The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS12.002

Temperature and Stress On-line Prediction in Steam Turbine Rotor using Neural Networks

K. Dominiczak 1 R. Rządkowski

2W. Radulski

3 R. Szczepanik4

Alstom Power LTD Institute of Fluid Flow Machinery Alstom Power LTD Air Force Institute of Technology

Elbląg, Poland Gdańsk, Poland Elbląg, Poland Warszawa, Poland

Abstract: Considered here are Nonlinear Auto-Regressive

neural networks with exogenous inputs (NARX) as a

mathematical model of a steam turbine rotor used for the

on-line prediction of turbine temperature and stress. In this

paper on-line prediction is presented on the basis of one

critical location in a high pressure steam turbine rotor,

according to power plant common measurements, i.e.,

turbine speed, turbine load as well as steam temperature

and pressure before turbine control valve. In order to

obtain neural networks that will correspond to the

temperature and stress the critical rotor location, an FE

rotor model was built. Neural networks trained using the

FE rotor model not only have FEM accuracy, but also

include nonlinearity related to nonlinear steam turbine

expansion, nonlinear heat exchange inside the turbine and

nonlinear rotor material properties during transient

conditions. Simultaneous neural networks are algorithms

which can be implemented in turbine controllers. This

allows for the application of neural networks to control

steam turbine stress in industrial power plants. Keywords: neural network, steam turbine, stress control, rotor

I. Introduction

The quality of on-line stress control is vital for steam

turbine operation flexibility. Operation flexibility has been

the subject 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 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 on-line stress control. The purpose of on-line

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.

1krzysztof.dominiczak@power.alstom.com 2z3@imp.gda.pl 3wojciech.radulski@power.alstom.com 4ryszard.szczepanik@itwl.pl

Thermal stress control in steam turbines has been

presented by Busse [1], Dawson [2], Pahl et al. [8],

Sindelar [10]. All of these stress control systems used

thermo-physical startup probes, which were physical

models of steam turbine rotors. A thermo-physical 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 [6], Lausterer et al. [7], Ehrsam [3] have

presented systems in which the mean temperatures of

particular turbine components were calculated using a

mathematical model and a start-up probe. Sindelar at al.

[11] describe a system which assesses stress in a critical

turbine component by using only standard power plant

measurements. Rusin at al. [9] have presented a steam

turbine stress control system based on Duhamel’s integral.

This paper for the first time presents a steam turbine

stress prediction based on a neural network. While neural

networks have already been used in power system

diagnostics, e.g. by Głuch at el. [4] [5] for diagnostics of

power object geometry deterioration, never before have

they been used for temperature and stress modeling. The

neural networks presented in this paper are able to simulate

and predict on-line 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.

II. Nomenclature

AE – absolute expansion

BT – axial bearing thrust

CS – cold start

DE – differential expansion

FD – feedback delay

FE – finite element

HP – high pressure

HS – hot start

ID – inputs delay

IP – intermediate pressure

LCF – low cycle fatigue

LR – load rejection

MSE – mean squared error

N – turbine load

n – turbine rotational speed

NARX – Nonlinear Auto-Regressive neural networks with

exogenous inputs

NN – neural network

p – steam pressure before turbine control valve

RES – restart

RMSE – root mean squared error

RTB – reaction type blading

SD – shut down

m – rotor critical point stress during turbine load cycle

T – steam temperature before turbine control valve

TDL – tapped delay inputs

Tm – rotor critical point temperature during turbine load

cycle

Tm (standstill) – rotor critical point temperature during

standstill

WS1 – warm start 1

WS2 – warm start 2

III. NARX neural networks

NARX neural network is a recurrent dynamic

network, with feedback connections enclosing layers of the

network (Fig. 1). NARX neural networks are commonly

used to monitor the nonlinear process where the

nonlinearity is unknown. In addition to its simplicity, this is

a major NARX neural network advantage. The defining

equation for the NARX model is:

where yt is the predicted value of the dependent output

signal based on previous output signal values yt-1,yt-2,…

and previous independent (exogenous) input signal values

ut, ut-1, ut-2 (Fig. 1)

