modelling and simulation of temperature variations of …439471/fulltext… · ·...

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Modelling and Simulation of Temperature Variations of Bearings in a Hydropower Generation Unit

A dissertation submitted to the Department of Energy Technology, Royal Institute of Technology,

Sweden for the partial fulfilment of the requirement for the Degree of Master of Science in Engineering

By

CGS Gunasekara

Department of Energy Technology Royal Institute of Technology,

Stockholm, Sweden

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Modelling and Simulation of Temperature Variations of Bear-ings in a Hydropower Generation Unit

by

CGS Gunasekara

Supervised by Dr. Primal Fernando, Dr. Joachim Claesson

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Declaration

The work submitted in this thesis is the result of my own investigation, except where otherwise stated.

It has not already been accepted for any other degree and is also not being concurrently submitted for any other degree.

CGS Gunasekara

Date

We/I endorse declaration by the candidate.

Dr. Primal Fernando

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Abstract

Hydropower contributes around 20% to the world electricity supply and is considered as the most important, clean, emissions free and economical renewable energy source. Total installed capacity of Hydropower generation is approximately 777GW in the world (2998TWh/year). Furthermore, estimated technically feasible hydropower potential in the world is 14000TWh/year. The hydro-power is the major renewable energy source in many countries and running at a higher plant-factor. Bearing overheating is one of the major problems for continues operations of hydropower plants. Objective of this work is to model and simulate dynamic variation of temperatures of bearings (generator guide bearing, turbine guide bearing, thrust bearing) of a hydropower generating unit. The temperature of a bearing is depends on multiple variables such as temperatures of ambient air, cooling water and cooling water flow-rate, initial bearing temperatures, duration of operation and electrical load. Aim of this study is to minimize the failures of hydropower plants due bearing tem-perature variations and to improve the plant-factor. The bearing heat exchange system of a hydro-power plant is multi-input (MI) and multi-output (MO) system with complex nonlinear characteris-tics. The heat transfer pattern is compel in nature and involves with large number of variables. Therefore, it is difficult to use conventional modelling methods to model a system of this nature. So that Neural Network (NN) method has been selected as the best where past input and output data is available, and the input characteristics can be mapped in order to develop a model. In this report a neural network model is developed to model the hydropower plant, using Matlab neural network tool box and matlab as the implementation language.

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Acknowledgments

Thanks are first due to my supervisors, Dr Primal Fernando and Dr Joachim Claesson for their great insights guidance and sense of humour. My sincere thanks should go to the Post Graduate Office, Royal Institute of Technology, Stockholm, Sweden for helping in various ways to clarify the things related to my academic works in time, with excellent cooperation and guidance. Next, I would like thank, staff of the Post Graduate Section of ICBT, Sri Lanka who facilitated to carry out my studies throughout the course.

Lastly, I should thank many individual friends and colleagues who have not been mentioned here personally in making this educational process success. May be I could not have make it without your support.

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List of Abbreviations a A dxw h H HE K L LGB M MIMO n N NN Q R s S T TGB THB U UGB w x

Output Surface area Wall thickness of heat exchanger Enthalpy Normalized enthalpy Heat exchanger Thermal conductivity Load Lower guide bearing Number of trials Multiple-input, multiple-output Output of neuron Number of layers Neural network Heat Number of input nodes Entropy Normalized entropy Temperature Turbine guide bearing Thrust bearing Heat transfer coefficient Upper guide bearing Weights Steam quality

Subscripts Amb Ambient Ca Circulating air cw Cooling water cwin Cooling water inlet cwout Cooling water outlet dotcw Cooling water flow rate dotoil Cooling oil flow rate e Electrical EL Electrical Load LGB Lower guide bearing LGBoin LGB oil in LGBoout LGB oil out m Mass O Oil TGB Turbine guide bearing TGBm TGB metal TGBoin TGB oil in TGBoout TGB oil out THB Thrust bearing UGB Upper guide bearing UGBm UGB metal UGBo UGB oil UGBoin UGB oil in UGBoout UGB oil out

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Greek symbols α Individual heat transfer coefficient δ Weight adjusting scalar η Efficiency of heat exchanger

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1 Introduction.........................................................................................................................10 1.2 The hydropower generating unit................................................................................. ...11 1.3 Bearing arrangement of Hydropower unit........................................................,...........12 1.4 Purpose and contribution of the thesis..........................................................................12 1.5 Organization of dissertation............................................................................................13

2 Overview of the Modelling..................................................................................................14 2.1 The research problem.......................................................................................................14

2.1.1 Aim and scope..........................................................................................................14 2.1.2 The research question.................................................................................................14

2.2 Approach............................................................................................................................14

3 Neural Networks.................................................................................................................24 3.1 Introduction................................................................................................................. .....24 3.2 Formal definition...............................................................................................................24 3.3 Biological Neuron..............................................................................................................24 3.4 Mathematical Model of a neuron....................................................................................25

3.4.1 Neuron with multi-inputs..........................................................................................27 3.4.2 Layer of Neurons......................................................................................................28 3.4.3 Muli-layer neurons....................................................................................................29 3.4.4 General Structure of NN.................................................................................,........29 3.4.5 Training a neural network.........................................................................................30 3.4.6 Training process........................................................................................................30

3.5 Demonstration of developing a NN by example.........................................................31 3.5.1 Problem.....................................................................................................................31 3.5.2 System as a NN model.............................................................................................32 3.5.3 Data used.................................................................................................................33 3.5.4 Training...................................................................................................................33 3.5.5 Simulation................................................................................................................36 3.5.6 Results......................................................................................................................36

4 Developing the model.........................................................................................................40 4.1 Selection of input variables..............................................................................................40 4.2 Selection of data.................................................................................................................41 4.3 Approach of developing a dynamic model....................................................................41

4.3.1 Developing a static NN model............................................................................41 4.3.2 Training the network and training results..................................................................43 4.3.3 Static model simulation results...................................................................................45 4.3.4 Developing the dynamic model...................................................................................45

5 Results.................................................................................................................................47 5.1 Static model simulation results........................................................................................47

5.1.1 Static model simulation results for bearing metal temperature......................................47 5.1.2 Co-relation coefficient of the static simulation results...................................................48 5.1.3 Static model simulation results for bearing oil temperature..........................................49 5.1.4 Correlation coefficients of simulation on bearing oil temperature..................................50 5.1.5 Summary results of static model.................................................................................51

5.2 Dynamic simulation results..............................................................................................52 5.2.1 Dynamic simulation results for bearing metal temperature..........................................52 5.2.2 Dynamic simulation results for bearing oil temperature...............................................53

5.3 Dynamic simulation results for reduced flow rate.......................................................53 5.3.1 Bearing metal temperature variation...........................................................................53 5.3.2 Bearing oil temperature variation...............................................................................54

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6 Discussion.....................................................................................................................56

7 Conclusions.................................................................................................................. 57

8 References.................................................................................................................... 58

Appendix A : NN initial weight and bias values (NN example).................................... 59

Appendix B: Training record ( NN example)................................................................. 62

Appendix C: Sample data used for training the model................................................... 76

Appendix D: training Matlab script for model.................................................................80

Appendix E: Initial values of trained model.................................................................... 84

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1 Introduction

1 . 1 G e n e r a l o v e r v i e w Hydro power contributes around 20% of the world electricity generation [1]. As a renewable energy source it has become more important economical resource compared to other renewable sources. Hydro power produces no direct waste and contribution to CO2, green house gases compared to fos-sil fuel plants. Global installed capacity of Hydropower generation (electrical) is approximately 777GW (2998TWh/year) [1]. It is around 88% of the renewable energy sources [2].

In Sri Lanka about 40% of electricity is generated by hydropower. At present, all most all hydro po-tentials available in the country have been utilized for electricity generation and few remaining are under construction.

Total Pow er Generation GWh

Hired pow er1%

Wind0%

Private Pow er37%

Thermal Complex

22%

Other Hydro8%

Laxapana Hydro Complex

15%

Mahaw eli Hydro Complex

17%

Fig.1.1 Hydro electricity contribution in 2009 (Source: Ceylon Electricity Board, statistics 2009)

The electricity generation by different sources in the year 2009 is shown in Fig. 1.1. Electricity gener-ated in three major hydropower complexes (Mahaweli Hydro complex, Laxapana Hydro Complex and Other Hydro Complexes) in Sri Lanka [3], contributes 40% to the national energy supply while the rest is coming from thermal power, mainly diesel. Hence, obtaining the maximum possible share from hydropower would be great saving to the national economy.

Around 95% of existing hydro power plants in Sri Lanka have passed the 25 year limit of their life span. Sri Lanka is not in a situation to replace old-hydro power plants, within a short period and also its energy production is mainly depends on hydropower. Age analysis of the hydropower plants in Sri Lanka is shown in Table 1.

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Table 1: Age analysis of hydropower stations in Sri Lanka (Source: Ceylon Electricity Board, Generation data)

Name of the Station Installed Capacity/MW

Commissioned year

Age (years)

Inginiyagala Norton Udawalawe Old Laxapana Polpitiya Ukuwela Bowatenna New Laxapana Canyon Kotmale Victoria Samanalawela Randenigala Nilambe Rantambe Kukule

11.25 50 6 50 75 40 40 100 60 201 210 120 122 3.2 50 70

1950 1950 1955 1955 1960 1976 1981 1984 1984 1985 1985 1985 1986 1988 1990 2002

65 65 60 60 50 34 29 26 26 25 25 25 24 22 20 08

Therefore, it is essential to obtain the maximum capacity from the existing plants by minimizing the downtime through proper operations. In that context, predicting the availability of hydroelectric gen-erating units for fault free operation is one of the crucial factors.

