List of gas path measured parameters of the engine selected as test case.
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Beebe, Tanya L. Russell, Thomas R. Burkot, Neil F. Lobo and\nRobert D. Cooper",authors:[{id:"152080",title:"Dr.",name:"Nigel",middleName:null,surname:"Beebe",fullName:"Nigel Beebe",slug:"nigel-beebe"},{id:"169012",title:"Dr.",name:"Tanya",middleName:null,surname:"L. Russell",fullName:"Tanya L. Russell",slug:"tanya-l.-russell"},{id:"169013",title:"Dr.",name:"Thomas",middleName:null,surname:"R. Burkot",fullName:"Thomas R. Burkot",slug:"thomas-r.-burkot"},{id:"169014",title:"Dr.",name:"Neil",middleName:null,surname:"F. Lobo",fullName:"Neil F. Lobo",slug:"neil-f.-lobo"},{id:"169015",title:"Dr.",name:"Robert",middleName:null,surname:"D. Cooper",fullName:"Robert D. Cooper",slug:"robert-d.-cooper"}]},{id:"43671",title:"Ecology of Larval Habitats",slug:"ecology-of-larval-habitats",signatures:"Eliška Rejmánková, John Grieco, Nicole Achee and Donald R.\nRoberts",authors:[{id:"151632",title:"Prof.",name:"Nicole",middleName:null,surname:"Achee",fullName:"Nicole Achee",slug:"nicole-achee"},{id:"152601",title:"Prof.",name:"Eliska",middleName:null,surname:"Rejmankova",fullName:"Eliska Rejmankova",slug:"eliska-rejmankova"},{id:"169016",title:"Dr.",name:"John",middleName:null,surname:"Grieco",fullName:"John Grieco",slug:"john-grieco"}]},{id:"43954",title:"From Anopheles to Spatial Surveillance: A Roadmap Through a Multidisciplinary Challenge",slug:"from-anopheles-to-spatial-surveillance-a-roadmap-through-a-multidisciplinary-challenge",signatures:"Valérie Obsomer, Nicolas Titeux, Christelle Vancustem, Grégory\nDuveiller, Jean-François Pekel, Steve Connor, Pietro Ceccato and\nMarc Coosemans",authors:[{id:"131417",title:"Dr.",name:"Valérie",middleName:null,surname:"Obsomer",fullName:"Valérie Obsomer",slug:"valerie-obsomer"},{id:"152754",title:"Prof.",name:"Marc",middleName:null,surname:"Coosemans",fullName:"Marc Coosemans",slug:"marc-coosemans"},{id:"153949",title:"Dr.",name:"Pietro",middleName:null,surname:"Ceccato",fullName:"Pietro Ceccato",slug:"pietro-ceccato"},{id:"153950",title:"Dr.",name:"Gregory",middleName:null,surname:"Duveiller",fullName:"Gregory Duveiller",slug:"gregory-duveiller"},{id:"153952",title:"Dr.",name:"Christelle",middleName:null,surname:"Vancutsem",fullName:"Christelle Vancutsem",slug:"christelle-vancutsem"},{id:"153980",title:"Dr.",name:"Nicolas",middleName:null,surname:"Titeux",fullName:"Nicolas Titeux",slug:"nicolas-titeux"},{id:"154158",title:"Dr.",name:"Steve J",middleName:null,surname:"Connor",fullName:"Steve J Connor",slug:"steve-j-connor"},{id:"167685",title:"MSc.",name:"Jean-Francois",middleName:null,surname:"Pekel",fullName:"Jean-Francois Pekel",slug:"jean-francois-pekel"}]},{id:"43960",title:"Simian Malaria Parasites: Special Emphasis on Plasmodium knowlesi and Their Anopheles Vectors in Southeast Asia",slug:"simian-malaria-parasites-special-emphasis-on-plasmodium-knowlesi-and-their-anopheles-vectors-in-sout",signatures:"Indra Vythilingam and Jeffery Hii",authors:[{id:"151116",title:"Dr.",name:"Indra",middleName:null,surname:"Vythilingam",fullName:"Indra Vythilingam",slug:"indra-vythilingam"},{id:"169006",title:"Dr.",name:"Jeffery",middleName:null,surname:"Hii",fullName:"Jeffery Hii",slug:"jeffery-hii"}]},{id:"44039",title:"Thermal Stress and Thermoregulation During Feeding in Mosquitoes",slug:"thermal-stress-and-thermoregulation-during-feeding-in-mosquitoes",signatures:"Chloé Lahondère and Claudio R. Lazzari",authors:[{id:"151619",title:"Prof.",name:"Claudio",middleName:null,surname:"R. Lazzari",fullName:"Claudio R. Lazzari",slug:"claudio-r.