Dependability Modelling under Uncertainty: An Imprecise Probabilistic Approach

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Springer Science & Business Media, Aug 20, 2008 - Computers - 140 pages
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Mechatronic design processes have become shorter and more parallelized, induced by growing time-to-market pressure. Methods that enable quantitative analysis in early design stages are required, should dependability analyses aim to influence the design. Due to the limited amount of data in this phase, the level of uncertainty is high and explicit modeling of these uncertainties becomes necessary.

This work introduces new uncertainty-preserving dependability methods for early design stages. These include the propagation of uncertainty through dependability models, the activation of data from similar components for analyses and the integration of uncertain dependability predictions into an optimization framework. It is shown that Dempster-Shafer theory can be an alternative to probability theory in early design stage dependability predictions. Expert estimates can be represented, input uncertainty is propagated through the system and prediction uncertainty can be measured and interpreted. The resulting coherent methodology can be applied to represent the uncertainty in dependability models.

 

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Contents

Introduction
1
11 Thesis Aims
3
Dependability Prediction in Early Design Stages
6
A Mechatronic Process Model
9
22 Dependability in an Early Design Stage
12
23 Definitions on Dependability Reliability and Safety
14
232 Dependability and Its Attributes
16
233 Means to Attain Dependability
17
46 Results
69
4611 Neural Networks
70
4612 Gaussian Processes
71
462 Real Test Set
73
4622 Gaussian Processes
76
Design Space Specification of Dependability Optimization Problems Using Feature Models
77
51 The Redundancy Allocation Problem
79
52 Feature Models
81

3 Representation and Propagation of Uncertainty Using the DempsterShafer Theory of Evidence
21
32 The ESReDA Framework on Uncertainty Modeling
24
33 The DempsterShafer Theory of Evidence
28
332 Foundations
29
333 An Illustrative Example
32
34 Aggregation
34
35 Dependency
36
351 The Concept of Copulas
37
352 Copula Types
38
353 Applying Copulas to Model Joint Imprecise Distributions
40
36 Propagation through System Functions
41
37 Measures of Uncertainty
44
38 Sensitivity Analysis Using Uncertainty Measures
47
39 Comparing DempsterShafer Theory and Probabilistic Settings
48
391 The Decision between DempsterShafer Theory and Probability
50
Predicting Dependability Characteristics by Similarity Estimates A Regression Approach
52
The Transformation Factor
54
42 Estimation Procedure
56
4212 Estimation of Similarity Relations
57
4213 Providing Training Data
59
43 Formulating Similarity Prediction as a Regression Problem
60
432 Implementing the Regression Problem
61
441 Neural Networks
62
4412 Customized Error Function
63
4413 Network Design
64
45 Test Sets
66
452 Real Test Set
68
53 Basic Feature Set Types
83
54 Feature Models Defining Optimization Problems
84
55 Generating Reliability Block Diagrams and Fault Trees from Realizations
85
56 Conclusion
87
Evolutionary Multiobjective Optimization of Imprecise Probabilistic Models
89
611 Deterministic Multiobjective Functions
90
612 Imprecise Multiobjective Functions
91
6121 Multiobjective Optimization in System Dependability
93
622 An Evolutionary Algorithm for Multiobjective Optimization under Uncertainty
95
63 Dominance Criteria on Imprecise Objective Functions
98
632 Imprecise Probabilistic Dominance
99
65 Illustrative Examples
101
651 RAP
102
652 Complex Design Space
104
66 Conclusion
106
Case Study
107
72 System under Investigation
108
73 Fault Tree Model
109
75 Quantification of the Input Sources
112
76 Practical Implementation Characteristics and Results of the Uncertainty Study
114
77 Specifying Design Alternatives
116
78 Optimizing System Reliability
119
Summary Conclusions and Outlook
123
82 Outlook
125
References
126
Index
137
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