Bearing oil temperature plays a vital role in continues operation of hydropower plants. Stable bearing temperatures in the turbine and generator are essential for their successful continues operations. All hydraulic and lubricating fluids have operating temperature limits. A machine could lose its stability and experiences conditional failures whenever the system’s fluid temperature exceeds these limits. Increase in temperatures in a machine may happen due to lack of heat losses, higher ambient temperatures and long operations at higher mechanical loads. The power plant staff should closely monitor the bearing oil and metal temperatures in order to ensure a safe operation [4]. Typical acceptable bearing temperatures of a vertical shaft hydropower turbine are shown in Table 2.

Table 2: Bearing temperature limits (refer Fig. 1.3) Bearing Type Temperature / deg C (Alarm)

Metal Oil Upper Guide Bearing (UGB) Lower Guide Bearing (LGB) Thrust Bearing (THB) Turbine Guide Bearing (TGB)

85 85 85 75

70 70 70 70

In this project, from the measured temperature variations of bearings (generator upper guide bearing UGB, lower guide bearing LGB, turbine guide bearing TGB, thrust bearing THB), a model is created to predict bearing temperatures at various operation conditions.

1 . 2 T h e h y d r o p o w e r g e n e r a t i n g u n i t Hydro electricity is generated by converting potential energy of water to kinetic energy by its turbines. A typical arrangement of a vertical shaft driven turbine, generator unit is shown in Fig.1.2 [5].

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Fig.1.2 Overview of a hydropower generating unit

1 . 3 B e a r i n g a r r a n g e m e n t o f H y d r o p o w e r u n i t A typical arrangement of the bearings in a vertical shaft generator-turbine unit of a hydropower plant is shown in Fig.1.3.

Fig.1.3 Turbine-Generator bearing arrangement

1 . 4 P u r p o s e a n d c o n t r i b u t i o n o f t h e t h e s i s The purpose of this thesis is to develop a model to predict the temperatures of bearings for different operating conditions. The model is developed using previously measured temperatures, loads, and cooling water flow data. To achieve these, following principle systems are stated.

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Choose the inputs and outputs.

Determine the appropriate method for this system considering the nature of the problem. It is suggested to use a neural network model for this problem as justified in the next section.

It is suggested to decompose the system into sub models to identify the heat transfer charac-teristics of the system.

In this work, Matlab neural network tool box, and Matlab scripts are used.

1 . 5 O r g a n i z a t i o n o f d i s s e r t a t i o n The rest of the chapters of this dissertation are organized as,

Describes the overview of the modelling strategy approach to the modelling method includ-ing the selection of modelling method and selection of input variables.

About application of neural network and the theory behind it.

Describes how to approach to developing the model by considering the heat transfer pattern, the interaction within system variables and implementing the model.

Presents the results obtained by simulating the model with comparison to the past actual characteristics of the system.

Discusses the performance of the model and concludes the work carried out by this study.

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2 Overview of the Modell ing

This section is devoted to describing the problem under investigation, importance of it to the energy sector, aims of the research, its scope and limitations, formulation of the research problem and the approach.

2 . 1 T h e r e s e a r c h p r o b l e m Monitoring the temperature of a bearing is an important task for ensuring continues running of hy-dropower generating. Old hydropower plants are frequently failed due to bearing temperature rise or stop when they reach to recommended temperature levels. This may causes frequent power failures or damagers to turbine-generator system.

2 . 1 . 1 A i m a n d s c o p e It is aimed to model and simulate the dynamic variation of temperatures of the bearings (generator guide bearing, turbine guide bearing, thrust bearing) of an in-service hydropower unit.

2 . 1 . 2 T h e r e s e a r c h q u e s t i o n One research question has been formulated for focusing the work:

How should multi-physical interactions in a hydropower bearing-heat exchanger system be modelled, simulated, in order to predict the bearing temperature variation?

2 . 2 A p p r o a c h

HE3, HE4 – LGB, TGB oil coolers, HE1 – THB and UGB oil cooler, HE2 – Stator cooler

Fig.2.0 Bearings-heat exchanger system,

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A simplified diagram that illustrate the physical arrangement of different types of heat exchangers, bearings, generator stator and cooling fluids flow directions of a hydropower plant is shown in Fig.2.0. The bearings (UGB, LGB, THB, and TGB) and generator stator are considered as heat sources and cooling water as well as ambient air act as heat sinks. Pictures of the TGB oil cooler and THB oil cooler are shown in Fig 2.1 and Fig. 2.2, respectively.

Fig.2.1 A picture of TGB-heat exchanger arrangement

Fig.2.2 A picture of THB & UGB heat exchanger arrangement

THB and UGB oil cooler consists of shell-and-tube type two parallel heat exchangers. Heat from the oil is transferred to the circulating cooling water. Interactions of system variables with each other are shown in heat transfer diagrams in Fig. 2.3 and Fig. 2.4.

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Fig.2.3 Simplified heat transfer diagram

Fig.2.4 Detailed Heat transfer diagram

The temperature variations in bearing metal, bearing oil, cooling water, circulating air and the load with time are shown in Fig. 2.5 during a typical running time. The temperatures were measured con-tinuously during the running period as well as during the stopping period.

Bearings

Generator Stator + Rotor

Cooling water

Ambient air

Bearing oil

Circulating air

Heat Source Heat Sink

UGB Metal

THB Metal

LGB Metal

TGB Metal

Generator stator + rotor

UGB oil

THB oil

LGB oil

TGB oil

Circulating air

Cooling water

Ambient air

Heat Source Heat Sink

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Load variation

0

10

20

30

40

50

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101

106

111

116

121

126

131

136

141

146

Time/ hours

MW

,MVa

r

Load MW

Load Mvar

Fig 2.5 Bearing metal /oil/cooling water/electrical load and circulating air temperature variation

When the plant started from stand still, the temperatures of the bearings rise rapidly and stabilize at a certain level for the given generator load profile is shown in Fig. 2.6. Sampling rate of the tempera-ture values are selected at 10-minute intervals. (Sample data record 1365 to 1465 Appendix D)

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Fig. 2.6 Variation of bearing metal and oil temperatures

When the external parameters such as cooling water flow rate and cooling water or ambient air tem-perature varies, the heat absorption rate of the bearing oil coolers varies. Data relevant to these dif-ferent operating conditions are given in table 2.1. According to this data, when the cooling water temperature is high (29°C) the bearing temperatures are also at a higher value.

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Table 2.1 Temperature variation of the bearings with load and cooling water temperature.

Load Temperature °C / Alarm °C MW MVar C win UGBm THBm LGBm TGBm UGBo LGBo TGBo

77 78 76 76 76 74 75 76

9 10 12 13 14 16 20 25

24.8 24.8 24.8 24.7 24.7 24.7 24.7 24.7

50/85 50/85 50/85 50/85 50/85 50/85 50/85 50/85

71/85 71/85 72/85 72/85 72/85 72/85 72/85 72/85

62/85 62/85 63/85 63/85 63/85 63/85 63/85 63/85

56/75 56/75 57/75 57/75 57/75 57/75 57/75 57/75

54/70 54/70 55/70 55/70 55/70 55/70 55/70 55/70

54/70 55/70 55/70 55/70 55/70 55/70 55/70 55/70

54/70 54/70 55/70 55/70 55/70 55/70 55/70 55/65

73 73 72 76 76 79

35 35 35 32 34 35

24.8 24.8 24.8 24.8 24.8 24.8

53/85 53/85 53/85 54/85 57/85 57/85

81/85 82/85 82/85 82/85 83/85 83/85

71/85 72/85 75/85 75/85 75/85 76/85

63/75 63/75 64/75 64/75 65/75 65/75

60/70 60/70 61/70 61/70 62/70 61/70

60/70 61/70 61/70 61/70 61/70 62/70

60/70 60/70 61/70 61/70 62/70 62/70

30 30 30 30 10 10 10

42 44 44 45 45 44 40

29 29 29 29 29 29 29

65/85 65/85 65/85 65/85 65/85 65/85 65/85

78/85 78/85 78/85 78/85 78/85 78/85 78/85

77/85 77/85 77/85 77/85 77/85 77/85 77/85

72/75 72/75 72/75 72/75 72/75 72/75 72/75

60/70 60/70 60/70 60/70 60/70 60/70 60/70

65/70 65/70 65/70 65/70 65/70 65/70 65/70

64/70 64/70 64/70 65/70 65/70 65/70 64/70

When one of the bearing temperatures reaches to the alarm level of the machine, the plant has to be stopped or automatic shut down takes place. A failure that occurred due to bearing over heating is shown in Fig. 2.7. It was observed that the THB temperature reached to 83°C with an increasing trend when the machine was running at a load of 77 MW, 37MVar and then the machine was manu-ally stopped.

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Fig.2.7 Failure due to bearing temperature rise

The bearing temperature variations show a clear relation to electrical load (both MW and MVars) and cooling water flow rates. Bearing metal temperatures depend on the initial conditions of the bearing, external conditions such as cooling water flow rate, cooling water temperature (ambient temperature) and electrical load of the generator. Parameters involved with system are shown in Fig.2.8.

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Fig. 2.8 Representation of the system: HE1, HE3, HE4 - bearing oil coolers, HE2 stator air cooler.

From first principles of thermodynamics,

Considering heat transfer from bearing metal to oil,

UGBoUGBmUGB TTAUQ 11 ( 1 )

Considering heat transfer in heat exchanger 1 (HE1),

cwoutcwindotcwwUGBOOutUGBOindotoilOil TTmCTTmC 1 ( 2 )

For HE2,

cwoutcwindotcwWAir TTmCQ 22 ( 3 )

Where AirQ is the heat absorbed from circulating air,

For HE3,

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cwoutcwindotcwwLGBOOutLGBOindotoilOil TTmCTTmC 333 ( 4 )

For HE4,

cwoutcwindotcwwTGBOOutTGBOindotoilOil TTmCTTmC 444 ( 5 )

Again, heat absorbed by circulating air can be written as,

ELLGBUGBAir QQQfQ ,, ( 6 )

Where, ELLGBUGB QQQ ,, are the heat generated by upper Guide bearing, Lower guide bearing and

due to Electrical Load of the generator, respectively. Also CWAirOil CCC ,, are the specific heat ca-pacities of bearing oil, air and cooling water, respectively and 1, 2, 3, 4 are the efficiencies of heat exchangers.

