LOCAL FUSION OF AN ENSEMBLE OF SEMI-SUPERVISED SELF ORGANIZING MAPS FOR POST-PROCESSING ACCIDENTAL SCENARIOS

Transcription

1 LOCAL FUSION OF AN ENSEMBLE OF SEMI-SUPERVISED SELF ORGANIZING MAPS FOR POST-PROCESSING ACCIDENTAL SCENARIOS Francesco Di Maio 1, Roberta Rossetti 1, Enrico Zio 1,2 1 Energy Department, Politecnico di Milano, Via La Masa 34, Milano, Italy francesco.dimaio@polimi.it 2 Chair System Science and the Energy Challenge, Fondation Electricité de France (EDF), CentraleSupélec, Université Paris Saclay, Paris, France

2 Dynamic Reliability for NPPs Safety Assessment Dynamic reliability Computational Risk Assessment Integrated Deterministic and Probabilistic Safety Assessment are collective names for the variety of different tools which use tightly coupled probabilistic and deterministic approaches to address in a consistent manner: - Uncertainties affecting the NPPs behavior - Effects of timing (dynamics) in the failure behavior of NPPs In PSA2017: 3 technical sessions on Dynamic PSA I-II-III 22 papers on dynamic reliability methods 1 plenary lecture 1 workshop

3 Integrated Deterministic and Probabilistic Safety Analysis (IDPSA) Failure scenarios sequences of failure events that lead the system into failed conditions Safe Scenarios sequences of failure events that keep the system into safe operational conditions

4 Integrated Deterministic and Probabilistic Safety Analysis (IDPSA) Failure scenarios sequences of failure events that lead the system into failed conditions Prime Implicants (PI) minimal sequences of component failures that lead the system into failure Safe Scenarios sequences of failure events that keep the system into safe operational conditions

5 Integrated Deterministic and Probabilistic Safety Analysis (IDPSA) Failure scenarios sequences of failure events that lead the system into failed conditions Prime Implicants (PI) minimal sequences of component failures that lead the system into failure Near Misses dangerous sequences of failure events that incidentally keep the system into safe but endangered and insecure operational conditions Safe Scenarios sequences of failure events that keep the system into safe operational conditions

6 IDPSA Scenarios generation Physical scenarios MONTE CARLO (MC) + PHYSICAL CODE SIMULATIONS MVL sequences Scenarios Post-processing PIs Failure Near Misses Safe Fuzzy C-Means (FCM) Mean Shift Methodology /MSM) Decision Trees Evolutionary Optimization Methods Visual Interactive Methods K-Means Unsupervised clustering

7 IDPSA: this work Scenarios generation Physical scenarios The U-Tube Steam generator MONTE CARLO (MC) + PHYSICAL CODE SIMULATIONS MVL sequences Scenarios Post-processing PIs Failure Near Misses Safe We propose an IDPSA method: able to comprehensively deal with all the classes at the same time simpler than other methods, thanks to an intuitive visual interface, which could be useful also for dynamic monitoring of the system. ENSEMBLE OF SEMI-SUPERVISED SELF-ORGANIZING MAPS (SSSOM)

8 The Case Study: U-Tube Steam Generator (UTSG) Controlled Variable Input variables Level of High Level Failure mode Safe Upper threshold Lower threshold Low Level Failure mode Control Variable Time 4000 s Aubry J. F., Babykina G., Barros A., Brinzei N., Deleuze G., De Saporta B., Dufour F., Langeron Y., Zhang H., Project APPRODYN: APPROches de la fiabilité DYNamique pour modéliser des systèmes critiques, Technical report, collaboration CRAN, EDF R&D, INRIACQFD, UTT-ICD, 2012

9 The Case Study: U-Tube Steam Generator (UTSG) Controlled Variable Input variables Level of High Level Failure mode Safe Upper threshold Lower threshold Low Level Failure mode Control Variable Time 4000 s Aubry J. F., Babykina G., Barros A., Brinzei N., Deleuze G., De Saporta B., Dufour F., Langeron Y., Zhang H., Project APPRODYN: APPROches de la fiabilité DYNamique pour modéliser des systèmes critiques, Technical report, collaboration CRAN, EDF R&D, INRIACQFD, UTT-ICD, 2012

