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An optimization of redundant measurements location for thermal capacity of power unit steam boiler calculations using data reconciliation method

Marcin Szega *,Grzegorz Tadeusz Nowak

Institute of Thermal Technology,Silesian University of Technology,44-100Gliwice,Konarskiego 22,Poland

a r t i c l e i n f o

Article history:

Received 11December 2014Received in revised form 20March 2015

Accepted 25March 2015Available online xxx

Keywords:

Data reconciliation Steam boiler

Optimization of measurements location Numerical simulation

a b s t r a c t

The optimization of a location of redundant measurements under varying loads for steam boiler of a supercritical power unit using the generalized method of data reconciliation has been carried out.The method of weighted objectives has been applied as a method of optimization.This method reduce the weighted multi-criteria optimization task to task one-dimensional.Measurement values have been determined by numerical experiment and the Monte Carlo method for the designed redundant mea-surements system.For this purpose,a mathematical simulation model of a supercritical steam power unit with power rating of 900MW in the Thermo ?ex program has been worked out.In the optimization calculations of location of redundant measurements as an objective functions minimizing the relative standard deviation of a boiler thermal capacity and maximizing the Kullback-Leibler divergence have been accepted.In the calculation the measurements were taken into account,which can be located in the water-steam system of the boiler and in the high-pressure heat recovery steam supercritical power unit.The results of calculations con ?rm the in ?uence of the number of redundant measurements and places of their location in the thermal system of the boiler on the accepted criteria of optimization.Increasing the number of redundant measurements,in terms of the data reconciliation method,leads to decrease the relative standard deviation of the thermal capacity of the boiler and increase the value of Kullback-Leibler divergence,i.e.;decrease the information entropy of the measuring system.

1.Introduction

Currently energy conversion processes occurring in the contemporary steam power plants cannot be realized without the automatic supervision and ability to in ?uence of their course.Modern power units are equipped with complex automation and control systems necessary for their proper operation.Increasing the nominal power of a power units and the use of supercritical steam parameters results in complexity of their thermal system [2,9].For the safe operation of a supercritical coal-?red steam power units a suf ?cient number of measurements,concerning the technical condition of their equipment and running the processes of energy conversion,is required.Besides of measurement information associated with the control process,the measurement information

concerning the supervision of operation has been signi ?cantly increased.Currently it enables the usage of a computer systems for decision support in terms of technical control operation and application of advanced methods of engineering analysis.An indispensable element of such systems should be an advanced validation of measurements data from distributed control systems using data reconciliation methods in case of measurements redundancy [1,9,13,17].Moreover the data reconciliation method should be used in the case of application measurements data in the identi ?cation of empirical models,e.g.regression or arti ?cial neural networks [4].Also diagnosis of complex energy systems as pre-sented e.g.in Refs.[11,12]requires reliable and reconciled opera-tional measurements and unknown values.Only credible measurements data and calculated parameters should be used in this type of applications.

The generalized method of data reconciliation [6,8]could be used at the design stage of redundant measurements system for newly built power units.Number of redundant measurements and

*Corresponding author.

E-mail addresses:marcin.szega@polsl.pl (M.Szega),grzegorz.t.nowak@polsl.pl (G.T.

Nowak).

Contents lists available at ScienceDirect

Energy

journal h omepage:w

https://www.wendangku.net/doc/4f7660178.html,/locate/energy

https://www.wendangku.net/doc/4f7660178.html,/10.1016/j.energy.2015.03.125

Energy xxx (2015)1e 7

their location in the thermal system of power units can be optimized

from the used criterion point of view.This criterion could be the minimization of uncertainty of the selected parameter which characterize the energy conversion process.Moreover another cri-terion can be determination of an extremum of parameters which describes in a comprehensive way the measurements system quality after validation his measurements.

Measurement values have been determined by numerical experiment and the Monte Carlo method for the designed redundant measurements system.For this purpose,a mathemat-ical simulation model of a supercritical steam power unit with a rated power of900MW in the Thermo?ex program[16]has been worked https://www.wendangku.net/doc/4f7660178.html,ing simulation model a calculations for different loads of power unit have been performed.In the optimization calculations of location of redundant measurements as an objec-tive functions minimizing the relative standard deviation of a boiler thermal capacity and maximizing the Kullback-Leibler divergence have been accepted[3].This divergence is the criterion which describes the quality of redundant measurement system as a whole[10].In the calculation the measurements were taken into account,which can be located in the water-steam system of the boiler and in the high-pressure heat recovery steam supercritical power unit.

The proposed algorithm consists in searching of vector of objective function values obtained from all possible solutions of the measurements con?guration location in the thermal system of the boiler.The results of calculations con?rm the in?uence of the number of redundant measurements and places of their location in the thermal system of the boiler on the accepted criteria of optimization.Increasing the number of redundant measurements,in terms of the data reconciliation method,leads to decrease the relative standard deviation of the thermal ca-pacity of the boiler and increase the value of Kullback-Leibler divergence,i.e.;decrease the information entropy of the measuring system.