-lazzari"},{id:"151620",title:"Ms.",name:"Chloé",middleName:null,surname:"Lahondère",fullName:"Chloé Lahondère",slug:"chloe-lahondere"}]},{id:"43955",title:"The Anopheles Mosquito Microbiota and Their Impact on Pathogen Transmission",slug:"the-anopheles-mosquito-microbiota-and-their-impact-on-pathogen-transmission",signatures:"Mathilde Gendrin and George K. Christophides",authors:[{id:"154007",title:"Dr.",name:"Mathilde",middleName:null,surname:"Gendrin",fullName:"Mathilde Gendrin",slug:"mathilde-gendrin"},{id:"154008",title:"Prof.",name:"George",middleName:"K",surname:"Christophides",fullName:"George Christophides",slug:"george-christophides"}]},{id:"43829",title:"Bacterial Biodiversity in Midguts of Anopheles Mosquitoes, Malaria Vectors in Southeast Asia",slug:"bacterial-biodiversity-in-midguts-of-anopheles-mosquitoes-malaria-vectors-in-southeast-asia",signatures:"Sylvie Manguin, Chung Thuy Ngo, Krajana Tainchum, Waraporn\nJuntarajumnong, Theeraphap Chareonviriyaphap, Anne-Laure\nMichon and Estelle Jumas-Bilak",authors:[{id:"50017",title:"Prof.",name:"Sylvie",middleName:null,surname:"Manguin",fullName:"Sylvie Manguin",slug:"sylvie-manguin"},{id:"75315",title:"Prof.",name:"Theeraphap",middleName:null,surname:"Chareonviriyaphap",fullName:"Theeraphap Chareonviriyaphap",slug:"theeraphap-chareonviriyaphap"},{id:"88985",title:"Prof.",name:"Anne-Laure",middleName:null,surname:"Michon",fullName:"Anne-Laure Michon",slug:"anne-laure-michon"},{id:"88986",title:"Prof.",name:"Estelle",middleName:null,surname:"Jumas-Bilak",fullName:"Estelle Jumas-Bilak",slug:"estelle-jumas-bilak"},{id:"156016",title:"MSc.",name:"Chung Thuy",middleName:null,surname:"Ngo",fullName:"Chung Thuy Ngo",slug:"chung-thuy-ngo"},{id:"156018",title:"MSc.",name:"Krajana",middleName:null,surname:"Tainchum",fullName:"Krajana Tainchum",slug:"krajana-tainchum"},{id:"156019",title:"Dr.",name:"Waraporn",middleName:null,surname:"Juntarajumnong",fullName:"Waraporn Juntarajumnong",slug:"waraporn-juntarajumnong"}]},{id:"43899",title:"Distribution, Mechanisms, Impact and Management of Insecticide Resistance in Malaria Vectors: A Pragmatic Review",slug:"distribution-mechanisms-impact-and-management-of-insecticide-resistance-in-malaria-vectors-a-pragmat",signatures:"Vincent Corbel and Raphael N’Guessan",authors:[{id:"152666",title:"Dr.",name:"Vincent",middleName:null,surname:"Corbel",fullName:"Vincent Corbel",slug:"vincent-corbel"},{id:"169017",title:"Dr.",name:"Raphael",middleName:null,surname:"N'Guessan",fullName:"Raphael N'Guessan",slug:"raphael-n'guessan"}]},{id:"43851",title:"Perspectives on Barriers to Control of Anopheles Mosquitoes and Malaria",slug:"perspectives-on-barriers-to-control-of-anopheles-mosquitoes-and-malaria",signatures:"Donald R. Roberts, Richard Tren and Kimberly Hess",authors:[{id:"151439",title:"Prof.",name:"Donald",middleName:null,surname:"R. Roberts",fullName:"Donald R. Roberts",slug:"donald-r.