Fig. 1. NARX neural network

IV. Neural networks modeling for stress and

temperature

This paper presents the NARX neural network 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 a

seven feed water preheater, designed to run a synchronous

GHTW-400 generator. The nominal live steam parameters

are 182bar(a)/557C, whereas nominal reheat steam

parameters are 42bar(a)/568C. 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 (10%CrMoVNbN) was used, whereas in the exhaust

cold region low-alloy steel (1%CrMoV) was used. The HP

rotor is 5625mm long and the assembled blade rows weigh

approximately 10.5 tons. The rotor diameter at the steam

inlet is 653mm, whereas at the steam path exhaust it is

686mm.

Fig. 2. HP cross section of 18K390 steam turbine

The NARX neural network 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. For lifetime

assessment purposes, theoretical startups and shut down

curves provided by turbine manufacturer were used. For all

considered rotor initial temperature depended theoretical

load cycles, critical location was rotor first blade groove.

The details of HP rotor stress during rotor transient states

is given in Fig. 3.

a)

b)

c)

Fig. 3. Axial stress distribution in HP rotor at idle run

during turbine cold start up (a). Hysteresis loop at

rotor critical location for three cold startup – shut

down load cycle (b). Stress in various HP rotor

locations during warm start II (c).

𝑦𝑡 = 𝐹(𝑦𝑡−1,𝑦𝑡−2,𝑦𝑡−3,… ,𝑢𝑡 ,𝑢𝑡−1,𝑢𝑡−2,𝑢𝑡−3,… )

During a steam turbine lifetime, two periods can be

distinguished: load cycles and standstill periods. During

turbine startups and shutdowns, which are a part of turbine

load cycle, transient temperature fields are induced due to

heat exchange between turbine elements and expanding

steam. These transient temperature fields cause thermal

stress, which is responsible for turbine low cycle fatigue.

During continuous turbine operation, which is also the part

of turbine load cycle, steady state temperature fields are

observed. Steady state temperature fields are responsible

for reducing turbine life due to the creep phenomenon. A

neural network based on-line stress control can assess in

real time stress and temperature in the critical location

during turbine load cycles. During steam turbine standstill,

rotor temperature is equalized and rotor is cooled down. In

comparison with the stress level which occurs during the

turbine load cycle, 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 a NARX neural

network 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 neural networks which represent

temperature and stress in rotor critical location. However

in case of neural network for stress representation these

measurements are not sufficient. During two identical

startups from fore mentioned measurements perspective,

stresses can differ depending on the initial temperature in

critical location. Therefore critical location temperature,

assess by the responsible neural network, is an exogenous

inputs for neural network responsible for assessment of

stress in rotor critical location. During standstill period,

temperature in rotor critical location can be assess based on

the current rotor thermal and mechanical growth, which are

calculated in considered case based on HP differential

expansion, HP and IP absolute expansion and the thrust

bearing float.

Fig. 4 shows a diagram of the NARX neural network

thermal stress control system. The control system consists

of three NARX neural networks. The first of these assess

critical point temperature during turbine standstill on the

basis of the rotor’s axial expansion, which is obtained from

absolute expansion (AE), differential expansion (DE) and

axial bearing thrust (BT). This temperature is used as an

initial temperature for the second NARX neural network,

which assesses 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 start-up. Assuming that rotor is stress free at the

beginning of turbine startup, the data concerning critical

point temperature, turbine speed, turbine load, steam

temperature and pressure before the turbine control valve

allows the third NARX network to assess critical point

stress.

Fig. 4. NARX neural network based steam turbine

thermal stress control

Fig. 5 presents a practical implementation of the

NARX neural network stress assessment in MATLAB.

There are two architectures: parallel and series-parallel.

