VIBRATION MEASUREMENT UNCERTAINTY AND RELIABILITY DIAGNOSTICS RESULTS IN ROTATING SYSTEMS

Transcription

1 VIBRATIO MEASUREMET UCERTAITY AD RELIABILITY DIAGOSTICS RESULTS I ROTATIG SYSTEMS. Introdction M. Eidkevicite, V. Volkovas anas University of Technology, Lithania The rotating machinery technical state can be described with varios parameters. There are five main non-destrctive control methods [, ], sally applied dring machinery state monitoring: vibration monitoring, termography, tribology, ltrasonics and visal inspection. Vibration monitoring and diagnostics is the niversal method, sed for different eqipment observation, it allows determining and evalating the problems and defects emerging in any stage of eqipment eploitation. As vibration monitoring ses vibration measrement for diagnostics, it is important to evalate the qality of measrement. Vibration measrement ncertainty describes this qality and is sally evalated sing procedre provided in the Gide to the Epression of Uncertainty in measrement GUM [3]). ere measrement ncertainty is defined as parameter related to the measrement reslt and variance of vales which can be reasonably attached to the measrand. The measrement ncertainty consists of these components: ncertainty de to measrement mean error; ncertainty de to environment factors inflencing measrement reslt; ncertainty of the standard; ncertainty de to assmptions of the measrement methods. The standard measrement ncertainty evalation procedre [3, 4]: evalate every effect i, which significantly inflences the measrement reslt y; evalate each ncertainty component, which significanly contribtes to the ncertainty of measrement, described by a standard deviation i ( i ) (standard ncertainty); determine the combined standard ncertainty c, by combining the individal standard ncertainties (and covariances) according to the formla: f f ( i ) + i= i= = i+ i f c ( y) = ( i, ), () here ( i, ) is estimated covariance associated with measrands i and ; nmber of parameters; determine the epanded ncertainty U by mltiplying c by a coverage factor k: U = k c. () The vale of k depends on desired level of confidence to be associated with the ncertainty interval. A vale of k is in the range to 3. When there is enogh measrements made, then normal distribtion describes combined ncertainty and coverage factor k =. If measrement ncertainty is evalated for a small set of measrements, then k and sally is stated separately net to the measrement reslt. Usally the GUM recommends sing two different ways to evalate ncertainty components. These methods are called A and B : A method ses statistical methods for ncertainty component evalation the specific data set is analyzed, its statistical parameters are evalated, and sing B method other data than statistical is sed, althogh the man reslt is statistical evalation. Measrements are sed in diagnostics have an important place, particlarly in differential diagnostics. The received data and their limit vales form decision making rles. The reslt of the rle application may correspond to the real state (diagnosis), bt also measrement ncertainty may inflence this reslt and in this case it might be different from real sitation (diagnosis). This reqires investigating ncertainty of measrements, sed in this diagnosis and observing its inflence to the reslts of decision making. The paper analyses correlation between vibration

2 measrement ncertainty in vibration monitoring and diagnostics systems and diagnostics false reslts.. Vibration monitoring ncertainty Vibration monitoring and diagnostics systems (monitoring can be permanent or periodic) consist of two sbsystems measrement and diagnostics. The reliability of those two sbsystems inflences common realibility of monitoring and diagnostic system and probability of false diagnosis. Vibration measrement inflence factors according to their natre can be distingished to: measrement mean error components; environmental inflence components; time components. If the variation of the process is significantly big, then statistical ncertainty component might be big and significant while calclating general ncertainty evalation. Althogh in case of stationary monitoring system the measrand is sally stable. As we do assmption that vibration measrement reslt set in case of permanent monitoring is stationary process, then ( ) = σ = becomes a fied vale and then systematic measrement error (statistical ncertainty component) may be epressed as: ( ) ( ) = = stat = (3) nowing the limit when the ncertainty component might be disposed as nsignificant, let s mark this ratio as b, ths we can calclate the necessary data volme in order to get insignificant ncertainty component. If b, then or (4) b b In case of periodic monitoring the inflence of statistical ncertainty is emphasized, in case of permanent monitoring systematic error is more important. The ncertainty of permanently installed monitoring system is calclated [5] according the formla: U = + (5) ss SVMS stat + mat + ˆ + + T + + T r( T, ) tr ere: stat - statistical contribtion, or random error, calclated sing measrement data; mat - contribtion de to amplitde-freqency characteristic nevenness; ˆ - error of transdcer transformation coefficient; - error of transverse transformation coefficient; SS T contribtion of temperatre T; contribtion of hmidity ; r(t,) - correlation between temperatre and hmidity. The ncertainty model of periodic vibration monitoring system cold be calclated according to the formla: U = k (6) VMS stat kal T T r( T, ) + laik op here op is error de to operator, as the measrements sally are performed manally by operator. The main difference between permanent and periodic monitoring systems is that here the main roles are played by different error types. In stationary system the measrements are performed constantly and the statistical ncertainty is very small, as the nmber of is large, bt the transdcers are calibrated periodically, for eample, once per year. Inflence factors, determined dring calibration,

