some problems of nondestructive testing

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Russian Journal of Nondestructive Testing, Vol. 38, No. 7, 2002, pp. 547–556. Translated from Defektoskopiya, No. 7, 2002, pp. 82–93. Original Russian Text Copyright c 2002 by Ivanov, Vlasov. GENERAL PROBLEMS OF NDT Some Problems of Nondestructive Testing V. I. Ivanov and I. E. Vlasov OAO ORGENERGONEFT’, Samara Branch, Samara, Russia Received November 23, 2001 Abstract—Problems involved in selection of NDT techniques and determination of NDT op- erations required for hazardous facilities are discussed. The nondestructive testing (NDT) and technical diagnostics (TD) are presently very important components of the system designed to guarantee safe operation of industrial facilities. NDT and TD enable one to upgrade the safety of industrial objects by increasing the quantity of available information about their conditions and the presence of flaws in their structures. Several stages of development of these techniques have been identified. (1) The early stage, when the underlying physical principles of NDT and TD were discovered. (2) From the early 20th century to 1945 was the stage when the fundamental base for these meth- ods was built. In particular, R¨ ontgen’s discovery of x-rays (1895), which can penetrate through bodies and materials, has allowed observation of human’s internal organs and detection of flaws in industrial objects. In 1928 S.Ya. Sokolov suggested using ultrasonic waves in detecting discontinu- ities in bodies and patented this NDT technique. At the same time, numerous attempts were made to exploit other physical fields in detecting internal and surface flaws. (3) The period between 1945 and 1960, when application domains of NDT techniques were established. The first manuals and other regulatory documents on NDT were written. Possibilities of NDT methods were investigated. NDT procedures were prescribed in regulatory documents and manuals for designers. This stage was marked by rapid development of industrial production all over the world. The mechanical engineering, power generation, chemical industry, transport, and other branches of industry progressed considerably. The explosive growth in the production of industrial facilities led to the increase in the number of flaws and accidents. The need in NDT methods was urgent, and their use in monitoring industrial objects became wide-spread. (4) In 1960–1980 the instruments and techniques of NDT were improved. The inadequate reliability and accuracy of NDT data were realized. (5) After 1980 the techniques have been improved using computer technologies and advanced NDT methods. A lot of engineers working in this field anticipated conversion of flaw detection technique to methods of flaw evaluation. (6) The year 2000 marked the beginning of a new, contemporary stage of NDT development. In Russia NDT was incorporated in the system of industrial safety, when Gosgortekhnadzor of Russia issued Concept of Management of Nondestructive Testing System and Main Lines of Its Development. The rapid development of NDT instruments on the base of the recent progress in electronics and computer technologies had started somewhat earlier. For a long time, NDT was treated as an independent field of technology, without relations to other techniques (such as strength evaluation) that are used to guarantee safety of industrial facil- ities. Information derived from nondestructive tests was treated mostly as a means for improving the technologies used in manufacture of hardware or as a signal for starting repair works. Presently NDT techniques are routinely used on all stages of service lives of industrial facilities using technologies that are hazardous for the personnel, local population, and environment [1]. The full life cycle of an object should include all stages, starting with its designing and ending with the termination of its operation or its failure. The following steps can be identified: (1) designing; (2) fabrication; (3) installation; (4) start of operation; (5) normal operation (within the prescribed service life); (6) operation beyond the design service life; (7) accelerated aging; (8) termination of operation (failure). On the stage of designing, NDT and TD are used largely for determining the range of NDT operations to be performed and required NDT techniques, alongside the parameters of admissi- 1061-8309/02/3807-0547$27.00 c 2002 MAIK “Nauka/Interperiodica”

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Page 1: Some Problems of Nondestructive Testing

Russian Journal of Nondestructive Testing, Vol. 38, No. 7, 2002, pp. 547–556. Translated from Defektoskopiya, No. 7, 2002, pp. 82–93.Original Russian Text Copyright c© 2002 by Ivanov, Vlasov.

GENERALPROBLEMS OF NDT

Some Problems of Nondestructive Testing

V. I. Ivanov and I. E. VlasovOAO ORGENERGONEFT’, Samara Branch, Samara, Russia

Received November 23, 2001

Abstract—Problems involved in selection of NDT techniques and determination of NDT op-erations required for hazardous facilities are discussed.

