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XII International Conference Condition Monitoring and Machinery Failure Prevention Technologies - СМ/MFPT 2015

RISK ASSESSMENT SELECTION OF GUIDELINE VALUES OF DIAGNOSTIC SIGNS

V.N. Kostyukov, A.P. Naumenko

“SPC “Dynamics” 644043, Omsk, Russia Tel.: +7 3812 254244 Fax: +7 3812 254372

E-mail: post@dynamics.ru

Abstract

The report discusses the method of calculation of guideline values of the diagnostic signs on the basis of statistical decision-making theory. It gives an example of calculation of the probability of the defect skipping and false alarms, the risk of the failure skipping while selecting the size of the regulatory characteristic of different methods of decision making.

It is shown that it is reasonable to use false decision minimum number method to compare the costs of false alarms and defect skipping. If the defect skipping cost is considerably higher than the cost of the false alarm it is advisable to use method of Neumann-Pearson. Selection of the boundary values of diagnostic signs according to their distribution functions for different states of the diagnostic object should be made when the probability rates are >0,93 and <0,95.

Key words: risks, monitoring, diagnostics, technical condition. Timeliness. In general case, on the basis of the diagnostic features(DF), with a certain proba-

bility characterizing the condition of a diagnosed object, it is necessary to build a decision rule help-ing to apply a set of features to one of possible states(diagnoses) [1, 2, 3, 4]. In a particular case, it is necessary to make a choice of one of two diagnoses (differential diagnostics or dichotomy), for in-stance, " operative condition " and "failure condition" [5, 6, 7].

Work purpose is in revealing of diagnostic feature normative values assessment methods, on the basis of theory of statistical decision-making and risk-taking which can be used in vibration-diagnostic monitoring [8, 9, 10, 11].

Prerequisites for the problem solving. Methods of statistical decisions, such as methods of a minimum number of wrong decisions, minimax, Neumann-Pearson, maximum likelihood - all this methods allow to choose a decision rule according to the optimality condition, for example, from the minimum risk condition, minimization of one of the errors in diagnosing with set level of another one.

Error cost estimation is often unknown, and their reliable determination is usually connected with great difficulties. That is why the center of all problems is a reasonable choice of an acceptable level of errors on the basis of the previous experience or intuition. The analysis of failures and re-pairs of piston compressors of Petrochemical Complex shows[1, 8], that valve failures counts 36% from the whole number of failures, and the cost of repair is up to 50% from the total cost. So, further investigation has to be conducted for valves.

To make a cost estimation of defect skipping and false alarm we take as initial data the follow-ing facts:

1. Technological complex - diesel fuel hydrofining unit with 250 t/h capacity, the unit is oper-ated 8000 hours a year.

2. Euro-3 (Euro-4) Diesel fuel release price is 9300 rub. per tonne. 3. The object is two constantly operated four-cylinder compressors, which have two decreas-

ing spaces in each cylinder. Each decreasing space has one suction valve and one delivery valve, and

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in case of failure of one of the valves, the gas is not delivered into this space. The gas delivery rate of one delivery space is 6,25 % from the total rate of both compressors.

4. The cost of one valve is 16 thousand rubles, its mean time between failures is 8000 hours. Cost estimation of decision making: 1. Valve over-reject cost: 16000 rub./8000 h.=2 rub./h., i.e. when the valve is over reject

(the valve was decommissioned for the repair one hour before its breakage) the cost of its underpro-duction is 2 rub./h.

2. Under-reject cost (the valve is not working for an hour of compressor's operation, conse-quently, the unit capacity dropped by 6,25 % ) is 145 312 rub.

3. Cost ratio is 72 656, subject to all unmentioned factors reducing this ratio, it allows to take the relative cost of defect skipping C12=1, and cost of false alarm C21=0,001.

