Analysis of Statistical Characteristics and Global Sensitivity for Forced Response of Bladed Disks Mistuned by Material Anisotropy

2019 ◽  
Author(s):  
Rahul Rajasekharan ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Computational Cost ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Design Parameters ◽  
Anisotropy Axis ◽  
Material Anisotropy ◽  
Axis Orientation ◽  
Global Sensitivity ◽  
Bladed Disk

Abstract High-pressure turbines of modern gas-turbine engines use single crystal blades that exhibit material anisotropy. Due to manufacturing tolerances, each blade in the bladed disk will have different crystal anisotropy axis orientation, thereby creating mistuning in the structure. In this paper, the blade anisotropy angles are considered as uncertain design parameters to study the variation in forced response of a mistuned bladed disk. For realistic, high fidelity model of a bladed disk, linear bonded contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (a) statistical analysis using polynomial chaos expansion and (b) global sensitivity analysis using Sobol indices. An effective strategy based on gradient information is used to minimize the computational cost involved in statistical and sensitivity analysis. For the first time, the possibility of introducing intentional blade material anisotropy mistuning to reduce the amplification of forced response is investigated.

scholarly journals Analysis of Deformation of Mistuned Bladed Disks With Friction and Random Crystal Anisotropy Orientation Using Gradient-Based Polynomial Chaos Expansion

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Rahul Rajasekharan ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Design Parameters ◽  
System Response ◽  
Chaos Expansion ◽  
Material Anisotropy ◽  
Bladed Disks ◽  
Bladed Disk

Single crystal blades used in high pressure turbine bladed disks of modern gas-turbine engines exhibit material anisotropy. In this paper, the sensitivity analysis is performed to quantify the effects of blade material anisotropy orientation on deformation of a mistuned bladed disk under static centrifugal load. For a realistic, high fidelity model of a bladed disk both: (i) linear and (ii) nonlinear friction contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (i) local sensitivity analysis (LSA), based on first-order derivatives of system response with respect to design parameters, and (ii) statistical analysis using polynomial chaos expansion (PCE). The PCE is used to transfer the uncertainty in random input parameters to uncertainty in static deformation of the bladed disk. An effective strategy, using gradient information, is proposed to address the “curse of dimensionality” problem associated with statistical analysis of realistic bladed disk.

scholarly journals Analysis of Deformation of Mistuned Bladed Disks With Friction and Random Crystal Anisotropy Orientation Using Gradient-Based Polynomial Chaos Expansion

2018 ◽  
Author(s):  
Rahul Rajasekharan ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Design Parameters ◽  
System Response ◽  
Chaos Expansion ◽  
Material Anisotropy ◽  
Bladed Disks ◽  
Bladed Disk

Single crystal blades used in high pressure turbine bladed disks of modern gas-turbine engines exhibit material anisotropy. In this paper the sensitivity analysis is performed to quantify the effects of blade material anisotropy orientation on deformation of a mistuned bladed disk under static centrifugal load. For a realistic, high fidelity model of a bladed disk both: (i) linear, and (ii) non-linear friction contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (i) local sensitivity analysis, based on first order derivatives of system response w.r.t design parameters, and (ii) statistical analysis using polynomial chaos expansion. The polynomial chaos expansion is used to transfer the uncertainty in random input parameters to uncertainty in static deformation of the bladed disk. An effective strategy, using gradient information, is proposed to address the “curse of dimensionality” problem associated with statistical analysis of realistic bladed disk.

Efficient and Accurate Global Sensitivity Analysis for Reservoir Simulations By Use of the Probabilistic Collocation Method

SPE Journal ◽  
2013 ◽  
Vol 19 (04) ◽  
pp. 621-635 ◽  
Author(s):  
Cheng Dai ◽  
Heng Li ◽  
Dongxiao Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Collocation Method ◽  
History Matching ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Global Sensitivity ◽  
Reservoir Simulations ◽  
Probabilistic Collocation Method ◽  
The Impact ◽  
Probabilistic Collocation

Summary Reservoir simulations involve a large number of formation and fluid parameters, many of which are subject to uncertainties owing to the combination of spatial heterogeneity and insufficient measurements. Accurately quantifying the impact of varying parameters on simulation models can reveal the importance of the parameters, which helps in designing field-characterization strategies and determining parameterization for history matching. Compared with the commonly used local sensitivity analysis (SA), global SA considers the whole variation range of the parameters and can thus provide more-complete information. However, the traditional global sensitivity analysis that is derived from Monte Carlo simulation (MCS) is computationally too demanding for reservoir simulations. In this study, we propose an alternative approach that is both accurate and efficient. In the proposed approach, the model outputs such as pressure and reservoir production quantities are expressed by polynomial chaos expansions (PCEs). The probabilistic collocation method is used to determine the coefficients of the polynomial expansions by solving outputs at different sets of collocation points by means of the original partial-differential equations. Then, a proxy is constructed with such coefficients. Accurate statistical sensitivity indices of the uncertainty parameters can be obtained by running the proxy. We validate the approach with 2D examples by comparing with the MCS-based global SA. It is found that with only a small fraction of the computational cost required by the MCS approach, the new approach gives accurate global sensitivity for each parameter. The proposed approach is also demonstrated on a large-scale 3D black-oil model, for which the MCS-based global SA is found to be computationally infeasible. It is found that the developed approach possesses the following key advantages: It requires a much smaller number of reservoir simulations for accurate global SA; it is nonintrusive and can be implemented with existing codes or simulators; and it can accommodate arbitrary distributions of parameters encountered in realistic geological situations.

