Uncertainty quantification for the analysis and design of a multibody system

다국어 초록 (Multilingual Abstract)

The performance and dynamic responses of a multibody system are determined by system parameters such as mass, stiffness, geometry of bodies and etc. Such system parameters are not deterministic since they always contain uncertainties caused by manufacturing tolerance, material irregularity and etc. Since the performance and dynamic responses of a multibody system depend on system parameters, parameter uncertainties directly result in the performance and dynamic response uncertainties. Then, the reliability of a multibody system deteriorates. In order to design a reliable multibody system, the performance and dynamic response uncertainties need to be quantified.
Most of existing uncertainty quantification methods of a multibody system can be used when the parameter random variables and random fields are given. However, such parameter uncertainties are practically unknown in most engineering problems. For that case, the uncertainty quantification of multibody system performance and dynamic responses using parameter samples needs to be conducted. However, only a few papers related to the sample based method were published. Also, for a flexible multibody system, the uncertainty quantification of the performance and dynamics responses considering parameter random variables and random fields should be conducted. However, existing methods are limited for a rigid multibody system and they cannot consider parameter random fields.
In the present study, the uncertainty quantification methods of multibody system performance and dynamic responses considering parameter random variables and random fields are proposed. The proposed methods consist of the uncertainty quantification method of a multibody system performance and that of multibody system dynamic responses. For the uncertainty quantification of a multibody system performance which can be represented by a random variable, sample based extreme value theory (EVT) was employed. Different from a multibody system performance, the dynamic responses of a multibody system are random fields. Also, the system parameters of the flexible bodies in a multibody system are random fields. In the present study, the spectral stochastic finite element method (SFEM) was employed to consider parameter and response random fields for the uncertainty quantification. To quantify the uncertainty of multibody system responses using the proposed method, parameter random fields need to be known. In the present study, a stochastic inverse method to quantify parameter random fields using modal data is also proposed. From numerical examples, it is proved that the proposed method can be successfully employed to the uncertainty quantification and reliability based design of a multibody system.

목차 (Table of Contents)

• Chapter 1. Introduction ………..………………………….. 1
• 1.1. Research motivation and related literature ……………………… 1
• 1.2. Research objectives ……………………………………………... 7
• 1.3. Organization of the thesis ……………………………………….. 9
• Chapter 2. Uncertainty Quantification of a Multibody System
• Performance using Extreme Value Theory ….. 11
• 2.1. Performance uncertainty quantification using EVT …………….. 11
• 2.1.1. Extreme value theory ……………………………………….. 11
• 2.1.2. Performance uncertainty quantification and reliability
• estimation method …………………………………………... 15
• 2.1.3. Probability of success ………………………………………. 24
• 2.1.4. Reliability estimation error …………………………………. 27
• 2.2. Examples of reliability based design of multibody systems …….. 35
• 2.2.1. Rotating double pendulum ………………………………….. 35
• 2.2.2. Vehicle ride comfort ………………………………………... 42
• Chapter 3. Uncertainty Quantification of Multibody System
• Responses using a Spectral Method ………..... 49
• 3.1. Random fields in a multibody system …………………………... 49
• 3.2. Uncertainty quantification of multibody system responses …….. 54
• 3.2.1. Derivation of stochastic differential algebraic equations …... 54
• 3.2.2. Numerical examples ………………………………………... 58
• 3.2.2.1 Transient analysis of a rigid pendulum …………………. 58
• 3.2.2.2 Transient analysis of a slider-crank mechanism with a
• flexible link ……………………………………………... 65
• 3.3. Uncertainty quantification of a structural system ……………….. 71
• 3.3.1. Derivation of stochastic equations of motion ………………. 71
• 3.3.2. Numerical results and discussions ………………………….. 78
• 3.3.2.1 Transient analysis of a rotating beam …………………... 78
• 3.3.2.2 Modal analysis of a rotating beam ……………………… 87
• 3.3.2.3 Resonance rotating speed of a beam excited by multiple
• nozzle forces ……………………………………………. 94
• 3.3.2.4 Resonance of a beam undergoing a prescribed rotational
• motion …………………………………………………... 97
• Chapter 4. Stochastic Inverse Method using Modal Data ... 102
• 4.1. Parameter random field quantification using modal data ………... 102
• 4.1.1. Karhunen-Loève expansion …………………………………. 103
• 4.1.2. Parameter random field quantification procedure …………... 105
• 4.1.3. Realization estimation method using modal data ………….... 109
• 4.1.4. Distribution estimation of random variables ………………... 117
• 4.2. Numerical examples ……………………………………………... 118
• 4.2.1. Case 1 (Gaussian random field example) …………………… 124
• 4.2.2. Case 2 (Non-Gaussian random field example 1) ……………. 130
• 4.2.3. Case 3 (Non-Gaussian random field example 2) ……………. 135
• 4.2.4. Parameter random variable vs. random field ………………... 140
• Chapter 5. Conclusions …………………………………….. 142
• References …………………………………………………... 145
• 국문요지 ……………………………………………………. 153