CN106019093B - A kind of online soft sensor method of three-phawse arc furnace arc length - Google Patents

Abstract

The present invention is a kind of online soft sensor method of three-phawse arc furnace arc length, its main feature is that, it comprises the step of：With controlling cycle T_cFor period acquisition electrode system N group inputoutput data；Anomaly data detection and processing；Data normalization processing；Determine electrode system model structure；With the minimum target of model predictive error function, the unknown parameter in electrode system model is solved；Using the parameter acquired, row write arc length soft-sensing model, obtain arc length value；With current time k_{It is existing}For basic point, chooses n (n≤N) group inputoutput datas successively in electrode system historical data, judge whether to update electric arc soft-sensing model online；If desired it updates, from (k_{It is existing}N) moment starts acquisition electrode system N group inputoutput datas, restarts to establish soft-sensing model, if need not update, waits for m controlling cycle, judges whether to update electric arc soft-sensing model again online.The present invention is not required to additionally increase detection device, realizes on-line measurement three-phawse arc furnace arc length.

Description

A kind of online soft sensor method of three-phawse arc furnace arc length

Technical field

The present invention relates to hard measurement fields, are a kind of online soft sensor methods of three-phawse arc furnace arc length.

Background technology

Electric arc furnaces is the main production equipments of steel industry, and electric arc furnaces will be electric by the electric arc generated between electrode and furnace charge It can be converted into thermal energy and carry out melting furnace charge.The arc length of electric arc determines arc power, in order to eliminate harmonic injection of the electric arc furnaces to power grid With voltage fluctuation and the deleterious effects such as flash, shorten the heat, improve labor productivity, improve quality of molten steel and reduction Electric power consumption per ton steel, it is the fundamental requirement of electric arc furnaces work to keep defined arc length.As shown in Figure 1, by regulating valve and electrode liter The hydraulic part that plunger beam hanger constitutes electrode system drops, and electrode controller realizes rise fall of electrodes by controlling hydraulic part, by stove Circuit Fault on Secondary Transformer, short net, electrode and electric arc constitute the electric part of electric arc furnaces.Control essence to electrode system is to electricity The control of arc length.But electric arc is high temperature, the electric discharge generation of high conductive gas, and during furnace operation, inconvenience is to its length It measures.

Currently, correlative study includes：

Chinese invention patent publication number CN200810226732, it is entitled " a kind of electric arc length control device and method ", The method is to install laser range finder on transportable welding gun, directly measured by laser range finder laser sensor with The distance between fixed workpiece, in this, as welding arc length.Chinese periodical document, Wang Yan, Mao Zhizhong, " exchange Electric arc furnaces arc power soft-sensing model ", industry heating, 2009 (38), 2,38-40.By on rise fall of electrodes plunger beam hanger The displacement for installing displacement sensor measuring electrode, in this, as arc length.Above two method is all by arc shape approximation For straight line, but the shape of actual arc is extremely complex, is not straight line, and in actual mechanical process, and electrode is constantly disappeared Consumption, the displacement of electrode are unable to the length of real embodiment electric arc, and both methods has some limitations, and of the present invention Method is insensitive to the shape of electric arc, and the scope of application is wider.

Northeastern University Ph.D. Dissertation, Wang Yan, " ac arc furnace Arc Modelling is studied and its application ", and 2009,05, base Establish the alternating current arc Model in Time Domain of nonlinear differential equation description in law of conservation of energy, the input of model be electric arc arc length and Electric current.Electric arc arc length is to utilize arc voltage-arc length formula, arc column gradient β₀It is calculated with alpha parameter, but these parameters and electric arc furnaces Working condition, the input of energy are more related than the several factors such as position of, duration of heat, electrode, and practical operation when is not easy to obtain .Compared with this method, the method for the invention has stronger practicability.