-roberts"},{id:"151656",title:"Mr.",name:"Richard",middleName:null,surname:"Tren",fullName:"Richard Tren",slug:"richard-tren"},{id:"154152",title:"Ms.",name:"Kimberly",middleName:null,surname:"Hess",fullName:"Kimberly Hess",slug:"kimberly-hess"}]},{id:"43874",title:"Residual Transmission of Malaria: An Old Issue for New Approaches",slug:"residual-transmission-of-malaria-an-old-issue-for-new-approaches",signatures:"Lies Durnez and Marc Coosemans",authors:[{id:"152754",title:"Prof.",name:"Marc",middleName:null,surname:"Coosemans",fullName:"Marc Coosemans",slug:"marc-coosemans"},{id:"169018",title:"Dr.",name:"Lies",middleName:null,surname:"Durnez",fullName:"Lies Durnez",slug:"lies-durnez"}]},{id:"44330",title:"Vector Control: Some New Paradigms and Approaches",slug:"vector-control-some-new-paradigms-and-approaches",signatures:"Claire Duchet, Richard Allan and Pierre Carnevale",authors:[{id:"151662",title:"Dr.",name:"Pierre",middleName:null,surname:"Carnevale",fullName:"Pierre Carnevale",slug:"pierre-carnevale"},{id:"169000",title:"Dr.",name:"Richard",middleName:null,surname:"Allan",fullName:"Richard Allan",slug:"richard-allan"},{id:"169008",title:"Dr.",name:"Claire",middleName:null,surname:"Duchet",fullName:"Claire Duchet",slug:"claire-duchet"}]},{id:"43870",title:"New Salivary Biomarkers of Human Exposure to Malaria Vector Bites",slug:"new-salivary-biomarkers-of-human-exposure-to-malaria-vector-bites",signatures:"Papa M. Drame, Anne Poinsignon, Alexandra Marie, Herbert\nNoukpo, Souleymane Doucoure, Sylvie Cornelie and Franck\nRemoue",authors:[{id:"151515",title:"Dr.",name:"Papa Makhtar",middleName:null,surname:"Drame",fullName:"Papa Makhtar Drame",slug:"papa-makhtar-drame"},{id:"151648",title:"Dr.",name:"Franck",middleName:null,surname:"Remoué",fullName:"Franck Remoué",slug:"franck-remoue"},{id:"154034",title:"Dr.",name:"Anne",middleName:null,surname:"Poinsignon",fullName:"Anne Poinsignon",slug:"anne-poinsignon"},{id:"154035",title:"MSc.",name:"Alexandra",middleName:null,surname:"Marie",fullName:"Alexandra Marie",slug:"alexandra-marie"},{id:"154037",title:"Dr.",name:"Souleymane",middleName:null,surname:"Doucoure",fullName:"Souleymane Doucoure",slug:"souleymane-doucoure"},{id:"154038",title:"MSc.",name:"Herbert",middleName:null,surname:"Noukpo",fullName:"Herbert Noukpo",slug:"herbert-noukpo"},{id:"154039",title:"Dr.",name:"Sylvie",middleName:null,surname:"Cornélie",fullName:"Sylvie Cornélie",slug:"sylvie-cornelie"}]},{id:"44149",title:"Transgenic Mosquitoes for Malaria Control: From the Bench to the Public Opinion Survey",slug:"transgenic-mosquitoes-for-malaria-control-from-the-bench-to-the-public-opinion-survey",signatures:"Christophe Boëte and Uli Beisel",authors:[{id:"98400",title:"Dr.",name:"Christophe",middleName:null,surname:"Boëte",fullName:"Christophe Boëte",slug:"christophe-boete"},{id:"167749",title:"Dr.",name:"Uli",middleName:null,surname:"Beisel",fullName:"Uli Beisel",slug:"uli-beisel"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"70287",title:"A New Approach for Model Developing to Estimate Unmeasured Parameters in an Engine Lifetime Monitoring System",doi:"10.5772/intechopen.90307",slug:"a-new-approach-for-model-developing-to-estimate-unmeasured-parameters-in-an-engine-lifetime-monitori",body:'\nLifetime monitoring systems are an effective way to perform condition base maintenance of gas turbine engines [1, 2, 3]; this allows a better use of the available lifetime and improvement of the engine’s reliability.