10 Scenarios generation SIMULINK model of the UTSG Communication X PID controller X Safety valve X X Steam valve Monte-Carlo engine simulating the failure of 4 components Di Maio F., Vagnoli M., Zio E., Risk-based clustering for near misses identification in Integrated Deterministic and Probabilistic Safety Analysis, Science of technology of nuclear installation Article ID

11 Scenarios generation: Monte Carlo engine Safety valve

12 Scenarios generation: Monte Carlo engine Safety valve Failure time Failure magnitude

13 Scenarios generation: Monte Carlo engine Safety valve Failure time Failure magnitude 2

14 Scenarios generation: Monte Carlo engine Safety valve Failure time Failure magnitude 2 3

15 Scenarios generation: Monte Carlo engine Safety valve Failure time Failure magnitude 2 3 1

16 Scenarios generation: Monte Carlo engine scenarios = (2,3,1,3,, 4), generic n-th vector representative of the n-th scenario

17 Post-processing Scenarios generation Physical scenarios MVL sequences Scenarios Post-processing ENSEMBLE OF SEMI-SUPERVISED SELF-ORGANIZING MAPS (SSSOM) PIs Failure Near Misses Safe

18 The ENSEMBLE approach MVL SSSOM 1 SSSOM 2... SSSOM H Outcome 1 Outcome 2... Outcome H Combination Aggregated outcome = assigned class (PI, NM, S, Failed)

19 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector Training scheme: Randomly initialize the M weight vectors, CLASSES are the additional layer

20 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector CLASSES are the additional layer Training scheme: Randomly initialize the M weight vectors, Sample a random MVL sequence x 11 x n1 x N1 x 12 x n2 x N2 x 1d x nd x Nd MVL sequences Identify the i-th Best Matching Unit where min X w = min X w n m n m k = 1 d

21 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector CLASSES are the additional layer Training scheme: Randomly initialize the M weight vectors, Sample a random MVL sequence x 11 x n1 x N1 x 12 x n2 x N2 x 1d x nd x Nd MVL sequences Identify the i-th Best Matching Unit where min X w = min X w n m n m k = 1 d Update of neurons in a neighborhood of the BMU, to increase their similarity to

22 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector CLASSES are the additional layer Training scheme: Randomly initialize the M weight vectors, Sample a random MVL sequence x 11 x n1 x N1 x 12 x n2 x N2 x 1d x nd x Nd MVL sequences Identify the i-th Best Matching Unit where min X w = min X w n m n m k = 1 d Update of neurons in a neighborhood of the BMU, to increase their similarity to

23 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector CLASSES are the additional layer Training scheme: Randomly initialize the M weight vectors, Sample a random MVL sequence x 11 x n1 x N1 x 12 x n2 x N2 x 1d x nd x Nd MVL sequences Identify the i-th Best Matching Unit where min X w = min X w n m n m k = 1 d Update of neurons in a neighborhood of the BMU, to increase their similarity to

24 The Semi-Supervised SOM (SSSOM) Lattice structure formed by M neurons associated to a (d+1)-dimensional weight vector CLASSES are the additional layer Training scheme: Randomly initialize the M weight vectors, Sample a random MVL sequence x 11 x n1 x N1 x 12 x n2 x N2 x 1d x nd x Nd MVL sequences Identify the i-th Best Matching Unit where min X w = min X w n m n m k = 1 d Update of neurons in a neighborhood of the BMU, to increase their similarity to

25 Ensemble approach: multiple classifiers The stand-alone SSSOM The MVL sequence is assigned to the class to which the BMU belongs to

26 Ensemble approach: multiple classifiers Geometric baricenters Baricenter based SSSOM The MVL sequence is assigned to the class with the smallest distance from the baricenter, i.e., to the class with the baricenter most similar to the MVL sequence.