Chinese invention patent publication number CN102521489, entitled " a kind of modeling of arc furnace load and parameter identification side Method and system ", establish reflection electric arc furnaces harmonic wave in kind, flickering and three-phase imbalance characteristic Arc Modelling, electric arc is described as Nonlinear time-varying resistance, wherein needing the parameter C of identification related with arc length.This method does not provide the calculating side of arc length clearly Method.

Chinese periodical document, Zhang Ping, Hou Yanbin, " the Electrade Regulation System for Electric Arc Furnace identification based on time-varying N-L-N models ", Information and control, 2014 (43), 6,711-714.Electrode system of arc furnace is expressed as to the N-L-N models of linear segment time-varying, And on-line identification method is proposed on this basis.The single-phase arc funace that this method is directed to, and three-phase electricity when three-phawse arc furnace work There are coupling influences between arc, are not suitable for three-phawse arc furnace in this way.And the output quantity of this method electrode system is electric arc Resistance, electrode system output quantity of the invention are the virtual values of three-phase line current.

Invention content

The importance controlled in electric arc analysis and electrode in face of three-phawse arc furnace arc length, according to the phase of three-phawse arc furnace arc length Situations such as closing research, and the working condition based on 1. three-phawse arc furnaces is more stable state, not considering current interruption and short circuit Arc length hard measurement；2. each rise fall of electrodes of three-phawse arc furnace is realized by individual plunger rod hydraulic cylinder, three electrodes are not considered Between influence each other；3. each electrode of three-phawse arc furnace generates an electric arc, exists between three electric arcs and influence each other.

The object of the present invention is to carry out substantive correction and innovation to the prior art, providing one kind can fully demonstrate very True property, easy to operate, the online soft sensor method of scientific and reasonable three-phawse arc furnace arc length.

Realize that the object of the invention is adopted the technical scheme that：A kind of three-phawse arc furnace arc length online soft sensor side Method, characterized in that it includes the following steps：

(a) with controlling cycle T_cFor period acquisition electrode system N group inputoutput data：

The electrode system of three-phawse arc furnace includes three single-input single-output regulating valves, three single-input single-output electrode liters Plunger beam hanger and one three three output alternating current arc of input drop, and input data is that k-th of sampling instant electrode controller is sent out Survey A phase control voltage values u_a(k), B phase controls voltage value u_b(k) and C phase control voltage values u_c(k), output data is k-th A phase line current virtual values i is surveyed in sampling instant_a(k), B phase line currents virtual value i_b(k) and C phase line current virtual values i_c(k)；

(b) anomaly data detection and processing：

It needs to judge abnormal data, it is Q first to calculate lower point of cut-off to each data₁-1.5R₁, upper point of cut-off is Q₃ +1.5R₁, wherein Q₁、Q₃Respectively upper and lower quartile, R₁=Q₃-Q₁It is very poor for quartile, then by data one by one with point of cut-off Compare, is abnormal data less than lower point of cut-off or more than the data of upper point of cut-off；It reuses data mean value and replaces abnormal data Abnormal data is handled；

(c) data normalization is handled：

Since the numberical range of actual measurement control voltage value is 0~10V, the numberical range of actual measurement triple line current effective value is 0~20000A, in order to eliminate the influence of dimension, to data be normalized for:

Wherein, u_{i max}And u_{i min}It is the numerical value maximum and minimum in N group samples in the i-th phase actual measurement control voltage value, i_{i max}And i_{i min}It is the numerical value maximum and minimum in N group samples in the i-th phase actual measurement line current virtual value, u_{I is marked}(k) it is kth The i-th phase actual measurement control voltage value after a sampling instant normalized, i_{I is marked}(k) it is after k-th of sampling instant normalized The i-th phase survey line current virtual value；

(d) electrode system model structure parameter n is determined_f、n_g、n_hAnd n_hj：

According to the practical structures of three-phawse arc furnace electrode system, mathematical description is：