2.Principle of data reconciliation

Evaluation of the energy process is carried out by means of its measurements.In reality there are no error-free measurements. The results of measurements contain errors due to inaccuracy of the applied method of measurements,failures of the device or in the signal processing.Such errors are then passed to calculations of unknown values(quantities that are not measured).In thermal engineering in most cases the number of balance equations is larger than the number of unknown values.Hence the surplus equations are not ful?lled because the substance and energy balance equa-tions are not reconciled.The application of the data reconciliation method permits calculations of the measurement corrections so that the all balance equations are ful?lled.

Data reconciliation can be mathematically expressed as a con-strained weighted least-squares optimization problem[7,17]:min

(

X m

i?1

x iàx i

s i

(1) subject to

g l

b x i;b y

?0for l?1;:::;r(2) The objective function(1)de?nes the total weighted sum of measurements corrections squares,whereas Formula(2)de?nes the set of mathematical model constrains.In the thermal engi-neering these constrains are generally mass and energy balances. Data reconciliation in thermal analysis permits to achieve the following aims[6,7,9,17,18]:

-calculation of the most reliable thermal measurements values, -unique solution of the most probable unknown quantities in thermal processes,

-an assessment of the accuracy of the corrected results of mea-surements and of calculated unknown quantities,

-a reduction of uncertainty of measured quantities,

-the control of ful?lling of the assumed measurements uncertainty.

3.Simulation model of the thermal system of power unit

As previously speci?ed,for the designed redundant measure-ments system,measurement values by means of numerical exper-iment have been determined.For this purpose,a mathematical simulation model of a supercritical steam power unit with a rated power of900MW in the Thermo?ex program has been worked out. Thermo?ex is a simulation program dedicated for simulation of power units[16].Simulation calculations in this program was divided into three parts.In the?rst one the structure of the power unit is build and values of thermodynamics parameters in partic-ular points of thermal system are assumed,for example:live and reheated steam parameters,pressure in the condenser,ambient parameters,electric power of the turbo-generator,etc.The results of calculations obtained from simulation model were veri?ed by examples presented in the literature and industrial applications. The next step was to transfer this model into off e designed mode which allowed to simulate different loads of power unit and observe the behavior depending on the change of electric power of the turbo-generator.In the last part of simulation the calculations for various loads of the steam power unit have been carried out.The ?ve loads were considered:60,70,80,90and100percentage of power unit nominal load.Results of this simulation are presented in Table1.

Considered part of the thermal system of power unit,which is the water-steam boiler system with a high-pressure regeneration and high-pressure part of the steam turbine with marked

Table1

Selected output data for the simulation calculations.

Parameters Unit Load,%

10090807060 Gross power MW900.0810.4720.0630.5539.8 Gross ef?ciency%46.8446.4645.8745.0043.92 Net power MW842.1758.9674.1589.1503.0 Live steam temperature o C650.0649.0649.0649.8648.8 Live steam pressure MPa30.026.923.921.018.2 Reheated steam temperature o C670.0670.0670.0669.2669.1 Reheated steam pressure MPa 5.9 5.4 4.8 4.2 3.7 Feed water temperature o C309.0304.0298.0291.0284.0

M.Szega,G.T.Nowak/Energy xxx(2015)1e7 2

measuring points is shown in Fig.1.In the scheme of considered thermal system(Fig.1)redundant measurements from the data reconciliation method point of view are shown in squares.

4.Conditional equations of the data reconciliation task

As described above the data reconciliation task requires the formulation of the set of mathematical model constrains.According to the scheme for the analyzed water-steam system of the boiler presented in Fig.1,the mass and energy balances equations in the steady state of steam boiler operation can be formulated.Total number of conditional equations is equal to r?13.Mass and energy balances are illustrated below.

-mass balance of the live steam:

_me1T?_me13Tt_me14T(3) -mass balance of the re-superheated steam:

_me4T?_me7Tt_me10T(4) -mass balance of the high pressure part of the steam turbine _me1T?_me42Tt_me39Tt_me19Tt_me7T(5)-mass balance of the condensate from heat exchanger RHE2: _me26T?me39Tt_me19T(6)

-mass balance of the condensate from heat exchanger RHE1: _me24T?me39Tt_me35Tt_me19T(7) -mass balance of the feed water mixing point before the boiler: _me13Tt_me14T?_me33Tt_me34Tt_me43T(8) -energy balance of the feed water mixing point before the boiler: _me20Th

te46T;pe15T

t_me43Th

te44T;pe45T

?_me1Th

te16T;pe15T

(9) -mass balance of the mixing point of the feed water behind the desuperheater DSH:

_me20T?_me33Tt_me34T(10)

-energy balance of the feed water mixing point behind the desuperheater DSH:

Fig.1.Scheme of the considered thermal system of the boiler,high pressure part of the steam turbine and high pressure heat regeneration system.

