APPLICATION OF THE METHOD AND APPLICATION OF THE METHOD AND COMBINED ALGORITHM ON THE BASIS OF COMBINED ALGORITHM ON THE BASIS OF

IMMUNE NETWORK AND NEGATIVE IMMUNE NETWORK AND NEGATIVE SELECTION FOR IDENTIFICATION OF SELECTION FOR IDENTIFICATION OF

TURBINE ENGINE SURGINGTURBINE ENGINE SURGING

Lytvynenko VolodymyrLytvynenko Volodymyr

KKHERSON NATIONAL TECHNICAL UNIVERSITYHERSON NATIONAL TECHNICAL UNIVERSITY

UkraineUkraine

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Contents:Contents:I. I. Problem statementProblem 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. II. Solving of the problemSolving of the problem 2.1. Use of artificial immune systems2.1. 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 selection2.2. 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. III. ExperimentsExperiments

3.1. The first experiment3.1. The first experiment 3.2. The second experiment3.2. The second experiment 3.3. 3.3. The third experiment The third experiment IV. IV. Current researchesCurrent researches V. V. The future researchesThe future researches

VI. VI. Conclusion.Conclusion.

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I. I. Problem statementProblem statement

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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 1.3 What are used now methods of the decision of the given problem?problem?

Method Fourier transform Wavelet-analysisNeural networksRobust statistics

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II. II. Solving of the problemSolving of the problem

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Our decision of a problemOur decision of a problem 1.1. To use for the decision of the given problem To use for the decision of the given problem

artificial immune systemsartificial immune systems

2.2. To examine the decision of the given problem as a To examine the decision of the given problem as a task of detection of anomaliestask 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.

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2.1. Use of artificial 2.1. Use of artificial

immune systemsimmune systems

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What methods the given problem by What methods the given problem by means of artificial immune systems means of artificial immune systems

dares?dares?

For the decision of the given problem methods For the decision of the given problem methods based on algorithm of negative selection are used.based on algorithm of negative selection are used.

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Algorithm of negative Algorithm of negative selectionselection

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Algorithm of negative selection Algorithm of negative selection Formally it is possible to present algorithm of Formally it is possible to present algorithm of

negative selection in the form of expression:negative selection in the form of expression:

pr,s,n,r,M,P,ClgNegA U – The general number of detectors of candidates

S – Set of detectors defined as “Self”

M – Set of detectors defined as "Non-Self" r – Cross-reacreactive a threshold n – The general number of appointed detectors

s The size of set of detectors

pr rule of matches of strings in r adjacent positions

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In what an essence of algorithm of negative selection?

1.1. InitializationInitialization: : randomly generate strings randomly generate strings and place them in a set and place them in a set PP of immature T- of immature T-cells, Assume all molecules (receptors cells, Assume all molecules (receptors and self-peptides) represented as binary and self-peptides) represented as binary strings of same length strings of same length LL;;

2.2. Affinity evaluation:Affinity evaluation: determine the determine the affinity of all T-cells in V with all affinity of all T-cells in V with all elements of the self set elements of the self set SS;;

3.3. Generation of the available repertoireGeneration of the available repertoire: : if the affinity of an immature T –cell if the affinity of an immature T –cell (element of (element of PP) with at least one self-) with at least one self-peptide is greater than or equal to a give peptide is greater than or equal to a give cross reactive threshold, then the T-cell cross reactive threshold, then the T-cell recognizes this self-peptide and has to recognizes this self-peptide and has to be eliminated (negative selection); else be eliminated (negative selection); else the T-cell is introduced into the the T-cell is introduced into the available repertoire available repertoire AA..

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.

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Graphic representation of Graphic representation of objects of algorithmobjects of algorithm

U – U – universum and set universum and set SS of of vectors which are classified vectors which are classified as “Selfas “Self””, and , and SS U U

The algorithm of negative selection assumes creation of set of detectors D such, that SdUdDd iii .

Each detector di has an own vicinity of recognition or "operative range". The sizes of an operative range of the detector are defined to parametres (Threshold). The zone form is defined by the chosen rule of comparison of strings (Matching Rule).