Problem solving. The chance of making wrong decision is made up of false alarm and defect skipping chances. If we attribute "prices" to this errors and take the costs for correct decisions as C11 and C22, which are taken as negative numbers in order to compare to the costs of losses(errors), we will get the formula of average risk (expected loss value):

0 0

0 0

11 1 1 21 1 1 12 2 2 22 2 2( / ) ( / ) ( / ) ( / ) .x x

x x

R C P f x D dx C P f x D dx C P f x D dx C P f x D dx∞ ∞

−∞ −∞

= + + +∫ ∫ ∫ ∫where f (x0/D1) – is a probability density for operative condition; f (x0/D2) – is a probability density for non-operative condition; diagnosis D1 is for operative condition, diagnosis D2 – is for non-operative condition of the object; C21 – cost of the false alarm; C12 – cost of the defect skipping (the first index is an adopted condition, the second one is a true condition).

x – current (measured) value of a diagnostic feature is random and consequently, the given equalities are average value (mathematical expectation) of a risk.

In [1] there are calculations of distribution function parameters of piston compressor valve malfunction diagnostic features for "Measures required"(MR) an "Unacceptable"(UA) states. The distribution functions for one of the features Abd2 are given above.

MR: 4,2289

( ) 1 exp29,29xF x

⎡ ⎤⎛ ⎞= − −⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦; UA:

16,616

( ) 1 exp56,5xF x

⎡ ⎤⎛ ⎞= − −⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦

Calculations for diagnostic feature Abd2 (table 2) show, that minimal decision risk

R=0,000089 can be gotten by method of minimum risk and minimum chance of defect skipping P(H12) from 0,0000051 to 0,0000059 can be gotten by methods of minimax and Neumann-Pearson, which corresponds to the boundary value x0=(33…38) m/sec2. For all other methods the average risk value is 0,000161…0,000364. At the same time, the minimum chance of false alarm P(H21) can be derived from assessments by minimum number of wrong decisions P(H21)=0,00523 and maxi-mum likelihood method P(H21)=0,0074.

Table 2

Method x0,

m/sec2 P(H21) P(H12) R

Minimum risk 37,8 0,05125 0,0000377 0,000089 Minimum number of wrong decisions 43,3 0,00523 0,0003584 0,000364

Maximum likelihood 42,6 0,0074 0,0002738 0,000281 Minimax 33,5 0,16611 0,0000051 0,000171

Neumann-Pearson 33,8 0,15522 0,0000059 0,000161

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Fig. 1. Failure skipping risk values R subject to costs for defect skipping P(H12) and false alarm

P(H21), chances of defect skipping and false alarm with assessment of diagnostic feature boundary value by the different methods

Analysis of the results. Calculation of the average values of defect skipping chance P(H12),

false alarm chance P(H21) and failure skipping Risk for diagnostic feature Abd2 has allowed to compare different methods of diagnostic features' boundary value selection (fig. 1).

Methods of Neumann-Pearson, minimax and minimum risk have shown the lowest chance of defect skipping P(H12) (0,0000059, 0,0000051 and 0,0000377 accordingly) and minimum value of failure skipping risk (Risk) (0,00016, 0,00017 и 0,000089 accordingly), but, false alarm chance P(H21) is within the range from 0,05 to 0,16, which leads to over-reject of non-fault valves.

Method of Minimum number of wrong decisions gives comparable values of defect skip-ping chance (P(H12=0,00036) and failure skipping risk (Risk=0,00036), along with quite low value of false alarm chance (P(H21)=0,0052).

Also method of Maximum likelihood gives comparable values of defect skipping chance (P(H12=0,00027) and failure skipping risk (Risk=0,00028), along with quite low value of false alarm chance (P(H21)=0,0074).

Methods of Neumann-Pearson and minimax have values of defect skipping chance (P(H12)=0,0000059 and 0,0000051) which are almost sixty times less and failure skipping risk (Risk=0,00016 and 0,00017) which are almost twice less than the method of minimum number of wrong decisions, but the value of false alarm chance is thirty times bigger (P(H21)=0,16).

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But the usage of minimum number of wrong decisions method is excused only in case when false alarm and defect skipping costs are commensurable [5]. In this case costs for defect skipping is considerably more than costs for the false alarm.

In the method of Neumann-Pearson there is designated value of false alarm chance, which minimize the defect skipping chance [5], which is the required task.