Wherein, i=a, b, c, u_{I is marked}(k) as the input quantity of model, i_{I moulds}(k) it is to adopt for k-th as the output quantity of model The i-th phase line current virtual value that sample moment electrode system model is calculated, x_i(k) it is that the i-th phase of k-th of sampling instant is practical not Oil mass in measurable addition hydraulic cylinder, v_i(k) it is the i-th phase of k-th of sampling instant actually immeasurablel arc length, it is comprehensive The demand for considering model accuracy and solving real-time is closed, determines polynomial basis function order n_fFor the order of 3, pulsed transfer function n_gFor 4, with v_i(k) it is the polynomial vector basic function H of independent variable_j(k) order n_hFor 3 and j-th of polynomial vector basic function The number of contained elementIt is 3, unknown parameter is in modelWith Indicate real Number field,It indicatesTie up real number matrix domain；

(e) with the minimum target of model predictive error function, the unknown parameter α in electrode system model is solved_ij、h_ijWith C_j, for N group sampled datas, it is defined as follows model predictive error matrix：

Definition Model prediction error functions are

In formula, upper footnote T indicates transposition operation, | | the determinant of representing matrix, the solution to formula (4) can using matrix Divide least-squares algorithm as follows：

1. model parameterization

Formula (2) is converted into

I_Mould(k)=[i_{A moulds}(k) i_{B moulds}(k) i_{C moulds}(k)]=φ (θ, u, k) β (5)

Wherein,I=a, b, c, y=1,2,3, herein, as i=a, y=1 works as i=b When, y=2, as i=c, y=3,

It is oneThe reality of dimension Several rows of vectors,C_j(y,:) representing matrix C_jThe all elements of y rows, j= 1,…,n_h,

Polynomial vector basic function H_jThe independent variable of (θ, u, k) is

Wherein：

It is n_gn_fThe row vector of dimension, θ=[θ_a θ_b θ_c]^TIt is 3n_gn_fThe column vector of dimension.

2. object function is converted

After model parameterization, the I in formula (4)_{Mould N}It is described as

I_{Mould N}=ψ (θ, u) β (7)

Wherein,Then the unknown parameter in model constitutes two parameter sets θ and β, leads to Variable drop is crossed, it will be containing there are two the formulas of parameter set (4) to be converted to containing there are one the forms of parameter set

Wherein, ψ⁺(θ, u) is the Moore-Penrose generalized inverse matrix of matrix ψ (θ, u), Moore-Penrose generalized inverses Matrix Chinese is Moore-Roger Penrose generalized inverse matrix, is a kind of inverse matrix, and the linear space being turned by the row of matrix ψ (θ, u) is just Friendship is projected as P_ψ=ψ (θ, u) ψ⁺(θ, u), the orthogonal complement space of matrix ψ (θ, u) are projected asI is unit matrix, then formula (8) is described as

IfIt is r₂(θ) obtains θ values when minimum value, i.e.,

3. solvingWith

Solution procedure is iterative search procedures, and steps are as follows：

The first step：The each element for choosing θ is 1, is defined as θ^(first), enable θ^(old)=θ^(first)；

Second step：By θ^(old)In substitution formula (9), r is calculated₂(θ^(old))；

Third walks：By r₂(θ^(old)) substitute into search end condition formula (11),

Wherein, ε₁It is the electrode system model tolerance index being manually set, L is model predictive error function r₂Hessian The Chinese of the Cholesky factorings of matrix, Hessian matrixes is Hessian matrix, is the real value letter that an independent variable is vector The square matrix of several second-order partial differential coefficient compositions, Cholesky decomposition Chinese tire out the decomposition of this base to be tall, and factoring L is diagonal element For the inferior triangular flap of positive number, η is the step-size in search for meeting Armijo-Goldstein criterion, and Armijo-Goldstein is optimization A kind of line search criterion when calculating, δ are the Newton method direction of search, | | | |²It is the 2- norms of matrix, n_θ=3n_fn_gIt is unknown ginseng Manifold θ includes the number of parameter, and N is collected electrode system inputoutput data group number in step (a), if formula (11) at It is vertical, thenGo to the 4th step.Otherwise, using search iteration formula (12),