UGBOilUGBUGBUGBUGB TTAUQ ( 7 )

LGBOilLGBLGBLGBLGB TTAUQ ( 8 )

Also, heat generated at TGB also can be expressed as,

TGBOilTGBTGBTGBTGB TTAUQ ( 9 )

Where TGBLGBUGBTGBLGBUGB AAAUUU ,,,,, are the heat transfer coefficients and surface areas of the Upper guide bearing, Lower guide bearing and turbine bearing, respectively.

Heat generated due to electrical load can be written as,

LefQEL ( 10 )

Where, Le is the electrical load.

Again, heat transfer coefficients, U also a complex non-linear function of temperatures, cooling water flow rates, thermal conductivity of the material, the individual convection heat transfer coefficient for each fluid and wall thickness as given in equation (11) [6].

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1111

AkAdx

AUAwall

(11)

Therefore, the system under investigation has multiple time dependent inputs and multiple outputs. Multiple input, Multiple output (MIMO) and interaction within the system are complex and non lin-ear in nature. So that, all the inputs has to be parallel processed to obtain the output. This type of computation can not be implemented by using conventional modelling techniques based on sequen-tial computer programs and based on first principles of thermodynamics. This topic will be discussed in detail in section 4.0 under developing of the model.

Hence, neural network (NN) approach is the best to model systems which exhibits the following characteristics. Due to the fascinating characteristics and capability of NNs, most of the models de-veloped in the past using other techniques are now being converted to NN model [7][8].

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Inputs and out puts have a cyclic repetitive pattern of variation over the time. Input/output past data of the system which describes the characteristics of the system is

available. The NN has the capability to identify the patterns exist in a given data set. The NNs can map the input data to the output data in a nonlinear system. The NNs can process data in parallel, so it can be applied to MIMO system easily.

Dynamic systems can be modelled using time delay inputs to the network to represent previ-ous time series values.

NN need to know little about the theory behind the process of the system.

The approach is described with the following steps:

1) As the system consists of several heat exchangers, which has different inputs and output bearing temperature variables, first the inputs (which characterize the behaviour of the sys-tem) and outputs of the model are clearly identified.

2) Then the past historical data over a period is collected from past operation data records.

3) Then an artificial NN is formed to model the system by mapping the input to known out-puts. The system is modelled using MATLAB neural network tool.

4) The simulated results are compared with past actual outputs and necessary adjustments are done to get the required accuracy.

5) The model and results are discussed with an objective perspective.

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3 Neural Networks

Neural networks (NN) play a vital role in the field of modelling and identifying characteristics of non linear systems. Hence, this section describes the capabilities of NN and mathematical theory behind it. In section 3.5.1, it is shown by an example, how NN technology can be used to solve a nonlinear problem.

3 . 1 I n t r o d u c t i o n Neural networks are capable of modelling complex MI-MO systems with non linear characteristics. So that NNs are a powerful tool in system modelling and identification field compared to conven-tional modelling techniques. NNs imitate the function of human brain or biological nervous system made up of small units called neurons. The network is formed by connecting the neurons with each other by adjustable weights between neurons. Neural network can be trained or adjusted to get a de-sired output or target for a given input. Hence, when the input, output characteristics of a system; historical data is available we can train a NN to model the system. NNs have the capability of identi-fying the patterns exist in the input/ output data, if a pattern exists. In section 3.2 gives a formal defi-nition of NN.

3 . 2 F o r m a l d e f i n i t i o n The following formal definition was proposed by Hechi-Nielson [9] which describes the functionality of neural network.

“An artificial neural network is a parallel distributed information processing structure consisting of processing units (which can posses a local memory and can carry out localized information process-ing operations) interconnected via unidirectional signal channels called connections. Batch processing unit has a single output connection that branches (“fans out”) into as many collateral connections as desired: each carries the same signal – the processing unit output signal. The processing unit output signal can be of any mathematical type desired. The information processing that goes on within each processing unit can be defined arbitrarily with the restriction that it must be completely local: that is, it must depend only on the current values of the input signals arriving at the processing element via impinging connections and on values stored in the processing unit’s local memory.”

3 . 3 B io l o g i c a l N e u r o n Human nervous system consists of about 1.3 x 1010 of neurons [10]. They are distributed among the human brain and the other parts of the body. It is found that about 1 x 1010 [10] neurons contain in the human brain itself. The basic building block of the nervous system is the neuron which contains four main parts. Normally it has a spherical shape. The cell body is called the ‘Soma’ and is sur-rounded by tree like branches called ‘Dendrites’ which receive signal from other neurons as shown in Fig. 3.1. The out of the neuron passes through the ‘Axon’ which has a length varying from fraction of mm to 1 m in human body [10][11].

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Fig 3.1 Biological Neuron

(source: Artificial Neural Networks, ch1, EE543 Lecture notes , METU EEE, Ankara , by Urgu Halici)

At the end of the Axon it is divided into branches called ‘Synapses’ which transmits the signals to other neurons. There are about 103-104 number of Synapses at each Axon end. The incoming signals to the cell body or Soma create an electrical potential due to the chemical changes takes place in the cell body. When this potential called ‘action potential’ exceeds a certain threshold that neuron fires and transmits pulse through the Axon [10].

These neurons form a parallel distributed network in the nervous system which helps to transmit in-formation gathered in the system to the brain to maintain a communication link. Signal transmission is caused by electric pulses. The pulses passing through the Axon has approximately constant ampli-tude but different time spacing decided by the statistics associated with the incoming signals from synaptic junctions of other neurons [10][11].

3 . 4 M a t h e m a t i c a l M o d e l o f a n e u r o n Characteristics of a biological neuron in mathematical form can be represented as shown in Fig. 3.2. The main three aspects of the biological neuron needed to be represented are the, synapses and the actual activity taken place inside the neuron. The weight w models the synapse. The value of the weight determines the strength of the connection. Then an adder adds up all the inputs.

Fig.3.2 neuron as a model

)( bwpfa (12 )

Typical characteristics of a neuron can be expressed as in equation (12). Where a, p and n are output of the neuron, input of the neuron and input to the activation function of the neuron, respectively. The output of neuron ‘a’, is the outcome of a function f called as activation function. Activation func-tion acts as a transforming function such that the output of a neuron should lie in between two de-

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fined values. Normally the lower and upper limits of the outputs are in between 0 to 1 or -1 to 1. Ac-tivation functions used in neural networks can be in several forms [12].

Generally there are three types of activation functions commonly used. The first type of function acts as a threshold function. If the summed up value exceeds a certain threshold value it is considered as 1 otherwise 0 which is called the step function. In mathematical form it can be shown as, given in equation (13).

nf 1 if 0n

0 if 0n (13)

First type of activation function characteristic is shown in Fig. 3.3

Fig. 3.3 Step function

Second type is the piecewise linear function. Output of this function lies in a linear region depending on the amplification factor, which can be expressed as shown in equation (14). A graphical form is shown in Fig. 3.4.

1 21n

nf n 2121 n

0 21n (14)

Fig. 3.4 Piecewise linear function

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The third type is ‘Sigmoid’ function which can take two forms, ‘logistic Sigmoid’ or ‘tangential Sig-moid’. The logistic sigmoid function is also called as ‘logsig’, whose characteristics are shown in Fig. 3.3.

Fig. 3.3 Logsig function

The ‘Logsig’ function f can be expressed as in equation (15),

nenf

11)( (15)

The tangential sigmoid function is also called as ‘tansig’, whose characteristics are shown in Fig. 3.4.

Fig. 3.4 Tansig function

The ‘tansig’ function f can be expressed as in equation (16),

nn

nn

eeeenf

)( (16)

The tangential sigmoid has the advantage due to it’s ability to deal with negative numbers which transforms output in between -1 and +1, while the ‘logsig’ function normalizes the output in between 0 and1. In our case we are using ‘logsig’ function as the activation function as we do not deal with negative numbers.

3 . 4 . 1 N e u r o n w i t h m u l t i - i n p u t s When there are several inputs to the same neuron, the model can be represented as shown in Fig. 3.5. p1, p2, …. pR are the input value and while w11,w 12,…..w1R represents the corresponding weights.

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Fig. 3.5 neuron with multi inputs (source: neural network toolbox user guide)

Mathematically this can be represented in vector form as,

nbwww

p

pp

R

R

11211

2

1

.. (17)

1 x R R x 1 1x1 1x1

3 . 4 . 2 L a y e r o f N e u r o n s Similarly a number of inputs also can be modelled as shown in Fig. 3.6 by layer of input neurons.

Fig. 3.6 Layer of neurons with multi inputs (source: neural network toolbox user guide)

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3 . 4 . 3 M u l i - l a y e r n e u r o n s

Fig. 3.7 Multi layer neurons (source: neural network toolbox user guide)

In a multi-layer neural network the relationship between inputs and the outputs can be expressed as,

bwfa pL 11111 (18)

For layer two as,

)212122 bawfa L (19)

Similarly for the 3rd layer,

bawfa L 323233 (20)

From equation (19)(20) and (21),

bbbwfwfwfa pILL 3211112123233 (21)

General Structure of NN

Followings are the typical major aspects common to any NN model.

A set of input processing units A state of activation for each unit An output function for each unit Topology of the network that describes pattern of connectivity among processing units. A rule defined to propagate or combine activities of processing units through out the net-

work. A defined rule to activate and update values received from input neurons. External data input that provides information of the environment. A rule to modify connectivity pattern based on the data which describes the environment.

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3 . 4 . 4 T r a i n i n g a n e u r a l n e t w o r k Generally neural networks trained by adjusting the weights. At the beginning of the training process the bias values (b) and weights are initialized randomly (random values are selected)

The training method can be classified in to several categories based on the method used by the net-work to learn behaviour of the actual system by adjusting the weights of the network so as to obtain the desired output. These methods can be classified into two main types called supervised-learning’ and ‘unsupervised-learning’.

