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\title{Damage Informatics for Steam Turbine Components}
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\begin{document}

             \author[1]{Kazunari  Fujiyama}

             \affil[1]{  Meijo University}

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\date{\small \em Received: 12 December 2013 Accepted: 31 December 2013 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


Statistical data analyses were conducted on the variety of damage modes occurred in steam turbine major components such as high pressure turbine blades/nozzles, casings and low pressure turbine rotors and blades. The data were fitted using log-normal distribution function of operation time and number of starts. Two dimensional distribution functions were constituted by combining the marginal distribution functions of operation time and number of starts. Time-cycle mapping for various events indicated that apparent order of event occurrence and the equi-probability loci representing the time or cycle dependency and data distribution range. The best fit line for mean values of time and cycles of each event was adopted to evaluate the probability function of operation time and used to calculate resultant risk function along the line. The rational results were obtained to determine optimum maintenance periods from the risk functions established for respective turbine sections. The entire procedure including time-cycle mapping expression has been proved to be a quite useful tool for damage assessment, causality assessment and resultant risk assessment to improve the maintenance technology and can be categorized in the brand-new ?Damage Informatics? concept.

\end{abstract}


\keywords{damage, steam turbine, two-dimensional probability, log-normal distribution, time and cycle mapping.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
ossil power plants still play important roles for providing electric power supply on demands all over the world. Although combined cycle plants coupling gas turbines and steam turbines have become more popular due to their higher efficiency, the conventional steam turbine plants still occupy the large part of power stations and have become aged by long term service, requiring cost-effective maintenance application. To make optimum maintenance planning, risk-based maintenance \hyperref[b0]{[1]}- \hyperref[b4]{[5]} procedures have been established and applied to actual plants but the objective parts have been restricted and comprehensive required. However the systematic lists of events to be considered have not been provided according to the wide variety of events and the lack of rational scenario making procedures. The fundamentals of manipulating damage information are statistical data processing and causality inference \hyperref[b5]{[6]} from the observed event items but the latter term has not been explicitly recognized in the maintenance technology development. As the damage events may dependent on two operational parameters such as operation time and number of starts, the two parameters are used as the variables for evaluating probability functions. To provide rational maintenance decision making, risk functions are introduced based on the two-parameter distribution functions and used as the comprehensive measures for synthesizing various damage events occurred in major turbine sections. The examples of some detailed damage scenarios are also presented here to understand the synthetic evaluation of total risks for optimum maintenance planning. This approach could be called as "Damage Informatics" for Steam Turbine Components as a new investigation field of plant integrity. 
\section[{II.}]{II.} 
\section[{A General Description of Damage Events Observed at Steam Turbine Major Components}]{A General Description of Damage Events Observed at Steam Turbine Major Components}\par
Figure  {\ref 4} shows typical damage modes in steam turbine components \hyperref[b3]{[4]}. For high-pressure (HP) and intermediate-pressure (IP) turbine rotors, creep damage is accumulated in the bore and wheel hooks. In the dovetail hook contacted area, high cycle or fretting fatigue occurs due to vibratory stress. In the strain concentrations region of casings and valves, cracks initiate due to thermo mechanical fatigue (TMF) during cyclic operations and then grow under internal pressure. For nozzles, downstream deflection of nozzle diaphragm due to steam force occurs at high temperature portion. Solid particle or droplet erosion is sometimes observed in nozzle plates at HP/IP steam inlet portion and wet steam section of LP turbine. For steam pipe weldments, creep damage is accumulated and resulted in the creep void formation. For low pressure turbine rotors, corrosion fatigue or SCC under centrifugal and vibratory stress are typical damage modes.  