M.Szega,G.T.Nowak/Energy xxx(2015)1e73

e33Th t e38T;p e15T t_m e34Th t e32T;p e15T ?_m e20Th

t e46T;p e15T (11)

-energy balance of the heat exchanger RHE1:

h _m

e35Th t e30T;p e29T t_m e26Th t e25T;p e17T à_m e24Th

t e23T;p e29T i ?h HE ?_m

e20Th h t e27T;p e22T àh t e21T;p e22T i (12)

-energy balance of the heat exchanger RHE2:

h _m

e35Th t e30T;p e29T t_m e26Th t e25T;p e17T à_m e24Th

t e23T;p e29T i ?h HE ?_m

e20Th h t e27T;p e22T àh t e21T;p e22T i (13)

-energy balance of the heat exchanger RHE3:

e39Th t e40T;p e41T àh t e31T;p e41T i

h HE ?_m

e20T?h h

t e32T;p e15T àh t e28T;p e22T

i (14)

-energy balance of the desuperheater DSH:

e35Th t e36T;p e37T àh t e30T;p e29T i

h HE ?_m

e33T?h h

t e38T;p e15T àh t e32T;p e15T

i (15)

Thermal capacity of the steam boiler results from the formula:

Subscripts in the balance equations refer to the measurement points shown in the scheme of the considered thermal system of the steam boiler (Fig.1).

Standard uncertainties of the measurements of pressure,tem-perature and mass ?ow for the data reconciliation calculations on the base of best practice in industrial measurement equipment and [14,15,18]have been assumed.

5.Optimization of a redundant measurements location As previously illustrated,as a result of application of the data reconciliation method the reconciled measurements data and reduction of its uncertainty have been achieved.For optimal loca-tion of redundant measurements in the water-steam boiler and the high-pressure heat regeneration system of power unit as a criterion of optimization,the minimization of uncertainty of the steam boiler thermal capacity can be used.Because in the data reconciliation calculations all measurements data are corrected,it is convenient for the analysis to accept the relative standard deviation of the

steam boiler thermal capacity RSD e_Q SB

T.Minimum of the value of RSD e_Q SB

Tcan be criterion of the optimal location of an additionally redundant measurements in the measurements system of the boiler and high-pressure heat regeneration system of power unit.Objective function of such described optimization task can be de ?ned as follows:

RSD _Q SB

k ?min RSD

_Q SB kj for

k ?1;:::;n j ?1;:::;L ek T

9>>

=>>>;

(17)

For the assessment of the measurements system as a whole the Kullback e Leibler divergence has been applied [3].Quality of a redundant system of measurements after introduction of new redundant measurement should be evaluated by applying criterion,which permits to measure the reliability increase of a measure-ments e both values of measurements as well as its uncertainties.It has been assumed that measurements system of thermal process represents a signals system of communication,which can be able to send the information about thermodynamic parameters of thermal process.For this assumption the entropy of information can be applied as an assessment criterion of quality of measurements system.In information theory,entropy is a measure of the uncer-tainty which is associated with a random variable [5].In probability and information theory also concept of a relative entropy called Kullback e Leibler divergence has been introduced [3].The Kull-back e Leibler divergence is a non-symmetric measure of the dif-ference between two probability distributions.Typically one of them represents the true distribution of data,observations,or a precise calculated theoretical distribution.Whereas the other dis-tribution typically represents a theory,model,description or approximation of data.

Introduction the variance-covariance matrices property in data

reconciliation method the Kullback e Leibler divergence (in bits)has the following form [10]:

D KL b N N ?

2,ln e2T

(ln

"Y m i ?1

s i

b s i

X m i ?1

b x i àx i

s i

2tu àr

)

(18)

In an assessment of increase of a measurements data reliability,

in principle,we are not interested in absolute value of information entropy,but only in the decrease of this entropy from state of raw measurements data to state of reconciled measurements.Hence,

assuming that distributions N and b N

concerns respectively raw and reconciled measurements data the calculation of decrease of in-formation entropy of measurements data after application of data reconciliation algorithm can be determined by use of Formula (18).In this case the Kullback-Leibler divergence can constitute the cri-terion of an assessment of increase of a measurements data reli-ability in a redundant system of measurements of thermal

systems.

M.Szega,G.T.Nowak /Energy xxx (2015)1e 7

Minimum of the entropy information of the reconciled mea-surements value,that is maximum of Kullback e Leibler divergence (18)from reconciled measurements to the raw measurements data, can be also criterion of the optimal location of a redundant mea-surements in the measurements system of the thermal systems. Objective function of such described optimization task can be de?ned as follows:

D KL

b N

?max

D KL

b N

for

k?1;:::;n

j?1;:::;LekT

>>>

;

(19)

The current methodology of optimization of the location of an additional redundant measurements(in the sense of the use of data reconciliation method),the nominal load of the power unit has been assumed[9,10].It is obvious,however,that due to the changing demand of the electric power in the power system,load of the power units is variable in time.Load variation causes changes of energy carriers?ows and their thermodynamics parameters in the power units.A method for optimizing the location of an additional redundant measurements under varying load of power unit has been worked out.The proposed methodology uses information contained in an ordered diagram of real working of power unit. Basing on this diagram of the power unit load,you can determine the time intervals of the selected average load occurrence and carry out the optimization procedure of the additional redundant mea-surements location for average loads occurring in these intervals. For the relative values of the time intervals this diagram indicates the likelihood of the load value.

The method of weighted objectives has been applied as a method of optimization.This method reduce the weighted multi-criteria optimization task to one-dimensional task.This reduction is being achieved by joining the respective criterion function to a single weighted objective function of the general form:

FezT?