Fig.3.8 Training process (source: Matlab user guide)

3 . 4 . 4 . 1 S u p e r v i s e d l e a r n i n g In the process of supervised learning, the network is allowed to adjust its weights by comparing the input and corresponding outputs. The inputs are fed to the network input nodes batch by batch and the actual output is compared with target. The error is used as a feedback to adjust the bias values and weights. This process is repeated until an accepted preset value is reached. The process can be pictorially depicted as shown in Fig. 3.8 which is called the supervised learning as the network is self-supervised during the training process. This method needs to have the historical data which repre-sents the behaviour of the system

3 . 4 . 4 . 2 U n s u p e r v i s e d l e a r n i n g In this method, when the inputs are fed into the network it creates its own outputs to represent those inputs. When the same inputs are fed to the network it produces the same out puts as earlier. In this way network classified the inputs into several categories or identifies the inputs. Compared to the previous method this training does not need any external supervision.

Our problem under investigation falls into the first category where historical data is used to train the network.

3 . 4 . 5 T r a i n i n g p r o c e s s Steps of the training process can be given as follows,

Feed first training sample to the NN. Initialize the threshold and weights for the input hid-den and output nodes of the network and set small random values.

For each hidden unit calculate,

i

R

ijij pwn

1

(22)

31

njj ea 1/1 for j=1.2…N (23)

For each output calculate,

N

jjkjk awO

1* (24)

For each neuron calculate a scaling factor in order to adjust the difference between net-work actual output and the desired output. In other words, actual and the target.

Adjust the weights of each neuron to reduce the local error,

kjkjkj ww (25)

Move to the next training sample, and repeat the procedure for all training samples. At the end compare the actual output with the target for each output neuron. Then calculate the mean square error.

The mean squared error is calculated by calculating difference between target and the actual output, squaring it summing over all the trials. Then by dividing by the number of trials M, to get the mean value as given in equation (26).

2

1

.1M

jjj taMdErrorMeanSquare (26)

When the mean squared error reaches the possible minimum value the corresponding trained net-work is saved. This is used to test the performance of the network for new data.

3 . 5 D e m o n s t r a t i o n o f d e v e lo p i n g a N N b y e x a m p l e In this section a demonstration is done to explain how a problem is solved using NN technology. This problem is related to the modelling of non linear thermodynamic characteristics, to show the capability of NNs.

3 . 5 . 1 P r o b l e m The problem selected is related to representation of thermodynamic properties of steam. Enthalpy, entropy characteristics of steam is non-linear. For different value of x (steam quality) characteristic curves can be represented as shown in Fig. 3.9, for different values of x, x=0.8, 0.85, 0.9 and for 0.95 respectively. These characteristics can not be modelled by using mathematical models due to its com-plexity and non-linear nature. Hence, some other method has to use to model these characteristics.

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Enthalpy vs Entropy for Steam

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

5.00

5.40

5.80

6.20

6.60

7.00

7.40

7.80

8.20

8.60

9.00

Entropy S

Enth

alpy

h /

KJ/

Kg

Enthalpy x=1.0x=0.95x=0.90x=0.85x=0.80

Fig 3.9 Enthalpy vs Entropy for Steam

Capability of modelling non-linear characteristics of a system in NNs can be useful in modelling a system of this nature. This system can considered as a model with 2 inputs, steam quality x and en-tropy s and enthalpy h as the output as shown in Fig. 3.10.

3 . 5 . 2 S y s t e m a s a N N m o d e l

Fig 3.10 NN model (inputs/outputs)

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3 . 5 . 3 D a t a u s e d Entropy, enthalpy data used to model the system is shown in the table 3.

Table 3: Data of Entropy and enthalpy for different values of x , steam quality

Entropy S

Enthalpy for

x = 1.0 x = 0.95 x = 0.90 x = 0.85 x = 0.80

5.0 2461 2461 2446 2446 2423 5.2 2561 2561 2534 2515 2450 5.4 2653 2630 2600 2538 2438 5.6 2723 2684 2630 2538 2400 5.8 2769 2715 2623 2500 2330 6.0 2800 2715 2600 2446 2265 6.2 2808 2693 2561 2400 2215 6.4 2793 2661 2523 2346 2165 6.6 2769 2638 2475 2300 2123 6.8 2746 2600 2446 2261 2076 7.0 2719 2569 2400 2230 2038 7.2 2692 2542 2369 2200 2015 7.4 2669 2507 2338 2176 7.6 2650 2476 2318 2146 7.8 2623 2453 2293 2130 8.0 2600 2438 2276 8.2 2576 2423 2261 8.4 2553 2400 8.6 2538 2384 8.8 2523 9.0 2515

This data has to be normalized in order to make the data range in between 0-1. We take normalized s = S/10 and h=H/10000 to feed into the NN model as inputs and targets in the training process.

3 . 5 . 4 T r a i n i n g Training data set consists of 63 set of input/output data values (s, x), where s and x are the entropy and steam quality respectively. Entropy (s) is ranging from 5 to 9 for different values of x ranging from 0.8 to 0.95. As the system has two inputs (x, s); input layer consists of two neurons and the out-put layer one neuron to represent the output (h). In this case two hidden layers are selected which comprises of 3 neurons and 2 neurons for the hidden layer 1 and hidden layer 2, respectively, as shown in Fig. 3.11. Initially, number of hidden layers and number of neurons in each layer are se-lected randomly. Later, they are changed so as to get the optimized performance of the model by minimizing the error.

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Fig. 3.11 NN model

In the implementation of this network in Matlab, it can be represented in Matlab code as,

nnet=newff(pr,[2321],{'tansig''tansig''tansig''tansig' },'trainbr');

which represents

newff, Create a feed-forward back propagation network.

pr, represents the input data

2321, number of neurons in each layer (input, hidden layer 1, hidden layer 2, output layer etc)

tansig, is a transfer function. Transfer functions calculate a layer's output from its net input.

Trainbr, is a network training function that updates the weight and bias values according to Leven-berg-Marquardt optimization. It minimizes a combination of squared errors and weights and, then determines the correct combination so as to produce a network which generalizes well. The process is called Bayesian regularization [13].

Full code listing of the Model training program is given below.

% develops a model to steam entropy enthalpy Characteristics (10 jun 2010) % Trains ,validates and tests new data close all; clear all; tic; file=xlsread('steam','a23:c86'); % loads xl data file toc; tic; B=file(:,1:2); % loads inputs x, s C=file(:,3:3); % loads outputs h p=B'; % inputs t=C'; % targets Q=6; n=63;

dtst=14:Q:n; % divides data for training validation dval= [ 13:Q:n ]; % and testing

dtrn=[1:Q:n 2:Q:n 3:Q:n 4:Q:n 5:Q:n 6:Q:n 7:Q:n 8:Q:n 9:Q:n 10:Q:n 11:Q:n 12:Q:n ]; val.P=p( : , dval); % validation data val.T=t( : , dval); test.P=p( : , dtst); % test data test.T=t( : , dtst); ptr=p( : , dtrn); % training data

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ttr=t( : , dtrn); nnet=network; % creates network pr=minmax(p); nnet=newff(pr,[2 3 2 1 ],{ 'tansig' 'tansig' 'tansig' 'tansig' },'trainbr'); nnet.trainParam.epochs = 1000; nnet.trainParam.show = 1; nnet.trainParam.lr = 0.01 % SETS ETA learning rate [nnet,tr]=train(nnet,ptr,ttr,[],[],val,test); plot(tr.epoch,tr.perf,tr.epoch,tr.vperf,tr.epoch,tr.tperf) legend('Training' , 'Validation' , 'Test', -2); ylabel('Squared Error'); xlabel('Epoch '); title(' Model Performance'); a = sim(nnet,p); % simulates figure(1) t1=t(1:1,1:63); % target a1=a(1:1,1:63); % simulated output plot(2:64,a1,'.',2:64,t1,'r-') ylabel('Output'); xlabel('Entropy S '); title(' Predicted vs Actual'); % writes data into xl file SUCESS=XLSWRITE('steam_op.xls',a1','b2:b64') SUCESS=XLSWRITE('steam_op.xls',t1','c2:c64') toc; % regresson analysis figure(2) % [m(1),b(1),r(1)]=postreg(a1,t1); % end In the training process the training is done iteratively for a number of epochs (iterations) until the er-ror (in this case SSE; sum of squared error) reaches to a predefined value. Variation of performance, training, validation and testing errors during the training process is shown in Fig 3.12. At the end of around 260 epochs (iterations), training, validation and testing errors have reached to 1.59084e-005, 1.40373e-006 and 6.53338e-007, respectively.

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Fig.3.12 Training error of the model

3 . 5 . 5 S i m u l a t i o n Simulation is done in order to test the trained model to see whether it performs well for the new data (unseen data) fed to the model. In this case data relevant to x=1.0 was selected as the new data to test the model.

Model simulation (testing) matlab code listing

% Tests the model for new data % of steam x= 1.0 (13 Jun 2010) close all; clear all; tic; A=XLSREAD('steam'); % loads xl data file load model; % trained network model net1= model; toc; % column 1 and 2 is input data rec_start=2; rec_end=22; n=rec_end-rec_start; % no of records tic; B=A(2:22,3:3); % loads data output (entropy,h) C=A(2:22,1:2); % loads inputs ( x, s) p=C'; t=B'; toc; pr=minmax(p); tic; a = sim(net1,p); % simulate the model figure(1) % graph 1 t1=t(1:1,1:n); % expected target a1=a(1:1,1:n); % simulated target plot(1:n,a1,'bx',1:n,t1,'r-') ylabel('Enthalpy / KJ/Kg Pu') xlabel('Entropy, S / KJ/Kg') legend('simulated ' , 'actual '); title('Entropy vs Enthalpy for steam x =1.0') % end

3 . 5 . 6 R e s u l t s Simulation results of the model shown in Fig.3.13 illustrate the characteristic curves relevant different steam qualities. The simulated characteristics generated by the NN model in comparison to actual values are almost same. This result shows how the model has modelled the characteristics of the given data set for training.