\section[{Statistical Analysis Procedure}]{Statistical Analysis Procedure}\par
Two dimensional log-normal probability distribution function F(Q) is expressed as the following equation and the ellipse locus is obtained by setting Q as a value corresponding to the constant probability \hyperref[b6]{[7]}. In this article, the value of F is assumed as 0.5( ) ? ? ? ? ? ? ? ? = 2 exp 1 Q Q F (1) ( ) ( )( ) ( ) ? ? ? ? + ? ? ? ? ? ? ? ? = 2 2 2 2 2 ln ln ln 2 ln 1 1 LeN Let LeN Let LeN Let Let Let N N t t Q ? µ ? ? µ µ ? ? µ ? (2) ( )( ) \{ \} LeN Let LeN Let N t E ? ? µ µ ? ? ? = ln ln\par
for the convenience in comparison of event data. The relationship between t op and N s obtained by fitting the mean values of events is defined as the most likely operation pattern from field database and expressed by N s as the function of t op as follows.  ( ) ( ) ( )( ) ( ) ? ? ? ? ? ? + + ? ? ? ? ? ? + ? ? ? ? = 2 2 2 2 2 ln ln ln ln ln 2 ln 1 1 LeN Let op LeN Let LeN op Let op Let Let op op t b A t b A t t t Q ? µ ? ? µ µ ? ? µ ? (5)\par
For evaluating risks, we must define the values of consequence, but here we put them as unity for the simplicity of data manipulation and then we can sum up the probabilities as the measure of risk value. The resultant risk function r (t op ) is expressed by the function of t op as follows( ) ( ) ( ) ? ? = = = = m i op i m i op i i op t F t F C t r 1 1 (6)\par
Where, C i : consequence of failure of event i(assumed=1), m: total number of subject events, F i (t op ): probability of failure of event i obtained by Eq.(1).\par
IV. 
\section[{Marginal Distribution}]{Marginal Distribution}\par
As the first step, the marginal distribution are obtained against operation tome t op and number of starts N s as shown in Fig.  {\ref 2} for high pressure inner casing cracking events. Log-normal type distribution are obtained for most of the event data like this case. The unreliability function of log-normal type is written as follows \hyperref[b1]{(2)} .The variable Y can be put as time of operation t op or number of starts N s .( ) ( ) ? ? ? ? = ? ? ? ? ? ? ? ? ? ? = Y x Le Le Le dx e Y Y F Le Le 2 2 2 ln 2 1 ln ? µ ? ? ? µ (7)\par
Fig.  {\ref 2} : Examples of marginal distributions for HP (High Pressure) inner casing cracking event V. 
\section[{Two-Dimensional Log-Normal Distribution Analysis for Various}]{Two-Dimensional Log-Normal Distribution Analysis for Various}\par
Events and Casualty Assessment\par
Based on Eqs.(  {\ref 5}) and the marginal distributions obtained in section4, two dimensional log-normal distribution are obtained and then causality assessment can be conducted by using the risk functions of Eq.(  {\ref 6}). Individual analytical results for HP (High Pressure) and LP(Low Pressure) turbine sections are described as follows. IP(Intermediate Pressure) turbine section showed almost similar trend with HP turbine section, therefore the IP turbine section was omitted here due to the lack of space. a) HP (High Pressure) Turbine\par
Figure \hyperref[fig_1]{3} shows N s -t op mean point damage mapping for HP blades and nozzles with 50\% unreliability contour. The mean trend is obtained from the regression of mean event data by Eq.(  {\ref 4}) excluding HP-2 nozzle erosion which shows irregular plot from the majority trend. This is caused by the data mismatch due to the small number of events (here, only 2 events available but the sets of N s and t op showed contrary combinations).  
\section[{Global Journal of Researches in Engineering}]{Global Journal of Researches in Engineering}\par
( ) A Vol obtained data. On the other hand, HP-1 blade lifting shows more apparent tendency of time dependence compared with other events and it has more data numbers. More detailed event scenario is shown as the flow chart form in Fig.  {\ref 4} referring Fig. \hyperref[fig_1]{3}. Resultant risk curve shown in Fig.  {\ref 5} indicates an apparent peak, so the t op value at the peak of risk function can be adopted as the recommendation of inspection timing.\par
Figure  {\ref 6} shows N s -t op mean point damage mapping for HP inner casing plots and almost all data are categorized as the thermo-mechanical fatigue cracking located in the narrow sets of t op and N s , so there is no motivation to draw mean trend by regression of the data. The shapes of 50\% contours show more horizontal orientation which suggests the stronger dependency on number of starts than operation time.      
\section[{Conclusions}]{Conclusions}\par