X q

i?1

w i f iezT(20)

where w i denotes i-th weight of the criterion function and ful?lls the following criterions:

w i2?0;1 (21) X q

i?1

w i?1(22)

In the form of Formula(20),it is evident that the different weight vectors will yield different optimal solution.Hence,it occurs a problem in the selection of appropriate weight values for each criterion functions in order to obtain good quality solutions.In the proposed methodology,the values of the criterion functions are the values obtained from the optimization calculations for the considered con?guration for a given number of redundant mea-surements and for a given load of power unit.The weights of the criterion functions are the probabilities of occurrence of the average load of the power unit resulting from the ordered diagram loads obtained from the power unit real operation.The accepted weights of criterion functions satis?es the conditions(21)and(22) the objective function(20).

Using the measurement of the electric power from the distrib-uted control system of the power unit working in one of the power plant an ordered diagram has been prepared.Basing on this dia-gram the probabilities of occurrence of a de?ned generator loads have been determined.The values of the probabilities of generator loads have been determined for?ve load values in the range of 60e100%of nominal load.The calculation results are shown in Table2.

Calculations of the criterion value of the objective function f iezTfor a given i-th power unit load and assumed p-th number of redundant measurements according to the developed algorithm described in Refs.[9,10]have been carried out.Determining the optimal value of the weighted objective function(20)needs the repetition of t-times the developed optimization procedure.In the considered problem the number of optimization criteria is equal to q?5and it concerns the number of assumed values of turbo-generator loads.

For a given number of redundant measurements p and the power unit load in the i-th time interval of the ordered diagram we obtain the components values of the objective function(20)in the form of below vector:

fepTi?

f1epTi

f2epTi

f LepTepTi

5(23)

The vector fepThas a number of components equal to the total number of measurements con?gurations LepTfor a given number p-th of redundant measurements.

Vector of solutions for all con?gurations of measurements of the weighted objective function for a given p-th number of redundant measurements has the form:

FepT?

F1epT

F2epT

F LepTepT

X q

i?1

w i

f1epTi

f2epTi

f LepTepTi

5(24)

From the elements of vector FepTthe value which ful?ll the assumed criterion of optimization is being chosen.When the cri-terion function fezTis the relative standard deviation of the boiler thermal capacity,namely:

fezT?RSD

(25)

the lowest value from the vector FepTis being selected.

If the function of criterion is the Kullback-Leibler divergence,that is:

fezT?D KL

b N

(26)

from the vector FepTthe highest value is being selected.

6.Example of optimization calculations

Value of the RSDe_Q SBT,as mentioned previously,constitutes the assumed criterion of assessment of uncertainty measurement decrease after data reconciliation.The criterion is depended on the Table2

Probability of power unit turbo-generator load.

No.The ratio of the average power in the

range of loads to the power rating,%

Value of the probability

of turbo-generator load 123

1600.305

2700.051

3800.052

4900.083

51000.509

M.Szega,G.T.Nowak/Energy xxx(2015)1e75

number of a surplus measurements quantities,as well as depended on the location in the analyzed thermal system.The procedure of an optimization calculations requires?rst of all the identi?cation of potential location for installation of an additional surplus mea-surements in a thermal system,considering the technical con-strains.These potential places determining the maximum number of available redundant measurements in the system.The deter-mined number of redundant measurements(lower than possible maximum)can be installed in measurements system in different con?gurations.Solution of the optimization task(17)requires determination of the RSDe_Q SBTfor all available con?gurations of installation of this measurements in the analyzed thermal system. Number of this installation con?gurations results from the bino-mial coef?cient.For any set containing n-elements,the number of considered k-elements subsets is given by the formula:

LekT?C k n?

k!enàkT!

;where k n;n;k2Nt

(27)

For n-elements set of all considered additional redundant measurements data,number of all available con?gurations of their installation in the thermal system will be the sum of con?gurations L(k)results from the formula:

X n

k?1C k n?

X n

k?1

X n

k?1

(28)

The optimization calculations for previously de?ned variants of con?gurations of the additional measurements in the analyzed thermal system on the basis of the algorithm presented in Ref.[8] have been carried out.

Number of the con?gurations of redundant measurements location for each amount of a measurements is calculated by means of Formula(27).Column2of Table3presents the number of analyzed con?gurations of an additional redundant measurements locations.Total number of analyzed measurements locations con-?gurations resulting from the Formula(28)is L?8191.The opti-mization calculations using the computer program elaborated in Fortran language have been carried out.

7.Conclusions

The steam boiler thermal capacity and its standard uncertainty for minimum measurement information(without data reconcilia-tion)for assumed direct measurements uncertainties[14,18]equals to_Q SB?1595.0±67.2MW.Relative standard deviation of the steam boiler thermal capacity in this case equals to RSDe_Q SBT?4.213%.Table3contains the results of optimization calculations.Column2of this table shows the con?guration numbers for considered additional redundant measurements.The column3of Table3presents the sets of the optimal con?gurations of the redundant measurements location for optimized quantities, that are:relative standard deviation of the thermal capacity of the boiler and Kullback-Leibler divergence.The column4shows the values of these optimized quantities.First of all it can be concluded that the sets of redundant measurements that provide the mini-mum value of the relative standard deviation of the steam boiler capacity and the maximum value of the Kullback-Leibler divergence (i.e.;the minimum information entropy of the measurements)are different.

