中圖分類號：029 文獻標志碼：A DOI： 10.19907/j.0490-6756.240239

Anidentificationmodel for weakinfluenceparameters ofnuclearpowerunitbased on parameterrecursion

LIANGQian-Yun， （1.StateGrid Sichuan Electric PowerCompany，Chengdu 6loo41，China; 2.SchoolofMathematics，SichuanUniversity，Chengdu6lOO65，China）

Abstract： In complex systems，there is a kind of parameters having only a minor impact on the outputs in most cases，but their accurate values are stil critical for the operation ofsystems.In this paper，the authors focus on the identification of these weak influence parameters in the complex systems and propose a identification model based on the parameter recursion.As an application，three parameters of the steam generator are identified，that is，the valve opening，the valve CV value，and the reference water level，in which the valve opening and the reference water level are weak influence parameters under most operating conditions.Numerical simulation results show that，in comparison with the multi-layer perceptron（MLP），the identification er rorrate is decreased.Actually，the average identification error rate for the valve opening decreases by 0.96% ，for the valve CV decreases by 0.002% ，and for the reference water level decreases by 12% after one recursion. After two recursions，the average identification eror rate for the valve opening decreases by 11.07% ，for the valve CV decreases by 2.601% ，and for the reference water level decreases by 95.79% This method can help to improve the control of the steam generator.

Keywords： Steam generator; Nuclear power; Parameter identification;Multi-layer perceptron

1 Introduction

With the industrial systems such as nuclear reactors becoming increasingly complex，it ismore and more difficult to determine their parameters when establishing dynamic models for these sys tems.Nowadays，the modeling，parameter identification and controller design of complex systems inevitablyrequirenewideaswiththehelpofAI technologies，especially the relevant knowledge of sta tistical pattern recognition combing control theory.

Many researchers have studied the parameter identification problem of complex systems and many methodswereproposed.Forinstance，Ref.[1]pro posed a parameter identification method based on the overall error degradation index of the successive typeofparametererrorsandbaddata.Ref.[2]used the traditional weighted least squares to identify the lineparameters.Ref.[3] combined the WLS method and residual sensitivity analysis to identify theparameters.In Ref.[4]，theamplitude ofvoltagedrop wasusedto identifythe parametersof distribution line impedance using the approximate relationship between voltage drop amplitude and current.In Ref.[5]，the mutual covariance between inputsand outputs and the output self-covariance func tion were constructed to identify the structural pa rameters of system. In Ref.[6]，a time-frequency domain method was proposed to identify the modal parameters of the time-frequency spectrum in theun steadyvibration signals.In Ref.[7]，a method depending only on the time-frequency spectrum of the non-stationary vibration signals was proposed.

Onthe other hand，few researchers considered theparameter identification problem of nuclear power units.Ref.[8]provided a method to evaluate theparameter in pressurized water reactor.Ref.[9] studied the dynamic parameter model of electrical performance of the reactor control rod drive system. Ref.[1O] proposed a predictive control method based on the linear parameter-varying model combined with the cascade control theory.To our best knowledge，there are veryfewreferences concerning the identification problem of the weak influence parameters.Here“weak influence”means that， given the inputs unchanged，the output changes less oreven does not change with the change of param eters，while the accuratevalueof the parametersare still critical for the operation of the system.In other words，thiskindofparametersare insensitivetothe relationship of input-output，thus they are hard to be recognized.

Generally，to address this problem，the usual methods require some extra information of param eterortoadd random factorsuchasGaussianwhite noise to the system.For instance，Ref.[11] pointed that the parameter identification needed to distinguish the parameterswith large or small influenceto system.Ref.[12]realizedtheidentification of line parameters by alternating the estimation of theparameterswith strongandweakinfluence.Ref. [13] proposed a weighted minimum absolute value resistance parameter identification method for the cases of parameterswith strong influence and weak influence.

In this paper，an identification model of the weak influence parameters is proposed based on the parameter recursion.Then the method is applied to identify three parameters，say，the valve opening， thevalve CVand thereferencewaterlevel，of the steam generator of nuclear power units，in which thevalve opening and the reference waterlevel are both weak influence parameters.Simulation results show that，in comparison with the multi-layer per ceptron，the average identification error rate is decreased.In fact，after one recursion，the average identification error rate for the valve opening decreases by 0.96% ，for the valve CV decreases by 0.002% ，and for the reference water level decreases by 12% . After two recursions，the average identification error rate for the valve opening decreasesby 11.07% ，for the valve CV decreases by 2.601% ，and for the reference water level decreasesby 95.79%

2 Parameterrecursionmodel

Suppose that there isa system with n outputs

（204號 z=（z₁，z₂，…，z_n） and m inputs x=（x₁，x₂，… x_m， ，andthe relationship between theseinputsand outputs is

z=f（x）

If there are k unidentified parameters …，α_k） in the system，then system（1）can be ex^- pressed as z=f（x;α） .Suppose that all parameters have weak influence to the outputs z .Toimprove the discrimination accuracy，we can add a positive perturbation to the system.For each X_i the perturbation is increased as E_i ， s=（ε₁，ε₂，…，ε_m） . Then system （1） canbefurtherexpressed as .In the following，we establish a model to make ε have the positive action to the pa rameteridentification.