θ^(new)=θ^(old)+ηδ (12)

Acquire θ^(new), enable θ^(old)=θ^(new), return to second step；

4th step：Search finishes, by what is acquiredIn substitution formula (13), parameter set is obtained

4. parameter set decomposes

ByConstruct following matrix

Carrying out singular value decomposition to formula (14) is

The unknown-model parameter then acquired is

Wherein, work as ξ_i1First nonzero element be timing, s_ξIt is 1, works as ξ_i1First nonzero element when being negative, s_ξ It is -1,

ByObtain the unknown parameter in formula (2)For

Wherein, it is specified thatIt indicates by matrixThe i-th row to jth row all column elements constitute Matrix；

(f) parameter for obtaining solution, substitutes into following equation, obtains three-phawse arc furnace arc length hard measurement value：

Wherein,For the hard measurement value of k-th of sampling instant arc length, u_i(k) it is k-th of sampling instant controller Control voltage value,The estimated value of hydraulic cylinder oil mass is added for k-th of sampling instant；

(g) judge whether that terminate arc length hard measurement just terminates this if arc length hard measurement need not be carried out according to need of work Process goes to step (l).Otherwise, sequence executes；

(h) with current time k_{It is existing}For basic point, n (n≤N) group input and output numbers are chosen successively in electrode system historical data According to, anomaly data detection and processing are first carried out, then carry out data normalization processing, by treated, input value substitutes into formula (2), The output valve i of computation model_{I moulds}(k)；

(i) judge whether formula (19) is true, if so, step (k) is gone to, if not, then sequence executes：

In formula, n is the inputoutput data group number that (h) step is chosen, ε₂It is the arc length hard measurement mould being manually set Type tolerates index；

(j) from (k_{It is existing}- n) moment starts acquisition electrode system N group inputoutput datas, go to step (b)；

(k) m controlling cycle is waited for, step (h) is gone to；

(l) terminate arc length hard measurement.

The online soft sensor method of the three-phawse arc furnace arc length of the present invention can fully demonstrate genuine property, operation side Just, scientific and reasonable.

Description of the drawings

Fig. 1 three-phawse arc furnace structural schematic diagrams；

Fig. 2 three-phawse arc furnace electrode system structural schematic diagrams；

A kind of flow charts of three-phawse arc furnace arc length online soft sensor method of Fig. 3；

500 groups of original sampling data figures of Fig. 4 steel mills three-phawse arc furnace electrode system；

Step-size in search indicatrix during Fig. 5 iterative solutions；

End condition indicatrix during Fig. 6 iterative solutions；

Object function indicatrix during Fig. 7 iterative solutions；

The arc length hard measurement value figure of 50 sampling instants of Fig. 8；

The comparison figure between line current virtual value is surveyed after Fig. 9 electrode models output valve and normalized.

Specific implementation mode

Below with drawings and examples, the invention will be further described.

Referring to Fig.1, three-phawse arc furnace structure is：It is equipped with electrode 4 in the top of molten steel 6, one end of electrode 4 passes through electrode holder Holder 3 is fixed on rise fall of electrodes plunger beam hanger 7, and electrode 4 passes through electrode jaw 3, rise fall of electrodes plunger beam hanger 7, regulating valve 8 It is connect with the output end of electrode controller, current supply circuit, current supply circuit is formed by electrode 4, short net 2 and furnace transformer secondary side 1 In triple line current effective value pass through the input terminal of power quality analyzer and electrode controller connect.In electrode 4 and molten steel 6 Between generate electric arc 5.