Values of the relative standard deviation of steam boiler thermal capacity in column4of Table3shows that adding only one addi-tional redundant measurement(in this case it is?ow of the feed water at the inlet of bypass heat exchanger BFWE e measurement point No.43)causes a signi?cant reduction of this relative standard https://www.wendangku.net/doc/4f7660178.html,paring to initial value(without data reconciliation), decrease of this relative standard deviation is approximately33 percent.Further introduction of additional redundant

Table3

Results of optimizations calculations.

Number of redundant measurements data,k Number of con?guration of installation

of redundant measurements data,L(k)

Sets of the optimal con?guration of redundant

measurements data

Optimal values of the

considered variables

1234

k?0Le0T?C0

13?1M min RSD?f RSDe_Q SBT?4.213%

M max DKL?f D KL?0.00bit

k?1Le1T?C1

13?13M min RSD?f43g RSDe_Q SBT?2.362%

M max DKL?f46g D KL?1.58bit

k?2Le2T?C2

13?78M min RSD?f4;43g RSDe_Q SBT?2.112%

M max DKL?f4;43g D KL?2.50bit

k?3Le3T?C3

13?286M min RSD?f4;7;43g RSDe_Q SBT?1.932%

M max DKL?f4;7;43g D KL?3.57bit

k?4Le4T?C4

13?715M min RSD?f4;7;26;43g RSDe_Q SBT?1.846%

M max DKL?f4;7;43;46g D KL?4.30bit

k?5Le5T?C5

13?1287M min RSD?f4;7;23;24;43g RSDe_Q SBT?1.741%

M max DKL?f4;7;23;24;43g D KL?5.19bit

k?6Le6T?C6

13?1716M min RSD?f4;7;23;24;43g RSDe_Q SBT?1.691%

M max DKL?f4;7;23;24;43;46g D KL?6.22bit

k?7Le7T?C7

13?1716M min RSD?f4;7;23;24;33;34;43g RSDe_Q SBT?1.642%

M max DKL?f4;7;23;24;39;43;46g D KL?6.91bit

k?8Le8T?C8

13?1287M min RSD?f4;7;23;24;39;43;46g RSDe_Q SBT?1.592%

M max DKL?f4;7;23;24;26;39;43;46g D KL?7.50bit

k?9Le9T?C9

13?715M min RSD?f4;7;13;23;24;26;33;34;43g RSDe_Q SBT?1.567%

M max DKL?f4;7;23;24;34;35;39;43;46g D KL?8.21bit

k?10Le10T?C10

13?286M min RSD?f4;7;13;23;24;26;33;34;43;46g RSDe_Q SBT?1.547%

M max DKL f4;7;23;24;26;33;34;39;43;46g D KL?8.85bit

k?11Le11T?C11

13?78M min RSD?f4;7;13;23;24;26;33;34;35;43;46g RSDe_Q SBT?1.535%

M max DKL?f4;7;19;23;24;26;33;34;39;43;46g}D KL?9.46bit

k?12Le12T?C12

13?13M min RSD?f4;7;13;19;23;24;26;33;34;35;39;43;46g RSDe_Q SBT?1.532%

M max DKL?f4;7;19;23;24;26;33;34;35;39;43;46g D KL?10.02bit

k?13Le13T?C13

13?13M min RSD?f4;7;13;19;23;24;26;33;34;35;39;43;46g RSDe_Q SBT?1.529%

M max DKL?f4;7;13;19;23;24;26;33;34;35;39;43;46g D KL?10.31bit M.Szega,G.T.Nowak/Energy xxx(2015)1e7

measurements in the optimal con?gurations is bene?cial for decreasing RSDe_Q SBTvalue.However decreasing this relative stan-dard deviations has limit for nine redundant measurements.Value of the RSDe_Q SBTcomparing to the initial value,decreases about62 percent.Loading a higher number of redundant measurements to the steam boiler and high-pressure heat regeneration system has no further bene?ts from the point of view of assumed RSDe_Q SBToptimization criterion.From column3in Table3the optimal con?guration of additional redundant measurements which pro-vide the minimization of RSDe_Q SBTis:4e?ow of the re-superheated steam at the outlet of the boiler,7e?ow of steam to the secondary superheating,13e?ow of injection to the live steam,14e?ow of the feed water,23e temperature of the condensate at the outlet of the heat exchanger RHE1,24e?ow of the condensate at the outlet of the heat exchanger RHE1,33e?ow of the feed water at the inlet of the desuperheater DSH,34e?ow of the feed water in the bypass of the desuperheater DSH,43e?ow of the feed water at the inlet of bypass heat exchanger BFWE.

An increase of the number of redundant measurements in the considered thermal system causes decrease of the entropy infor-mation of the measurements,i.e.;the increase of the Kullback-Lei-bler divergence(column4in Table3).However in this case,there is no certain limit value above which the increase of the value of Kullback-Leibler divergence is very low.This divergence value in-creases almost linearly.Developed optimization method of redundant measurement system location could be used on the stage of designing redundant measurement system for new control operation system in power units.

