Online Prediction of Temperature and Stress in Steam Turbine Components Using Neural Networks

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1 Krzysztof Dominiczak 1 ALSTOM Power Ltd., ul. Stoczniowa 2, Elblag , Poland krzysztof.dominiczak@power.alstom.com Romuald Rządkowski Institute of Fluid Flow Machinery of PASc, ul. Fiszera 14, Gdansk , Poland z3@imp.gda.pl Wojciech Radulski ALSTOM Power Ltd., ul. Stoczniowa 2, Elblag , Poland wojciech.radulski@power.alstom.com Ryszard Szczepanik Air Force Institute of Technology, ul. KsieR cia Bolesława 6, P.O. Box 96, Warszawa , Poland ryszard.szczepanik@itwl.pl Online Prediction of Temperature and Stress in Steam Turbine Components Using Neural Networks Considered here are nonlinear autoregressive neural networks (NETs) with exogenous inputs (NARX) as a mathematical model of a steam turbine rotor used for the online prediction of turbine temperature and stress. In this paper, the online prediction is presented on the basis of one critical location in a high-pressure (HP) steam turbine rotor. In order to obtain NETs that will correspond to the temperature and stress the critical rotor location, a finite element (FE) rotor model was built. NETs trained using the FE rotor model not only have FEM accuracy but also include all nonlinearities considered in an FE model. Simultaneous NETs are algorithms which can be implemented in turbine controllers. This allows for the application of the NETs to control steam turbine stress in industrial power plants. [DOI: / ] Introduction The quality of online stress control is vital for steam turbine operation flexibility. Operation flexibility has been the subject in recent steam turbine research and development. Flexibility reduces steam turbine startup time and enables fast loading and unloading. There is a growing market for renewable energy sources. However, renewable energy is often unpredictable and causes grid fluctuation. This requires flexibility in conventional units. Thermal stress in thick-walled steam turbine elements limits the operation flexibility. The rotor is the most important thick-walled element in a steam turbine both in terms of operation and safety. Therefore, the rotor is usually controlled and protected by an online stress control. The purpose of online stress control is to assess the actual stress level in the steam turbine and protect it from high thermal stress by monitoring steam temperature and flow through the turbine. Stress-controlled steam turbine startup is not only faster but it also extends turbine lifetime due to low thermal-induced cycle fatigue. Thermal stress control in steam turbines has been presented by Busse [1], Dawson [2], Pahl et al. [3], and Sindelar [4]. All of these stress control systems used thermophysical startup probes, which were physical models of steam turbine rotors. A thermophysical startup probe measures two temperatures: that of the steam turbine rotor surface and the mean rotor temperature. More accurate stress control can be achieved by using mathematical models of steam turbine components. Lausterer [5], Lausterer et al. [6], and Marinescu and Ehrsam [7] have presented systems in which the mean temperatures of particular turbine components were calculated using a mathematical model and a startup probe. Sindelar et al. [8] described a system which assesses stress in a critical turbine component by using only standard power plant measurements. Rusin et al. [9] presented a steam turbine stress control system based on Duhamel s integral. 1 Corresponding author. Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 5, 2015; final manuscript received September 6, 2015; published online November 11, Editor: David Wisler. This paper for the first time presents a steam turbine stress prediction based on an NET. The NETs have already been used in power system diagnostics, e.g., by Głuch et al. [10,11] for diagnostics of power object geometry deterioration. The NETs also have already been used by Kosowski et al. [12] for investigations of steam turbine cascades. Rusin et al. [13] used the NETs for stress modeling in a steam turbine inner casing. However, the NETs have never before been used for temperature and stress modeling in a steam turbine rotor. The NETs presented in this paper are able to simulate and predict online the temperature and stress of a critical turbine rotor based only on standard power plant measurements, such as speed, power, steam temperature, and pressure in front of turbine control valves. NARX NETs NARX NET is a recurrent dynamic network, with feedback connections enclosing layers of the network (Fig. 1). The NARX NETs are commonly used to monitor the nonlinear process where the nonlinearity is unknown. In addition to its simplicity, this is a major NARX NET advantage. The defining equation for the NARX model is y t ¼ Fðy t 1 ; y t 2 ; y t 3 ; ; u t ; u t 1 ; u t 2 ; u t 3 ; Þ where y t is the predicted value of the dependent output signal based on previous output signal values y t 1, y t 2, and previous independent (exogenous) input signal values u t, u t 1, u t 2 (Fig. 1). NET Modeling for Stress and Temperature This paper presents the NARX NET stress control using the example of a 18K390 HP steam turbine rotor (Fig. 2). The 18K390 condensing turbine has a reaction-type blading (RTB) reheated in the turbine with seven feedwater preheaters, designed to run a synchronous GHTW-400 generator. The nominal live steam parameters are 182 bar(a)/557 C, whereas nominal reheat steam parameters are 42 bar(a)/568 C. The HP rotor is a RTB drum design rotor with 24 blade rows. The HP rotor was welded with two forgings. In the inlet hot region, high-alloy steel Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 / Copyright VC 2016 by ASME