\nSeveral approaches exist to predict the remaining lifetime, such as neural networks [4, 5, 6, 7], finite element analysis (FEA) [8, 9, 10], and statistical methods [11]; however, in order to significantly enhance the accuracy of the lifetime prediction, it is necessary to estimate the lifetime in real time (on-line prediction) using actual conditions [12, 13]. All of the previously cited approaches require a large amount of computing resources, making them not suitable for an on-line application; another limitation is that none of the cited approaches take into consideration the existing engine-to-engine differences and the performance deterioration.
\nOleynik proposes in a study [14] an approach to perform on-line lifetime prediction of engine component condition (Figure 1); he proposes to use simple models to estimate the temperature and stresses at critical points. A major advantage of this approach is the use of actual engine operating and atmospheric conditions as input data. The methodology has been proven by practical application in monitoring of some Ukrainian engines.
\nScheme for on-line lifetime prediction.
As shown in Figure 1, one of the blocks performs the thermal condition (TC) monitoring, while the second block, the stress condition (SC) monitoring.
\nInside the block of TC, it is necessary to set the thermal boundary conditions (gas temperature around the critical element and the heat transfer coefficient between the gas and metal), which are not measured parameters; the author [14] proposed a methodology to develop mathematical models based on the theory of similarity to estimate these boundary conditions.
\nIn this chapter a new approach to develop physics-based models to estimate the unmeasured parameters is proposed and analyzed. This new approach emphasizes the accuracy of the models regardless of the engine-to-engine differences, taking into consideration a healthy and faulty engine condition.
\nWith the help of the thermodynamic model of the engine chosen as test case, all the necessary data for model developing and validation is simulated; the simulation of the engine’s component degradation is widely used in gas turbine monitoring and diagnostics [15, 16].
\nA comparison between the physics-based models and the reference method based on the theory of similarity proposed by [14] is conducted to validate the accuracy of the methods.
\nFinally, the influence of the accuracy in the prediction of the thermal boundary conditions on the errors of the engine lifetime prediction is evaluated.
\nIt is well-known that the thermomechanical stresses in gas turbine hot elements are very high, particularly in the turbine blade having a significant effect on the safety and economics of the fleet operation [17]. For this reason, a turbine blade with three cooling channels has been chosen as the test case; the blade is mounted in the first stage of the high-pressure turbine (HPT) of a two-spool free turbine engine.
\nIn Table 1 the seven measured gas path parameters of the engine chosen as test case are listed.
\nDesignation | \nGas path parameter | \n
---|---|
\n\n | \nFuel consumption | \n
\n\n | \nCompressor discharge temperature | \n
\n\n | \nCompressor discharge pressure | \n
\n\n | \nHPT discharge temperature | \n
\n\n | \nHPT discharge pressure | \n
\n\n | \nLow-pressure turbine (LPT) discharge temperature | \n
\n\n | \nRotational speed of the high-pressure (HP) rotor | \n
List of gas path measured parameters of the engine selected as test case.