The NN has satisfactorily modelled the characteristics of steam. Regression analysis for the simula-tion is shown in Fig.3.14 proves the performance of the model.

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Fig.3.13 Simulated vs Actual characteristics

Fig. 3.14 Regression analysis result for the model

The simulated results for unseen (new) data to the model which corresponds to x=1.0 is shown in Fig.3.15. It compares actual characteristics with the simulated result. So the model accurately simu-lates the steam characteristics where the corresponding regression analysis results are shown in Fig. 3.16.

Hence, using this model any other characteristics curves corresponding to intermediate values of x such as x=0.775, 0.825, 0.875, 0.925, 0.975 can be obtained is shown in Fig 3.17

.

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Fig.3.15 Simulated (predicted) characteristics for new data for x=0.1

Fig.3.16 regression analysis results for x=1.0

Fig.3.17 Predicted characteristics for new data x=0.775, x=0.825,

X=0.875, x=0.925, x=0.975 and x=1.0

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4 Developing the model

This section describes the approach and steps followed to develop a dynamic model to simulate hy-dro-electric power generating unit bearing temperature variation with time, electrical load, with the duration of operation and other environmental factors.

4 . 1 S e l e c t i o n o f i n p u t v a r i a b l e s Input variables which affect to the characteristics of the system under investigation are listed out be-low.

TLGBm Lower guide bearing metal temperature TUGBm Upper guide bearing metal temperature TTGBm Turbine guide bearing metal temperature TTHBm Thrust bearing metal temperature TLGBoil Lower guide bearing oil temperature TUGBoil Upper guide bearing oil temperature TTGBoil Turbine guide bearing oil temperature TTHBoil Thrust bearing oil temperature Tcooling water Cooling water temperature Tair Circulating air temperature mdotCW Cooling water flow rate mBCW Bearing cooler water flow rate Le Electrical load (MWs) Lvars Electrical load (Vars) The main concern is to simulate the temperature variation pattern of,

TLGB, TUGB,TTHB, TTGB, TLGBoil, TUGBoil, TTGBoil and TTHBoil. But, values of the above variables depend not only on the instantaneous values of them, but current values as well as the previous values. It can be illustrated more general form as shown in Fig. 4.1, where, Xi as temperature related inputs, mi as flow rate related inputs and Li as load variable related inputs .

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Fig.4.1 System as a static model

Where,

Xi = { TUGBm(0), TTHBm(0), TLGBm(0), TUGBO(0), TLGBO(0), TTGBO(0), TUGBm(t-2T), TUGBm(t-T), TUGBm(t), TTHBm(t-2T), TTHBm(t-T), TTHBm(t), TLGBm(t-2T), TLGBm(t-T), TLGBm(t), TTGBm(t-2T), TTGBm(t-T), TTGBm(t), TUGBo(t-2T), TUGBo(t-T), TUGBo(t), TLGBo(t-2T), TLGBo(t-T), TLGBo(t), TTGBo(t-2T), TTGBo(t-T), TTGBo(t), TCW(t-2T), TCW(t-T), TCW(t), TCA(t-2T), TCA(t-T), TCA(t), } Mi = { mdot1(t-2T), mdot1(t-T), mdot1(t), mdot2(t-2T), mdot2(t-T), mdot2(t) } Li = { Lmw(t-2T), Lmw(t-T), Lmw(t), Lmv(t-2T), Lmv(t-T), Lmv(t), }

4 . 2 S e l e c t i o n o f d a t a As a case study, a set of data records were obtained from the Victoria hydro power station, Sri Lanka. It is a vertical shaft turbine generator unit which has an electrical power generating capacity of 71 MW. The data set was extracted from eight channels of the DAQSTANDARD R8.11 data recorder, which contains bearing metal temperatures, oil temperatures, cooling water flow rates and generator electrical load. The data set consists of 3623 data records as given in Appendix D. The sampling pe-riod of data was 10 minutes intervals.

4 . 3 A p p r o a c h o f d e v e l o p i n g a d y n a m i c m o d e l In section 4.3.1 up to 4.3.4, it is described the approach and how the model is developed in step by step by starting from the selection of variables to developing a model to characterize the system.

4 . 3 . 1 D e v e l o p i n g a s t a t i c N N m o d e l As discussed earlier, in section 4.1 and as shown in Fig. 4.1, there are two types of input variables to the model, temperature dependent variables ( bearing metal temperatures, bearing oil temperatures, cooling water temperature and circulating air temperature) as denoted by Xi. Second, type of inputs is the bearing water flow rates that do not change due to the performance of the system and the elec-trical load that directly affect to the bearing metal and bearing oil temperatures.

42

The variables that interact with system can also be classified into two categories. They are external variables and internal variables. Electrical load, cooling water temperature, circulating air tempera-tures are acts as external factors while initial bearing metal temperature, bearing oil temperature act as internal variables of the system. In a system of this nature, output values depend on the present status as well as previous status of the system.

In mathematical form, general behavior of the system can be defined as,

State equation,

)),(),(()( wtXtSfTtS (27)

Output equation,

)),(()( wtShty (28)

Where, S represents the state vector, x external input vector and w neural parameter vector synaptic connection vectors and operational parameters, f(.) is the function that represents the structure of the neural network, and h(.) is a function that represents the relationship between state vector S(t) and output vector y(t) [13].

The output of the system does not depend on the current inputs but also on the previous values. Therefore, previous time series values also have to be considered. Some times in order to get a rea-sonable accuracy several previous states have to be considered. Therefore, some sort of memory ca-pability has to be introduced to the model. The variation of temperatures are continues varying func-tions. But, as we consider sample inputs at a chosen time interval the model becomes a discrete sys-tem. Hence, the memory capability can be incorporated by giving a series of time delay inputs to rep-resent previous states [14].

Fig 4.2 Representation of a NN for prediction

Selection of time delay, inputs to represent the previous states in a NN structure and predicting the output can be shown in Fig. 4.2, where one time dependent variables is shown there. Equations (27) and (28) describe behavior of a first order system which takes into account the previous state (with one step time delay) of the variables. In generally nth order system can be described as,

State equation,

)),()]1[().........2(),(),(()( wtXTntSTtSTtStSfTtS (29)

Output equation,

43

)),(()( wtShty (30)

We have developed two models; second order and third order. Then by comparing the performance or output error, the better model with the lowest error can be selected. But, higher the number of time series values or degree of the network, number of hidden layers, and number of neurons in each layer the computing power (memory and processor speed) required is higher. Hence, a compromiza-tion between accuracy and computing power is needed.

In a second order system we have to consider the two previous states. Therefore, in order to predict the bearing temperature value at time t, bearing temperatures at time, (t-T) and (t-2T) also has to con-sidered. Then, with the bearing metal temperature, bearing oil temperature, cooling water tempera-ture, circulating air temperature and electrical load MWs, MVars altogether makes 32 inputs to the model. Our intention is to predict the four bearing metal temperatures but as bearing oil tempera-tures, cooling water temperature and circulating air temperatures also affect to it, altogether the num-ber of outputs become 9 (TUGBm, TTHBm, TLGBm, TTGBm, TUGBOil, TLGBOil, TTGBOil, Tcw, TCA). So that, the ini-tial architecture of the NN takes shape of 32 input nodes, and 9 output nodes as shown in Fig. 4.2. Let’s arbitrarily select two hidden layers. This can be changed if necessary during the process of training the network. [15][16][17].

Then, the initial architecture becomes (32, 24, 15, 9), where number of inputs and outputs are a fixed value and the number of input also can be changed according to the consideration of previous status of inputs at interval such as t-T, t-2T, etc depending on the accuracy or the error of training. Training, validation and testing errors explain to what extent that the model fit to the actual system behavior.

Fig 4.2 General NN architecture

4 . 3 . 2 T r a i n i n g t h e n e t w o r k a n d t r a i n i n g r e s u l t s For training the network 500 data records which consists of past data inputs and outputs were used. Initially, time interval t, time intervals t, t-T, t-2T was considered 23 input 9 outputs and 32 inputs, 9 outputs, respectively. Four different architectures were selected by varying the number of previous status considered, number of hidden layers and number of nodes in hidden layers etc. For training the model four different architectures were considered as shown in Table 4.1

Table 4.1: Model Architecture

Model no Architecture 1 23,15,12,9 second order 4 Layers 2 32,21,9 third order 3 Layers 3 32,28,16,9 third order 4 Layers 4 32,25,15,9 third order

44

Training, testing and validation results are shown in Table 4.2 for models 1,2,3 and 4, respectively. The model with the (32, 25, 15, 9) architecture gives the performances giving the lowest training error of 0.0689 SSE.

Table 4.2: Model Performance Model no Architecture Training Error (SSE) 1 23, 15, 12, 9 second order 1.4634 2 32, 21, 9 third order 0.2478 3 32, 28, 1 6, 9 third order 0.1189 4 32, 30, 16, 9 third order 0.0689 5 32, 40, 26, 9 third order 0.0011

In order to improve the training performance of the model, the whole system was divided into two sub units and two separate models are developed for the individual sub units. The new approach is shown in Fig 4.3.

Fig 4.3 Sub models to represent the system

Decomposed model with two sub models shows better training performance compared to single model. The architecture selected for the sub models are (19, 50, 25, 5) and (17, 50, 30, 6) respectively.

Where, UGBm, THBm, UGBo, CW, CA with delayed time series inputs and MW, Mvar, cooling bearing water flow rate act as inputs to the model 1. Then, similarly LGBm, TGBm, LGBo, TGBo, with delayed time series inputs and MW, Mvar, cooling bearing water flow rate act as inputs to the model 2. The training performance of the model is shown in Table 4.3 for model 1 and model2, re-spectively.