The nondestructive testing (NDT) and technical diagnostics (TD) are presently very importantcomponents of the system designed to guarantee safe operation of industrial facilities. NDT andTD enable one to upgrade the safety of industrial objects by increasing the quantity of availableinformation about their conditions and the presence of flaws in their structures. Several stages ofdevelopment of these techniques have been identified.

(1) The early stage, when the underlying physical principles of NDT and TD were discovered.(2) From the early 20th century to 1945 was the stage when the fundamental base for these meth-

ods was built. In particular, Rontgen’s discovery of x-rays (1895), which can penetrate throughbodies and materials, has allowed observation of human’s internal organs and detection of flaws inindustrial objects. In 1928 S.Ya. Sokolov suggested using ultrasonic waves in detecting discontinu-ities in bodies and patented this NDT technique. At the same time, numerous attempts were madeto exploit other physical fields in detecting internal and surface flaws.

(3) The period between 1945 and 1960, when application domains of NDT techniques wereestablished. The first manuals and other regulatory documents on NDT were written. Possibilitiesof NDT methods were investigated. NDT procedures were prescribed in regulatory documentsand manuals for designers. This stage was marked by rapid development of industrial productionall over the world. The mechanical engineering, power generation, chemical industry, transport,and other branches of industry progressed considerably. The explosive growth in the productionof industrial facilities led to the increase in the number of flaws and accidents. The need in NDTmethods was urgent, and their use in monitoring industrial objects became wide-spread.

(4) In 1960–1980 the instruments and techniques of NDT were improved. The inadequatereliability and accuracy of NDT data were realized.

(5) After 1980 the techniques have been improved using computer technologies and advancedNDT methods. A lot of engineers working in this field anticipated conversion of flaw detectiontechnique to methods of flaw evaluation.

(6) The year 2000 marked the beginning of a new, contemporary stage of NDT development.In Russia NDT was incorporated in the system of industrial safety, when Gosgortekhnadzor ofRussia issued Concept of Management of Nondestructive Testing System and Main Lines of ItsDevelopment. The rapid development of NDT instruments on the base of the recent progress inelectronics and computer technologies had started somewhat earlier.

For a long time, NDT was treated as an independent field of technology, without relations toother techniques (such as strength evaluation) that are used to guarantee safety of industrial facil-ities. Information derived from nondestructive tests was treated mostly as a means for improvingthe technologies used in manufacture of hardware or as a signal for starting repair works.

Presently NDT techniques are routinely used on all stages of service lives of industrial facilitiesusing technologies that are hazardous for the personnel, local population, and environment [1].The full life cycle of an object should include all stages, starting with its designing and ending withthe termination of its operation or its failure. The following steps can be identified: (1) designing;(2) fabrication; (3) installation; (4) start of operation; (5) normal operation (within the prescribedservice life); (6) operation beyond the design service life; (7) accelerated aging; (8) termination ofoperation (failure).

On the stage of designing, NDT and TD are used largely for determining the range of NDToperations to be performed and required NDT techniques, alongside the parameters of admissi-

1061-8309/02/3807-0547$27.00 c© 2002 MAIK “Nauka/Interperiodica”

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ble flaws. The contemporary approach prescribes that a designed object should be accessible tomonitoring techniques. If the accessibility of an industrial facility to NDT methods is inadequate,its design must be altered.

NDT methods used on production lines are important for improving the discipline of the per-sonnel. A flaw may be detected because either materials other than those prescribed by the designhave been used or a the prescribed technological procedures have been violated. NDT techniquescan be used both on the stage of a technological operation performed on the production line andafter its termination. In these cases, NDT acts as a component of the feedback, which is requiredto prevent fabrication of products that are inferior to the prescribed level of quality. On productionlines, it is usually possible to repair a fabricated component (eliminate a fault) when a flaw hasbeen detected. The rejection norms are usually determined by the susceptibility of available testingtechniques and economical parameters of more sophisticated methods that can be used.

On the stage of installation, the conditions for nondestructive tests are more difficult that onproduction lines, even so, it is still possible to conduct tests with a fairly high sensitivity andeliminate inadmissible flaws. In these conditions, the rejection norms can be the same as on thestage of fabrication. The range of NDT operations can be much more narrow (by an order ofmagnitude) than on the production line because only the sites of junctions manufactured in theprocess of installation are tested. On the contrary, the number of diagnostic operations is muchhigher because the system should be tuned up on this stage.