Parametric Dynamics of Mistuned Bladed Disk

2014 ◽  
Author(s):  
Peiyi Wang ◽  
Lin Li
Keyword(s):  
Coupling Strength ◽  
Amplification Factor ◽  
Dynamic Properties ◽  
Forced Response ◽  
Design Parameters ◽  
Classical Dynamic ◽  
Mode Localization ◽  
Bladed Disk ◽  
Saddle Surface ◽  
Wear And Tear

The mistuning of bladed disk comes from manufacturing tolerances and in-service wear and tear. Consequently the cyclic symmetry has been destroyed by mistuning, even small mistuning levels could result in drastic changes in the dynamics of bladed disks. Specifically, mistuning can cause mode localization and an increase of the maximum forced response. It has been known that frequency veering, modal localization and magnification of response are three most classical dynamic properties of bladed disk. However few researches has focused on the relationships between dynamic characters and design parameters, because the proper variation ranges of the design parameters are difficult to be determined. The aim of this paper is to investigate the relationship between designed parameters and dynamic properties of mistuned bladed disk. Based on a lumped parametric model of bladed disk and utilizing parameterized eigenvalue solution, a reasonable range of designed parameter corresponding to specific nodal diameter index was provided. The numerical results showed that the curves of the gap of frequency veering versus coupling strength or blade stiffness have bowel-style. It was also found that there exists a quasi-saddle-surface while the vibration amplification factor varies with coupling strength and mistuning strength. The quasi-saddle-surface reveals that the existence of threshold of vibration amplification factor depends on the value of coupling strength. The result means that a proper choice of combination of coupling strength and mistuning strength could lead to a suppression of mistuned vibration amplification.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

Global Sensitivity Analysis for Stay Vane and Casing Design of Reaction Hydraulic Turbine

2019 ◽  
Author(s):  
Hyunkyoo Cho ◽  
Ujjwal Shrestha ◽  
Young-Do Choi ◽  
Jungwan Park
Keyword(s):  
Sensitivity Analysis ◽  
Design Process ◽  
Performance Measures ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Surrogate Models ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
Design Variables ◽  
Hydraulic Turbines

Abstract Global sensitivity analysis (GSA) estimates influence of design variables in the entire design domain on performance measures. Hence, using GSA, important design variables could be found for an engineering application with high dimension which require computationally expensive analyses. Then, similar engineering applications could use selected variables to carry out design process with smaller dimension and affordable computational cost. In this study, GSA has been carried out for the performance measures in design of stay vane and casing of reaction hydraulic turbines. Global sensitivity index method is used for GSA because it can fully capture the effect of interaction between the design variables. For efficiency, genetic aggregation surrogate models are constructed using the responses of computational fluid dynamic (CFD) analysis. Global sensitivity indices for the performance measures of stay vane and casing have been evaluated using the surrogate models. It is found that less than three design variables among 12 are effective in the design process of stay vane and casing in reaction hydraulic turbines.

scholarly journals Global Sensitivity Analysis of the Vibration Reduction System with Seated Human Body

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Igor Maciejewski ◽  
Tomasz Krzyzynski
Keyword(s):  
Sensitivity Analysis ◽  
Vibration Isolation ◽  
Global Sensitivity Analysis ◽  
Operating Conditions ◽  
Design Parameters ◽  
Global Sensitivity ◽  
Seat Suspension ◽  
Sensitivity Indices ◽  
Vibration Transmissibility ◽  
Nonlinear Force

The paper deals with the global sensitivity analysis for the purpose of shaping the vibroisolation properties of suspension systems under strictly defined operating conditions. The variance-based method is used to evaluate an influence of nonlinear force characteristics on the system dynamics. The proposed sensitivity indices provide the basis for determining the effect of key design parameters on the vibration isolation performance. The vibration transmissibility behaviour of an exemplary seat suspension system is discussed in order to illustrate the developed methodology.

Sensitivity Analysis of Ballistics Performance with Respect to Statistical Design Parameters

2011 ◽  
Vol 130-134 ◽  
pp. 373-376
Author(s):  
Chang Qing Liu ◽  
Wen Cai Luo
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Design ◽  
Statistical Characteristics ◽  
Design Parameters ◽  
Statistical Parameters ◽  
Baseline Design ◽  
Flight Range ◽  
Sensitivity Derivatives ◽  
Performance Results ◽  
Sensitive Parameters

To investigate the effect of design parameters with statistical characteristics on ballistics performance, sensitivity analysis of the flight range objective with respect to relevant parameters was conducted to demonstrate it. Statistical parameters were modeled using an iterative method in order to determine descriptive statistics for further sampling. Simulation of flight range based on a dynamics model was then carried out. Finally, sensitivity derivatives from the baseline design scheme were calculated to locate the most sensitive parameters which can be controlled specially for better performance. Results show that by sensitivity analysis, thrust parameters affect the flight range objective obviously while others not, which provides suggestions about whether some parameters should be limited in a range or not.

Sign in / Sign up

Export Citation Format

Share Document