With reference to flow shown in Fig. 2, a kind of specific implementation of the flexible measurement method of three-phawse arc furnace arc length of the present invention Steps are as follows：

(a) with controlling cycle T_cFor period acquisition electrode system N group inputoutput data：

As shown in figure 3, the electrode system of three-phawse arc furnace includes three single-input single-output regulating valves, three single input lists Output electrode lifts plunger beam hanger and one three three output alternating current arcs of input, the oil of the addition hydraulic cylinder in Fig. 3 in dotted line frame Measure x_a(k)、x_b(k)、x_c(k), arc length v_a(k)、v_b(k)、v_c(k) and measurement noise υ_a(k)、υ_b(k)、υ_c(k) being can not The amount of measurement, input data are the actual measurement A phase control voltage values u that electrode controller is sent out_a(k), B phase controls voltage value u_b(k) and C phase control voltage values u_c(k), output data is actual measurement A phase line current virtual values i_a(k), B phase line currents virtual value i_b(k) and C Phase line current virtual value i_c(k).As shown in figure 4, enabling controlling cycle T_c=10 seconds, 500 groups of input and output numbers of acquisition electrode system According to i.e. N=500, input data is actual measurement control voltage value, and output data is actual measurement triple line current effective value.

(b) anomaly data detection and processing：

It needs to judge abnormal data, it is Q first to calculate lower point of cut-off to each data₁-1.5R₁, upper point of cut-off is Q₃ +1.5R₁, wherein Q₁、Q₃Respectively upper and lower quartile, R₁=Q₃-Q₁It is very poor for quartile, then by data one by one with point of cut-off Compare, is abnormal data less than lower point of cut-off or more than the data of upper point of cut-off；It reuses data mean value and replaces abnormal data Abnormal data is handled.

(c) data normalization processing is carried out to collected 500 groups of data according to formula (1)：

(d) electrode system model structure parameter n is determined_f、n_g、n_hWith

The initial model of row writing electrode system determines that vector basic function is polynomial form and n_f=3, n_g=4, n_h=3.

(e) the model predictive error matrix defined according to formula (3) obtains model predictive error functional expression (4), first by model Parameter turns to formula (5), i.e.,

I_Mould(k)=[i_{A moulds}(k) i_{B moulds}(k) i_{C moulds}(k)]=φ (θ, u, k) β

Wherein,

The independent variable of polynomial vector basic function is formula (6), i.e.,

Wherein：

It is The row vector of 12 dimensions,

Be 36 dimensions row to Amount, i.e. n_θ=36.

I is described by formula (7)_{Mould N}, the unknown parameter in model constitutes two parameter sets θ and β.

Parameter set is solved in accordance with the following stepsWith

The first step：Choose θ^(first)Each element be 1, enable θ^(old)=θ^(first)；

Second step：For simplicity, matrix ψ (θ^(old), u) and it is denoted as ψ, UV decomposition (a kind of decomposition operation of matrix) is carried out to it ForIn formula, U_ψFor orthogonal matrix, Σ_ψFor diagonal matrix, then the Moore-Penrose generalized inverse matrix of ψ areAnd the projection factorI is unit matrix.In this way, formula (8) is converted to formula (9), and obtain To r₂(θ^(old))；

Third walks：By model predictive error matrix Z_N(θ^(old)) it is denoted as Z_N, a kind of QR decomposition (decomposition of matrix is carried out to it Operation) beIn formula,For orthogonal matrix,For upper triangular matrix, thenT is matrix's Order, i.e., Representing matrixThe square operation of diagonal line element, ∏ indicates product calculation, and model prediction misses Poor matrix Z_NMoore-Penrose generalized inverses beWherein, Q is matrixPreceding t row, R is matrixPreceding t Row, matrixThe matrix of remaining row composition is denoted as Q^*。

Model predictive error matrix Z_NIn include 36 unknown parameters, be to its p-th of parameter derivation

Wherein, ψ_(p)Indicate p-th of parameter derivation to function ψ.