The initial stage of operation is characterized by the higher probability of failures. On thisstage, commissioning tests are performed, and the NDT and TD subsystems should be tuned upbefore the main stage of the service life. The numbers of operations, methods, and susceptibilityof NDT and TD should be determined jointly by the producer (designing organization) and theoperator. The sensitivity of NDT instruments and rejection parameters can be degraded several-fold with respect to those used on the stage of manufacture. But this relaxation of the rejectionnorms requires that the frequency of tests should be increased in order to determine the effectsof operating conditions on generation and development of flaws, and the amount of informationobtained in the process of tests should also be increased.

On the middle stage of operation, NDT and TD operations are performed routinely. The re-markable feature of this period is that the faults typical of the initial stage have been eliminated,and those caused by aging do not take place yet. The range of NDT and TD operations is deter-mined by the design features of the object and parameters of its operation. The sensitivity of NDTinstruments can be reduced by an order of magnitude, in comparison with those on the stage ofmanufacture.

Although the designers attempt to produce a perfect facility, select adequate materials, and takeadvantage of the most advanced technologies, although measures are taken to avoid deviations fromprescribed technologies and to ensure that a facility be operated in accordance with prescribed rulesby skilled personnel, it is impossible to get rid of all flaws in operating hardware. Therefore, on thestage of routine operation, nondestructive tests should be performed with a view to parametersanalyzed in the fracture mechanics (FM) [2].

In most cases the repair is difficult, the more so the replacement of hardware components, con-sequently the assessment of effects of flaws on the operated structure is important. Detected flawsshould be investigated with a view to obtaining more detailed information about their parameters.The amount of information derived from NDT and TD data depends on the required FM inputparameters for assessing the strength of the structure containing the flaw. In order to calculateaccurately the strength of the structure with the detected flaw, one needs its coordinates, dimen-sions, shape, and orientation. Determination of all these parameters (except the coordinates) isnot prescribed by the contemporary standard methods of NDT, which makes the assessment of theobject’s serviceability on the base of NDT data very difficult.

The need in evaluation of dimensions, shapes, and orientation of internal flaws was first real-ized in high-tech industries, such as nuclear power generation, construction of air- and spacecraft,and later in thermal power generation. Presently this approach should be extended to the oil andgas processing, chemical industry, and other businesses operating hazardous industrial facilities.

The development of industrial production requires that effects of detected flaws on the strengthand serviceability of structure should be evaluated. Therefore it becomes important not only todetect flaws, but also to evaluate their parameters. Previously the measured flaw parameters havebeen their coordinates and their equivalent (fictitious) dimensions, but presently attention is focusedon measurements of real flaw dimensions. After this shift of emphasis, the main consumers of NDT

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data become engineers specializing in strength of materials and structures, which use informationderived from nondestructive tests in calculations of strength parameters of structures. Therefore,NDT studies should focus on flaw detection and evaluation of such parameters that are used inestimating material strength. First of all, these are the real (but not equivalent) dimensions andshapes of flaws, and their orientations.

Intensive research in the field of fracture mechanics has led to the conclusions that the majorfactors affecting strength of flawed objects are the material properties, ambient conditions, characterand configuration of loading, alongside parameters of flaws themselves, including their dimensionsalong all directions, ratios between flaw dimensions and wall thicknesses, flaw shapes, their positionswith respect to wall surfaces, and orientations.

Given these parameters, material properties, and conditions of operation, one can calculatestrength parameters of objects, critical dimensions of flaws, levels of rejection, frequencies of tests,and remaining service lives. In this connection, it becomes more important to obtain numericalcharacteristics in nondestructive tests. Conversion of NDT from the technique of flaw detection toflaw evaluation becomes a necessity [3].

When the design service life of an object terminates and its operation beyond the prescribedservice life begins, more information should be derived from nondestructive tests. Additional infor-mation should be obtained by increasing the dimensionality of the space of measured parameters,rather than by upgrading the susceptibility of instruments. Not only do we need information aboutdetected flaws and their parameters listed above, but also about changes in these parameters inthe course of the service life. Moreover, information about changes in the properties of structuralmaterials is also needed. Alongside the flaw parameters, these properties should be used in esti-mating the serviceability of the tested object and determining the times of the subsequent tests(unless the object is monitored permanently).