Table 4.3. : Sub Model Performance Model no Architecture Training Error (MSE) 1 19, 50, 25, 5 3.04 X 10-7 2 17, 50, 30, 6 3.80 x 10-7

Graphical representation of the performance and convergence of the errors to a minimum value dur-ing the training process is shown in Fig. 4.4.

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Fig. 4.4 Training Performance of Model 1

4 . 3 . 3 S t a t i c m o d e l s i m u l a t i o n r e s u l t s Our approach is to develop (training) a static model to simulate the behavior of the real system and then to convert it to a dynamic model by arranging a feedback of internal variables as inputs to the model. The simulated outputs are compared with the actual outputs to evaluate the performance of the static model.

4 . 3 . 4 D e v e l o p i n g t h e d y n a m i c m o d e l As described in the previous section in order to model the temporal nature of the system as well as the effect of the internal variables the general architecture of the model should be as shown in Fig. 4.5 where Xi(0) denotes the initial conditions.

Fig 4.5 NN Dynamic model

46

Algorithm of the simulation:

Read Xi(0), initial conditions (bearing metal and oil temperature) read Xi(t),Xi(t-T),Xi(t-2T), bearing metal and oil temperature Mi(t),Li(t) cooling water flow rates, circulating air temperature and electrical load, make input matrix load trained neural network decide time duration n loop up to n records

simulate and get output of Xi(t+T) update inputs record output

end plot graph of Xi(t)simulated & actual For corresponding Matlab implementation (Matlab codes) see appendix C.

Next section presents the dynamic simulation results obtained from the model.

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5 Results

5 . 1 S t a t i c m o d e l s i m u l a t i o n r e s u l t s

5 . 1 . 1 S t a t i c m o d e l s i m u l a t i o n r e s u l t s f o r b e a r i n g m e t a l t e m p e r a t u r e

Fig. 5.1. Simulation results of the static model

48

Out put results obtained from the static model are shown in Fig. 5.1. It represents the UGB, LGB, THB and TGB metal temperature variation with time for a given generator load profile.

5 . 1 . 2 C o - r e l a t i o n c o e f f i c i e n t o f t h e s t a t i c s i m u l a t i o n r e s u l t s Corresponding correlation coefficient results for bearing metal temperatures for UGB, LGB and THB and TGB are shown in Fig 5.2.and Fig. 5.3 respectively.

Fig.5.2. Co-relation results for UGB and LGB metal temperature

Fig.5.3. Co-relation results for THB and TGB metal temperature

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5 . 1 . 3 S t a t i c m o d e l s i m u l a t i o n r e s u l t s f o r b e a r i n g o i l t e m p e r a t u r e

Fig 5.4. Simulation results of static model for bearing oil temperature

Simulation results of static model for bearing oil temperature for UGB, THB and TGB and corre-sponding co-relation coefficients graphs are shown in Fig. 5.4. and Fig. 5.5, respectively.

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5 . 1 . 4 C o r r e l a t i o n c o e f f i c i e n t s o f s i m u l a t i o n o n b e a r i n g o i l t e m p e r a t u r e .

Fig.5.5. Correlation coefficients of simulation on bearing oil temperature

Summary of the static model simulation results are shown in Fig.5.6 and Fig.5.7 for bearing metal and bearing oil.

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5 . 1 . 5 S u m m a r y r e s u l t s o f s t a t i c m o d e l

Fig. 5.6. Simulation results of static model for all four bearing metal temperatures

Fig. 5.7 Simulation results of static model for bearing oil temperatures

52

5 . 2 D y n a m i c s i m u l a t i o n r e s u l t s

5 . 2 . 1 D y n a m i c s i m u l a t i o n r e s u l t s f o r b e a r i n g m e t a l t e m p e r a t u r e

Fig. 5.8 Dynamic simulation results for bearing metal temperature

53

5 . 2 . 2 D y n a m i c s i m u l a t i o n r e s u l t s f o r b e a r i n g o i l t e m p e r a t u r e

Fig 5.9 Dynamic simulation results for bearing oil temperature

Dynamic model simulation results for bearing metal temperature variation and bearing oil tempera-ture variation for new data (unseen data) for the model are shown in Fig.5.9 and Fig.5.10 respectively.

5 . 3 D y n a m i c s i m u l a t i o n r e s u l t s f o r r e d u c e d f l o w r a t e

5 . 3 . 1 B e a r i n g m e t a l t e m p e r a t u r e v a r i a t i o n

54

Fig 5.10 Dynamic simulation results of bearing metal temperature rise for reduced cooling water flow rate

A new input data set, which represent a different operating environment (i.e. reduced cooling water flow rate) were presented to the trained model. The simulated out put given by the model is shown in Fig.5.10 for bearing metal temperature variation and in Fig.5.11 for bearing oil temperature respec-tively.

Both the bearing metal and oil temperatures show a temperature rise over the normal operating con-ditions due to reduced cooling effect of heat exchangers as results of reduced (10%) cooling water flow rate.

5 . 3 . 2 B e a r i n g o i l t e m p e r a t u r e v a r i a t i o n

Fig 5.11 Dynamic simulation results of bearing oil temperature

rise for reduced cooling water flow rate

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6 Discuss ion

In this research work Neural Network modelling approach was used to model the bearing heat ex-changer system of a hydro electric power generating unit. The results shown in section 5 consist of performance obtained from the static model for bearing metal temperature. Static simulation was done in order to test the accuracy of the static model. Correlation coefficient results shown in Fig. 5.2 and 5.4 respectively show the accuracy of actual verses simulation results.

Then, as discussed in section 4.3.4, dynamic simulation model was developed using the above results. The results obtained for the dynamic simulation for the untrained on untested data are shown in Fig. 5.7 and 5.8 for bearing metal temperatures and bearing oil temperatures respectively. Those results shows with accuracy of ±1.0 °C for bearing metal temperature and ±2.0 °C variation for bearing metal temperature with compared to the actual past performance of the system.

For improving the accuracy, more past data needs to feed to cover all possible input combinations and also several previous values of inputs. Higher number of inputs of the NN model, number of in-put layer neurons and intermediate layer neurons increase. Therefore, higher computing capacity is needed in terms of memory and processor speed to train the network.

In section 5.3, it was tested the behavior of the heat exchanger system due to a reduced cooling water flow rate for the same load profile, as it usually happens in operation of power plants. In section 5.3, as shown in Fig.5.10 and 5.11, both the bearing metal temperatures and the bearing oil temperatures have risen over the normal stabilized temperature level due to the reduced heat absorbing rate caused by the reduced (10%) cooling water flow rate.

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7 Conclusions

Continuous operation of old hydropower plants have constrained with the failures due to bearing overheating. The objective of this work was modelling and simulation of dynamic variation of tem-peratures of bearings (generator guide bearing, turbine guide bearing, thrust bearing) of a hydro elec-tric generating unit. The temperature of a bearing is depends on multiple variables such as ambient air temperature, cooling water temperature, cooling water flow-rate, initial bearing temperatures, du-ration of operation and generating unit electrical load.

As the problem under investigation was a multi-input (MI) and multi-output (MO) system, conven-tional first principles based model approach and sequential computer programs could not be applied. So that the neural network (NN) method was selected as the best where past input and output data is available, and the input characteristics can be mapped in order to develop a model. The NN’s capa-bility of parallel processing was used to develop a model the system. This was implemented in MAT-LAB environment. According to the simulation results, it demonstrates a reasonable (±2 °C) accuracy to predict the temperature variation for a given generator load profile.

Hence, this model can be used to predict the temperature variation characteristics of the system. Temperature increase in ambient air, or cooling water (due to reduced cooling water flow rate) would increase the temperature level of bearing metal and oil. Using this model, it is possible to predict the temperature increase for a given generator load profile for a given period. It will help to determine maximum safe load level, while maximizing the plant factor minimizing the sudden failures due to bearing overheating.

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8 References

[1] www.eia.doe.gov/ Energy Information Administration international statics database, visited 04-03-2010 [2] Renewable Global Status Report 2006 Update, REN21, published 2007, accessed 04-03-2010; see Table 4, p. 20 [3] Statistical Digest 2009, Ceylon Electricity Board, Sri Lanka [4] http://www.machinerylubrication.com/Read/367/temperature-stability, Machinery Lubrica-tion, as accessed 2010-03-02 [5] R.K.Sharma, T.K.Sharma, A text book of Water Power Engineering, S.Chand & Company Ltd, pp 450-455, 2000 [6] http://www.engineeringtoolbox.com/overall-heat-transfer-coefficient- d_434.html,The Engi-neering Tool Box, as accessed 22-10-2010 [7] Girish kumar Jar, Artificial neural networks and it’s applications, IARI, New Delhi- 100-012, pp 41-42, [8] Raủl Rojas, Neural network a systematic introduction, Sprinter -Verlag, Berlin, New-York, pp 5-27, March 1996. [9] Heichi Neilson R. [1990], Neurocomputing, Addison-Wesley, Reading, Mass.pp 18, 1990 [10] Ugur Hlici, Artificial Neural Networks, EE543 Lecture notes, METU EEE, Ankara. [11] http://www.learnartificialneuralnetworks.com/, Artificial Neural network tutorial as accessed 24-06-2010 [12] Matlab Neural Network User’s Guide, The Mathworks inc, 1992-2010 [13] Stuart Russel, Peter Norvig, Artificial Intelligence A Modern Approach Persons Inc, pp24,693-695,727-736,1995, [14] G. Bekely and K. Goldberg, Eds, Norwell , MA Kluwer , Stable nonlinear system identification using neural network models in Neural Networks in Robotics, pp 147-164,1992 [15] http://www.obitko.com/tutorials/neural-network-prediction/prediction-using-neural-networks.html, Prediction using Neutal Networks, as accessed 17-11-2010 [16] Madan M Gupta, Liang jin and Noriyasu Homma, Static and Dynamic Neural Networks From Fundamental to Advanced theory, John Wiley& Sons Inc, Hobokan New Jersey,pp 27-31,297-387, 2003 [17] James A Freeman, David M Skapura, Neural networks Algorithms, Applications, and pro-gramming techniques, Pearson Inc, pp 12-30,89-93,1999

