CN114660941A - Alternating current electric arc furnace electrode system identification method based on hierarchical identification principle - Google Patents

Alternating current electric arc furnace electrode system identification method based on hierarchical identification principle Download PDF

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CN114660941A
CN114660941A CN202210323000.XA CN202210323000A CN114660941A CN 114660941 A CN114660941 A CN 114660941A CN 202210323000 A CN202210323000 A CN 202210323000A CN 114660941 A CN114660941 A CN 114660941A
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李俊红
蒋一哲
宋伟成
储杰
芮佳丽
褚云琨
宗天成
蒋泽宇
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Nantong University
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Abstract

The invention provides an alternating current electric arc furnace electrode system identification method based on a hierarchical identification principle, and belongs to the technical field of alternating current electric arc furnace electrode system identification. The problem of lower model precision caused by over-simplification of a real electrode system structure is solved. And the hierarchical identification is applied to the model, so that the identification precision is further improved. The technical scheme is as follows: the method comprises the following steps: step 1) establishing a single-input single-output Hammerstein-Wiener model of an electrode system of an alternating current electric arc furnace; and 2) constructing a hierarchical identification process of maximum likelihood least squares and random gradients. The invention has the beneficial effects that: the maximum likelihood least square hierarchical identification algorithm provided by the invention has higher convergence speed and higher convergence precision, and can be better suitable for modeling and parameter identification of an alternating current electric arc furnace electrode system.

Description

Alternating current electric arc furnace electrode system identification method based on hierarchical identification principle
Technical Field
The invention relates to the technical field of alternating current electric arc furnace electrode system identification, in particular to an alternating current electric arc furnace electrode system hierarchical identification method based on a maximum likelihood least square algorithm and a random gradient algorithm.
Background
In recent years, electric arc furnaces have been widely used in the metallurgical industry, becoming the primary equipment for steel production. The electric energy is converted into heat energy by generating electric arcs between the electrodes and furnace materials, the conversion efficiency depends on the length of the electric arcs, however, the electric arcs are generated by high-temperature and high-gas conductor discharge, and the length of the electric arcs is difficult to control directly in the operation process of an electric arc furnace system. The general method is to control the up-and-down movement of the electrode to maintain the arc current of the arc furnace at a certain set value, thereby eliminating the adverse effects of the arc furnace on the harmonic injection of a power grid, voltage fluctuation, flicker and the like, improving the quality of molten steel and reducing the power consumption of each ton of steel. The essence of the control of the electric arc furnace is the control of the electrodes. And an effective way to control the electrodes is to model the electrode system. For this reason, many researchers have proposed different identification methods, such as: random gradient algorithm, least square algorithm, particle swarm algorithm and the like.
The random gradient algorithm has poor identification precision and low convergence rate, so that the identification effect in actual production is usually poor; the least square algorithm has the problem that data saturation is caused by the fact that the data volume is increased in the process of tracking time-varying parameters; although the particle swarm algorithm serving as the swarm intelligence algorithm can be well applied to different working conditions, the problems of local optimization and large calculation amount are also caused.
How to solve the above technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide an alternating current electric arc furnace electrode system identification method based on a hierarchical identification principle, which is a novel identification method developed based on identification model decomposition, is provided for solving the problems of complex structure, high dimension and large-scale system identification, and can be better suitable for modeling and parameter identification of an alternating current electric arc furnace electrode system.
The invention is realized by the following measures: an alternating current electric arc furnace electrode system identification method based on a hierarchical identification principle comprises the following steps:
step 1) establishing a single-input single-output Hammerstein-Wiener time lag model of an alternating current electric arc furnace electrode system;
step 2) identifying parameter vectors by using a maximum likelihood least square algorithm;
and 3) identifying the time delay by using a random gradient algorithm.
As a further optimization scheme of the alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle, the specific modeling steps of the step 1) are as follows:
step 1-1) constructing a single-input single-output Hammerstein-Wiener time lag system model of an electrode system of an alternating current electric arc furnace:
h[y(t)]＝ω(t)+ξ(t) (1)
where h [ y (t) ] is the output of the system, ω (t) and ξ (t) are intermediate variables defined as follows:
ω(t)＝G(z-1)x(t) (2)
ξ(t)＝E(z-1)v(t) (3)
wherein x (t) is an intermediate variable, G (z)-1) Is a linear partial transfer function, z-1Denotes the postoperator, v (t) is the system noise, E (z)-1) Is z-1Is defined as follows:
Figure BDA0003570745370000021
wherein e iskIs the parameter vector of linear part to be identified, neIs order, assumed to be known;
x (t) is defined as follows:
x(t)＝f[u(t)] (5)
where u (t) is the system input and f (t) is the input nonlinear function of the system.