Parallel architecture is used for normal neural network

work. During neural network training the network outputs

are known. Therefore feedback is uncoupled and true

output is used instead of being estimated. This leads to

more effective neural network training, because the inputs

to the network are more accurate. Series-parallel

architecture also allows for the use a static

back-propagation training algorithm.

a)

b)

Fig. 5. MATLAB implementation of NARX neural

network responsible assessment of critical point

stress: (a) parallel architecture, (b) series parallel

architecture

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 neural

network was used, whereas for stress control the neural

network required five specialized sets of weights and bias

values for the following transient states:

cold starts

warm starts I

warm starts II

hot starts

restarts, shutdowns and load rejections

A proper set of neural network weights and bias values was

selected, based on the initial critical temperature location.

Neural networks for stress control are designed to

work on-line, therefore their structures must be optimized.

Fig. 6 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 wasn’t part of training data set. Neural

networks 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. 6a) and five neurons in input layer for stress

networks (Fig. 6b). The two time samples of input delays

and feedback delays are sufficient to model on-line rotor

strength and temperature parameters during turbine load

cycles.

The same optimization process has been performed

for neural network responsible for assessment of

temperature during turbine standstill period. Also in this

case neural network with two neurons in hidden layer, two

input and feedback delays is sufficient to assess rotor

critical location temperature during turbine standstill

period.

a)

b) Fig. 6. Neural networks structure optimization results:

a) temperature, b) stress

V. FEM based neural network training

Neural network 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

neural network training was performed using the

Levenberg–Marquardt algorithm, which was possible

because of the series-parallel architecture. However, for

the NARX neural network 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 on-line stress monitoring are

used. In this investigation the neural network training data

was prepared using an FE model. The quality of the stress

and temperature neural network models can only be as

good as that of the FE model used for neural network

training. FE analyses were also used to assess neural

networks performance for a real turbine operating data

testing set, which were not a part of 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 considered case backpressure is

equal to pressure in cold reheat). Thermodynamic model

performance was checked based on the measurements

installed in the vicinity of HP part. The steam flow through

the turbine was verified based on the steam flow

measurement installed on 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 measurement at the steam path inlet. In case of

steam path exhaust, there is temperature measurement

located in 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, HP

steam path characteristic was recognized. This

characteristic was used for thermodynamic model of 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

LCF lifetime consumption was assess using

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. Fig. 7

shows comparison between calculated and measured steam

temperature before HP steam path during turbine warm

start II.

Fig. 7. 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

blades grooves was omitted since it is insignificant in

comparison with convective heat transfer from steam. As

an example Fig. 8 shows the heat transfer coefficient on the

rotor surface after the first stationary radial stage.

Fig. 8. Heat transfer coefficient for rotor

surface after first HP stationary blades row

FE modeling of a steam turbine rotor used for neural

networks 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, shown in Fig. 9, has been prepared

using ABAQUS. The FE rotor model is an axisymmetric

model comprising approximately 9000 elements and

31000 nodes. 8-node bilinear temperature elements were

applied for the temperature analyses and 8-node

biquadratic displacement stress elements were applied for

the structural analyses.

a)

b) c)

Fig. 9. FE model of 18K390 turbine HP rotor:

a) whole model, b) steam inlet view, c) 1st and 2nd

blade grooves

The only experimental possibility of verify the

assumed heat exchange and FE models was through

expansion of the rotor (thermal and mechanical rotor

growth). Nevertheless rotor expansion is mainly caused by

rotor axial temperature distribution, whereas radial

temperature distribution is responsible for stress in rotor

critical location. Therefore stress in rotor can’t be directly

verified. However if accurate rotor axial expansion can be

obtain based on assumed heat exchange model, this heat

exchange model should also ensure accurate rotor radial

temperature distribution responsible for stress.

The rotor expansion can be obtain from the FE model,

whereas for real data can be calculated based on HP

differential expansion, HP and IP absolute expansion ant

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, bearing pedestal between HP and

IP and HP outer casing are assembled together. Due to the

thermal growth pedestals and casings expands in one

direction. Rotor relative fix point is located in thrust

bearing, which is pushed by IP outer casing. HP rotor

expands in the same direction what HP outer casing,

whereas IP rotor expands in opposite direction in

comparison with IP outer casing.

Fig. 10 compares results of the FE analysis with axial

expansion calculated from measurements during a cold

startup 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. HP rotor axial expansion during cold startup:

calculations and measurements.