Owing to the exponential development of new technologies, this conversion should be conductedconcurrently, i.e., before the appropriate techniques and instruments are developed in their finalforms, additional NDT parameters should be selected, and the schedule of their inclusion in docu-ments regulating technological processes should be drawn up.

After discussing the aims of NDT on different stages, we can select a number of factors thatshould be taken into consideration in planning the NDT and TD system. They include the hazard offailures on the early stage of operation; the design of the facility, structural materials, and operatingconditions; flaws and their characteristics; degrees of hazard due to various flaws.

After assessing these factors, one can draw up the short-term and long-term plans of NDT oper-ations, select NDT parameters, including sensitivity characteristics of instruments, measured flawparameters, and their accuracy. The parameters to be measured include, first of all, the coordinates,dimensions in all directions, shapes, and orientations of flaws.

An important component is a system of classification of all flaws and rejection criteria. The cri-teria adopted earlier on the initial development stage of industrial NDT are obsolete. In most casesthey were based on sensitivity characteristics of specific NDT techniques, but not on estimates ofimpact of specific flaws on strength parameters of structures.

One of the first steps in this direction can be inclusion of new requirements to evaluationof flaw parameters in NDT manuals. First of all, calibration curves, accuracy and confidencecharacteristics of the measuring techniques should be obtained. The calibration curves must re-late real flaw dimensions to measurements obtained by NDT instruments. The confidence andaccuracy characteristics of measurements are also necessary because they affect the accuracyof strength calculations and confidence in estimates of the degree of safety of operated facili-ties.

That said, we can list the main aims of development of NDT methods in the immediate future.(1) Upgrading the susceptibility of NDT instruments in view of new requirements to NDT data.(2) Increasing the quantity of information derived from NDT measurements (more accurate

dimensions and shapes of flaws, etc.).(3) Automation of tests (automatic scanning).(4) Automation of data processing (identification of flaws by computers and utilization of neural

networks).(5) Development of new NDT methods (holography, tomography, acoustic emission techniques,

etc.).

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(6) Development of new approaches and NDT methods of a new generation basing on the factthat NDT is, in effect, a process of measurement (introduction of calibration characteristics forNDT data), and an essentially random process at that (which requires introduction of specificparameters for estimating the degree of confidence in NDT data).

(7) Development of new systems for assessing NDT data, e.g., a classification of flaws in accor-dance with the degree of real hazard due to these flaws and development of new rejection criteriabased on NDT data.

(8) Search for new links between NDT and related techniques, which can also be used in esti-mating the degree of safety of industrial facilities, their remaining service lives, and in identificationof conditions under which they should be decommissioned.

Let us discuss some of these issues in detail.Presently the NDT techniques are on the stage of transition from one state to the other [3].

The start of the contemporary stage of the NDT development in Russia can be dated as theyear 2000, when NDT was incorporated in the expert system of safety of industrial facilities regu-lated by Gosgortekhnadzor of Russia. The latest period can be characterized as a stage of transitionfrom statistical flaw detection to stochastic flaw evaluation.

For most of the NDT methods, the statistic flaw detection includes detection of flaws anddetermination of some of their parameters. Usually only one of the parameters can be measuredwith a more or less acceptable accuracy. This is the flaw coordinate. The other parameters areeither ignored or estimated by methods of comparison. Parameters of real flaws are compared toparameters of fabricated flaws or reference flaws, e.g., reflectors of ultrasound in the shapes of holesdrilled in side surfaces, scratches, notches, flat-bottom holes, slots, etc.

The stochastic flaw evaluation is defined as a field of technology involving detection of flaws,their identification, and measurement of their parameters. Since the flaw detection is a probabilisticprocess, which should be controlled with the help of the theory of random processes, it can bedescribed as a stochastic flaw evaluation. In measuring flaw parameters, one should use approachespracticed in the theory of measurement of random process parameters.

Most of the traditional NDT and TD methods do not include measurements of flaw parameters.One of rare examples of techniques measuring real flaw dimensions is the x-ray screening. The mea-surements of the flaw projection on the x-ray film, however, yield only information about the flawdimensions in the plane of the object’s wall, whereas strength calculations strongly depend on theflaw dimension along the normal to the wall plane.