Step 1-2) for the nonlinear part of the inputs and outputs in the model, it is assumed to be continuous and reversible and is represented using an integration of known nonlinear functions, so f [ u (t) ] and h [ y (t)) ]arerepresented thereby:
Figure BDA0003570745370000022
Figure BDA0003570745370000023
wherein, csAnd dlParameter vector, n, for non-linear part to be identifiedcAnd ndIn order, it is assumed to be known.
And for the linear part, it is expressed in the form of a transfer function:
Figure BDA0003570745370000024
in the formula (8), τ is a time delay, A (z)-1)，B(z-1) Are all z-1Is defined as follows:
Figure BDA0003570745370000025
Figure BDA0003570745370000031
wherein, aiAnd bjIs the parameter vector of linear part to be identified, naAnd nbIs order, assumed to be known; step 1-3) deducing to obtain the mathematical description of the system model as follows:
Figure BDA0003570745370000032
definition of d 11, the first term d of the nonlinear function is output1h1[y(t)]Separating to obtain:
Figure BDA0003570745370000033
for the system described in equation (12), a, b, and e are all linear part of the parameter vector, defined as follows:
Figure BDA0003570745370000034
Figure BDA0003570745370000035
Figure BDA0003570745370000036
c. d is a parameter vector for the nonlinear part of the system, defining c1＝1、d1The vector is defined as 1:
Figure BDA0003570745370000037
Figure BDA0003570745370000038
parameter vectors theta, thetabc、θae、θd、θadIs defined as:
Figure BDA0003570745370000039
wherein:
Figure BDA00035707453700000310
Figure BDA00035707453700000311
Figure BDA00035707453700000312
Figure BDA00035707453700000313
then, the information vector of the whole system is defined as follows:
Figure BDA00035707453700000314
wherein:
Figure BDA0003570745370000041
Figure BDA0003570745370000042
Figure BDA0003570745370000043
Figure BDA0003570745370000044
Figure BDA0003570745370000045
Figure BDA0003570745370000046
the system model can be described as: h is1[y(t)]＝ΦT(t,τ)θ+v(t)。
As a further optimization scheme of the alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle, the model in the step 1) is a model of a single-input single-output system.
The alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle according to claim 1, wherein the step 2) of identifying the parameter vector by using the maximum likelihood least square algorithm comprises the following specific steps:
step 2-1) assuming maximum likelihood estimation values
Figure BDA0003570745370000047
Then the Taylor expansion of v (t) at this time is approximated as:
Figure BDA0003570745370000048
ignoring the higher order terms, approximating v (t) as:
Figure BDA0003570745370000049
step 2-2) taking the actually measured single-phase control voltage value sent by the electrode controller as input data of an alternating current electric arc furnace electrode system model, and taking the single-phase line current effective value as output data;
step 2-3) defining the estimated value of the parameter vector theta at the time t as
Figure BDA00035707453700000410
Figure BDA00035707453700000411
Step 2-4) gives v (t) partial derivatives of the parameter vector θ at time t, i.e. partial derivatives are calculated for a, b, c, d, e respectively:
Figure BDA0003570745370000051
Figure BDA0003570745370000052
Figure BDA0003570745370000053
Figure BDA0003570745370000054
Figure BDA0003570745370000055
step 2-5) substitutes (25), (26), (27), (28) and (29) to define a partial derivative information vector
Figure BDA0003570745370000056
Figure BDA0003570745370000057
Step 2-6) the criterion function of the system is expressed as:
J(θ,t)＝J(θ,t-1)+v2(t) (31)
step 2-7) is obtained by Taylor formula:
Figure BDA0003570745370000058
wherein:
Figure BDA0003570745370000059
Figure BDA00035707453700000510
η(t)*＝-r(t)TP-1(t)r(t)+v2(t)+η(t-1) (35)
applying a matrix inversion formula to obtain:
Figure BDA00035707453700000511
step 2-8) defining a gain vector k (t):
Figure BDA00035707453700000512
step 2-9) substituting the gain vector K (t) into equation (36) to obtain:
Figure BDA0003570745370000061
replacing the value of the parameter vector with an estimated value
Figure BDA0003570745370000062
To minimize the value of the criterion function J (θ, t), we should:
Figure BDA0003570745370000063
therefore, the method can obtain:
Figure BDA0003570745370000064
step 2-10) obtaining the identification summary of the parameter vector by using the maximum likelihood least square algorithm as follows:
Figure BDA0003570745370000065
Figure BDA0003570745370000066
as a further optimization scheme of the alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle provided by the invention, the step 3) of identifying the time delay by using the random gradient algorithm comprises the following specific steps:
step 3-1) defining the time delay as tau, and the estimated value as
Figure BDA0003570745370000067
From the gradient descent formula
Figure BDA0003570745370000068
Figure BDA0003570745370000069
(41) Wherein alpha is a self-defined iteration step,
step 3-2) alignment function partial derivation is obtained:
Figure BDA00035707453700000610
wherein:
Figure BDA00035707453700000611
step 3-3) into formula (41)
Figure BDA00035707453700000612
In the calculation formula (2), the identification of the time delay is summarized as follows:
Figure BDA00035707453700000613
and 3-4) finishing the identification and outputting an identification result.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention establishes a model for identifying the parameters of the electrode system of the alternating current electric arc furnace, takes the actually measured single-phase control voltage value sent by an electrode controller as input data, takes the effective value of the single-phase line current as output data, and identifies the parameters of the model by utilizing a hierarchical method of a maximum likelihood least square algorithm and a random gradient algorithm; as shown in FIG. 4, the method can identify the internal parameters of the model well.
(2) In the invention, a hierarchical identification method of maximum likelihood least squares and a random gradient algorithm is introduced into the identification of an alternating current electric arc furnace electrode system; for the parameter vector, a maximum likelihood least square algorithm is used, a probability model is obtained according to known input and output data, a log-likelihood function is obtained, the minimum value is obtained, and the model parameter vector is reversely deduced; for time delay, a random gradient algorithm is selected to quickly obtain a result; in terms of the overall identification step, the two methods are required to be performed alternately, namely, the time delay of the current moment is deduced by using the parameter identification result of the previous moment, and then the parameter estimation of the next moment is deduced by using the time delay of the current moment, so that the two methods are performed alternately and are suitable for the identification process of the electrode system of the alternating current electric arc furnace.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
Fig. 1 is an overall flowchart of an alternating current electric arc furnace electrode system identification method based on a hierarchical identification principle according to the present invention.
Fig. 2 is a schematic structural diagram of an ac electric arc furnace based on a hierarchical identification principle of the method for identifying an electrode system of an ac electric arc furnace according to the present invention.
FIG. 3 is a schematic diagram of a single-input single-output Hammerstein-Wiener time lag model of the alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle provided by the invention.
FIG. 4 is a schematic diagram of the error between the identification value and the true value of the parameter vector according to the present invention.
FIG. 5 is a schematic diagram of the error between the time delay identification value and the true value according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Example 1
Referring to fig. 1 to 4, the present invention provides a method for identifying an electrode system of an ac electric arc furnace based on a hierarchical identification principle, comprising the following steps:
step 1) establishing a single-input single-output Hammerstein-Wiener time lag model of an alternating current electric arc furnace electrode system;
step 2) identifying parameter vectors by using a maximum likelihood least square algorithm;
and 3) identifying the time delay by using a random gradient algorithm.
Preferably, the specific modeling step of step 1) is as follows:
step 1-1) constructing a single-input single-output Hammerstein-Wiener time lag model of an electrode system of an alternating current electric arc furnace:
h[y(t)]＝ω(t)+ξ(t) (1)
where h [ y (t) ] is the output of the system, ω (t) and ξ (t) are intermediate variables defined as follows:
ω(t)＝G(z-1)x(t) (2)
ξ(t)＝E(z-1)v(t) (3)
wherein x (t) is an intermediate variable, G (z)-1) Is a linear partial transfer function, z-1Denotes the postoperator, v (t) is the system noise, E (z)-1) Is z-1Is defined as follows:
Figure BDA0003570745370000081
wherein e iskIs the parameter vector of linear part to be identified, neIs order, assumed to be known;
x (t) is defined as follows:
x(t)＝f[u(t)] (5)
where u (t) is the system input and f (t) is the input nonlinear function of the system.