Let （Δ_{Zα，i，ΔXα，i}） be a set of outputs and inputs， depending on the parameters α ，where i∈I is the setof indicators，where I represents the number of sets of inputs and outputs. Through arbitrary AI methods，we can establish an approximate relationship Let .By arbitrary re gression method，bring （z_α，i，x_α，i） into the above equation，the following approximate relationship can be established：

Let

Wecheck whether or not the accuracy of the identification is satisfied，if not，let and bring （Δ_{Zα，i，δXα，i}） into the above equation. By the regression method，the following approximate relationship can be established：

Let

Wecheck one more time whether or not the accuracyof identification is satisfied，if not we repeat the above process. Implementing this process repeatedly，the accuracy of identification can be successivelyraised.Therefore，there must existsaninteger s making the following equation holds：

3 Applications

Steam generator is the core of nuclear reactor bylinking the primary and the secondary loops of nuclear power units. According to the relationship between the energy and mass conservation，and transfer among these control bodies，its mechanism model can be established，which is divided into primary side single-phase mechanism model，descendingtube mechanism model，secondary side hot watersection mechanism model，secondary side boilingsection mechanism model， phase separator mechanism model，and steam chambermechanism model，etc.These modelscontain hundredsof inter mediate process parameters and variables such as theexit density ofworkmass in the descent section， theenthalpy of recirculationwork mass，theweight offeed water in the descent section，the flow rate in the descent section，the density of work mass in the exitoftheprimary side，the heattransferred from the primary-side fluid to the metal tubes，the exit enthalpy，and so on.

Most of the parameters and variables in nuclear power units cannot be controlled directly，such as the temperature and pressure.As an application of the parameter recursion model，we choose three key parameters to identify，say，the valve opening， thereference water level andthevalve CV. Through three parameters，the working condition of the steam generator can be reflected，as shown in Fig. 1.

The outputs used in this paper are the gasphase velocities，the gas-phase flow rates，and the liquid-phase velocities at outlet 1；the liquid-phase velocities，and the gas-phase flow rates，at outlet 2；the above data are composed as Z_α，i .Since the system varies with time，the time data is composed of X_α，i .Theoutputsat outlet1 andoutlet2 are influencedbythevalveCVmost.Oncethevalve CVis determined， the gas-phase velocities，the gas-phase flow rates，the liquid-phase velocities at outlet 1;

and the liquid-phase velocities，and the gas-phase flow rates at outlet 2 in the vast majority of occa sions has been almost completely determined.The influences of the valve opening and the reference water level are thought to be minor.

We choose to regress three parameters by MLP with the regression model Z_α，i=f（Δx_α，i;Δαα） For the training data X_α，i ，there are 2OOl temporal data from the moment O to 2O seconds with a samplinginterval of O.Ol seconds.For the trainingdata Z_α，i ，there are 576 different combinations for param eter α ，and the gas-phase velocities，the gas-phase flow rates，and the liquid-phase velocities at outlet 1；and the liquid-phase velocities and the gas-phase flowratesatoutlet2are sampled for 2oOl times for each combination，totaling lO OO5 data.The total data Z_α，i used for training contains 57 628 80 data.

For the testing data X_α，i ，there are 2001 time data from O to 2O seconds with a sampling interval of O.O1 seconds；for the testing data z_α，i ，thereare 15different combinations for parameter α_a ，each combination includes the gas-phase flow rate，the liquid-phase flow rate，and the gas-phase flow rate at outlet1，and the liquid-phase velocities and the gas-phase flow rates at outlet 2.Moreover，each combination is sampled for 2Ool times，totaling

10005 data.The total data Z_α，i used for training con tains 57 62 88O data.Particularly，the testing data setisnot included in the trainingdata set.

The MLP is set to train lOoO times，the accuracy is set to 10^-6 ，the gradient is set to 10^-7 ，and the damping factor is set to 10¹⁰ .Before 1000 times havereached，there have been lO consecutive train ingerrors that cannot be reduced，the training task isended.The network isadequately trained with the above settings.After loading the test data，Tab.1 lists the average error level of the valve opening， thevalve CV，and thereference waterlevel relative to the truevalues.

In Tab.1，we notice that the identification ac curacy ishighin recognizing the valve CV with ma jor influence，but the identification accuracy is poor inrecognizing the valve opening and the reference waterlevelwithweakinfluence.Inaccordancewith theparameter recursion method，we utilize the MLP to carry out another recursion. In order to be better reflect the performance of the method，we use the same setting as the first training.After loadingthe testing data，Tab.2 lists the average error levels of the valve opening，the valve CV，and the referencewaterlevel relativetothetruevalue.

In Tab.2，we notice that the identification er ror rate decreases relative to the first regression. The average identification error rate of the valve opening decreases by 0.96% ，theaverage identification error rate of the valve CV decreases by 0.002% ，and the average identification error rate of thereference water level decreases by 12%

In accordance with the parameter recursion model，weutilizetheMLPagain with the same setting as the first training.Tab.3 lists the average identification error levels of the valve opening，the valveCV，and the referencewaterlevel relative to the true value.

In Tab.3，we notice that thereisa significant decrease in the identification error rate relative to the first regression. The average identification error rate of the valve opening decreases by 11.07% ，the valve CV decreases by 2.601% ，and the reference water level decreases by 95.79% . That is to say， after two iterations，there is a significant decrease in the identification error rate of the weak influence pa rameters.

4 Conclusions

In this paper，we have proposed a parameter recursion model for the identification problem of the weak influence parameters of the complex systems. Asan application，this method is used to identify threeparameters，namely，thevalve opening，the valve CV，and the reference waterlevel of the steam generator of nuclear power units. After two 990

recursions，the recognition accuracy significantly in creases. The method is expected to help the design of control systems of the steam generator.

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（責任編輯：周興旺）