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Problems of use of algorithm Problems of use of algorithm of negative selectionof negative selection

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Limitation of algorithm of Limitation of algorithm of negative selectionnegative selection

Casual generation of detectors does not give possibility to Casual generation of detectors does not give possibility to define their is minimum necessary quantity, sufficient for a define their is minimum necessary quantity, sufficient for a covering of all set of "Non-Self“covering of all set of "Non-Self“

High probability of education of "cavities" that worsens High probability of education of "cavities" that worsens quality of recognition since "cavities" are areas in space of quality of recognition since "cavities" are areas in space of "Non-Self" which are not recognized by any of detectors"Non-Self" which are not recognized by any of detectors

Generation too a considerable quantity of detectors Generation too a considerable quantity of detectors essentially slows down a recognition phase since any essentially slows down a recognition phase since any entering image is necessary for comparing to each of entering image is necessary for comparing to each of the created detectorsthe created detectors

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2.2. The decision of problems of 2.2. The decision of problems of algorithm of negative selectionalgorithm of negative selection

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What it is necessary to make to What it is necessary to make to eliminate limitations of this eliminate limitations of this

algorithm?algorithm? We have set for ourselves a problem to We have set for ourselves a problem to

improve a method of generation of detectors improve a method of generation of detectors which is applied at training of algorithm of which is applied at training of algorithm of negative selection which is capable is adaptive negative selection which is capable is adaptive to select their options, quantity and an to select their options, quantity and an arrangement in phase space of an investigated arrangement in phase space of an investigated signalsignal

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How we suggest to solve the How we suggest to solve the given problem?given problem?

We offer at generation of detectors for their We offer at generation of detectors for their adaptive and options, and also definitions of adaptive and options, and also definitions of their optimum quantity and an arrangement in their optimum quantity and an arrangement in phase space of an investigated signal to use an phase space of an investigated signal to use an artificial immune network.artificial immune network.

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Artificial immune network Artificial immune network

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What is the artificial immune What is the artificial immune network?network?

2020

Artificial immune network

Initialization of population of cells of memory

Calculation of affinity of cells of memory and choice

of one – the best cells

Cloning of the chosen cells

Mutation of clones

Addition of the changed clones to population of

antibodies

Calculation of affinity of population of antibodies

Clonal deleting

Average affinity of population above threshold value?

No Yes

Repeated cloning of a part of antibodies from

population of antibodies

To choose from population of antibodies the best antibody

The chosen antibody is better, than an initial cells

of memory?

Yes No

To add an antibody in population of cells of

memory Compression of population

of cells of memory

BEGING

Input: k, mAB, , n, d, d, s

Initialization of population of antibodies

stop?

No

End

Output: memory cells

Yes

Arrangement of data (A two-dimensional case)

Antibody

Initial data (antigenes)

Network generation

Network activation

Network compression

Memory formation

The trained network

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Adaptation of detectorsAdaptation of detectors

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Adaptation of detectors of an immune network for a problem of negative selection

1. Representation of an individual (antibody):

r yt yt-1 … yt-k+1

Possibility of adaptive adjustment of value threshold Cross-Reactivity

2. Population of antigenes:

...

...,,,

...,,,

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11

kttt

kttt

yyy

yyy

Set of vectors of the training image representing a phase portrait of a normal signal in k-dimensional space

Ab

Ag

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Adaptation of detectors of an immune network for a problem of negative selection

3. Calculation of affinity "antibody-antigene": )( AgAbEr

AgAb Dr

kf

)( AgAbED

rk

- Euclidean distance

- The parameter defining the importance cross-reactivity a threshold r

«Self»

r «Self»

r

detectors

kr kr’

kr > kr’

«Self»

In such situation to the detector the penalty with the subsequent clonal deleting of all fined detectors is appointed

min

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Adaptation of detectors of an immune network for a problem of negative selection