2 Fig. 1 NARX NET Fig. 2 HP cross section of 18K390 steam turbine (10%CrMoVNbN) was used, whereas in the exhaust cold region, low-alloy steel (1%CrMoV) was used. The HP rotor is 5625 mm long and the assembled blade rows weigh approximately 10.5 tons. The rotor diameter at the steam inlet is /653 mm, whereas at the steam path exhaust it is /686 mm. The NARX NET thermal stress control does not focus on the entire HP rotor but only on its critical thermal stress point. In order to identify this point, a rotor lifetime assessment was performed. This showed that there is only one critical point in the region of the first HP rotor groove. During a steam turbine lifetime, two periods can be distinguished: load cycles and standstill periods. During the turbine startups and shutdowns (SD), which are a part of turbine load cycle, transient temperature fields are induced due to heat exchange between the turbine elements and expanding steam. These transient temperature fields cause thermal stress, which is responsible for turbine low cycle fatigue (LCF). During continuous turbine operation, which is also the part of turbine load cycle, steady-state temperature fields are observed. The steady-state temperature fields are responsible for reducing turbine life due to the creep phenomenon. An NET-based online stress control can Fig. 3 NARX NET-based steam turbine thermal stress control / Vol. 138, MAY 2016 Transactions of the ASME

3 Fig. 4 MATLAB implementation of NARX NET responsible assessment of critical point stress: (a) parallel architecture and (b) series parallel architecture assess in real-time stress and temperature in the critical location during turbine load cycles. During steam turbine standstill, the rotor temperature is equalized and the rotor is cooled down. In comparison with the stress level which occurs during the turbine load cycle, the stress during turbine cool down is negligible. Nevertheless, temperature in the critical location must be assessed during the standstill period with sufficient accuracy. The accurate prediction of temperature is necessary to recognize initial state of the rotor before turbine startup. A stress control system based on an NARX NET does not require any additional instrumentation, such as a startup probe. Only common measurements, available in every power plant, are used by the system. However, different sets of measurements in the turbine are used in the control system for each period of the steam turbine lifetime. Steam temperature, steam pressure, turbine speed, and load are used for load cycle. All of these physical quantities, which characterize steam parameters as well as heat exchange inside the turbine, are sufficient to describe rotor boundary conditions during turbine load cycles. Therefore, these measurements were chosen as exogenous inputs to NETs which represent temperature and stress in rotor critical location. However in case of NET for stress representation, these measurements are not sufficient. During two identical startups from aforementioned measurements perspective, stresses can differ depending on the initial temperature in critical location. Therefore, the critical location temperature, assessed by the responsible NET, is an exogenous input for the NET responsible for the assessment of stress in the rotor critical location. During the standstill period, temperature in the rotor critical location can be assess based on the current rotor thermal and mechanical growth, which are calculated in a considered case based on the HP differential expansion (DE), HP and IP (intermediate pressure) absolute expansion (AE), and the thrust bearing float. Figure 3 shows a diagram of the NARX NET thermal stress control system. The control system consists of three NARX Fig. 5 NETs structure optimization results: (a) temperature and (b) stress Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /

4 Fig. 6 Temperature before HP steam path during turbine warm start II Fig. 7 Heat transfer coefficient for rotor surface after first HP stationary blades row for various local steam temperatures, local steam pressures at nominal steam flow and nominal rotational speed NETs. The first of these assesses the critical point temperature during turbine standstill on the basis of the rotor s axial expansion, which is obtained from AE, DE, and axial bearing thrust (BT). This temperature is used as an initial temperature for the second NARX NET, which assesses the critical point temperature on the basis of turbine speed (n), turbine load (N), steam temperature (T), and pressure (p) before the turbine control valve during turbine startup. Assuming that rotor is stress free at the beginning of turbine startup, the data concerning the critical point temperature, turbine speed, turbine load, steam temperature, and pressure before the turbine control valve allow the third NARX network to assess critical point stress. Figure 4 presents a practical implementation of the NARX NET stress assessment in MATLAB. There are two architectures: parallel and series parallel. The parallel architecture is used for normal NET work. During NET training, the network outputs are known. Therefore, feedback is uncoupled and true output is used instead of being estimated. This leads to more effective NET training, because the inputs to the network are more accurate. The series parallel architecture also allows for the use of a static backpropagation training algorithm. Stresses in the considered HP rotor have been investigated during different turbine transient states. This investigation shows that the high scatter of stress transient variations depends on the initial thermal state of the HP turbine when transient temperature variations are small. Therefore for temperature modeling, a single NET was used, whereas for stress control, the NET required five specialized sets of weights and bias values for the following transient states: / Vol. 138, MAY 2016 Transactions of the ASME

5 Fig. 8 FE model of 18K390 turbine HP rotor: (a) whole model, (b) steam inlet view, and (c) first and second blade grooves Fig. 9 HP rotor axial expansion during CS: calculations and measurements Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /

6 cold starts (CS) warm starts I warm starts II hot starts (HS) restarts (RES), SD, and load rejections (LR) A proper set of NET weights and bias values was selected, based on the initial critical temperature location. The NETs for stress control are designed to work online; therefore, their structures must be optimized. Figure 5 shows optimization results for networks responsible for determining temperature and stress in the HP rotor critical location during turbine load cycles. Networks performance was assessed based on the sum of mean squared errors (MSE) for a set of real turbine operating data, which was not part of training data set. The NETs with different numbers of neurons in the input layer were considered. The investigation showed that two neurons in input layer are sufficient for temperature networks (Fig. 5(a)) and five neurons in input layer for stress networks (Fig. 5(b)). The two time samples of input delays and feedback delays (FDs) are sufficient to model online rotor strength and temperature parameters during turbine load cycles. The same optimization process has been performed for NET responsible for assessment of temperature during the turbine standstill period. Also in this case, the NET with two neurons in hidden layer, two input and FDs, is sufficient to assess the rotor critical location temperature during the turbine standstill period. FEM-Based NET Training NET training is a process which allows selection of network weights and biases in order to reflect known output data based on corresponding inputs. Here, the NET training was performed using the Levenberg Marquardt algorithm, which was possible because of the series parallel architecture. However, for the NARX NET, the most important factor is the training data. Stresses are not measured on turbine rotors in industrial power plants. This is due to technical problems such as a high temperature and rotor rotational speed, and also turbine rotor critical location inaccessibility. Therefore, indirect methods of turbine online stress monitoring are used. In this investigation, the NET training data were prepared using an FE model. The quality of the stress and temperature NET models can only be as good as that of the FE model used for NET training. FE analyses were also used to assess the NETs performance for a real turbine operating data testing set, which were not a part of the training data set. In order to perform FE analyses, boundary conditions, e.g., transient steam parameter distributions inside the turbine as well as heat transfer characteristics, must be known. The steam parameters were derived from a thermodynamic turbine model, whereas the boundary condition was derived from a heat transfer model. The thermodynamic model is met to derive actual steam flow through the turbine as well as steam parameters inside the turbine based on actual steam parameters before control valves, actual turbine speed, actual turbine load, and turbine backpressure (in the considered case, the backpressure is equal to pressure in cold reheat). The thermodynamic model performance was checked based on the measurements installed in the vicinity of the HP part. The steam flow through the turbine was verified based on the steam flow measurement installed on the live steam pipeline. As far as steam parameters inside the HP turbine are concerned, they were verified at two points: at the inlet to HP steam path and at the steam path exhaust. There are temperature and pressure measurements at the steam path inlet. In case of steam path exhaust, there is temperature measurement located in the HP turbine outer casing. Pressure at the HP exhaust is measured at pipelines before HP safety valves. Steam flow through the turbine for near design conditions has been calculated based on Stodola s law, with appropriate correction for lower flows. Based on the heat balance diagrams for different turbine states, the HP steam path characteristic was recognized. This characteristic was used for thermodynamic model of the HP turbine part. However, adiabatic model has been assumed for purposes of modeling. Possibility of performing calculation in sequence is more beneficial than better accuracy of thermodynamic. The influence of adiabatic model on turbine LCF lifetime consumption was checked for few real load cycles. For each considered load cycles, the LCF lifetime consumption was assessed using the thermodynamic model and site measurements. Errors of lifetime consumption made due to adiabatic thermodynamic model strongly depend on initial rotor temperatures. Nevertheless, these errors can be corrected by considering it during permissible stress evaluation. Figure 6 shows comparison between calculated and measured steam temperature before HP steam path during turbine warm start II. In order to create a heat exchange model, the HP rotor was divided into heat exchange regions described by appropriate Nusselt correlations. Heat transfer through the blade grooves was omitted since it is insignificant in comparison with convective heat transfer from steam. For example, Fig. 7 shows the heat transfer coefficient on the rotor surface after the first stationary radial stage. FE modeling of a steam turbine rotor used for NETs training and verification consists of two analyses: Thermal, in which the transient temperature field in the turbine rotor is calculated on the basis of heat transfer between steam flowing through the turbine and the turbine components. Structural, in which the stress distribution is derived from the transient temperature analysis. The FE rotor model, as shown in Fig. 8, has been prepared using ABAQUS. The FE rotor model is an axisymmetric model comprising approximately 9000 elements and 31,000 nodes. Eight-node bilinear temperature elements were applied for the temperature analyses and eight-node biquadratic displacement stress elements were applied for the structural analyses. The only experimental possibility to verify the assumed heat exchange and FE models was through expansion of the rotor (thermal and mechanical rotor growth). The rotor expansion can be obtain from the FE model, whereas for real data can be calculated based on HP DE, HP and IP AE, and the thrust bearing float, and based on steam turbine fixed points arrangement. For the considered example, turbine absolute fix point is located in bearing pedestal at IP exhaust. This pedestal, IP outer casing, the bearing pedestal between HP and IP, and HP outer casing are assembled together. Due to the thermal growth pedestals, casings expand in one direction. Rotor relative fix point is located in thrust bearing, which is pushed by the IP outer casing. The HP rotor expands in the same direction as HP outer casing, whereas the IP rotor expands in opposite direction in comparison with IP outer casing. Figure 9 compares results of the FE analysis with axial expansion calculated from measurements during a CS of the turbine. The dotted lines show the expansion, taking into account measurement errors. The results obtained from the numerical calculations end experiments are very close. Fig. 10 NET performance based on real turbine operating data / Vol. 138, MAY 2016 Transactions of the ASME

7 Fig. 11 Result of NET tests for CS In order to build a training data set for NETs operating during turbine load cycles, 168 FE calculations for transient turbine rotor states were performed. These calculations cover all possible variations of every exogenous input. The variation range of each NET training data set was established on the basis of turbine operational history. For NET operating during turbine standstill, two FE calculations were performed in order to build the training data set for this NET. NET Testing Using Real Turbine Operating Data The HP rotor NET control system was verified using real turbine operating data. For NETs operating during turbine load cycles, this included each turbine startup category (cold, warm I, warm II, and hot), one sliding pressure SD, and one LR together with turbine reloading. As a measure of NET performance, the root mean squared error (RMSE) was used. Figure 10 presents the Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /

