APPLICATION OF THE METHOD AND COMBINED ALGORITHM ON THE BASIS OF IMMUNE NETWORK AND NEGATIVE SELECTION FOR IDENTIFICATION OF TURBINE ENGINE SURGING Lytvynenko Volodymyr KHERSON NATIONAL TECHNICAL UNIVERSITY Ukraine

2 Contents: I. Problem statement 1.1 Turbine engine surging 1.2 How it is possible to minimized consequences Surging gas turbine engine (GTE)? 1.3 What are used now methods of the decision of the given problem? 1.3 What are used now methods of the decision of the given problem? II. Solving of the problem 2.1. Use of artificial immune systems 2.1. Use of artificial immune systems - Algorithm of negative selection - Algorithm of negative selection - Problems of use of algorithm of negative selection - Problems of use of algorithm of negative selection 2.2. The decision of problems of algorithm of negative selection 2.2. The decision of problems of algorithm of negative selection - Artificial immune network - Artificial immune network - Adaptation of detectors - Adaptation of detectors - The developed combined algorithm - The developed combined algorithm III. Experiments III. Experiments 3.1. The first experiment 3.1. The first experiment 3.2. The second experiment 3.2. The second experiment 3.3. The third experiment 3.3. The third experiment IV. Current researches V. The future researches VI. Conclusion.

3 I. Problem statement

4 1.1 Turbine engine surging In the given report the algorithm of definition turbine engine surging is offered What is Surging ? Surging (fr.: “pompage”) is stalled operating mode of aviation gas turbine engine (GTE), infringement of its gas-dynamic stability of functioning accompanied by claps, sharp decrease of thrust and powerful vibrations which are capable to destroy the engine 1.2 How it is possible to minimized consequences Surging gas turbine engine (GTE)? Prevention of the coming surging demands a possibility of forecasting of approaching to these modes and their instant registration. 1.3 What are used now methods of the decision of the given problem?  Method Fourier transform  Wavelet-analysis  Neural networks  Robust statistics

5 II. Solving of the problem

6 Our decision of a problem 1. To use for the decision of the given problem artificial immune systems 2. To examine the decision of the given problem as a task of detection of anomalies We examine anomaly as a status of system which is not compatible to normal behavior of this system. According to this, an anomaly detection system will perform a continuous monitoring of the system and an explicit classification of each state as normal or abnormal.

Use of artificial immune systems

8 What methods the given problem by means of artificial immune systems dares? For the decision of the given problem methods based on algorithm of negative selection are used. For the decision of the given problem methods based on algorithm of negative selection are used.

9 Algorithm of negative selection

10 Algorithm of negative selection Formally it is possible to present algorithm of negative selection in the form of expression: Formally it is possible to present algorithm of negative selection in the form of expression:

11 In what an essence of algorithm of negative selection? 1. Initialization: randomly generate strings and place them in a set P of immature T-cells, Assume all molecules (receptors and self-peptides) represented as binary strings of same length L; 2. Affinity evaluation: determine the affinity of all T-cells in V with all elements of the self set S; 3. Generation of the available repertoire: if the affinity of an immature T –cell (element of P) with at least one self- peptide is greater than or equal to a give cross reactive threshold, then the T-cell recognizes this self-peptide and has to be eliminated (negative selection); else the T-cell is introduced into the available repertoire A. The process of generating the available repertoire in the negative selection algorithm was termed censoring phase by the authors. The algorithm is also composed of a monitoring phase. In the monitoring phase, a set S* of protected strings is matched against the elements of the available repertoire A. The set S* might be the own set S, a completely new set, or composed of elements of S. If recognition occurs, then a non-self pattern (string) is detected. The negative selection algorithm suggests the random generation of strings, until an available repertoire A of appropriate size is generated. This approach could be adopted in both algorithms. Even the random generation of the repertoire P results in algorithms with some drawbacks. First, this approach results in an exponential cost to generate the available repertoire A in relation to the number of self strings in S. Second, randomly generating P does not account for any adaptability in the algorithm and neither any information contained in the set S.

12 Graphic representation of objects of algorithm U – universum and set S of vectors which are classified as “Self”, and S  U U – universum and set S of vectors which are classified as “Self”, and S  U

13 Problems of use of algorithm of negative selection

14 Limitation of algorithm of negative selection Casual generation of detectors does not give possibility to define their is minimum necessary quantity, sufficient for a covering of all set of "Non-Self“ Casual generation of detectors does not give possibility to define their is minimum necessary quantity, sufficient for a covering of all set of "Non-Self“ High probability of education of "cavities" that worsens quality of recognition since "cavities" are areas in space of "Non-Self" which are not recognized by any of detectors High probability of education of "cavities" that worsens quality of recognition since "cavities" are areas in space of "Non-Self" which are not recognized by any of detectors Generation too a considerable quantity of detectors essentially slows down a recognition phase since any entering image is necessary for comparing to each of the created detectors Generation too a considerable quantity of detectors essentially slows down a recognition phase since any entering image is necessary for comparing to each of the created detectors