27 Ensemble approach: multiple classifiers Minimum neurons: neurons with minimum weight vector Minimum neuron based SSSOM The MVL sequence is assigned to the class with the smallest distance from the minimum neuron, i.e., to the class with the minimum neuron most similar to the MVL sequence.

28 Ensemble approach: multiple classifiers Maximum neurons: neurons with maximum weight vector Maximum neuron based SSSOM The MVL sequence is assigned to the class with the smallest distance from the maximum neuron, i.e., to the class with the maximum neuron most similar to the MVL sequence.

29 Ensemble approach: multiple classifiers MQE based SSSOM 7 6 NMs PDF FAILED PDF MQE MQE 14 PIs SAFE PDF PDF MQE MQE MQE g empirical probability density functions: the larger the value of the g-th PDF, the more the probability that a MVL scenario with a specific MQE belongs to class g.

30 The ENSEMBLE approach MVL Stand alone SSSOM Baricenter based SSSOM Minimum neuron based SSSOM Maximum neuron based SSSOM MQE based SSSOM Outcome 1 Outcome 2 Outcome 3 Outcome 4 Outcome 5 Locally weighted based on the single SSSOM performances (precision, sensitivity and specificity) Aggregated outcome = assigned class (PI, NM, S, Failed)

31 SSSOMs performances Precision: ability to not include MVL sequences of other classes in the g-th class Sensitivity: ability to correctly recognize MVL sequences belonging to the g-th class Specificity: ability of each g-th class to reject the MVL sequences of all the others Stand-alone SSSOM Maximum neuron-based SSSOM

32 SSSOMs performances Precision: ability to not include MVL sequences of other classes in the g-th class Sensitivity: ability to correctly recognize MVL sequences belonging to the g-th class Specificity: ability of each g-th class to reject the MVL sequences of all the others Stand-alone SSSOM

33 SSSOMs performances Precision: ability to not include MVL sequences of other classes in the g-th class Sensitivity: ability to correctly recognize MVL sequences belonging to the g-th class Specificity: ability of each g-th class to reject the MVL sequences of all the others Stand-alone SSSOM MQE based SSSOM Minimum neuron-based SSSOM

34 SSSOMs performances Precision: ability to not include MVL sequences of other classes in the g-th class Sensitivity: ability to correctly recognize MVL sequences belonging to the g-th class Specificity: ability of each g-th class to reject the MVL sequences of all the others Stand-alone SSSOM

35 The ENSEMBLE approach MVL Stand alone SSSOM Baricenter based SSSOM Minimum neuron based SSSOM Maximum neuron based SSSOM MQE based SSSOM Outcome 1 Outcome 2 Outcome 3 Outcome 4 Outcome 5 Locally weighted based on the single SSSOM performances (precision, sensitivity and specificity) The MVL is assigned to the class with the lowest local (class) error

36 RESULTS (training) Correctly assigned MVL sequences Total NMs PIs Stand-alone SSSOM Ensemble of locally weighted SSSOMs Results are satisfactory for the operational risk quantification Total number of correctly assigned scenarios increases with respect to the stand-alone SSSOM The number of correctly assigned NMs and PIs scenarios decreases, but: PIs normally are made of many component failures with low probability of occurrence not accounted risk is very low; NMs are either classified as safe (with no extra risk quantification being both safe and NMs leading to safe states) or failed scenarios (with a conservative overestimation of the system operational risk).

37 RESULTS (test) 2000 unknown sequences (with random components failure times) Correctly assigned sequences Total NMs PIs Truth 8 11 Ensemble of locally weighted SSSOMs Results are satisfactory for the operational risk quantification All NMs and PIs are correctly classified The wrongly assigned sequences are SAFE sequences that are (conservatively) assigned to the FAILURE class (with a conservative overestimation of the system operational risk).

38 Conclusions PIs Failure Near Misses Safe An IDPSA scenarios post-processing method based on an ensemble of SSSOMs has been proposed that is able to comprehensively deal with all the classes at the same time (safe, failed, NMs, PIs), applies to the classification of unknown sequences and whose interpretation of the provided classification results is simpler than other methods, thanks to an intuitive visual interface, which could be useful also for dynamic monitoring of the system. Scenario generation Post-processing