Step 1-2) deducing and obtaining mathematical description of a system model:
f [ u (t)) ] and h [ y (t)) ] are represented by an integration of known nonlinear functions:
Figure BDA0003570745370000082
Figure BDA0003570745370000083
wherein, csAnd dlParameter vector, n, for non-linear part to be identifiedcAnd ndIn order, it is assumed to be known.
And for the linear part, it can be expressed in the form of a transfer function:
Figure BDA0003570745370000091
in the formula (8), t is a time delay, A (z)-1)，B(z-1) Are all z-1The constant expression of (c), defined as follows:
Figure BDA0003570745370000092
Figure BDA0003570745370000093
wherein, aiAnd bjIs the parameter vector of linear part to be identified, naAnd nbIs order, assumed to be known;
step 1-3) definition of d 11, the first term d of the nonlinear function is output1h1[y(t)]Separating to obtain:
Figure BDA0003570745370000094
defining parameter vectors a, b and c of a linear part, parameter vectors c and d of a nonlinear part, defining parameter vectors and nonlinear parameters in a parameter vector theta, and finally defining information vectors of the whole system.
The system model can be described as: h is1[y(t)]＝ΦT(t,t)θ+v(t)。
Preferably, the model of step 1) is a model of a general single-input single-output system.
Preferably, the step 2) of constructing the maximum likelihood least square algorithm identification parameter vector specifically comprises the following steps:
step 2-1) assuming maximum likelihood estimation values
Figure BDA0003570745370000095
Then the taylor expansion of v (t) at this time ignores the higher order terms and can approximate v (t) as:
Figure BDA0003570745370000096
step 2-2) taking the actually measured single-phase control voltage value sent by the electrode controller as input data of an alternating current electric arc furnace electrode system model, and taking the single-phase line current effective value as output data;
step 2-3) defining the estimated value of the parameter vector theta at the time t as
Figure BDA0003570745370000097
Figure BDA0003570745370000098
Step 2-4) gives v (t) partial derivatives of the parameter vector θ at time t, i.e. partial derivatives are calculated for a, b, c, d, e respectively:
Figure BDA0003570745370000101
Figure BDA0003570745370000102
Figure BDA0003570745370000103
Figure BDA0003570745370000104
Figure BDA0003570745370000105
step 2-5) substitutes into (14), (15), (16), (17) and (18) to define a partial derivative information vector
Figure BDA0003570745370000106
Figure BDA0003570745370000107
Step 2-6) represents the criterion function of the system as:
J(θ,t)＝J(θ,t-1)+v2(t)(20)
steps 2-7) are derived from the taylor formula:
Figure BDA0003570745370000108
wherein:
Figure BDA0003570745370000109
Figure BDA00035707453700001010
η(t)*＝-r(t)TP-1(t)r(t)+v2(t)+η(t-1)(24)
applying a matrix inversion formula to obtain:
Figure BDA00035707453700001011
step 2-8) defining a gain vector K (t):
Figure BDA0003570745370000111
step 2-9) substituting the gain vector K (t) into the formula (25) to obtain:
Figure BDA0003570745370000112
replacing the value of the parameter vector with an estimated value
Figure BDA0003570745370000113
To minimize the value of the criterion function J (θ, t), we should:
Figure BDA0003570745370000114
therefore, the method can obtain:
Figure BDA0003570745370000115
step 2-10) obtaining the identification summary of the parameter vector by using the maximum likelihood least square algorithm as follows:
Figure BDA0003570745370000116
Figure BDA0003570745370000117
preferably, the step 3) of identifying the time delay by the stochastic gradient algorithm comprises the following specific steps:
step 3-1) defining the time delay as t and the estimated value as
Figure BDA0003570745370000118
From the gradient descent formula
Figure BDA0003570745370000119
Figure BDA00035707453700001110
Where α is a self-defined iteration step.
Step 3-2) alignment function partial derivation is obtained:
Figure BDA00035707453700001111
wherein:
Figure BDA00035707453700001112
substitution of step 3-3) into formula (31)
Figure BDA00035707453700001113
In the calculation formula (2), the identification of the time delay is summarized as follows:
Figure BDA0003570745370000121
the ac electric arc furnace described in this embodiment is schematically shown in fig. 2.