The aim of the carried out calculations was also to check whether the measurement values that are different from the nominal values have an in?uence on the location of the redundant measurements.The calculations showed that in the considered case the thermal capacity of the boiler does not have in?uence on the location of the redundant measurements,i.e.;for each boiler thermal capacity(in the range of60e100%of nominal power unit load)the same optimal con?guration of redundant measurements is being achieved.

Acknowledgment

The results presented in this paper were obtained from research work co-?nanced by the National Centre of Research and Devel-opment in the framework of Contract SP/E/1/67484/10e Strategic Research Programme e Advanced technologies for obtaining en-ergy:Development of a technology for highly ef?cient zero-emission coal-?red power units integrated with CO2capture.

Nomenclature

D KL Kullback-Leibler divergence,bit,

f iezTi-th criterion function,

h speci?c enthalpy,kJ/kg,

k current number of redundant measurement,

L number of location con?gurations of a redundant

measurements data,m s number of measurements data,

_m mass?ow,kg/s,

n number of considered redundant measurements,

p pressure,Pa

q number of optimization criteria,

thermal capacity of the steam boiler,MW,

r number of a conditional equations,

RSD relative standard deviation,

t temperature,K,

u number of not measured variables,

w weight of the criterion function,

x raw measurement data,

b x reconciled measurement data,

b y reconciled not measured variable,

z variable representing the solution of the optimization,

s standard uncertainty of raw measurement data,

b s standard uncertainty of a reconciled measurement data. References

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740)this.width=740" border=undefined> 该燃烧方式燃烧器射出的煤粉气流经过燃烧室中部区域变成强烈燃烧的高温烟气，一部分直接补充到相邻燃烧器射流的根部，使相邻燃烧器射出的煤粉升温引燃。射流本身的卷吸和邻角的相互点燃特点，使直流式燃烧器四角布置、切圆燃烧方式具有良好的着火性能。同时二次风口与一次风口相对独立，相互间的排列自由，可以在布置上变化出多种形式，控制二次风与一次风混合的迟早，满足不同的燃料对混合的不同要求，改善着火性能。此外，由于一次风衰减慢和二次风的加强作用，使煤粉气流的后期混合强烈，加之炉内的气流旋转，煤粉在炉内螺旋上升，通过的路程长，故直流式燃烧器切圆燃烧又具有燃烬程度好的特煤粉管道从磨煤机出口供至燃烧器进口，每台磨煤机出口由4根煤粉管道接至同一层四角布置的煤粉燃烧器。每角燃烧器风箱分成14层，其中A、B、C、D、E、F 6层为一次风喷嘴，其余8层为二次风喷嘴。一二次风呈间隔排列，在AB、CD、EF 3层二次风室内设有启动及助燃油枪，共12支。为了降低四角切圆燃烧引起的炉膛出口及水平烟道中烟气的残余旋转造成的烟气侧的屏间热偏差，采用同心反切加燃尽风(OFA)和部分消旋二次风，使炉内气流的旋转强度具有一定的可调性，下部的启转二次风与一次风喷嘴偏转

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附件1：外文资料翻译译文机床机床是用于切削金属的机器。工业上使用的机床要数车床、钻床和铣床最为重要。其它类型的金属切削机床在金属切削加工方面不及这三种机床应用广泛。车床通常被称为所有类型机床的始祖。为了进行车削，当工件旋转经过刀具时，车床用一把单刃刀具切除金属。用车削可以加工各种圆柱型的工件，如：轴、齿轮坯、皮带轮和丝杠轴。镗削加工可以用来扩大和精加工定位精度很高的孔。钻削是由旋转的钻头完成的。大多数金属的钻削由麻花钻来完成。用来进行钻削加工的机床称为钻床。铰孔和攻螺纹也归类为钻削过程。铰孔是从已经钻好的孔上再切除少量的金属。攻螺纹是在内孔上加工出螺纹，以使螺钉或螺栓旋进孔内。铣削由旋转的、多切削刃的铣刀来完成。铣刀有多种类型和尺寸。有些铣刀只有两个切削刃，而有些则有多达三十或更多的切削刃。铣刀根据使用的刀具不同能加工平面、斜面、沟槽、齿轮轮齿和其它外形轮廓。牛头刨床和龙门刨床用单刃刀具来加工平面。用牛头刨床进行加工时，刀具在机床上往复运动，而工件朝向刀具自动进给。在用龙门刨床进行加工时，工件安装在工作台上，工作台往复经过刀具而切除金属。工作台每完成一个行程刀具自动向工件进给一个小的进给量。磨削利用磨粒来完成切削工作。根据加工要求，磨削可分为精密磨削和非精密磨削。精密磨削用于公差小和非常光洁的表面，非精密磨削用于在精度要求不高的地方切除多余的金属。车床车床是用来从圆形工件表面切除金属的机床，工件安装在车床的两个顶尖之间，并绕顶尖轴线旋转。车削工件时，车刀沿着工件的旋转轴线平行移动或与工件的旋转轴线成一斜角移动，将工件表面的金属切除。车刀的这种位移称为进给。车