Since NDT is an important component of the system of safe operation of hazardous industrialfacilities, NDT data should be used more widely than they are at present. In particular, NDT shouldsupply information that could be used in estimating strength characteristics of an object (static,dynamic, and cyclic) and its service life (or the time to its decommissioning) [2].

In view of this, the systemic approach is optimal. A system is defined as a “separate functionalhierarchic aggregation of components each of which has specific purposes and contributes to theprocess of development”. One of such systems is that created by Gosgortekhnadzor of Russia:“The system of testing that permits the expert assessment of the industrial safety and technicaldiagnostics of industrial facilities, equipment, and structures without degrading their fitness forfurther operation (nondestructive testing) for making decisions concerning the extension of theirtimes of safe operation as parts of hazardous industrial objects (determination of their remainingservice lives) on the territory of Russian Federation” [4].

In order to implement the prescriptions of the NDT system, a concept of management [5]was developed aimed at creation of organizational structures, developing and enacting regulatorydocuments, planning of measures for development and introduction of NDT procedures, etc.

“The concept of management of the system of nondestructive testing and main lines of its de-velopment” issued by Gosgortekhnadzor of Russia prescribes that four basic regulatory documents(Rules) should be drawn up:• Rules for certification and main requirements to NDT laboratories;• Rules for certification of personnel working with NDT techniques;• Rules for certification of NDT instruments;• Rules for attesting technical manuals on NDT methods.These documents should describe the main organizational principles for the technical certification

regulated by each respective document.

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Fig. 1. Calibration characteristic of an NDT technique.

The personnel working with NDT techniques should be certified in accordance with the level ofqualification, the range and quality of permitted nondestructive tests. The certification of NDTinstruments is common practice, and these operations are routine, to a certain extent. This cannotbe said about attesting technical manuals on NDT methods.

It will be the first time that an expert system is created for assessing the completeness andsufficiency of technical manuals on NDT methods and NDT techniques, and this will require iden-tification of basic requirements to this regulatory document and its contents.

Attempts were made to develop an algorithm for the techniques of acoustic-emission (AE)NDT [6]. The document listed the major pieces of preliminary information required for normativedocuments regulating such tests (in particular, with the help of acoustic emission). The followingmain stages of development of an AE testing technique were identified:• investigation of basic properties of a structural material (for the AE method, these are the

acoustic properties of the material);• investigation of specific properties of the structural material (for the AE method, these are

the AE parameters of the material);• development of techniques used in tests;• composition of a regulatory technical document.The expected rules for attesting technical manuals on nondestructive testing should set forth

the requirements to the NDT methods corresponding to the contemporary level of technology,and attention should be focused on the issues of stochastic flaw evaluation. The document mustcontain clear and unambiguous definitions of such terms as standard, technical requirements (spec-ifications), testing technique, technical manual, technology (technological chart), and others, anddefine the application domains for these terms.

The documents should legitimize the term flaw evaluation and clearly define its meaning. In itsbroadest interpretation, the flaw evaluation is a complex multi-stage process which can include thefollowing processes:

(1) Detection of (search for) flaws.(2) Observation (resolution) of flaws.(3) Identification (typization) of flaws.(4) Measurement of flaw parameters (evaluation of parameters on the first stages).In measuring (estimating) the parameters, one determines:• flaw dimensions;• flaw shape;• orientation;• flaw coordinates.An important tool in the flaw evaluation is a calibration characteristic, which relates real the

flaw dimensions dreal to measurements obtained by the instrument, dmeas. The curve plotted inFig. 1 is an example of the calibration characteristic.

This characteristic also identifies processes related to flaw detection. In Fig. 1, zone 1 is whereflaws are detected, and zone 2 is the region where flaw parameters are measured. One can concludefrom Fig. 1 that dimensions of “small” flaws are difficult to measure. In order to obtain accuratemeasurements, one should have a flaw in the measurement zone 2. It is possible if the flaw dimensionis relatively large, or relatively small flaws are translated to the measurement zone by increasing

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Fig. 2. Diagram of information flow in a nondestructive test.