With the above mentioned general single input single output model, the following model can be established for this embodiment:
Figure BDA0003570745370000122
f[u(t)]＝c1[u(t)+u2(t)]+c2[u(t)+u2(t)]＝(1+1.35)*[u(t)+u2(t)]
h[ξ(t)]＝d1[E(z-1)v(t)+[E(z-1)v(t)]2]+d2[E(z-1)v(t)+[E(z-1)v(t)]2]
＝(1+0.09)*[E(z-1)v(t)]2]
A(z-1)＝1+a1z-1＝1+0.9z-1
B(z-1)＝b1z-1＝0.11z-1
E(z-1)＝1+e1z-1＝1+0.9z-1
comparing the model with step 1) above, we can get:
a1＝0.9,b1＝0.11,c1＝1,c2＝1.35,d1＝1,d2＝0.09,e1＝0.9
in order to conveniently substitute the parameters to be identified into the hierarchical identification method of the maximum likelihood least square algorithm and the random gradient algorithm, the parameters to be identified are combined into a parameter vector theta, and the parameters to be identified are defined as follows:
Figure BDA0003570745370000123
determining an approximate expression of v (t) according to step 2-1);
obtaining input and output data of the alternating current electric arc furnace electrode system model according to the step 2-2);
defining an estimated value of a parameter vector theta at the time t according to the step 2-3);
respectively solving partial derivatives for a, b, c, d and e according to the step 2-4);
defining a partial derivative information vector according to step 2-5)
Figure BDA0003570745370000124
Obtaining a criterion function expression according to the step 2-6);
sorting the simplification rule function according to the step 2-7) to obtain values of all parts;
defining a gain vector K (t) according to the step 2-8);
minimizing the value of a criterion function J (theta, t) according to the step 2-9) and the step 2-10), and substituting to obtain a parameter vector identification result;
obtained from the gradient descent formula according to step 3-1)
Figure BDA0003570745370000131
Calculating the partial derivative of J according to the step 3-2);
substitution into according to step 3-3)
Figure BDA0003570745370000132
The identification result of the time delay is obtained through calculation by the calculation formula.
The parameter identification result of the alternating current electric arc furnace electrode system hierarchical identification method based on the maximum likelihood least square algorithm and the random gradient algorithm is shown in fig. 4 and fig. 5, and it can be seen that the identification precision of the method is high, the estimated value of the parameter to be identified is very close to the true value, and meanwhile, the identification method has good applicability to the alternating current electric arc furnace electrode system model.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. An alternating current electric arc furnace electrode system identification method based on a hierarchical identification principle is characterized by comprising the following steps:
step 1) establishing a single-input single-output Hammerstein-Wiener time lag system model of an alternating current electric arc furnace electrode system;
step 2) identifying parameter vectors by using a maximum likelihood least square algorithm;
and 3) identifying the time delay by using a random gradient algorithm.
2. The alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle according to claim 1, wherein the specific modeling steps of the step 1) are as follows:
step 1-1) constructing a single-input single-output Hammerstein-Wiener time lag model of an electrode system of an alternating current electric arc furnace:
h[y(t)]＝ω(t)+ξ(t) (1)
where h [ y (t) ] is the output of the system, ω (t) and ξ (t) are intermediate variables defined as follows:
ω(t)＝G(z-1)x(t) (2)
ξ(t)＝E(z-1)v(t) (3)
wherein x (t) is an intermediate variable, G (z)-1) Is a linear partial transfer function, z-1Denotes the postoperator, v (t) is the system noise, E (z)-1) Is z-1Is defined as follows:
Figure FDA0003570745360000011
wherein e iskIs the parameter vector of linear part to be identified, neIs order, assumed to be known;
x (t) is defined as follows:
x(t)＝f[u(t)] (5)
where u (t) is the system input and f (t) is the input nonlinear function of the system;
step 1-2) for the nonlinear part of the inputs and outputs in the model, which are assumed to be continuous and invertible, and represented using an integration of known nonlinear functions, so f [ u (t) ] and h [ y (t)) ] are represented as:
Figure FDA0003570745360000012
Figure FDA0003570745360000013
wherein, csAnd dlParameter vector, n, for non-linear part to be identifiedcAnd ndIs order, assumed to be known;
and for the linear part, it is expressed in the form of a transfer function:
Figure FDA0003570745360000021
in the formula (8), τ is a time delay, A (z)-1) And B (z)-1) Are all z-1The polynomial of (a) is defined as follows;
Figure FDA0003570745360000022
Figure FDA0003570745360000023
wherein, aiAnd bjIs the parameter vector of linear part to be identified, naAnd nbIs order, assumed to be known;
step 1-3) deducing to obtain the mathematical description of the system model as follows:
Figure FDA0003570745360000024
definition of d11, the first term d of the nonlinear function is output1h1[y(t)]Separating to obtain:
Figure FDA0003570745360000025
for the system described in equation (12), a, b, and e are all linear partial parameter vectors, defined as follows:
Figure FDA0003570745360000026
Figure FDA0003570745360000027
Figure FDA0003570745360000028
c. d is defined as the parameter vector of the nonlinear part of the system, let c1＝1、d11, the following is defined:
Figure FDA0003570745360000029
Figure FDA00035707453600000210
parameter vectors theta, thetabc、θae、θd、θadIs defined as:
Figure FDA00035707453600000211
wherein:
Figure FDA0003570745360000031
Figure FDA0003570745360000032
Figure FDA0003570745360000033
Figure FDA0003570745360000034
then, the information vector of the whole system is defined as follows:
Figure FDA0003570745360000035
wherein:
Figure FDA0003570745360000036
Figure FDA0003570745360000037
Figure FDA0003570745360000038
Figure FDA0003570745360000039
Figure FDA00035707453600000310
Figure FDA00035707453600000311
the system model can be described as: h is1[y(t)]＝ΦT(t,τ)θ+v(t)。
3. The alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle according to claim 1, wherein the model of the step 1) is a model of a single-input single-output system.