In order to build a training data set for neural

networks 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

neural network training data set was established on the

basis of turbine operational history. For neural network

operating during turbine standstill, 2 FE calculations were

performed in order to build training data set for this neural

network.

VI. Neural networks testing using real operating data

The HP rotor neural network control system was

verified using real turbine operating data. For neural

networks operating during turbine load cycles, this

included each turbine startup category (cold, warm I, warm

II, hot), one sliding pressure shut down and one load

rejection together with turbine reloading. As a measure of

neural network performance, the root mean squared error

(RMSE) was used. Fig. 11 presents the neural network

determined temperature (Tm) and stress (Sig) in HP rotor

critical location.

The maximal RMSE for neural network determined

temperature was 5.4°C and occurred during warm start up I

(WS1) (Fig. 11). The other temperatures were: 5.4°C for

load rejection together with turbine reloading (LR+RES),

4.8°C for cold start up (CS), 4.2°C for hot start (HS), 4.1°C

for sliding pressure shut down (SD) and 2.1°C for warm

start up II (WS2).

The maximal RMSE for neural network determined

stress was 18.8MPa and occurred during cold start up (CS)

(Fig. 11). The other stress values were: 10,2 MPa (WS1),

11,3 MPa (WS2), 13,2 MPa (HS), 8MPa (SD) and 6.4

MPa (LR+RES).

Fig. 11. Neural network performance based on real

turbine operating data

Fig. 12 presents the neural network determined

temperature (Tm) and stress (Sig), including relatively

errors, in the HP rotor critical location during cold start up.

The relative error in determining temperature (Tm) is

presented in Fig. 12a. 100% of the hits occur in the relative

error interval (-5, +5%). The relative error in determining

stress (Sig) during cold start up is presented in Fig. 12b.

44% of the hits occur in the relative error interval (-5,

+5%), 32% in (5-15%), 18% in (-15, +-5%).

Fig. 12c and Fig 11d present the FE-neural network

correlations for temperature stress, respectively. The red

line denotes the finite element (FE) results and the blue line

the neural network (NET) results. Here we see very good

temperature correlation between the NET and FE analyses

(i.e. the red line coincides with the blue one). In the case of

stress (Fig. 12d) there is good correlation up to 420MPa,

above this value the neural network results are slightly

lower than those of the FE. Fig. 12e and 12f show good

FE-NET correlation for cold start-up.

Higher error values were observed in NET

determined stress (Fig. 12g). 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. 12g).

Fig. 12. Result of neural network tests for cold

start-up

Fig. 13 presents neural network determining

temperature (Tm) and stress (Sig), with errors, in HP rotor

critical location for load rejection together with turbine

reloading. The relative error of determined temperature

(Tm) is presented in Fig. 13a. 100% of the hits were in

relative error interval (-5, +5%), as in the case of cold

startup (Fig. 12a).

The relative error of determined stress (Sig) is

presented in Fig. 13b. 54% of the hits were in the relative

error interval (-5%, +5%). Therefore the relative error

for load rejection together with turbine reloading was

lower than for cold startup (Fig. 12b), where a higher

percentage of hits in the relative error interval (-5%, +5%).

Fig. 13c and Fig 12d present the FE-NET correlations for

temperature and stress, respectively. Both correlations are

very good (the red and blue lines coincide).

Fig. 13e and 13f show that neural network results for

load rejection together with turbine reloading were close to

Relative error Tm [%] Relative error Sig [%]

FE Sig [MPa] FE Tm [°C]

Ne

t Si

g [M

Pa]

Ne

t Tm

[°C

]

hit

s [%

]

hit

s [%

] Tm

[°C

] Si

g [M

Pa]

re

lati

ve e

rro

r [%

]

time [min]

time [min]

time [min]

NET FE

NET FE

Tm sig

NET FE=NET

NET FE=NET

finite element analysis. The relative error for temperature

(Fig. 13g) is very small and for stress it is small (below 5%)

in the area of large stress. By contrast, in cold startup at the

stress maximum the error is more than 10%.

