The Baum Welch algorithm

For more info about our services contact : help@bestpfe.com

Table of contents

1 State of the Art
1.1 Maintenance
1.2 Degradation
1.3 Diagnostic
1.4 Prognostic
1.5 PHM approaches
1.5.1 Model-based prognostic approaches
1.5.2 Data driven prognostic approaches
1.5.3 Hybrid approaches
1.5.4 Conclusion
1.6 Model types
1.6.1 Deterministic models
1.6.2 Stochastic models
1.6.3 Hybrid models
1.6.4 Conclusion
1.7 Stochastic models
1.7.1 Fuzzy Logic models
1.7.2 Neural Networking models
1.7.3 Markov Models
1.7.4 Conclusion
2 Background of the Model from MC to IOHMM
2.1 Markov Chain notations
2.2 Hidden Markov Model
2.2.1 HMM Structure
2.2.2 The Forward-backward (FB) algorithm
2.2.3 The Baum Welch algorithm
2.2.4 The Viterbi algorithm
2.3 Input-Output Hidden Markov Model
2.4 Conclusion
3 The First Contribution: Learning Model Parameters
3.1 The learning algorithms adaptation
3.1.1 Multiple input conditions
3.1.2 Multiple inputs case
3.1.3 Multiple sequences case
3.1.4 Multiple outputs cases
3.1.5 Normalization
3.1.6 The Baum Welch adaptation
3.2 Numerical Illustration (IOHMM learning)
3.2.1 Modeling under multiple operating conditions
3.2.2 Modeling under missing data
3.2.3 Modeling by using the bootstrap method
3.3 Conclusion
4 The Second Contribution: Diagnostic and Prognostic
4.1 Diagnostic
4.2 Prognostic: RUL prediction
4.3 Offline and Online Operation
4.4 Application
4.4.1 The first application: Diagnostic and prognostic under multiple operating conditions
4.4.2 The second application: Managing the RUL
4.5 Conclusion
5 The Third Contribution: Estimating RUL of Aircraft
5.1 C-MAPSS
5.2 Model Structure
5.2.1 The operating conditions
5.2.2 Degradation indicator
5.2.3 Emitted symbols
5.2.4 Defined IOHMM
5.3 Model evaluation
5.4 Cross Validation
5.5 Results
5.5.1 Parameter Learning
5.5.2 Diagnostic: current health state estimation
5.5.3 Prognostic: the meantime RUL estimation
5.5.4 Benchmarking Between Different Models
5.5.5 Cross Validations
5.6 Conclusion
6 The Fourth Contribution: Estimating RUL of Structured Systems
6.1 Model construction for prognosing the system RUL
6.1.1 Series structure of two components with HMM models
6.1.2 Series structure of two components with IOHMM models
6.1.3 Parallel structure of two components with HMM models
6.1.4 Parallel structure of two components with IOHMM models
6.1.5 A drinking water network illustration
6.1.6 Diagnostic
6.2 Application
6.2.1 Data simulation
6.2.2 Model Learning
6.2.3 Diagnostic
6.2.4 Prognostic
6.3 Conclusion
Conclusion
Perspectives
Reference