4. The alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle according to claim 1, wherein the step 2) of identifying the parameter vector by using a maximum likelihood least square algorithm comprises the following specific steps:
step 2-1) assuming maximum likelihood estimation values
Figure FDA00035707453600000312
Then the Taylor expansion of v (t) at this time is approximated as:
Figure FDA00035707453600000313
ignoring higher order terms, then v (t) is approximated as:
Figure FDA00035707453600000314
step 2-2) taking the actually measured single-phase control voltage value sent by the electrode controller as input data of an alternating current electric arc furnace electrode system model, and taking the single-phase line current effective value as output data;
step 2-3) defining the estimated value of the parameter vector theta at the time t as
Figure FDA0003570745360000041
Figure FDA0003570745360000042
Step 2-4) gives v (t) partial derivatives of the parameter vector θ at time t, i.e. partial derivatives are calculated for a, b, c, d, e respectively:
Figure FDA0003570745360000043
Figure FDA0003570745360000044
Figure FDA0003570745360000045
Figure FDA0003570745360000046
Figure FDA0003570745360000047
step 2-5) substitutes into (25), (26), (27), (28) and (29) to define a partial derivative information vector
Figure FDA0003570745360000048
Figure FDA0003570745360000049
Step 2-6) the criterion function of the system is expressed as:
J(θ,t)＝J(θ,t-1)+v2(t) (31)
step 2-7) is obtained by Taylor formula:
Figure FDA00035707453600000410
wherein:
Figure FDA00035707453600000411
Figure FDA00035707453600000412
η(t)*＝-r(t)TP-1(t)r(t)+v2(t)+η(t-1) (35)
applying a matrix inversion formula to obtain:
Figure FDA0003570745360000051
step 2-8) defining a gain vector k (t):
Figure FDA0003570745360000052
step 2-9) substituting the gain vector K (t) into equation (36) to obtain:
Figure FDA0003570745360000053
replacing the value of the parameter vector with an estimated value
Figure FDA0003570745360000054
To minimize the value of the criterion function J (θ, t), we should:
Figure FDA0003570745360000055
therefore, the method can obtain:
Figure FDA0003570745360000056
step 2-10) obtaining the identification summary of the parameter vector by using the maximum likelihood least square algorithm as follows:
Figure FDA0003570745360000057
Figure FDA0003570745360000058
5. the alternating current electric arc furnace electrode system identification method based on the hierarchical identification principle according to claim 1, wherein the step 3) of identifying the time delay by using the random gradient algorithm comprises the following specific steps:
step 3-1) defining the time delay as tau, and the estimated value as
Figure FDA0003570745360000059
From the gradient descent formula
Figure FDA00035707453600000510
Figure FDA00035707453600000511
(43) Wherein alpha is a self-defined iteration step,
step 3-2) obtaining a partial derivative of the criterion function as follows:
Figure FDA00035707453600000512
wherein:
Figure FDA0003570745360000061
substitution of step 3-3) into formula (41)
Figure FDA0003570745360000062
In the calculation formula (2), the identification of the time delay is summarized as follows:
Figure FDA0003570745360000063
and 3-4) finishing the identification and outputting an identification result.
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