Experience has shown that it is sufficient to consider a two-dimensional analysis of the mid-span section of the blade in order to save computing time; however, the same methodological approach can be applied for a three-dimensional geometry.
\nThe finite element model of the mid-span turbine blade section was built with the help of FEA software. After setting all the necessary boundary conditions, the distribution of the temperature and stresses was obtained. The critical points with the smallest safety factor were found as well; as shown in Figure 2, the critical points correspond to the numbers 101, 102, 103, and 69.
\nCritical points at the turbine blade mid-span section.
Three critical points are located at the leading edge of the blade and one critical point at the trailing edge. For an easier analysis, the four critical points are organized into two groups: group a (GA) contains the critical points 101, 102, and 103, and group b (GB) contains the critical point number 69.
\nThe thermodynamic model of the engine chosen as test case [18] is used to generate all the data for model developing and validation.
\nA brief description of the lifetime monitoring system proposed by the author [14] is presented to have a better understanding. As shown in Figure 1, the block to perform the TC contains the sub-block named “thermal boundary conditions” (unmeasured parameters). The new approach for model developing proposed in this chapter focuses all the efforts in improving the accuracy in this sub-block, as improving the efficiency in the prediction of the thermal boundary conditions directly affects the accuracy of the whole monitoring system.
\nIn the following subsection, the simple mathematical models used to estimate the blade temperature and the thermal stress at the critical points are explained.
\nIn [19] an analysis of the models proposed by [14] to estimate the blade temperature and stress applied to the same turbine blade and critical points was conducted. As a result, it was concluded that the best model to calculate the blade temperature at the critical points is:
\nHere \n
Here \n
The model to estimate the thermal stress at critical points is:
\nHere \n
The dimensionless parameters \n
The parameters \n
As mentioned in the introduction, a new approach for model developing is proposed. Since the models will be used in an on-line monitoring system, it is necessary to meet the following requirements:
The models must be developed on physics-based relations, such as thermodynamic and kinematic relations and others.
All models must use the gas path measured parameters as input data.
The structure of the models must be simple.
The measuring error of the gas path parameters, which are the input data of the models, must be taken into account.
The models must have high robustness to the influence of engine’s component deterioration.
Taking into account the main requirements, the following general dependence for any unmeasured parameter is proposed:
\nHere \n
As shown in Eq. (4), such dependence is not possible to be used in an on-line monitoring system since it includes the vector \n
Besides, all the parameters are corrected to standard atmosphere to take into account the influence of atmospheric conditions [20]. After rewriting Eq. (4), the general dependence for any unmeasured parameter is:
\n\nFigure 3 shows the algorithm to estimate the unmeasured parameters using the previously presented model developing methodology.
\nAlgorithm to estimate the unmeasured parameters.
The best models are selected during the model verification process. The total mean square error (MSE) is the main criteria to select the best models; the MSE consists of two components, a truncation error and an instrumental error:
\nHere \n
The mean square truncation error is:
\nHere \n
The average truncation error in percentage for any engine health conditions is obtained by:
\nHere n is the number of engine health conditions.
\nThe MSE for the instrumental error for a healthy engine condition is calculated as follows:
\nHere \n
The average instrumental error in percentage is obtained by:
\nHere N is the sample size—the number of engine operating points corresponding to a healthy engine condition.
\nEngine health conditions in real life are different from engine to engine; therefore, it is necessary to take into account these shifts from the ideal engine. For the model robustness analysis, the truncation error is calculated for several engine health conditions. In [21] the most common engine faulty conditions of a two-spool free turbine engine were analyzed; as a result, 10 faulty engine conditions were selected.
\nIn Table 2 the 11 engine conditions considered for analysis are listed. The deteriorated engine condition represents a 3% shift from engine health condition.