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Appendix A : NN init ial weight and bias values (NN example)

nnet = Neural Network object: architecture: numInputs: 1 numLayers: 4 biasConnect: [1; 1; 1; 1] inputConnect: [1; 0; 0; 0] layerConnect: [4x4 boolean] outputConnect: [0 0 0 1] targetConnect: [0 0 0 1] numOutputs: 1 (read-only) numTargets: 1 (read-only) numInputDelays: 0 (read-only) numLayerDelays: 0 (read-only) subobject structures: inputs: {1x1 cell} of inputs layers: {4x1 cell} of layers outputs: {1x4 cell} containing 1 output targets: {1x4 cell} containing 1 target biases: {4x1 cell} containing 4 biases inputWeights: {4x1 cell} containing 1 input weight layerWeights: {4x4 cell} containing 3 layer weights functions: adaptFcn: 'trains' initFcn: 'initlay' performFcn: 'mse' trainFcn: 'trainbr' parameters: adaptParam: .passes initParam: (none) performParam: (none) trainParam: .epochs, .show, .goal, .time, .min_grad, .max_fail, .mem_reduc, .mu, .mu_dec, .mu_inc, .mu_max, .lr weight and bias values:

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IW: {4x1 cell} containing 1 input weight ma-trix LW: {4x4 cell} containing 3 layer weight ma-trices b: {4x1 cell} containing 4 bias vectors other: userdata: (user stuff)

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Appendix B: Train ing record ( NN example)

TRAINBR, Epoch 0/1000, SSE 18.3133/0, SSW 1279.74, Grad 4.87e+001/1.00e-010, #Par 2.60e+001/26



TRAINBR, Epoch 3/1000, SSE 0.0269173/0, SSW 135.249, Grad 8.41e-001/1.00e-010, #Par 3.66e+000/26







TRAINBR, Epoch 10/1000, SSE 0.00455401/0, SSW 133, Grad 3.08e-001/1.00e-010, #Par 8.08e+000/26






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TRAINBR, Epoch 39/1000, SSE 9.4329e-005/0, SSW 131.778, Grad 3.31e-002/1.00e-010, #Par 1.67e+001/26

















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TRAINBR, Validation stop.

Elapsed time is 74.438000 seconds.

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Appendix C: Sample data used for training the model

DAQSTANDARD R8.11 Data Viewer R8.11 CEYLON ELECTRIC-ITY BOARD Device Type DX2000 Serial No. S5J603679 File Message U1-TOP DATA Time Correction None Starting Condition Auto Dividing Condition Auto Meas Ch. 0 Math Ch. 0 Ext Ch. 0 Data Count 3623 Sampling Interval 10 minutes Start Time 10/25/2010 10:20:00 Stop Time 2010/11/19 14:20:00 Trigger Time 2010/11/19 14:20:00 Trigger No. Started by Admin1 Stopped by [ Running ]

Num. Of Converted Data 3623

CH015 CH018 CH023 CH024 CH026 CH027 CH028

UGB.PAD-5

LGB.PAD-4

THRUST BRG.PAD-11 TGB

THRUST/LGB.-OIL

C.W.-INLET LO AD

Date Time C C C C C C MW MVar

2010/11/03 16:30:00 40.3 43.1 39.6 25.0 38.6 24.6 52 0

2010/11/03 16:40:00 40.2 42.9 39.4 24.8 38.4 24.7 61 21

2010/11/03 16:50:00 40.2 42.8 39.2 24.6 38.2 24.7 74 22

2010/11/03 17:00:00 40.2 42.6 39.0 24.4 38.0 24.8 76 21

2010/11/03 17:10:00 40.1 42.5 38.9 24.3 37.8 24.8 74 21

2010/11/03 17:20:00 40.1 42.3 38.7 24.1 31.0 24.8 75 20

2010/11/03 17:30:00 47.6 51.2 58.9 44.3 42.2 24.6 77 19

2010/11/03 17:40:00 48.5 55.2 64.6 50.0 46.9 24.6 75 19

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2010/11/03 17:50:00 48.5 57.5 67.1 52.5 49.3 24.6 77 20