火力发电厂锅炉课程设计

* 《火力发电厂锅炉课程设计》学校：XXXXX大学班级：热能与动力工程（专升本）姓名： XXXXXX 日期：X年X月X日

400t/h一次中间再热煤粉锅炉第一章设计任务书一、设计题目：400t/h一次中间再热煤粉锅炉二、原始资料 1.锅炉蒸发量 1 D 400t/h 2.再热蒸汽流量 2 D 350t/h 3.给水温度 gs t 235℃ 4.给水压力 gs P 15.6MPa 5.过热蒸汽温度 1 t540℃ 6.过热蒸汽压力 1 p 13.7MPa 7.再热蒸汽(进)温度 2 t'330℃ 8.再热蒸汽(出)温度 2 t''540℃ 9.再热蒸汽(进)压力 2 p' 2.5MPa 10.再热蒸汽(出)压力 2 p'' 2.3MPa ※注：以上压力为表压。 11.周围环境温度20℃ 12.燃料特性 (1) 燃料名称:设计煤种数据（17） (2) 设计煤种数据: (表一) 工业分析(ar)% 固定碳 45.30 灰分 22.39 挥发分 25.5 水分 8.0 低位发热量 21.65

元素分析（ar ）碳 55.66 氢 3.69 氧 8.46 氮 0.89 硫 0.91 灰渣特性灰变形温度 1160℃ 灰软化温度 1250℃ 灰熔融温度 1330℃ (3) 煤的可燃基挥发分：r V =100ar V / (100-ar W -ar A )=36.63% (4) 煤的低位发热量y dw Q =21650kj/kg (5) 灰熔点：1t 、2t 、3t ＜1500℃ 13.制粉系统中间储仓式,热风送粉,筒式钢球磨煤机 14.汽包工作压力 15.2MPa 提示数据:排烟温度假定值py t =146℃；热空气温度假定值rk t =320℃ 注:以上压力为表压。第二章设计计算说明书第一节煤的元素分析数据校核和煤种判断一、煤的元素各成分之和为100%的校核 ar C +ar O +ar S +ar H +ar N +ar W +ar A =55.66+8.46+0.91+3.69+0.89+8+22.39=92% 二、元素分析数据校核 (一)干燥无灰基（可燃基）元素成分计算干燥无灰基元素成分与收到基（应用基）元素成分之间的换算因子为 K=100/(100-ar W -ar A )=100/(100-8-22.39)=1.4366 则干燥无灰基元素成分应为（％） daf C ＝K ar C ＝1.4366×55.66=79.96 daf H =K ar H =1.4366×3.69=5.30 daf O ==K ar O =1.4366×8.46=12.15 daf N =K ar N =1.4366×0.89=1.28 daf S =K ar S =1.4366×0.91=1.31 （二）干燥基灰分的计算

组合机床外文文献

Int J Adv Manuf Technol (2006) 29: 178–183 DOI 10.1007/s00170-004-2493-9
ORIGINAL ARTICLE
Ferda C. C ? etinkaya
Unit sized transfer batch scheduling in an automated two-machine ?ow-line cell with one transport agent
Received: 26 July 2004 / Accepted: 22 November 2004 / Published online: 16 November 2005 ? Springer-Verlag London Limited 2005 Abstract The process of splitting a job lot comprised of several identical units into transfer batches (some portion of the lot), and permitting the transfer of processed transfer batches to downstream machines, allows the operations of a job lot to be overlapped. The essence of this idea is to increase the movement of work in the manufacturing environment. In this paper, the scheduling of multiple job lots with unit sized transfer batches is studied for a two-machine ?ow-line cell in which a single transport agent picks a completed unit from the ?rst machine, delivers it to the second machine, and returns to the ?rst machine. A completed unit on the ?rst machine blocks the machine if the transport agent is in transit. We examine this problem for both unit dependent and independent setups on each machine, and propose an optimal solution procedure similar to Johnson’s rule for solving the basic two-machine ?owshop scheduling problem. Keywords Automated guided vehicle · Lot streaming · Scheduling · Sequencing · Transfer batches entire lot to ?nish its processing on the current machine, while downstream machines may be idle. It should be obvious that processing the entire lot as a single object can lead to large workin-process inventories between the machines, and to an increase in the maximum completion time (makespan), which is the total elapsed time to complete the processing of all job lots. However, the splitting of an entire lot into transfer batches to be moved to downstream machines permits the overlapping of different operations on the same product while work proceeds, to complete the lot on the upstream machine. There are many ways to split a lot: transfer batches may be equal or unequal, with the number of splits ranging from one to the number of units in the job lot. For instance, consider a job lot consisting of 100 identical items to be processed in a three-stage manufacturing environment in which the ?ow of its operations is unidirectional from stage 1 through stage 3. Assume that the unit processing time at stages 1, 2, and 3 are 1, 3, 2 min, respectively. If we do not allow transfer batches, the throughput time is (100)(1+3+2) = 600 min (see Fig. 1a). However, if we create two equal sized transfer batches through all stages, the throughput time decreases to 450 min, a reduction of 25% (see Fig. 1b). It is clear that the throughput time decreases as the number of transfer batches increases. Flowshop problems have been studied extensively and reported in the literature without explicitly considering transfer batches. Johnson [1], in his pioneering work, proposed a polynomial time algorithm for determining the optimal makespan when several jobs are processed on a two-machine (two-stage) ?owshop with unlimited buffer. With three or more machines, the problem has been proven to be NP-hard (Garey et al. [2]). Besides the extension of this problem to the m -stage ?owshop problem, optimal solutions to some variations of the basic two-stage problem have been suggested. Mitten [3] considered arbitrary time lags, and optimal scheduling with setup times separated from processing was developed by Yoshida and Hitomi [4]. Separation of the setup, processing and removal times for each job on each machine was considered by Sule and Huang [5]. On the other hand, ?owshop scheduling problems with transfer batches have been examined by various researchers. Vickson
1 Introduction
Most classical shop scheduling models disregard the fact that products are often produced in lots, each lot (process batch) consisting of identical parts (items) to be produced. The size of a job lot (i.e., the number of items it consists of) typically ranges from a few items to several hundred. In any case, job lots are assumed to be indivisible single entities, although an entire job lot consists of many identical items. That is, partial transfer of completed items in a lot between machines on the processing routing of the job lot is impossible. But it is quite unreasonable to wait for the
F.C. ?etinkaya (u) Department of Industrial Engineering, Eastern Mediterranean University, Gazimagusa-T.R.N.C., Mersin Turkey E-mail: ferda.cetinkaya@https://www.wendangku.net/doc/4f7660178.html,.tr Tel.: +90-392-6301052 Fax: +90-392-3654029