\nDesignation | \nFault parameter | \nDeteriorated condition | \n
---|---|---|
C1 | \n— | \nHealthy engine | \n
C2 | \n\n\n | \nCompressor efficiency decrease | \n
C3 | \n\n\n | \nCompressor airflow decrease | \n
C4 | \n\n\n | \nCombustion chamber (CC) efficiency decrease | \n
C5 | \n\n\n | \nDecrease in the CC total pressure | \n
C6 | \n\n\n | \nHPT efficiency decrease | \n
C7 | \n\n\n | \nHPT nozzle box (NB) area increment | \n
C8 | \n\n\n | \nDecrease in the total pressure between HPT and LPT duct | \n
C9 | \n\n\n | \nLPT efficiency decrease | \n
C10 | \n\n\n | \nLPT NB area increment | \n
C11 | \n\n\n | \nIncrement of the air bleed for gas pumping needs | \n
Engine healthy and faulty condition considered for analysis.
As shown in SubSection 3.1, it is necessary to calculate the input data for Eqs. (1) and (3). For our particular test case, the selected thermal boundary conditions are shown in Table 3.
\nCooling temperature | \n\n\n | \n
Heating temperature | \n\n\n | \n
Relation of heat transfer coefficients for hot gases | \n\n\n | \n
Relation of heat transfer coefficients for cooling air | \n\n\n | \n
Thermal boundary conditions for our test case.
Here \n
It is necessary to develop alternative models for each one of the selected thermal boundary conditions. Although the compressor discharge temperature is a measured gas path parameter for our test case (Table 1), it is of particular interest to analyze the effect of its inclusion or exclusion from the list of gas path measured parameters in the overall lifetime prediction.
\nSince many alternative models were developed, only one example will be shown in order to save available text space; for more details consult [21].
\nLet us consider the gas temperature at the inlet of the turbine \n
Here \n
Let us take into account that:
\nHere \n
Solving Eq. (11) for \n
All the unmeasured parameters in Eq. (14) will be described with the help of the internal model \n
Let us remember that all the internal models will be calculated as a polynomial functions using one of the available gas path measured parameters as argument.
\nFinally, after making the correction to standard atmospheric conditions of Eq. (14), we arrive at the following expression:
\nHere \n
Several models can be developed for the same unmeasured parameter based on different source equations (alternative models). Figure 4 shows the general scheme for the developing of alternative models.
\nScheme for the developing the alternative models.
Using the scheme shown in Figure 4, a total of 31 models were developed for our test case (see reference [21]). A name is given to each developed model for easier identification, for example, the model shown in Eq. (16) is named MTG1. The names and arguments for each alternative developed model are shown in Figure 5.
\nStructure of the alternative models developed for our test case.
Let us consider the model MTG1 shown in Eq. (16), which includes the internal model \n
All of the necessary data for the analysis was obtained using the thermodynamic model of the engine selected as test case [18]. A total of 245 engine operating modes for a healthy engine condition were simulated; these operating modes describe the whole range of the engine operating conditions.
\nThe generated data was randomly divided into two sets. The first set of 123 operating points is used as reference. The second set of 122 operation modes is for model validation. Using the data from the reference set, the coefficients for the polynomial functions were obtained using the least square method.
\nThe polynomial degree was changed from 1 to 4 using each one of the gas path measured parameters (see Table 1) as argument in the polynomial.
\nOnce all the polynomial coefficients describing the internal model \n
The total error (see Eq. (6)) was the main criteria to assess the accuracy of the developed models. A total of 11 engine conditions (Table 2) were considered for the model validation (model robustness analysis).
\n\nFigure 6(a) depicts the total error in the prediction of \n
Total error in the prediction of \n\n\nT\ng\n∗\n\n\n using model MTG1. (a) Using seven different measured parameters as argument; (b) detailed view for the best argument.
\nFigure 6(b) shows that it is sufficient to use a third-degree polynomial as further increment does not reduce the total error in the prediction.
\nFrom this analysis the polynomial degree and the gas path measured parameter to be used as argument in Eq. (17) are selected:
\nThe selection of the argument in the i-internal models and the best polynomial degree for all the developed models was done using the same methodology. After the model verification of all the developed models, the best models were selected. Figure 7 shows the selected models to calculate the thermal boundary conditions for the test case.