Model predictive error function r₂(θ^(old)) gradient vector be denoted as ω, p-th of element isThe wherein mark of tr [] representing matrix.

r₂(θ^(old)) Hessian matrixes be denoted as Ω, the element of pth row q row is

Seek r₂(θ^(old)) the characteristic value of Hessian matrixes Ω determine that the direction of search is δ if characteristic value is all positive value =-Ω^-1ω.If there are negative values for characteristic value, find the negative feature value of maximum absolute value, be denoted as λ, determine the direction of search be δ=- (Ω-2λI)^-1ω, wherein I are unit matrix.

To r₂(θ^(old)) Hessian matrixes Ω carry out Cholesky decomposition, that is, be expressed as a lower triangular matrix and The product of this lower triangular matrix transposition.When the characteristic value of Ω is all positive value, Ω=LL^T.When there are negative values for the characteristic value of Ω When, Ω -2 λ I=LL^T。

Step-size in search η is determined in accordance with the following steps：

Step 1：The selected region of search is [0,1], ρ=0.25, γ=1.2, η⁽⁰⁾=0.001, it enablesTime=0；

Step 2：Inspection formula r₂(θ^(old)+η^(time)δ)≤r₂(θ^(old))+ρω(θ^(old))^Tη^(time)Whether δ is true, if so, turn step 3；Otherwise, it enablesTurn step 5；

Step 3：Inspection formula r₂(θ^(old)+η^(time)δ)≥r₂(θ^(old))+(1-ρ)ω(θ^(old))^Tη^(time)Whether δ is true, if so, Stop iteration, η=η^(time), turn step 6；Otherwise, it enables

Step 4：IfTurn step 5；Otherwise, η is enabled^(time+1)=γ η^(time), time=time+1, turn step 2；

Step 5：It takesTime=time+1 is enabled, step 2 is turned；

Step 6：Terminate the search of step-length η.

Set electrode system model tolerance index ε₁=0.01, whether verification expression (11) is true, if so, then acquireGo to the 4th step.Otherwise, using formula (12), θ is acquired^(new), enable θ^(old)=θ^(new), return to second step；

4th step：Search finishes, by what is acquiredSubstitution formula (13), obtains parameter set

Step-size in search, end condition and object function index during iterative solution is as shown in Fig. 5, Fig. 6 and Fig. 7.

By formula (14) --- (17), it is as follows that decomposition obtains parameter：

1 regulating valve parameter of table

A phase regulating valve parameters	B phase regulating valve parameters	C phase regulating valve parameters
			-2156.54	2325.27	-836.02
-2295.12	2439.03	-864.14
			-1103.50	1216.99	-447.42

2 rise fall of electrodes plunger beam hanger parameter of table

A phase plunger beam hanger parameters	B phase plunger beam hanger parameters	C phase plunger beam hanger parameters
			0.38	0.37	0.53
0.27	-0.11	0.15
			-0.86	-0.77	-0.82
0.21	0.51	0.15

3 arc parameters of table

(f) obtained model parameter will be solved and substitutes into formula (18), obtain three-phawse arc furnace arc length soft-sensing model：

Actual measurement control voltage value is substituted into above-mentioned model successively, the hard measurement value of arc length can be obtained, such as Fig. 8 institutes It is shown as the arc length hard measurement value of 50 sampling instants.

If (g) electric arc furnaces is in reduction period working stage at this time, needs to carry out hard measurement to arc length, arc length cannot be terminated Hard measurement process, sequence execute.If electric arc furnaces is in the scratch start phase or wears well phase working stage at this time, arc length need not be carried out soft It measures, goes to step (l).

(h) with current time k_{It is existing}For basic point, 100 groups of inputoutput datas are chosen successively in electrode system historical data, Anomaly data detection and processing are first carried out, then carries out data normalization processing, input value substitutes into formula (2) by treated, meter The output valve of model is calculated, it is more as shown in Figure 9 with the actual measurement triple line current effective value after normalized.

(i) judge whether to need to update soft-sensing model according to formula (19).Calculated value is 0.0504 on the left of formula (19), this reality Example chooses ε₂It is 0.05, formula (19) is invalid, needs to update soft-sensing model, sequence executes.If this example chooses ε₂It is 0.06, Soft-sensing model need not be then updated, step (k) is gone to.