Field inspection database can be fully utilized to constitute damage scenario and to make up maintenance decision making for steam turbine major compound sections. Statistical analyses are utilized to quantify the event occurrence timing and the order with the scatter band of each event data. The accumulation of field data is quite important and scenario inference should be performed by combining the data analyses and the knowledge of experts in the form of damage sequence flow chart. The "Informatics" for plant damage may contribute to make more improvement in the accuracy for predicting the life of components and to identify the casualty of the events. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}FFig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-3.png}
\caption{\label{fig_1}( 3 )}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{345}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Fig. 3 :Fig. 4 :Fig. 5 :F}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{67}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Fig. 6 :Fig. 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{89}\includegraphics[]{image-7.png}
\caption{\label{fig_6}LFig. 8 :Fig. 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10}\includegraphics[]{image-8.png}
\caption{\label{fig_7}Fig. 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.07828947368421052\textwidth}P{0.10625\textwidth}P{0.5899671052631579\textwidth}P{0.008388157894736842\textwidth}P{0.011184210526315788\textwidth}P{0.05592105263157894\textwidth}}
\tabcellsep 99.99\tabcellsep \multicolumn{2}{l}{HP inner casing}\tabcellsep \\
\% Cumulative probability F,\tabcellsep 99.9 99 90 70 50 30 10 1 0.1\tabcellsep \multicolumn{4}{l}{Upper inner surface crack : Ns Upper inner surface crack regression : Ns Upper inner surface crack regression : top Upper inner surface crack : top}\\
\tabcellsep 0.01\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep 1\tabcellsep 10\tabcellsep 100\tabcellsep 1000\tabcellsep 10000 100000 1000000\\
\tabcellsep \tabcellsep \multicolumn{4}{l}{Number of starts N s or operation time t op (h)}\end{longtable} \par
  {\small\itshape [Note: © 2014 Global Journals Inc. (US)]} 
\caption{\label{tab_0}}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Fujiyama et al. ()]{b1}\label{b1} 	 		‘An Integrated Approach of Risk Based maintenance for Steam Turbine Components’.  		 			K Fujiyama 		,  		 			T Kubo 		,  		 			Y Akikuni 		,  		 			T Fujieara 		,  		 			H Kodama 		,  		 			M Okazaki 		,  		 			T Kawabata 		.  	 	 		\textit{OMMI (Operation, Maintenance and Materials Issues)}  		2007. 4 p. .  	 
\bibitem[Wadsworth and Bryan ()]{b6}\label{b6} 	 		\textit{Applications of Probability and Random Variables, Second Edition},  		 			G P Wadsworth 		,  		 			J G Bryan 		.  		1974. McGraw-Hill. p. .  	 
\bibitem[Pearl ()]{b5}\label{b5} 	 		\textit{Causality: Models, Reasoning and Inference},  		 			J Pearl 		.  		2000. Cambridge University Press.  	 
\bibitem[Fujiyama et al. ()]{b2}\label{b2} 	 		‘Design, Material Selection and Life Assessment of High Temperature Components Using the Unified Statistical Master Curves of Material Properties’.  		 			K Fujiyama 		,  		 			T Fujiwara 		,  		 			Y Nakatani 		,  		 			K Daito 		,  		 			A Sakuma 		,  		 			Y Akikuni 		,  		 			S Hayashi 		,  		 			S Matsumoto 		.  	 	 		\textit{Maintenance and Materials Issues)}  		2008. OMMI(Operation. 5 p. .  	 
\bibitem[Bedford and Cooks ()]{b7}\label{b7} 	 		\textit{Probabilistic Risk Analysis: Foundations and Methods},  		 			T Bedford 		,  		 			R Cooks 		.  		2009. Cambridge University Press.  	 
\bibitem[Fujiyama ()]{b0}\label{b0} 	 		‘Risk Based Engineering for Design, Material Selection and Maintenance of Power Plants’.  		 			K Fujiyama 		.  	 	 		\textit{Materials at High Temperatures},  				2011. 28 p. .  	 
\bibitem[Fujiyama et al. ()]{b4}\label{b4} 	 		‘Risk-based design and maintenance measures for high temperature components under creep-fayigue conditions using Bayesian approach’.  		 			K Fujiyama 		,  		 			H Ueno 		,  		 			H Hirano 		,  		 			H Kimachi 		.  	 	 		\textit{HIDA (High Temperature Defect Assessment)-6 Conference},  				 (Nagasakim Japan, CD-ROM)  		2013.  	 
\bibitem[Fujiyama et al. ()]{b3}\label{b3} 	 		‘Risk-Based Maintenance Procedures for Compound Damage Modes of High Temperature Components’.  		 			K Fujiyama 		,  		 			H Suzuki 		,  		 			T Tsuboi 		.  	 	 		\textit{Proc. 7 th China-Japan Bilateral Symposium on High Temperature Strength of Materials},  				 (7 th China-Japan Bilateral Symposium on High Temperature Strength of Materials)  		2010. p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