8 Fig. 12 Result of NET tests for LR and turbine reloading NET-determined temperature (T m ) and stress (Sig) in the HP rotor critical location. The maximal RMSE for the NET-determined temperature was 5.4 C and occurred during warm startup I (WS1) (Fig. 10). The other temperatures were: 5.4 C for LR together with turbine reloading (LR þ RES), 4.8 C for CS, 4.2 C for HS, 4.1 C for sliding pressure SD, and 2.1 C for warm startup II (WS2). The maximal RMSE for the NET-determined stress was 18.8 MPa and occurred during CS (Fig. 10). The other stress values were: 10.2 MPa (WS1), 11.3 MPa (WS2), 13.2 MPa (HS), 8 MPa (SD), and 6.4 MPa (LR þ RES). Figure 11 presents the NET-determined temperature (T m ) and stress (Sig), including relatively errors, in the HP rotor critical location during CS. The relative error in determining temperature / Vol. 138, MAY 2016 Transactions of the ASME

9 Fig. 13 Result of NET tests for standstill after turbine SD with steam cooling phase (T m ) is presented in Fig. 11(a). Hundred percent of the hits occur in the relative error interval ( 5, þ5%). The relative error in determining stress (Sig) during CS is presented in Fig. 11(b). Forty-four percent of the hits occur in the relative error interval (þ5, 5%), 32% in (þ5, þ15%) and 18% in ( 15, 5%). Figures 11(c) and 11(d) present the FE NET correlations for temperature stress, respectively. The dot line denotes the FE results and the solid line the NET results. Here, we see very good temperature correlation between the NET and FE analyses (i.e., the dot line coincides with the solid one). In the case of stress (Fig. 11(d)), there is a good correlation up to 420 MPa, above this value the NET results are slightly lower than those of the FE. Figures 11(e) and 11(f) show good FE NET correlation for CS. Higher error values were observed in NET-determined stress (Fig. 11(g)). This was because while temperature was determined only on the basis of exogenous inputs and feedback values, stress was not only based on exogenous inputs and feedback values but also on temperatures determined by the other networks. Therefore, errors in the temperature network affected the stress network (Fig. 11(g)). Figure 12 presents NET determining temperature (T m ) and stress (Sig), with errors, in the HP rotor critical location for LR together with turbine reloading. The relative error of determined temperature (T m ) is presented in Fig. 12(a). Hundred percent of the hits were in relative error interval ( 5, þ5%), as in the case of CS (Fig. 11(a)). The relative error of determined stress (Sig) is presented in Fig. 12(b). Fifty-four percent of the hits were in the relative error interval ( 5%, þ5%). Therefore, the relative error for LR together with turbine reloading was lower than for CS (Fig. 11(b)), where a higher percentage of hits in the relative error interval ( 5%, þ5%). Figures 12(c) and 12(d) present the FE NET correlations for temperature and stress, respectively. Both correlations are very good (the red and blue lines coincide). Figures 12(e) and 12(f) show that NET results for LR together with turbine reloading were close to FE analysis. The relative error for temperature (Fig. 12(g)) is very small and for stress it is small (below 5%) in the area of large stress. By contrast, in CS at the stress maximum, the error is more than 10%. For NETs operating during turbine standstill, testing data set includes two turbine natural cooling: with and without steam cooling phase during turbine SD. As a measure of NET performance, also the RMSE was used. The RMSE for natural cooling without steam cooling phase was equal to 5.1 C, whereas the RMSE for natural cooling phase was equal to 5.3 C. Figure 13 presents the NET-determined temperature (T m ) in the HP rotor critical location during turbine standstill after SD with steam cooling phase. The relative error of determined temperature during standstill is presented in Fig. 13(a). Forty-nine percent of the hits were in relative error interval ( 5, þ5%). Figure 13(b) presents the FE NET correlations for temperature during standstill. Figure 13(c) shows that NET results for standstill were close to FE analysis. The relative error for temperature (Fig. 13(d)) is very small and for stress it is no larger than 10%. Prediction of Temperature and Stress at the Rotor Critical Location The quality of turbine stress control system is much more effective if it is able to predict temperature and stress in the critical location for several subsequent time steps. Based on the predicted Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /

10 Fig. 14 NET prediction performance based on real turbine operating data: (a) temperature and (b) stress Fig. 15 Temperature prediction in the 54th minute of warm start II Fig. 16 Stress prediction in the 54th minute of warm start II / Vol. 138, MAY 2016 Transactions of the ASME