(j) from (k_{It is existing}- 100) moment starts 500 groups of inputoutput datas of acquisition electrode system, goes to step (b).

(k) 20 controlling cycles are waited for, step (h) is gone to.

(l) terminate arc length hard measurement.

Claims (1)

1. a kind of three-phawse arc furnace arc length online soft sensor method, characterized in that it includes the following steps：

(a) with controlling cycle T_cFor period acquisition electrode system N group inputoutput data：

The electrode system of three-phawse arc furnace includes three single-input single-output regulating valves, three single-input single-output rise fall of electrodes columns Beam hanger and one three three output alternating current arc of input are filled in, input data is the actual measurement A that k-th of sampling instant electrode controller is sent out Phase control voltage value u_a(k), B phase controls voltage value u_b(k) and C phase control voltage values u_c(k), when output data is k-th of sampling Carve actual measurement A phase line current virtual values i_a(k), B phase line currents virtual value i_b(k) and C phase line current virtual values i_c(k)；

(b) anomaly data detection and processing：

It needs to judge abnormal data, it is Q first to calculate lower point of cut-off to each data₁-1.5R₁, upper point of cut-off is Q₃+ 1.5R₁, wherein Q₁、Q₃Respectively upper and lower quartile, R₁=Q₃-Q₁It is very poor for quartile, then by data one by one with point of cut-off Compare, is abnormal data less than lower point of cut-off or more than the data of upper point of cut-off；It reuses data mean value and replaces abnormal data Abnormal data is handled；

(c) data normalization is handled：

Due to actual measurement control voltage value numberical range be 0~10V, actual measurement triple line current effective value numberical range be 0~ 20000A, in order to eliminate the influence of dimension, to data be normalized for:

Wherein, u_imaxAnd u_iminIt is the numerical value maximum and minimum in N group samples in the i-th phase actual measurement control voltage value, i_imaxWith i_iminIt is the numerical value maximum and minimum in N group samples in the i-th phase actual measurement line current virtual value, u_{I is marked}(k) when being k-th of sampling Carve the i-th phase actual measurement control voltage value after normalized, i_{I is marked}(k) it is the i-th phase after k-th of sampling instant normalized Survey line current virtual value；

(d) electrode system model structure parameter n is determined_f、n_g、n_hWith

According to the practical structures of three-phawse arc furnace electrode system, mathematical description is：

Wherein, i=a, b, c, u_{I is marked}(k) as the input quantity of model, i_{I moulds}(k) as the output quantity of model, when being k-th of sampling Carve the i-th phase line current virtual value that electrode system model is calculated, x_i(k) it can not actually be surveyed for the i-th phase of k-th of sampling instant The oil mass of amount being added in hydraulic cylinder, v_i(k) it is the i-th phase of k-th of sampling instant actually immeasurablel arc length, it is comprehensive to examine Consider model accuracy and solve the demand of real-time, determines polynomial basis function order n_fFor the order n of 3, pulsed transfer function_gFor 4, with v_i(k) it is the polynomial vector basic function H of independent variable_j(k) order n_hContained by 3 and j-th of polynomial vector basic function The number of elementIt is 3, unknown parameter is in modelWith Indicate real number field,It indicatesTie up real number matrix domain；

(e) with the minimum target of model predictive error function, the unknown parameter α in electrode system model is solved_ij、h_ijAnd C_j,

For N group sampled datas, it is defined as follows model predictive error matrix：

Definition Model prediction error functions are

Solution to formula (4) can divide least-squares algorithm as follows using matrix：

1. model parameterization

Formula (2) is converted into

I_Mould(k)=[i_{A moulds}(k)i_{B moulds}(k)i_{C moulds}(k)]=φ (θ, u, k) β (5)

Wherein,I=a, b, c, y=1,2,3, herein, and as i=a, y=1, as i=b, y= 2, as i=c, y=3,

It is oneThe real number row of dimension Vector,Representing matrix C_jThe all elements of y rows,