Fig. 13. Result of neural network tests for load

rejection and turbine reloading

For neural networks operating during turbine

standstill, testing data set includes two turbine natural

cooling: with and without steam cooling phase during

turbine shut down. As a measure of neural network

performance, also the root mean squared error (RMSE)

was used. RMSE for natural cooling without steam cooling

phase was equal to 5.1°C, whereas RMSE for natural

cooling phase was equal to 5.3°C.

Fig. 14 presents the neural network determined

temperature (Tm) in HP rotor critical location during

turbine standstill after shutdown with steam cooling phase.

The relative error of determined temperature during

standstill is presented in Fig. 14a. 49% of the hits were in

relative error interval (-5, +5%). Fig. 14b presents the

FE-NET correlations for temperature during standstill.

Fig. 14c shows that neural network results for

standstill were close to finite element analysis. The relative

error for temperature (Fig. 14d) is very small and for stress

it is no larger than 10%.

Fig. 14. Result of neural network tests for standstill

after turbine shutdown with steam cooling phase

VII. Prediction of temperature and stress at 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 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 NARX neural

networks.

With current values of temperature and stress from

neural networks, it is possible to make neural networks

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 neural

networks is 0 instead of 1, which determines the

temperature and stress for the current time step. In this way,

outputs for predictive neural networks 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 five minutes into

the future with the assumption that exogenous data are not

changed.

Errors in the considered a real turbine operating data

set are prone to increase with larger time steps (Fig. 15).

On account of relatively slow changes of the temperature at

the critical location, the neural network is able to exactly

predict temperature one minute ahead of time. For five

minutes 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 shutdown and load rejection, where temperature

changes are much higher (Fig. 15a). 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

one minute ahead of time prediction error equals 2.0MPa,

whereas a five minutes ahead of time error equals 14.7MPa

(Fig. 15b).

a)

b)

Fig. 15. Neural network prediction performance based

on real turbine operating data: a) temperature, b)

stress

The first example of neural network temperature and

stress change prediction quality occurred after the 38th

minute of hot start. Up until that moment, the turbine load

was increasing with constant gradient. Neural networks

predicted a continued stress decrease (Fig. 17) and

temperature (Fig. 16) increase at the critical location of the

rotor. In the 39th minute the turbine load gradient

increased. Despite the previous stress decrease trend, the

neural network successfully predicted its subsequent

increase. The load gradient increase has no significant

impact on temperature in rotor critical location, therefore

in both considered time moments i.e. 38th (Fig. 16) and

39th (Fig. 18) minutes of hot start, temperature prediction

was very accurate. The neural network responsible for

stress correctly predicted the stress curve peak (Fig. 19).

Fig. 16. Temperature prediction in the 38

minute of hot start up

Fig. 17. Stress prediction in the 38 minute

of hot start up

Fig. 18. Temperature prediction in the 39

minute of hot start up

Fig. 19. Stress prediction in the 39 minute

of hot start up

The second example of neural network temperature

and stress change prediction quality occurred after the 45th

minute of hot start. Up until that moment, the turbine load

was increasing. Neural networks predicted a continued

stress (Fig. 21) and temperature (Fig. 20) increase at the

critical location of the rotor. In the 46th minute the turbine

loading was held. The neural network responsible for

temperature correctly predicted the change of temperature

gradient at rotor critical location (Fig. 22). The neural

network responsible for stress correctly predicted the stress

curve peak (Fig. 23).

Fig. 20. Temperature prediction in the 45

minute of hot start up

Fig. 21. Stress prediction in the 45 minute

of hot start up

Fig. 22. Temperature prediction in the 46

minute of hot start up

Fig. 23. Stress prediction in the 46 minute

of hot start up

VIII. Conclusions

A HP steam turbine stress control system based on a

NARX neural network has been presented. The HP rotor

neural network control system was verified using real

turbine operating data. Neural networks are able to

simulate on-line 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

and outer casings, etc., where it is difficult or impossible to

make direct stress measurements on-line. 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 neural networks are very similar to those obtained

using the finite element 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.

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