4. Calculation of affinity "antibody-antibody": ),min(2

)(

21

2121 )(

AbAb

AbAbAbAbEAbAb rr

rrDf

Ab1

Ab2

fAb-Ab <= 0 – Compression is not

required

Ab1 Ab2

0 < fAb-Ab < 1 – Compression depends on degree of

overlapping of detectors

Ab1

Ab2

fAb-Ab >= 1 – Compression by removal of the absorbed

detector is made

r

If fAb-Ab > a compression threshold there is a removal of that detector whose fAb-Ag is less

Depending on value fAb-Ab following situations are possible:

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The developed combined The developed combined algorithmalgorithm

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

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III. III. ExperimentsExperiments

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Experimental researches 1

50 60 70 80 90 100 110 120 130 140 150

0,0

0,2

0,4

0,6

0,8

1,0

Y

t

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

Y(t

+1

)

Y(t)

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

kr = 0.01 kr = 0.1

Less steady decision

Steadier decision

Class«Self»

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Experimental researches 1

Signal with anomaly (a test signal) Phase portrait of a test signal

Results of testing

50 60 70 80 90 100 110 120 130 140 150

0,0

0,2

0,4

0,6

0,8

1,0

Y

t

0,0 0,2 0,4 0,6 0,8 1,0

0,0

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0,4

0,6

0,8

1,0

Y (

t+1)

Y(t)

Anomaly deviations on

a phase portrait are observed

50 60 70 80 90 100 110 120 130 140 1500

1

2

3

4

5

Act

ive

de

tect

ors

t

It is recognized by 5th detectors

It is recognized by 3th detectors

The histogram of the found out anomaly (activation of detectors)

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Experimental researches 2(Anomaly of parametre)

Investigated signal: ttt yyy 11 Normal signal : = 4.0

0 10 20 30 40 50 60 70 80 90 100

0,0

0,2

0,4

0,6

0,8

1,0

Y(t

)

t

100 110 120 130 140 150 160 170 180 190 200

0,0

0,2

0,4

0,6

0,8

1,0

Y(t

)

t

Training data: 1-100 Test data: 100-200

Anomaly of parametre ( = 3.6), data: 112-121

Structure trained AIS

100 110 120 130 140 150 160 170 180 190 2000,0

0,5

1,0

1,5

2,0A

ctive

de

tecto

rs

t

Activation of detectors in a place of occurrence of anomaly

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Experimental researches 3IDENTIFICATION OF TURBINE ENGINE SURGINGIDENTIFICATION OF TURBINE ENGINE SURGING

For the third experiment the data have been used received on the test bed for the aviationFor the third experiment the data have been used received on the test bed for the aviation gas gas turbine engineturbine engine. The data represent four time series (Vk_3, Vk_P, Vv_3, Vv_P); the signals . 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. received from gauges of vibration of support on which the engine has been fixed.

0

2

4

6

8

10

12

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157 163 169 175 181 187 193 199 205 211

Vв_Р Vв_З Vк_Р Vк_З

The graphs of time series, representing the vibration

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Structure of the trained immune network for various Structure of the trained immune network for various

valuesvalues rk

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THE HISTOGRAMS OF DETECTORS THE HISTOGRAMS OF DETECTORS

ACTIVATIONACTIVATION

IV. IV. Current researchesCurrent researches ::

A Hardware-Based realizations of the A Hardware-Based realizations of the developed algorithmdeveloped algorithm

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V. V. The future researchesThe future researches and developmentand development

In the further researches we plan:In the further researches we plan:1.1. To carry out comparative researches at the To carry out comparative researches at the

decision of the given problem with such decision of the given problem with such methods as Method Fourier transform, the methods as Method Fourier transform, the Analysis of a small wave,Analysis of a small wave, the Neural networks, the Neural networks, the Steady statistics. the Steady statistics.

2.2. To investigate identification possibility turbine To investigate identification possibility turbine engine surging on other parameters.engine surging on other parameters.

3.3. To investigate possibility of the forecast on To investigate possibility of the forecast on approximating wavelets-coefficients.approximating wavelets-coefficients.

4.4. To unite the given algorithm with the Bayes To unite the given algorithm with the Bayes networknetwork

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VI. VI. ConclusionConclusion1. 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.

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Thanks for attention!Thanks for attention!