Polynomial vector basic function H_jThe independent variable of (θ, u, k) is

Wherein： It is n_gn_f The row vector of dimension, θ=[θ_aθ_bθ_c]^TIt is 3n_gn_fThe column vector of dimension；

2. object function is converted

After model parameterization, the I in formula (4)_{Mould N}It is described as

I_{Mould N}=ψ (θ, u) β (7)

Wherein,Then the unknown parameter in model constitutes two parameter sets θ and β, passes through change Amount projection, will be containing there are two the formulas of parameter set (4) to be converted to containing there are one the forms of parameter set

Wherein, ψ⁺(θ, u) is the Moore-Penrose generalized inverse matrix of matrix ψ (θ, u), the line being turned by the row of matrix ψ (θ, u) Property orthogonal space is projected as P_ψ=ψ (θ, u) ψ⁺(θ, u), the orthogonal complement space of matrix ψ (θ, u) are projected asI is unit matrix, then formula (8) is described as

IfIt is r₂(θ) obtains θ values when minimum value, i.e.,

3. solvingWith

Solution procedure is iterative search procedures, and steps are as follows：

The first step：The each element for choosing θ is 1, is defined as θ^(first), enable θ^(old)=θ^(first)；

Second step：By θ^(old)In substitution formula (9), r is calculated₂(θ^(old))；

Third walks：By r₂(θ^(old)) substitute into search end condition formula (11),

Wherein, ε₁It is the electrode system model tolerance index being manually set, L is model predictive error function r₂Hessian matrixes Cholesky factorings, η is the step-size in search for meeting Armijo-Goldstein criterion, and δ is the Newton method direction of search, n_θ =3n_fn_gIt is the number that unknown parameter collection θ includes parameter, N is collected electrode system inputoutput data in step (a) Group number, if formula (11) is set up,The 4th step is gone to, otherwise, using search iteration formula (12),

θ^(new)=θ^(old)+ηδ (12)

Acquire θ^(new), enable θ^(old)=θ^(new), return to second step；

4th step：Search finishes, by what is acquiredIn substitution formula (13), parameter set is obtained

4. parameter set decomposes

ByConstruct following matrix

Carrying out singular value decomposition to formula (14) is

The unknown-model parameter then acquired is

Wherein, work as ξ_i1First nonzero element be timing, s_ξIt is 1, works as ξ_i1First nonzero element when being negative, s_ξIt is -1,

ByObtain the unknown parameter in formula (2)For

Wherein, it is specified thatIt indicates by matrixThe i-th row to jth row all column elements constitute square Battle array；

(f) parameter for obtaining solution, substitutes into following equation, obtains three-phawse arc furnace arc length hard measurement value：

Wherein,For the hard measurement value of k-th of sampling instant arc length, u_i(k) it is the control of k-th of sampling instant controller Voltage value processed,The estimated value of hydraulic cylinder oil mass is added for k-th of sampling instant；

(g) judge whether that terminate arc length hard measurement just terminates this mistake if arc length hard measurement need not be carried out according to need of work Journey goes to step (l), and otherwise, sequence executes；

(h) with current time k_{It is existing}For basic point, n (n≤N) group inputoutput datas are chosen successively in electrode system historical data, Anomaly data detection and processing are first carried out, then carries out data normalization processing, input value substitutes into formula (2) by treated, meter Calculate the output valve i of model_{I moulds}(k)；

(i) judge whether formula (19) is true, if so, step (k) is gone to, if not, then sequence executes：

In formula, n is the inputoutput data group number that (h) step is chosen, ε₂It is the arc length soft-sensing model tolerance being manually set Index；

(j) from (k_{It is existing}- n) moment starts acquisition electrode system N group inputoutput datas, go to step (b)；

(k) m controlling cycle is waited for, step (h) is gone to；

(l) terminate arc length hard measurement.