11 Fig. 17 start II Temperature prediction in the 55th minute of warm Fig. 20 Stress prediction in the 61st minute of warm start II Fig. 18 Stress prediction in the 55th minute of warm start II Fig. 21 start II Temperature prediction in the 62nd minute of warm Fig. 19 start II Temperature prediction in the 61st minute of warm Fig. 22 Stress prediction in the 62nd minute of warm start II future stress value, stress control system protection could be much more effective. It is possible to predict the future values of the temperature and stress in the rotor critical location using the NARX NETs. With current values of temperature and stress from NETs, it is possible to make NETs appropriately alter the temperature and stress values before the next time step occurs by removing one delay from the exogenous inputs. The minimal tap delay for these NETs is 0 instead of 1, which determines the temperature and stress for the current time step. In this way, outputs for the predictive NETs are moved forward one time step ahead. From this position, the system can predict the next time-step temperature and stress values, and so on. This system can thus reasonably predict the temperature and stress values for about 5 min into the future with the assumption that exogenous data are not changed. Errors in the considered real turbine operating data set are prone to increase with larger time steps (Fig. 14). On account of relatively slow changes of the temperature at the critical location, the NET is able to exactly predict the temperature 1 min ahead of time. For 5 min ahead of time, the RMSE for temperature prediction is about 0.5 C in the case of startup and 2.5 C in the case of SD and LR, where temperature changes are much higher (Fig. 14(a)). In the case of stress, prediction errors result not only from stress prediction itself but also from temperature prediction. Stress variations at the rotor critical location are higher than temperature variations. All this causes higher stress prediction errors than temperature predication errors. A 1 min ahead of time prediction error equals 2.0 MPa, whereas a 5 min ahead of time error equals 14.7 MPa (Fig. 14(b)). The first example of NET temperature and stress change prediction quality occurred after the 54th minute of warm start II. Up until that moment, steam temperature and the turbine load were increasing. The NETs predicted a continued stress (Fig. 15) and temperature (Fig. 16) increase at the critical location of the rotor. In the 55th minute, the temperature started to decrease but the load continued increasing. Despite the previous stress increase trend, the NET successfully predicted its subsequent decrease. The NETs also predicted a lower temperature increase gradient caused by a drop in live steam temperature (Fig. 17). The NET responsible for stress correctly predicted the stress curve peak (Fig. 18). The next example of NET stress prediction occurred in the 61st minute, before which both steam temperature and turbine load had been decreasing, thus also decreasing stress at the rotor critical location. In the 61st minute, the NET predicted this trend to continue for the next 5 min (Fig. 20). Yet the 62nd minute, the steam temperature and turbine load began to increase. Despite the preceding step calculations, the NET managed to predict the stress increase correctly (Fig. 21). It also predicted the temperature Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /

12 increase at the rotor critical location. As soon as this information was available to the NETs, they correctly predicted rotor temperature (Fig. 25) and stress (Fig. 26) response. Fig. 23 Temperature prediction just before turbine LR, i.e., 68th minute Conclusions An HP steam turbine stress control system based on an NARX NET has been presented. The HP rotor NET control system was verified using real turbine operating data. The NETs are able to simulate online the temperature and stress of a critical turbine component based only on standard power plant measurements, such as speed, power, steam temperature, and pressure in front of turbine control valves. This is a very promising system for controlling various transient thermal stresses in steam turbine and gas turbine rotors. This system can also be applied to control stress in many other power plant components, e.g., boilers, turbine inner casing, and turbine outer casing, where it is difficult or impossible to make direct stress measurements online. Another advantage of this system is its low hardware requirements, which allow it to be implemented in existing controllers. Temperature and stress analyses show that results obtained from NETs are very similar to those obtained using the FE method. The results presented here are for only one critical point (the first groove of an HP rotor), but, after due training, it could be applied in many other points. Fig. 24 minute Fig. 25 minute Stress prediction just before turbine LR, i.e., 68th Temperature prediction after turbine LR, i.e., 69th Nomenclature AE ¼ absolute expansion BT ¼ axial bearing thrust CS ¼ cold start DE ¼ differential expansion FD ¼ feedback delay FE ¼ finite element HP ¼ high pressure HS ¼ hot start ID ¼ inputs delay IP ¼ intermediate pressure LCF ¼ low cycle fatigue LR ¼ load rejection MSE ¼ mean squared error n ¼ turbine rotational speed N ¼ turbine load NARX ¼ nonlinear autoregressive neural networks with exogenous inputs NN ¼ neural network p ¼ steam pressure before turbine control valve RES ¼ restart RMSE ¼ root mean squared error RTB ¼ reaction-type blading SD ¼ shut down T ¼ steam temperature before turbine control valve T m ¼ rotor critical point temperature during turbine load cycle T m (standstill) ¼ rotor critical point temperature during standstill TDL ¼ tapped delay inputs WS1 ¼ warm start 1 WS2 ¼ warm start 2 r m ¼ rotor critical point stress during turbine load cycle Fig. 26 Stress prediction after turbine LR, i.e., 69th minute gradient caused by a rise in live steam temperature (Fig. 22) in comparison with the prediction made in the 61st minute (Fig. 19). Figures 23 and 24 show temperature and stress prediction, respectively, just before turbine LR to turbine idle run (68th minute). Temperature and stress are well predicted. There is a LR in the 69th minute. This caused a temperature drop and the stress References [1] Busse, L., 1973, Anfahrsonde, BBC Studie, Paper No. HTGD [2] Dawson, R., 1989, Monitoring and Control of Thermal Stress and Component Life Expenditure in Steam Turbine, Tenth International Conference on Modern Power Stations, Liege, Belgium, Sept [3] Pahl, G., Reitze, W., and Salm, M., 1964, Ueberwachungseinrichtung fuer Zulaessige Temperaturaenderungen bei Dampfturbinen, BBC Nachrichten, Vol. 46, pp [4] Sindelar, R., 1972, Control of the Level of Heat Stress of the Steam Turbine Metal During Start-Up and Load Changes, Skoda Rev., 4, pp [5] Lausterer, G. K., 1997, On-Line Thermal Stress Monitoring Using Mathematical Models, Control Eng. Pract., 5(1), pp / Vol. 138, MAY 2016 Transactions of the ASME

13 [6] Lausterer, G. K., Franke, J., and Eitelberg, E., 1980, Mathematical Modeling of a Steam Generator. Digital Computer Applications to Process Control, 6th IFAC/ IFIP International Conference, Duesseldorf, Germany, Oct , pp [7] Marinescu, G., and Ehrsam, A., 2012, Experimental Investigation on Thermal Behavior of Steam Turbine Components: Part 2 Natural Cooling of Steam Turbines and the Impact on LCF Life, ASME Paper No. GT [8] Sindelar, R., and Toewe, W., 2000, TENSOMAX A Retrofit Thermal Stress Monitoring System for Steam Turbine, Vol. 1, VGB Power Tech, Essen, Germany, pp [9] Rusin, A., Banaszkiewicz, M., Lipka, M., Łukowicz, H., and Radulski, W., 2005, Continuous Control and Optimization of Thermal Stresses in the Process of Turbine Start-Up, Congress of Thermal Stresses, Vienna, Austria, May 26 29, pp [10] Głuch, J., and Krzy_zanowski, J., 2004, Application of an for Diagnostics of the Geometry Deterioration of the Power System Apparatuses, ASME Paper No GT [11] Głuch, J., and Krzy_zanowski, J., 2006, New Attempt for Diagnostics of the Geometry Deterioration of the Power System Based on Thermal Measurement, ASME Paper No GT [12] Kosowski, K., Tucki, K., and Kosowski, A., 2010, Application of Artificial Neural Networks in Investigations of Steam Turbine Cascades, ASME J. Turbomach., 132(1), p [13] Rusin, A., Nowak, G., and Lipka, M., 2014, Practical Algorithms for Online Thermal Stress Calculations and Heating Process Control, J. Therm. Stresses, 37(11), pp Journal of Engineering for Gas Turbines and Power MAY 2016, Vol. 138 /