2010/11/03 18:00:00 48.8 58.8 68.2 53.6 50.8 24.6 75 21

2010/11/03 18:10:00 48.9 59.6 68.9 54.3 51.7 24.7 76 21

2010/11/03 18:20:00 49.0 60.2 69.5 54.9 52.3 24.7 74 24

2010/11/03 18:30:00 49.1 60.6 69.9 55.3 52.7 24.7 76 21

2010/11/03 18:40:00 49.2 60.8 70.2 55.6 53.0 24.7 77 19

2010/11/03 18:50:00 49.3 61.0 70.4 55.8 53.2 24.7 77 19

2010/11/03 19:00:00 49.3 61.2 70.5 55.9 53.4 24.7 76 18

2010/11/03 19:10:00 49.5 61.3 70.7 56.1 53.5 24.7 76 17

2010/11/03 19:20:00 49.5 61.4 70.7 56.1 53.6 24.7 76 17

2010/11/03 19:30:00 49.7 61.4 70.7 56.1 53.6 24.7 76 17

2010/11/03 19:40:00 49.8 61.5 70.9 56.3 53.7 24.8 78 17

2010/11/03 19:50:00 49.9 61.6 70.9 56.3 53.7 24.8 76 16

2010/11/03 20:00:00 50.0 61.6 71.0 56.4 53.8 24.8 77 16

2010/11/03 20:10:00 50.0 61.7 71.1 56.5 53.9 24.7 75 15

2010/11/03 20:20:00 50.1 61.8 71.1 56.5 53.9 24.8 77 15

2010/11/03 20:30:00 50.1 61.8 71.1 56.5 54.0 24.8 73 16

2010/11/03 20:40:00 50.1 61.9 71.1 56.5 54.0 24.7 77 14

2010/11/03 20:50:00 50.2 61.9 71.2 56.6 54.0 24.8 76 13

2010/11/03 21:00:00 50.2 61.9 71.2 56.6 54.1 24.8 76 13

2010/11/03 21:10:00 50.3 62.0 71.3 56.7 54.1 24.8 78 10

2010/11/03 21:20:00 50.4 62.0 71.2 56.6 54.1 24.8 77 9

2010/11/03 21:30:00 50.4 62.0 71.4 56.8 54.2 24.7 75 6

2010/11/03 21:40:00 50.5 62.1 71.3 56.7 54.2 24.8 74 7

2010/11/03 21:50:00 50.5 62.1 71.3 56.7 54.2 24.8 75 8

2010/11/03 22:00:00 50.5 62.1 71.3 56.7 54.2 24.8 76 10

2010/11/03 22:10:00 50.5 62.1 71.3 56.7 54.2 24.7 74 9

2010/11/03 22:20:00 50.4 62.2 71.4 56.8 54.2 24.7 74 7

2010/11/03 22:30:00 50.5 62.2 71.5 56.9 54.2 24.8 78 7

2010/11/03 22:40:00 50.5 62.2 71.4 56.8 54.2 24.8 76 8

2010/11/03 22:50:00 50.5 62.3 71.4 56.8 54.2 24.8 73 15

2010/11/03 23:00:00 50.5 62.3 71.4 56.8 54.3 24.7 76 12

2010/11/03 23:10:00 50.6 62.3 71.4 56.8 54.3 24.8 74 8

2010/11/03 23:20:00 50.6 62.3 71.5 56.9 54.3 24.8 74 9

2010/11/03 23:30:00 50.6 62.3 71.5 56.9 54.3 24.8 77 7

2010/11/03 23:40:00 50.6 62.3 71.5 56.9 54.3 24.8 77 5

2010/11/03 23:50:00 50.6 62.3 71.5 56.9 54.3 24.8 75 4

2010/11/04 00:00:00 50.6 62.3 71.4 56.8 54.3 24.8 75 3

2010/11/04 00:10:00 50.6 62.3 71.5 56.9 54.3 24.8 77 5

2010/11/04 00:20:00 50.5 62.3 71.4 56.8 54.3 24.8 75 5

2010/11/04 00:30:00 50.4 62.4 71.4 56.8 54.3 24.8 76 5

2010/11/04 00:40:00 50.6 62.4 71.4 56.8 54.3 24.7 74 6

2010/11/04 00:50:00 50.6 62.4 71.5 56.9 54.3 24.7 75 6

2010/11/04 01:00:00 50.6 62.4 71.5 56.9 54.3 24.7 77 5

2010/11/04 01:10:00 50.5 62.4 71.5 56.9 54.3 24.7 77 5

2010/11/04 01:20:00 50.5 62.4 71.5 56.9 54.3 24.7 78 5

78

2010/11/04 01:30:00 50.6 62.4 71.5 56.9 54.3 24.8 74 5

2010/11/04 01:40:00 50.4 62.4 71.5 56.9 54.4 24.8 75 5

2010/11/04 01:50:00 50.5 62.4 71.5 56.9 54.4 24.7 74 5

2010/11/04 02:00:00 50.5 62.4 71.5 56.9 54.4 24.7 74 5

2010/11/04 02:10:00 50.5 62.5 71.5 56.9 54.4 24.7 77 4

2010/11/04 02:20:00 50.4 62.5 71.5 56.9 54.4 24.8 76 3

2010/11/04 02:30:00 50.4 62.4 71.5 56.9 54.4 24.7 75 3

2010/11/04 02:40:00 50.4 62.4 71.5 56.9 54.4 24.7 75 3

2010/11/04 02:50:00 50.4 62.4 71.5 56.9 54.4 24.7 76 1

2010/11/04 03:00:00 50.5 62.4 71.5 56.9 54.4 24.8 75 1

2010/11/04 03:10:00 50.5 62.5 71.5 56.9 54.4 24.7 78 1

2010/11/04 03:20:00 50.5 62.5 71.5 56.9 54.4 24.8 78 0

2010/11/04 03:30:00 50.5 62.4 71.5 56.9 54.4 24.7 74 1

2010/11/04 03:40:00 50.5 62.5 71.5 56.9 54.4 24.8 72 2

2010/11/04 03:50:00 50.4 62.5 71.5 56.9 54.4 24.8 76 1

2010/11/04 04:00:00 50.5 62.5 71.5 56.9 54.4 24.7 73 0

2010/11/04 04:10:00 50.5 62.5 71.5 56.9 54.4 24.7 76 0

2010/11/04 04:20:00 50.5 62.4 71.5 56.9 54.4 24.8 77 1

2010/11/04 04:30:00 50.4 62.5 71.5 56.9 54.4 24.7 74 0

2010/11/04 04:40:00 50.4 62.5 71.5 56.9 54.4 24.7 77 1

2010/11/04 04:50:00 50.5 62.5 71.5 56.9 54.3 24.7 74 2

2010/11/04 05:00:00 50.4 62.5 71.5 56.9 54.4 24.8 76 2

2010/11/04 05:10:00 50.5 62.5 71.5 56.9 54.4 24.7 77 4

2010/11/04 05:20:00 50.4 62.5 71.5 56.9 54.4 24.7 77 7

2010/11/04 05:30:00 50.4 62.5 71.5 56.9 54.4 24.8 76 6

2010/11/04 05:40:00 50.4 62.5 71.5 56.9 54.4 24.8 75 6

2010/11/04 05:50:00 50.4 62.5 71.5 56.9 54.4 24.8 74 6

2010/11/04 06:00:00 50.4 62.5 71.5 56.9 54.4 24.7 76 7

2010/11/04 06:10:00 50.4 62.5 71.5 56.9 54.4 24.7 79 7

2010/11/04 06:20:00 50.4 62.6 71.5 56.9 54.4 24.7 73 5

2010/11/04 06:30:00 50.4 62.5 71.5 56.9 54.4 24.8 74 4

2010/11/04 06:40:00 50.4 62.5 71.5 56.9 54.4 24.8 74 2

2010/11/04 06:50:00 50.4 62.5 71.5 56.9 54.4 24.8 76 3

2010/11/04 07:00:00 50.5 62.6 71.5 56.9 54.4 24.7 75 12

2010/11/04 07:10:00 50.4 62.6 71.5 56.9 54.5 24.7 60 10

2010/11/04 07:20:00 50.4 62.5 71.6 57.0 54.5 24.7 74 10

2010/11/04 07:30:00 50.5 62.6 71.6 57.0 54.5 24.8 73 7

2010/11/04 07:40:00 50.4 62.6 71.7 57.1 54.5 24.7 71 8

2010/11/04 07:50:00 50.4 62.6 71.6 57.0 54.5 24.8 69 10

2010/11/04 08:00:00 50.4 62.7 71.6 57.0 54.5 24.7 74 12

2010/11/04 08:10:00 50.4 62.5 71.6 57.0 54.5 24.8 76 12

2010/11/04 08:20:00 50.3 62.6 71.7 57.1 54.5 24.7 75 13 08:30:00 50.4 62.6 71.8 57.2 54.5 24.7 76 14

2010/11/04 08:40:00 50.4 62.6 71.7 57.1 54.5 24.7 74 16

2010/11/04 08:50:00 50.4 62.6 71.7 57.1 54.5 24.7 75 20

2010/11/04 09:00:00 50.4 62.7 71.7 57.1 54.5 24.7 74 20

79

2010/11/04 09:10:00 50.5 62.7 71.6 57.0 54.5 24.7 76 25

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Appendix D: training Matlab script for model

% develops a model for temperature data % Trains ,validates and tests new data % written by CGS Gunasekara, 20 Nov 2010 close all; clear all; tic;

file=xlsread('VICDATA','Q1364:BE1464'); % loads xl data from file toc; tic; B=file(:,1:31); % loads inputs ok % output vector C=file(:,33:41); % loads outputs p=B'; % inputs t=C'; % targets Q=6; n=100;

dtst=14:Q:n; % divides data for training validation dval= [ 13:Q:n ]; % and testing

dtrn=[1:Q:n 2:Q:n 3:Q:n 4:Q:n 5:Q:n 6:Q:n 7:Q:n 8:Q:n 9:Q:n 10:Q:n 11:Q:n 12:Q:n ]; val.P=p( : , dval); % validation data val.T=t( : , dval); test.P=p( : , dtst); % test data test.T=t( : , dtst); ptr=p( : , dtrn); % training data ttr=t( : , dtrn); nnet=network; % creates network pr=minmax(p);

nnet=newff(pr,[31 20 16 9 ],{ 'tansig' 'tansig' 'tansig' 'tansig' },'trainlm'); nnet.trainParam.epochs = 25000; nnet.trainParam.show = 1; load vic_100B; %trains partly trained network nnet=vic_100B; nnet.trainParam.lr = 0.35 % SETS ETA learning rate [nnet,tr]=train(nnet,ptr,ttr,[],[],val,test); figure(1)

plot(tr.epoch,tr.perf,tr.epoch,tr.vperf,tr.epoch,tr.tperf) legend('Training' , 'Validation' , 'Test', -2); ylabel('Squared Error');

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xlabel('Epoch '); title(' Model Performance'); a = sim(nnet,p); % simulates t=t*100, a=a*100; t=t+7; a=a+7; figure(2) t1=t(1:1,1:100); % target a1=a(1:1,1:100); % simulated output plot(1:n,a1,'r-',1:n,t1,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' UGB metal temperature'); legend('simulated ' , 'actual'); figure(3) [m,b,r]=postreg(a1,t1); figure(4) t2=t(2:2,1:100); % target a2=a(2:2,1:100); % simulated output plot(1:n,a2,'r-',1:n,t2,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' LGB metal temperature'); legend('simulated ' , 'actual'); figure(5) [m,b,r]=postreg(a2,t2); figure(6) t3=t(3:3,1:100); % target a3=a(3:3,1:100); % simulated output plot(1:n,a3,'r-',1:n,t3,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' THB metal temperature'); legend('simulated ' , 'actual'); figure(7) [m,b,r]=postreg(a3,t3); figure(8) t4=t(4:4,1:100); % target a4=a(4:4,1:100); % simulated output plot(1:n,a4,'r-',1:n,t4,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' TGB metal temperature'); legend('simulated ' , 'actual'); figure(9) [m,b,r]=postreg(a4,t4); figure(10) t5=t(5:5,1:100); % target a5=a(5:5,1:100); % simulated output plot(1:n,a5,'r-',1:n,t5,'bo')

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ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title('UGB Oil temperature'); legend('simulated ' , 'actual'); figure(11) [m,b,r]=postreg(a5,t5); figure(12) t6=t(5:5,1:100); % target a6=a(5:5,1:100); % simulated output plot(1:n,a6,'r-',1:n,t6,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' THB Oil temperature'); legend('simulated ' , 'actual'); figure(13) [m,b,r]=postreg(a6,t6); figure(14) t7=t(7:7,1:100); % target a7=a(7:7,1:100); % simulated output plot(1:n,a7,'r-',1:n,t7,'bo') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' TGB Oil temperature'); legend('simulated ' , 'actual'); figure(15) [m,b,r]=postreg(a7,t7); figure(16) % all graphs in one diagram

plot(1:n,a1,'r-',1:n,t1,'bo',1:n,a2,'r-',1:n,t2,'bX',1:n,a3,'r-',1:n,t3,'b*',1:n,a4,'r-',1:n,t4,'b+') ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' Bearing Metal Temperatures');

legend('UGB Actual ','Simulated' , 'LGB Actual','Simulated','THB Ac-tual','Simulated','TGB Actual','Simulated');

figure(17) plot(1:n,a5,'r-',1:n,t5,'bO',1:n,a6,'r-',1:n,t6,'bX',1:n,a7,'r-',1:n,t7,'b+')

ylabel('Temperature/ deg C'); xlabel('Time / (10 minutes samples) '); title(' Bearing Oil Temperatures');

legend('UGB Actual','Simulated' , 'THB/LGB Actual','Simulated','TGB Ac-tual','Simulated');

% writes data into xl file %SUCESS=XLSWRITE('_op.xls',a1','b2:b64') %SUCESS=XLSWRITE('_op.xls',t1','c2:c64') toc; % end

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Appendix E: Init ial values of trained model

Initial values of network

nnet = Neural Network object: architecture: numInputs: 1 numLayers: 4 biasConnect: [1; 1; 1; 1] inputConnect: [1; 0; 0; 0] layerConnect: [4x4 boolean] outputConnect: [0 0 0 1] targetConnect: [0 0 0 1] numOutputs: 1 (read-only) numTargets: 1 (read-only) numInputDelays: 0 (read-only) numLayerDelays: 0 (read-only) subobject structures: inputs: {1x1 cell} of inputs layers: {4x1 cell} of layers outputs: {1x4 cell} containing 1 output targets: {1x4 cell} containing 1 target biases: {4x1 cell} containing 4 biases inputWeights: {4x1 cell} containing 1 input weight layerWeights: {4x4 cell} containing 3 layer weights functions: adaptFcn: 'trains' initFcn: 'initlay' performFcn: 'mse' trainFcn: 'trainlm' parameters: adaptParam: .passes initParam: (none) performParam: (none) trainParam: .epochs, .goal, .max_fail, .mem_reduc, .min_grad, .mu, .mu_dec, .mu_inc, .mu_max, .show, .time, .lr weight and bias values: IW: {4x1 cell} containing 1 input weight matrix LW: {4x4 cell} containing 3 layer weight matrices b: {4x1 cell} containing 4 bias vectors other: userdata: (user stuff)

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