characterization ◽  
Order Markov Chain ◽  
Hourly Rainfall ◽  
General Stochastic Model ◽  
Storm Rainfall ◽  
Rainfall Occurrences

The present study, a continuation of a previous work by the author, suggests a new theoretical approach to the characterization of the temporal pattern of storms. A storm is defined as a continuous run of non-zero one-hour rainfall depths. A general stochastic model is developed to determine the probability distributions of cumulative storm rainfall amounts at successive time intervals after the storm began. The previous model for characterizing storm temporal patterns was based on the assumption that hourly rainfall depths were independent and identically exponentially distributed random variables, while sequences of wet hours were modeled by a first-order stationary Markov chain. Hence, the model did only introduce dependence of wet hour occurences into the rainfall process through the first-order Markov chain. The present paper proposes a more general model that can take into account both the persistence in hourly rainfall occurrences and the dependence between successive hourly rainfall depths. Results of an illustrative example show that by accounting for the correlation structure of consecutive rainfall depths the present model gives a better fit to the observations than the previous one.

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

Analysis of the Partial Safety Factor Method Using Probabilistic Techniques

2010 ◽  
Author(s):  
B. A. Lindley ◽  
P. M. James
Keyword(s):  
Probabilistic Method ◽  
Probability Of Failure ◽  
Safety Factors ◽  
First Order Reliability Method ◽  
First Order ◽  
Target Probability ◽  
Reliability Method ◽  
Input Parameters ◽  
Partial Safety Factors ◽  
Hand Calculation

Partial Safety Factors (PSFs) are scaling factors which are used to modify the input parameters to a deterministic fracture mechanics assessment in order to consider the effects of variability or uncertainty in the values of the input parameters. BS7910 and SINTAP have adopted the technique, both of which use the First Order Reliability Method (FORM) to derive values for PSFs. The PSFs are tabulated, varying with the target probability of failure, p(F), and the Coefficient of Variance (COV) of the variable. An accurate assessment of p(F) requires a probabilistic method with enough simulations. This has previously been found to be time consuming, due to the large number of simulations required. The PSF method has been seen as a quick way of calculating an approximate, conservative value of p(F). This paper contains a review of the PSF method, conducted using an efficient probabilistic method called the Hybrid probabilistic method. The Hybrid probabilistic method is used to find p(F) at a large number of assessment points, for a range of different PSFs. These p(F) values are compared to those obtained using the PSF method. It is found that the PSF method was usually, and often extremely, conservative. However there are also cases where the PSF method was non-conservative. This result is verified by a hand calculation. Modifications to the PSF method are suggested, including the establishment of a minimum PSF on each variable to reduce non-conservatisms. In light of the existence of efficient probabilistic techniques, the non-conservatisms that have been found in the PSF method, coupled with the impracticality of completely removing these non-conservatisms, it is recommended that a full probabilistic assessment should generally be performed.

scholarly journals Extending Fibre Nonlinear Interference Power Modelling to Account for General Dual-Polarisation 4D Modulation Formats

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1324
Author(s):  
Gabriele Liga ◽  
Astrid Barreiro ◽  
Hami Rabbani ◽  
Alex Alvarado
Keyword(s):  
Optical Communication ◽  
Average Power ◽  
Noise Model ◽  
Analytical Models ◽  
Modulation Formats ◽  
First Order ◽  
Modulation Format ◽  
The One ◽  
Mathematical Derivation ◽  
Mutually Independent

In optical communications, four-dimensional (4D) modulation formats encode information onto the quadrature components of two arbitrary orthogonal states of polarisation of the optical field. Many analytical models available in the optical communication literature allow, within a first-order perturbation framework, the computation of the average power of the nonlinear interference (NLI) accumulated in coherent fibre-optic transmission systems. However, all such models only operate under the assumption of transmitted polarisation-multiplexed two-dimensional (PM-2D) modulation formats, which only represent a limited subset of the possible dual-polarisation 4D (DP-4D) formats. Namely, only those where data transmitted on each polarisation channel are mutually independent and identically distributed. This paper presents a step-by-step mathematical derivation of the extension of existing NLI models to the class of arbitrary DP-4D modulation formats. In particular, the methodology adopted follows the one of the popular enhanced Gaussian noise model, albeit dropping most assumptions on the geometry and statistic of the transmitted 4D modulation format. The resulting expressions show that, whilst in the PM-2D case the NLI power depends only on different statistical high-order moments of each polarisation component, for a general DP-4D constellation, several other cross-polarisation correlations also need to be taken into account.

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