The calculations made by method of Neumann-Pearson for the analysis of efficiency of decision-making about the diagnosed ob-ject's condition by the distribution functions obtained are showing (fig.2) that the minimum of failure skipping risk corresponds to the di-agnostic feature chance within 0,93 ... 0,95.

Conclusion. The analysis of statistical decision method usage for the assessment of di-agnostic feature boundary values has shown that in case of comparable costs for false alarm and defect skipping it is appropriate to use minimum num-ber of wrong decisions method. If the costs for defect skipping are considerably more than costs for false alarm it is appropriate to use the method of Neumann-Pearson. The choice of diagnostic feature boundary values by their distribution functions for different conditions of the diagnosed object should be made when the chance value is from 0,93 to 0,95.

References

1. A.P. Naumenko ‘Scientific and methodical bases of real-time vibrodiagnostic monitoring of pis-ton machines: dissertation for the degree of Dr.Sci.Tech.:05.11.13’, Omsk, 423 p., 2012.

2. V.N. Kostyukov and A. P. Naumenko ‘Basic issues of machinery vibroacoustic diagnostics and monitoring (study guide)’, Omsk, OmSTU, 360 p., 2011.

3. Pat. 2337341 Russian Federation, MPK G01M15/14, G01M7/02. A way of vibration diagnostics of technical condition of piston mashines on spectral invariants / Kostyukov V. N., Boychenko S.N. and Naumenko A.P. – No 2007113529; decl. 11.04.07; publ. 27.10.08, Bulletin No. 30. 4. V.N. Kostyukov and A.P. Naumenko ‘Vibration diagnostics of piston compressors’, Compressor equipment and pneumatics, No 3, pp 30-31, 2002. 5. I.A. Birger ‘Technical diagnostics’, Moscow, Mechanical engineering, 240 p, 1978.

6. V.N. Kostyukov, A.P. Naumenko, Аn.V. Kostyukov, S.N. Boychenko and Аl.V. Kostyukov ‘Standards in the field of health monitoring of hazardous production facilities equipment’, Industrial Safety, No 7, pp 30-36, 2012. 7. V.N. Kostyukov and A.P. Naumenko ‘Standard and methodical ensuring of piston compressor diagnostics and monitoring’, Safety of work in the industry, No 5, pp 66-70, 2013. 8. V.N. Kostyukov and A.P. Naumenko ‘Problems and solutions of piston compressors safe opera-tion’, Compressor Techniques and Pneumatics, No 3, pp 21-28, 2008. 9 V.N. Kostyukov and A.P. Naumenko ‘Condition monitoring system of reciprocating machines’, Control. Diagnostics, No 3(105), pp 50-59, 2007.

Fig. 2. Dependence of failure skipping risk value

subject to costs for defect skipping and false alarm from correct diagnosing chance and diag-

nostic feature chance

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10. V.N. Kostyukov and A.P. Naumenko ‘Analysis of modern methods and means of piston com-pressors health monitoring and diagnostics. On-line monitoring systems. Part 1’, Non-Destructive Testing World, No 1 (47), pp 64-70, 2010.

11. V.N. Kostyukov and A.P. Naumenko ‘Analysis of modern methods and means of piston com-pressors health monitoring and diagnostics. On-line monitoring systems. Part 2’, Non-Destructive Testing World, No 2 (48), pp 28-35, 2010.

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Welcome to CM 2015 and MFPT 2015

9-11 June 2015, The Oxford Hotel, Oxford, UK

About the International Conference The British Institute of Non-Destructive Testing (BINDT) is pleased to invite you to this premier event, the Twelfth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies.

The Conference is being organised by BINDT in close co-operation and partnership with the US Society for Machinery Failure Prevention Technology (MFPT). The combination of the efforts of two leading organisations creates the largest event of its kind at a truly international level and builds on the highly successful series of international Condition Monitoring Conferences (CM2001, CM2003, CM2005, CM2007, CM2008, CM2009, CM2010, CM2011, CM2012, CM2013 and CM2014) organised by BINDT and highly successful 69 Annual Conferences organised by the Society for MFPT.