3 still affect the measrement procedre if it is performed in environmental conditions other than of calibration. So the systematic error here plays the main role rather than the random. In case of periodic monitoring system, the transdcer calibration is sally performed before every measrement set. Bt in contrary, as the measrements are rarer, their variance is bigger and the volme of data set is very small the random error dominates in ncertainty vale. 3. Analysis of measrement ncertainty inflence to diagnostic parameters. According to the definition, the evalation of reliability is a qantitative evalation of the prodct or system. For sch evalation sally mathematical modelling is sed, directly applied reslts of the tests, etc. Data sets in monitoring systems are sally large, so the distribtion of the diagnostic parameter might be described as: ( ) σ f ( / D i ) = e (7) σ π ere: - mean vale of the data set, frther is also denoted as m; σ - standard deviation of the data set; D i state of the system (D stable state; D defective state). f( Di) f[+u D f( D ) ] f[-u D ] f( D ) Fig.. Uncertainty inflence to decision making probability Possible ncertainty inflence to decision making probability is depicted in Fig.. The area of the first distribtion which falls otside the line is the probability to make a false decision [6]. When the ncertainty estimate U is added to the measrement reslt, the graph moves to the right. So, the area otside the line changes it becomes bigger, in other words, the probability of making false decision increases. The same principles can be applied to the second crve in solid line; therefore we will analyze only the first case. The probability to make a false decision (Fig. ) can be epressed by formla: P ( ) = P f ( / D ere P is constant. Inflence of measrement ncertainty to decision making is described as: ) d (8)

4 3 σ ( ( + U )) σ σ f (, σ, U, ) = e d e d σ π σ π (9) 3 σ ( ( + U )) 3 σ ( ) = σ σ e d e d σ π The fnction f, σ, U, ) describes the change of false decision probability when the area is ( constrained by limit vale and 3σ. The fnction will depend on the mean, variance, limit vale and ncertainty. m Dring the analysis the maimm ncertainty was chosen to be half of the mean vale U. The reslts showed that then there is a clear dependence on the ratio of the mean and ncertainty m the bigger is ncertainty, the bigger fail probability we can epect. We sggest sing this ratio U as a parameter to calclate a decision making probability change. Applying this to different vibration monitoring systems, we shold notice that in permanent vibration monitoring systems the variance of the normal distribtion will be small enogh de to large data sets, so in critical cases, the ncertainty inflence will show the effect immediately. In case of periodic monitoring system, the data sets are small and variance is mch bigger. De to that, the ncertainty might have a big inflence to decision making with portable systems having initial data. The data set might be epanded sing the particlar methodology, while transformation fnction will enlarge data set, in this way redcing the statistical ncertainty component. Using this method additional ncertainty contribtion shold be added, which calclates the impact of the increase of the set to measrement reliability. In the other hand, this contribtion has a less impact than the difference between the primal statistical ncertainties and ncertainties calclated after the transformation. As eample of the real monitoring and diagnostic system was sed vibration monitoring system, installed in anas hydroelectric power station. This data was analysed to 3 σ ( ) evalate the significance of the threshold b i = i. The vales of threshold b i in stationary monitoring and diagnostics system Table Threshold b b b 7 b 8 b 9 b b b Vale 5 5,68,36,78,48 8,75 6,44,36 The noise component in ncertainty model was evalated sing statistical data and 3 tr =,568 mm/s This shows that it is nsignificant and does not have any inflence to the evalate of ncertainty. After calclating the parameters inclded into ncertainty epression, the reslt of the permanent vibration monitoring system is U SVMS =,53 mm/s The eample of the periodic monitoring system was the measrement made for the leak cleaning eqipment compressor. According to the analyzed reslts the conclsions abot the periodic system data featres were made. In order to evalate the effect of data volme change to the threshold b the graph was made in Fig..

5 b, mmm/s,8,6,4,,,8,6,4, Fig.. The dependence of threshold b i to measrement amont Conclsions. In the permanent vibration monitoring and diagnostic system de to large qantity of the data the statistical ncertainty component is diminishing and the epanded ncertainty is inflenced only by environmental and instrmental ncertainty components. Therefore each similar measrement channel which measres the same qantity will have the same ncertainty evalate.. The variable b was evalated which allows evalating the significance of measrement ncertainty statistical component. This variable b depends on the amont of measrement data. When the qantity of this data increases, the variable b decreases. The rate of decreasing depends on the dispersion of the data. If the dispersion is large, then the decrease rate might be insfficient and then the measrement ncertainty is different in each measrement channel as the statistical ncertainty component is qite large. 3. The criterion b is based on the ratio of measrement data average and ncertainty as it evalates the significance of ncertainty inflence to false decision making. This inflence is significant only in case when this ratio is eqal or bigger than mm/s. Reference. Mobley R.. An introdction to predictive maintenance. Btterworth-einemann,, 337 p.. Plant Engineer s andbook. Elsevier, Btterworth-einemann,, 4 p. 3. International Organization of Standartization (ISO). Gide to the epression of ncertainty in measrement. ISB , Geneva, Switzerland J. von Martens. Evalation of ncertainty in measrements problems and tools // Optics and Lasers in Engineering, Elsevier 38,, p Eidkevičiūtė, Maria, Volkovas, Vitalis. On the impact of vibration measrement ncertainty to diagnostics in vibromonitoring systems //Vibroengineering 6 : proceedings of the 6th international conference, anas University of Technology. ISS 8-6. anas: Technologia. 6, p Volkovas, Vitalis; Eidkevicitė, Maria. Uncertainty in vibromonitoring systems of rotating machinery // Vibroengineering 4 : proceedings of 5th International Conference, October 4-5, 4, anas, Lithania. ISS p. -3.