\nSelected models to monitor the thermal boundary conditions of the test case.
Let us conduct a comparative analysis between two approaches for model developing: the first approach for model developing [14] uses the theory of similarity (reference model), and the second approach is proposed in this chapter and uses a physics-based methodology.
\nThe thermal boundary conditions for our test case (see Table 3) were calculated using models developed with both methodologies.
\nThe total error was calculated according to Eq. (6), and the model robustness analysis took into account the 11 engine health conditions listed in Table 2. It is of particular interest to analyze the model robustness, since such analysis for the reference methodology does not exist.
\nIn Figure 8 the truncation errors for the thermal boundary condition prediction are presented.
\nTruncation error in the prediction of thermal boundary conditions for different engine health conditions. Blue color, physics-based models; red color, models developed on theory of similarity. (a) \n\n\nT\nW\n∗\n\n\n; (b) \n\n\nT\nC\n∗\n\n\n; (c) \n\n\nk\n\nα\n\ng\n\n\n\n; (d) \n\n\nk\n\nα\n\na\n\n\n\n.
From Figure 8, it is clear that the models developed using the approach introduced in this chapter are more robust; it means that the models are less sensitive to the deviations from a healthy engine condition. This is a major advantage compared to the reference methodology based in the theory of similarity [14].
\nThe thermal-stress engine condition was calculated using Eqs. (1) and (2). The prediction of the turbine blade lifetime is a very complex process, which involves different factors; however, a conservative lifetime prediction will be enough to assess the impact that a new model developing methodology has on the accuracy of the lifetime prediction. According to the author [22], a practical way to predict lifetime is the Larson-Miller relation:
\nHere PLM is the Larson-Muller parameter; C is a coefficient, which for the test case is equal to 20.
\nAs mentioned in Section 5, it is of particular interest to analyze what is the influence of the inclusion or exclusion of the compressor temperature \n
\nFigure 9 presents the total error in the prediction of TC, SC, and lifetime tr\n. From Figure 9(a) it is clear that the physics-based models give a better prediction of TC. Figure 9(c) shows that the improvement in the prediction of SC is not as significant, especially for the critical points GB. Figure 9(e) shows that the prediction of the lifetime tr\n is highly improved compared to the results obtained when the models based on the theory of similarity are used to calculate the thermal boundary conditions.
\nTotal error in the prediction of TC, SC, and tr. Blue color, physics-based models; red color, models developed on the theory of similarity. (a, c, e) \n\n\nT\nC\n∗\n\n\n is an unmeasured parameter; (b, d, f) \n\n\nT\nC\n∗\n\n\n is a measured parameter.
From this analysis, it is clear that the methodology used for developing the models of the unmeasured parameters has a great impact in the final accuracy of the lifetime tr\n prediction.
\nWe repeated the calculation, but this time the value of the compressor temperature is measured. Figure 9(b) shows that the total error in the prediction of TC for both groups is still better when using physics-based models.
\n\nFigure 9(d) shows that the accuracy in the prediction of the SC is not significantly affected. From Figure 9(f) it is clear that the improvement in the prediction of TC has a significant impact in the prediction of the lifetime tr\n, for example, for the critical point GA when using physics-based models, an improvement in the prediction of TC from 0.58 to 0.44% leads to a better lifetime prediction from 45.95 to 27.96%.
\nWe can conclude that the accuracy in the prediction of the lifetime is highly improved when the temperature after the compressor is a measured parameter.
\nA new approach for model developing to estimate the unmeasured parameters in an engine lifetime monitoring system was introduced. This is an effort to increase the accuracy of the lifetime prediction.
\nAll the developed models have a very simple structure and are physics-based, making them ideal to be applied in an on-line lifetime monitoring system.
\nA turbine blade mounted on the first stage of the high-pressure turbine of a two-spool free turbine power plant is the test case.