机床加工外文翻译参考文献

机床加工外文翻译参考文献(文档含中英文对照即英文原文和中文翻译) 基本加工工序和切削技术基本加工的操作机床是从早期的埃及人的脚踏动力车和约翰·威尔金森的镗床发展而来的。它们为工件和刀具提供刚性支撑并可以精确控制它们的相对位置和相对速度。基本上讲，金属切削是指一个磨尖的锲形工具从有韧性的工件表面上去除一条很窄的金属。切屑是被废弃的产品，与其它工件相比切屑较短，但对于未切削部分的厚度有一定的增加。工件表面的几何形状取决于刀具的形状以及加工操作过程中刀具的路径。大多数加工工序产生不同几何形状的零件。如果一个粗糙的工件在中心轴上转动并且刀具平行于旋转中心切入工件表面，一个旋转表面就产生了，这种操作称为车削。如果一个空心的管子以同样的方式在内表面加工，这种操作称为镗孔。当均匀地改变直径时便产生了一个圆锥形的外表面，这称为锥度车削。如果刀具接触点以改变半径的方式运动，那么一个外轮廓像球的工件便产生了；或者如果工件足够的短并且支撑是十分刚硬的，那么成型刀具相对于旋转轴正常进给的一个外表面便可产生，短锥形或圆柱形的表面也可形成。

平坦的表面是经常需要的，它们可以由刀具接触点相对于旋转轴的径向车削产生。在刨削时对于较大的工件更容易将刀具固定并将工件置于刀具下面。刀具可以往复地进给。成形面可以通过成型刀具加工产生。多刃刀具也能使用。使用双刃槽钻钻深度是钻孔直径5-10倍的孔。不管是钻头旋转还是工件旋转，切削刃与工件之间的相对运动是一个重要因数。在铣削时一个带有许多切削刃的旋转刀具与工件接触，工件相对刀具慢慢运动。平的或成形面根据刀具的几何形状和进给方式可能产生。可以产生横向或纵向轴旋转并且可以在任何三个坐标方向上进给。基本机床机床通过从塑性材料上去除屑片来产生出具有特别几何形状和精确尺寸的零件。后者是废弃物，是由塑性材料如钢的长而不断的带状物变化而来，从处理的角度来看，那是没有用处的。很容易处理不好由铸铁产生的破裂的屑片。机床执行五种基本的去除金属的过程：车削，刨削，钻孔，铣削。所有其他的去除金属的过程都是由这五个基本程序修改而来的，举例来说，镗孔是内部车削；铰孔，攻丝和扩孔是进一步加工钻过的孔；齿轮加工是基于铣削操作的。抛光和打磨是磨削和去除磨料工序的变形。因此，只有四种基本类型的机床，使用特别可控制几何形状的切削工具1.车床，2.钻床，3.铣床，4.磨床。磨削过程形成了屑片，但磨粒的几何形状是不可控制的。通过各种加工工序去除材料的数量和速度是巨大的，正如在大型车削加工，或者是极小的如研磨和超精密加工中只有面的高点被除掉。一台机床履行三大职能：1.它支撑工件或夹具和刀具2.它为工件和刀具提供相对运动3.在每一种情况下提供一系列的进给量和一般可达4-32种的速度选择。加工速度和进给速度，进给量和切削深度是经济加工的三大变量。其他的量数是攻丝和刀具材料，冷却剂和刀具的几何形状，去除金属的速度和所需要的功率依赖于这些变量。切削深度，进给量和切削速度是任何一个金属加工工序中必须建立的机械参量。它们都影响去除金属的力，功率和速度。切削速度可以定义为在旋转一周时