Fig. 3. Distributions of amplitudes of detected signal and noise.

the gain. Obviously, the NDT technique should be designed to have a sufficiently wide zone ofmeasurements. Figure 1 also shows the spread of measurements, which should be normed too, i.e.,as a result of measurement, one should obtain both the measured parameter and the measurementerror (accuracy).

The processes of flaw detection, observation, and identification are strongly affected by the signal-to-noise ratio (s/n), which is defined as a ratio between the characteristic parameters (e.g., rms valueor energy) of the signal and noise. In nondestructive tests, information is collected about both signaland noise, as it is schematically shown in Fig. 2.

If a tested natural object does not contain a flaw, only noise (n) is detected in the process oftesting, whereas in the presence of a flaw, a signal (s) due to the flaw is measured, alongside thenoise. When the instrument detects only noise, the operator can come to a correct conclusionthat only noise is detected with the probability Pn/n, which is termed the probability of correctundetection in the radar technique [7, 8], but with the probability Ps/n he can mistake the noise fora signal due to a flaw (the probability of a false alarm). In the presence of a flaw, the operator cancome to the correct conclusion that a flaw is present with the probability Ps/s (the probability ofcorrect detection), but with the probability Pn/s (the probability of missing) he can miss the flawand interpret a signal as noise.

The probabilities of detecting signals and noises as random processes are described in terms ofdistributions of parameters. Most commonly, the amplitude distribution is used (Fig. 3), whichshows probability densities for the signal and noise amplitudes.

The probability equals the area under this or that curve (for signal or noise) between the limitsuthr and ∞, where uthr is the sensitivity threshold of the instrument.

Using the distributions plotted in Fig. 3, one can obtain diagrams shown in Fig. 4, whichare termed receiver operating characteristics (ROC) [8] and determine the probabilities of correctdetection denoted as Ps/s and false alarm (in NDT this is the probability of over-reject) denotedas Ps/n. Such diagrams are presently used in nondestructive tests [9, 10].

The abscissa in Fig. 4 plots the probability of false alarm (over-reject) Ps/n, and the ordinateplots the probability of correct detection Ps/s. Curves 1, 2, and 3 correspond to different mutual

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Fig. 4. Operational characteristics of flaw detection process (comparative operational characteris-tics [9]).

Fig. 5. Curves of ∆P = Ps/s − Ps/n: (1 ) a = 1, b = 1/2; (2 ) a = 1, b = 1/4; (3 ) a = 1, b = 1/8.

positions of signal and noise amplitude distributions (Fig. 3) and their shapes. Curve 1 correspondsto the situation when the two probabilities are equal, i.e., the amplitude distributions for the signaland noise are identical (in Fig. 3). Curve 2 corresponds to the imaginary situation with Ps/s = P 0.5

s/n,and curve 3 to the situation when Ps/s = P 0.125

s/n . The arrow marked by (a) shows the tendency to amore definite separation of signal and noise, and the arrow (b) the tendency to a lower sensitivitythreshold of the instrument.

It is noteworthy that the curves in Fig. 4 do not plot Ps/s as a function of Ps/n, but each pointon the curve plots specific values of Ps/s and Ps/n for specific distributions of signal and noiseamplitudes at a given sensitivity threshold. If the average signal amplitude is higher than that ofnoise, the curves relating Ps/s and Ps/n can be described by the formula

Ps/s = aP bs/n, (1)

where a and b are constants, a > 1, b < 1.If the sensitivity threshold is set to zero, the probabilities of detecting signal and noise are equal

to unity: Ps/s = Ps/n = 1. This means that signal and noise are recorded with the same probability

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554 IVANOV, VLASOV

Fig. 6. Entropy curves: (1 ) for Ps/n; (2 ) for a = 1, b = 1/2; (3 ) for a = 1, b = 1/8.

equal to unity. As the sensitivity threshold is raised, the two probabilities Ps/s and Ps/n graduallydrop to Ps/s = Ps/n = 0.