\nSeveral alternative models were developed using different basic equations. Some of the models include in their structure an internal model, which characterizes the thermodynamic properties of the working fluid, such as efficiencies, pressure loss factors, and others. The internal models were defined by a polynomial function. The best measured parameter used as argument in the polynomial and the degree of the polynomial function were selected using the mean square error as criteria.
\nAll the necessary data for model developing and validation was generated with the engine thermodynamic model.
\nThe truncation and instrumental error are the main criteria to select the best models. Ten engine faulty conditions were considered for the robustness analysis of the models.
\nA comparative analysis between two model developing methodologies was conducted: physics-based methodology (proposed in this chapter) and models developed on the theory of similarity (reference). The results show that the physics-based models are less sensitive to shifts from the engine healthy condition.
\nIt was found that the use of the proposed model developing methodology provides a better estimation of the thermal boundary conditions, which leads to a significantly better prediction of the lifetime.
\nIt was proven that the compressor temperature has a great impact in the lifetime prediction. If this parameter is not measured, then the accuracy of the lifetime prediction is significantly worse compared to the results obtained when the compressor temperature is measured.
\nThe obtained results show that it is possible to use the proposed model developing methodology in real applications; however, it is necessary to take into account a proper interpretation of the results obtained in this chapter. The reference data, which was used to determine the accuracy of the models, is simulated data; therefore, it is possible that the errors of the lifetime monitoring under real conditions will grow. To avoid such inconvenience, it is possible to replace the data generated with the help of the engine thermodynamic model with real data. This approach is valid, since the engine thermodynamic model is not part of the proposed model developing methodology. In order to obtain the necessary real data, it will be necessary to use additional instrumentation under engine test bed conditions.
\nSubscripts | |
\na\n | air |
\ncor\n | corrected parameter |
\ncr\n | critical point |
\nC\n | compressor |
\nCC\n | combustion chamber |
\nCH\n | channel |
\nf\n | fuel |
\ng\n | gas |
\nH\n | atmospheric conditions |
\nHP\n | high pressure |
\nHPT\n | high-pressure turbine |
\ni\n | i-engine mode |
\nINS\n | instrumental error |
\nj\n | j-engine health condition |
\nLPT\n | low-pressure turbine |
\nm\n | value calculated with the help of models, mechanical |
\nNB\n | nozzle box |
\nref\n | reference engine mode |
\nST\n | gas pumping station |
\nS1\n | cooling |
\nS2\n | heating |
\nt\n | thermal |
\nT\n | turbine |
\nTR\n | truncation error |
\nTT\n | total mean square error |
\nW\n | relative velocity |
Designations | |
G | consumption |
T | temperature |
p | pressure |
n | rotational speed, number of engine health conditions |
t | blade temperature |
k | coefficient, isentropic factor |
\n\n\n\nS\n¯\n\n\n\n | dimensionless parameter |
z | unmeasured parameter |
Y | gas path measured parameters |
W | unmeasured parameters describing thermodynamic properties of the working fluid |
A | internal model |
x | measured parameter, argument of polynomial |
\n\n\n\np\n0\n\n\n\n | standard atmospheric pressure (101.3 KPa) |
\n\n\n\nT\n0\n\n\n\n | standard atmospheric temperature (288.15 K) |
y | measured parameter |
N | sample size (number of engine operation modes), power |
C | engine condition, coefficient |
L | thermodynamic work |
Cp\n | specific heat at constant pressure |
A | coefficient |
Re | Reynolds number |
Kα\n | relation of heat transfer coefficient at current and at a reference operation mode |
tr\n | lifetime |
Greek symbols | |
* | stagnation parameter |
\nα\n | heat transfer coefficient |
\n\n\nΘ\n\n\n | dimensionless parameter |
σ | stress, mean square error, total pressure conservation |
\nη\n | efficiency |
δ | shift from healthy engine condition |
\nμ\n | dynamic viscosity |
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\n\nOver the years we have learned what is important. What makes a difference to the researchers that work with us, what they value. Something that is very high not only on their lists, but our own, is the quality of the published content.
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After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. 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