BINDT has always recognised the importance of encouraging students to participate in this major international event. As a repeat to the gesture in 2014, the Twelfth International Conference will be providing generous sponsorship of student registrations in 2015, resulting in a major reduction of fees for student attendance.

Programme There will be four sessions running in parallel covering a wide range of advances in CM fields, which will include:

• Plenary keynote addresses

• Plenary distinguished invited presentations

• Specialised keynote addresses (for structured session organisers)

• Invited presentations

• Contributed presentations, including case-study presentations

• World-leading sessions for major industrial sectors, including a session for the BINDT certification scheme

• Expert panel sessions on hot topics in condition monitoring, organised by recognised scientists

• Extensive exhibition and vendor presentations

• Social eventsThe Exhibition of 13 organisations will take place alongside the Conference and will provide an ideal opportunity to investigate the up-to-date technology available.

Sponsored by:

CM 2015 and MFPT 2015 Conference Programme

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Tuesday 9thMorning Session

Wednesday 10thMorning Session

Wednesday 10thAfternoon Session

Thursday 11thFirst Session

Thursday 11thSecond Session

Tuesday 9th June – Afternoon Session

2A – Room A – From wind turbine condition diagnosis to prognosis Chair: Dr M Papaelias

3A – Room A – Condition monitoring of turbomachinery Chair: Dr S Muthuraman

2B – Room B – Real-time health monitoring of machinery Chair: Prof V Kostyukov

3B – Room B – Real-time health monitoring of machinery Chair: Prof V Kostyukov

2C – Room C – Vibration condition monitoring Chair: Dr S Ganeriwala

3C – Room C – Signal processing for condition monitoring Chair: Dr G Zusman

3D – Room D – Signal processing and modelling for condition monitoring Chair: Dr L Zanotti-Fragonara

2D – Room D – Acoustic condition monitoring Chair: Dr I Petrunin

14.00

15.30

15.50

16.10-16.30

14.20

14.40

[127] Adequate settings of condition monitoring systems for different wind turbine types based on the lifecycle cost

[139] Low-pressure steam turbine last stage blade vibration monitoring

[143] Generator rotor thermal sensitivity

[147] Gas turbine combustion dynamics monitoring

[131] Vibration-based tools for the optimisation of large-scale industrial wind turbine devices

[135] Integrated condition monitoring of industrial wind turbines – the OPTIMUS project

[128] Real-time vibration-diagnostic condition monitoring of production and transport complex machinery

[140] The technology of complex assessment of EMU trains in depot

[144] A unit for experimental investigations of vibration of rolling stock assemblies in operation

[148] A fatigue life assessment methodology for rolling element bearing under irregular loading

[132] Risk assessment selection of guideline values of diagnostic signs

[136] Diagnostics of rolling bearings by the parameters of the characteristic function

[129] Title to be confirmed

[141] Wavelet – Fourier transforms for an industrial robot fault detection

[145] Automated cepstral editing procedure (ACEP) for removing discrete components from vibration signals

[149] FREE SLOT AVAILABLE FOR A LATE SUBMISSION

[142] Discretisations impact on amplitude accuracy for computer analysis

[146] Dynamic modelling of complex engineering assets using associative memory models

[150] FREE SLOT AVAILABLE FOR A LATE SUBMISSION

[133] Title to be confirmed

[137] Compensating an assembly fault in a gas turbine rotor by in-situ balancing: a case study

[130] Relationship between 3D tool geometry, in-process acoustic emissions and workpiece surface integrity in finish end milling

[134] Damage detection in hydrogen vehicle pressure vessels using acoustic emission technique

[138] Improvement of axle bearing monitoring systems through the use of high-speed imaging for directing acoustic beamforming

13.30-14.00 Plenary Keynote Lecture – [126] Advances in rolling bearing current signature analysis, Prof L Swedrowski, Poland (Room A). Chair: Prof L Gelman

16.30 Conference close for day

17.00-18.00 Dinner for one hour – Hotel Restaurant

18.00 Meet in Hotel Foyer to board the coach, which will take us into Oxford for a two-hour walking tour of Oxford

18.15 Coach leaves the hotel for Oxford city centre

15.00-15.30 Tea & Coffee – Oriel Marquee

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