The decision of problems of algorithm of negative selection

16 What it is necessary to make to eliminate limitations of this algorithm? We have set for ourselves a problem to improve a method of generation of detectors which is applied at training of algorithm of negative selection which is capable is adaptive to select their options, quantity and an arrangement in phase space of an investigated signal We have set for ourselves a problem to improve a method of generation of detectors which is applied at training of algorithm of negative selection which is capable is adaptive to select their options, quantity and an arrangement in phase space of an investigated signal

17 How we suggest to solve the given problem? We offer at generation of detectors for their adaptive and options, and also definitions of their optimum quantity and an arrangement in phase space of an investigated signal to use an artificial immune network. We offer at generation of detectors for their adaptive and options, and also definitions of their optimum quantity and an arrangement in phase space of an investigated signal to use an artificial immune network.

18 Artificial immune network

19 What is the artificial immune network?

20 Artificial immune network Initial data (antigenes) Network generation Network activation Network compression Memory formation The trained network

21 Adaptation of detectors

22 Adaptation of detectors of an immune network for a problem of negative selection 1. Representation of an individual (antibody): 2. Population of antigenes: Set of vectors of the training image representing a phase portrait of a normal signal in k-dimensional space Ab Ag

23 Adaptation of detectors of an immune network for a problem of negative selection 3. Calculation of affinity "antibody-antigene": - Euclidean distance - The parameter defining the importance cross-reactivity a threshold r  min

24 Adaptation of detectors of an immune network for a problem of negative selection 4. Calculation of affinity "antibody-antibody": Depending on value f Ab-Ab following situations are possible:

25 The developed combined algorithm

26 THE GENERALIZED SCHEME OF THE COMBINED NEGATIVE SELECTION ALGORITHM AND AN IMMUNE NETWORK

27 III. Experiments

28 Experimental researches 1 Signal without anomalies (a training signal)Phase portrait of a training signal (yt, yt+1) Results of learning AIS Training sample of 200 points. The size of a window = 2 k r = 0.01k r = 0.1 Less steady decision Steadier decision Class «Self»

29 Experimental researches 1 Signal with anomaly (a test signal)Phase portrait of a test signal Results of testing Anomaly deviations on a phase portrait are observed It is recognized by 5th detectors It is recognized by 3th detectors The histogram of the found out anomaly (activation of detectors)

30 Experimental researches 2 (Anomaly of parametre) Investigated signal: Normal signal : = 4.0 Training data: Test data: Anomaly of parametre ( = 3.6 ), data: Structure trained AIS Activation of detectors in a place of occurrence of anomaly

31 IDENTIFICATION OF TURBINE ENGINE SURGING For the third experiment the data have been used received on the test bed for the aviation gas turbine engine. The data represent four time series (Vk_3, Vk_P, Vv_3, Vv_P); the signals received from gauges of vibration of support on which the engine has been fixed. Experimental researches 3 IDENTIFICATION OF TURBINE ENGINE SURGING For the third experiment the data have been used received on the test bed for the aviation gas turbine engine. The data represent four time series (Vk_3, Vk_P, Vv_3, Vv_P); the signals received from gauges of vibration of support on which the engine has been fixed. The graphs of time series, representing the vibration

32 Structure of the trained immune network for various values

33 THE HISTOGRAMS OF DETECTORS ACTIVATION

IV. Current researches : A Hardware-Based realizations of the developed algorithm

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37 V. The future researches and development In the further researches we plan: 1. To carry out comparative researches at the decision of the given problem with such methods as Method Fourier transform, the Analysis of a small wave, the Neural networks, the Steady statistics. 2. To investigate identification possibility turbine engine surging on other parameters. 3. To investigate possibility of the forecast on approximating wavelets-coefficients. 4. To unite the given algorithm with the Bayes network

38 VI. Conclusion 1. The algorithm using mechanisms of artificial immune networks for the decision of a problem of detection of anomalies by a method of negative selection is developed 2. Distinctive feature of algorithm is updating of process of training thanks to which possibility of adaptive selection of options is realized, quantities and arrangements of detectors 3.The experimental study has shown a high efficiency of the offered algorithm which is linked to its computing stability thanks to adaptive selection of the cross-reactive threshold. Also optimality is achieved owing to adaptive adjustment of the size of an immune network, i.e. quantity of necessary detectors; high accuracy of detecting is shown, owing to reduction of quantity and the sizes of "cavities" created. 4.To compare the results of the algorithm an exact benchmark diagnostics was used, supported by experts. Results of diagnostics testify to affinity of the estimates produced by the experts, and the estimates generated by means of the method and algorithm developed.

39 Thanks for attention!