The probabilistic characteristics of testing techniques can be determined by the parameters aand b, and the requirements to detecting instruments by the probabilities Ps/s and Ps/n. A testingtechnique can be characterized, e.g., by the parameter ∆P = Ps/s − Ps/n (which is similar to thatin the Neumann–Pearson criterion [7]). Figure 5 plots curves of ∆P = Ps/s − Ps/n for the caseswith a = 1, b = 1/2 (curve 1); a = 1, b = 1/4 (curve 2); a = 1, b = 1/8 (curve 3). Conditions fortesting can be selected to maximize the parameter ∆P . For curve 1 we have the maximal valueat Ps/n = 0.25: ∆P = 0.250; for curve 2 these are Ps/n = 0.157 and ∆P = 0.472; for curve 3Ps/n = 0.093 and ∆P = 0.650.

Since information is processed in the NDT and TD techniques, it is natural to use approachesof the information technology, which involves determination of entropy H or the related quantityof information I. The entropy in NDT methods can be obtained using formulas of the informationtheory [11]. In the absence of flaws, one can plot the noise entropy hs/n, and this curve correspondsto the graph of entropy in an experiment with two possible outcomes (curve 1 in Fig. 6):

hs/n = ps/nlog2 ps/n − (1− ps/n)log2 (1− ps/n). (2)

In the absence of flaws, the signal entropy hs/s for the case of Ps/s = P1/2

s/n is plotted by curve 2

in Fig. 6, and for the case of Ps/s = P1/8

s/n by curve 3.In selecting parameters of tests using the entropy approach (Fig. 6), one can choose either the

entropy maximum or the crossing points of curves 2 and 3 plotting the signal entropy (for differentsignal distributions) with curve 1 for the noise entropy. These situations are marked by the verticaldashes in Fig. 6.

Matrix for estimating comparative degrees of confidence in testing methods using the number of testeditems (an alternative parameter)

Testing method and estimates of its results for nΣ

Initial (reference) method

Number of itemsaccepted by reference

method, nra = na + nα

Number of itemsrejected by reference

method, nrr = nr + nβ

Tested methodNumber of accepted items na, twice accepted nβ , under-reject

Number of rejected items nα, over-reject nr, twice rejected

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Fig. 7. Degree of confidence P versus the number m of statistically independent tests: a priori(at m = 1) degree of confidence (1 ) P = 0.3; (2 ) P = 0.5; (3 ) P = 0.75; (�) two tests with differentdegrees of confidence (P1 = 0.3 and P2 = 0.75); (+) three tests (P1 = 0.3, P2 = 0.5, and P3 = 0.75).

Traditionally the matrix of comparative confidence in testing techniques (in comparison with analternative testing method) is used [12] (see table).

If the confidence matrix is used, the degree of confidence is calculated by the formula

Pc =na + nr

. (3)

Using the confidence parameters, one can determine whether it is preferable to use multipletests by the same method or several different NDT techniques. On the base of investigations offlaw localization at several ultrasound frequencies [13], we suggest the following expressions forestimating the degree of confidence in tests using probabilities of flaw detection:

PΣ = 1− (1− P1)(1− P2) . . . (1− Pm), (4)

PΣ = 1− (1− P1)m, (5)

where PΣ is the resulting probability of flaw detection, P1, . . . , Pm are the probabilities of detectinga flaw by the methods labeled 1, . . . ,m. Expression (4) is used when m methods are applied(or tests are performed by m operators), and these methods have different a priori probabilitiesof flaw detection, whereas expression (5) is used in the case of multiple tests by the same method(one operator).

Curves illustrating expressions (4) and (5) are plotted in Fig. 7, which demonstrates that thedetection probability is much higher in repeated tests. Even if the a priori probability of flawdetection is unacceptable for testing hazardous industrial facilities (P < 0.3–0.5), this parameterbecomes essentially higher in repeated tests and can be raised to acceptable levels (P ∼ 0.7–0.8).

In conclusion, we reiterate the necessity of including articles regulating calibration characteristicsand parameters of confidence in testing techniques in Rules for attesting technical manuals fornondestructive testing.

REFERENCES1. Ivanov, V.I., Nondestructive Testing in System of Safe Operation of Hazardous Objects, Bezopasnost’

Truda v Promyshlennosti (Safety of Industrial Labor), 1987, no. 9, pp. 52–54.2. Getman, A.F. and Kozin, Yu.N., Nerazrushayushchii kontrol’ i bezopasnost’ ekspluatatsii sosudov i trubo-

provodov vysokogo davleniya (Nondestructive Testing and Safety of Operation of High-Pressure Vesselsand Pipelines), Moscow: Energoatomizdat, 1997.

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