CN113569195B - Preconditioning method for distributed network system - Google Patents

Preconditioning method for distributed network system Download PDF

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CN113569195B
CN113569195B CN202110814501.3A CN202110814501A CN113569195B CN 113569195 B CN113569195 B CN 113569195B CN 202110814501 A CN202110814501 A CN 202110814501A CN 113569195 B CN113569195 B CN 113569195B
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information matrix
matrix
distributed network
network system
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CN113569195A (en
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陈晶
胡满峰
过榴晓
仲红秀
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Jiangnan University
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Abstract

The application discloses a preconditioning method for a distributed network system, which comprises the following steps: acquiring system control data to construct an original information matrix; according to the original information matrix, utilizing a Newton secondary iteration method to calculate an approximate value of the inverse of the information matrix, and constructing a new information matrix; solving the maximum and minimum eigenvalues of the new information matrix by using a power method, and constructing an optimal step length; updating system parameters based on the new information matrix and the optimal step length; repeating the iteration to obtain the optimal estimation parameters. The application designs a method for solving the conditions of the distributed network system, which can avoid solving the solution of the derivative function equation and further expand the application range; the speed is superior to the original gradient algorithm, and when the original information matrix has pathological characteristics, the method can obtain higher convergence speed as well, and the precondition matrix P k The condition number of the matrix is reduced, and the parameter convergence speed can be remarkably improved by designing the optimal step length gamma.

Description

Preconditioning method for distributed network system
Technical Field
The application relates to the technical field of parameter identification, in particular to a preconditioning method for a distributed network system.
Background
In recent years, with the high-speed development of sensor technology and internet of things technology, signals are collected through sensors between distributed industrial control systems, signals are transmitted through a network, mutual connection and mutual communication are achieved, the functions of an original centralized system can be achieved through a plurality of distributed network systems, and therefore efficiency is improved. Conventional identification algorithms such as Least Square (LS) and Gradient (GD) are directed to parameter identification of the distributed network system, where the Least square is applied to parameter identification of the distributed network system, and it is necessary to assume that a derivative equation of the cost function has an analytical solution, which affects the application range; the gradient algorithm can only set the step length according to the original information matrix when updating the parameters each time, and when the original information matrix has the pathological characteristics, the convergence speed is very slow, even the convergence is not.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
The present application has been made in view of the above-described problems occurring in the prior art.
Therefore, the technical problems solved by the application are as follows: in the traditional identification algorithm, the application range of the least square algorithm is severely limited by conditions; the convergence rate of the gradient algorithm is affected by the original information matrix, and when the information matrix has pathological characteristics, the convergence of the information matrix is not guaranteed.
In order to solve the technical problems, the application provides the following technical scheme: acquiring system control data to construct an original information matrix; according to the original information matrix, utilizing a Newton secondary iteration method to calculate an approximate value of the inverse of the information matrix, and constructing a new information matrix; solving the maximum eigenvalue and the minimum eigenvalue of the new information matrix by using a power method, and constructing an optimal step length based on the maximum eigenvalue and the minimum eigenvalue; updating system parameters based on the new information matrix and the optimal step length; repeating the iteration to obtain the optimal estimation parameters.
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: the matrix of raw information comprises,
setting the information vector asFor L sets of data, the vector is constructed as +.>Said information vector->The original information matrix Φ (L) of (b) is:
H(L)＝Φ T (L)Φ(L)
wherein Φ (L) ∈R L×n N is the number of unknowns, and<l, H (L) represents an information matrix, H (L) ∈R n×n T is the rank of the matrix.
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: inverse P of the information matrix k Comprising the steps of (a) a step of,
P k ＝2P k-1 -P k-1 H(L)P k-1
P 0 ＝rI,
where k represents the number of iterations, P 0 Initial value representing the inverse of the information matrix, I represents and P 0 Identity matrix lambda with same dimension max [H(L)]Representing the maximum eigenvalue of matrix H (L), r represents the step size of the algorithm during the update.
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: in the L groups of data, the input and output of the system control are respectively: u (1), …, u (L) and Y (1), …, Y (L), based on the output of the system control, a constructed data vector Y (L) is:
Y(L)＝[y(1)，…,y(L)] T 。
as a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: the new information matrix P is obtained by exponentiation k The maximum eigenvalue of H (L),
ν m ＝P k H(L)ν m-1
wherein lambda is max [P k H(L)]Representing the new information matrix P k Maximum characteristic value of H (L), max (v) m ) Representing vector v m The element with the largest absolute value in m represents the iteration number, and m=0 and v in the initial state 0 Representing an arbitrary non-zero vector.
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: solving the new information matrix P by using error power method k The minimum eigenvalue of H (L),
d＝||P k H(L)|| 1
D＝dI-P k H(L)
λ min [P k H(L)]＝d-λ max [D]
wherein d represents a value of 1 norm, ||P k H(L)|| 1 Representation matrix P k H (L) 1 norm, D is the adjusted information matrix, I represents and matrix P k H (L) same-dimensional identity matrix lambda max [D]Representing the maximum eigenvalue, lambda, of matrix D min [P k H(L)]Representing the new information matrix P k Minimum eigenvalue of H (L).
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: according to the new information matrix P k Maximum eigenvalue λ of H (L) max [P k H(L)]And a minimum eigenvalue lambda min [P k H(L)]The optimal step length gamma is obtained,
as a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: according to the precondition matrix and the optimal step length, obtaining new parameters
Wherein,for the estimated value of the parameter after the mth iteration, the initial parameter vector +.>
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: the step of updating the system parameters includes,
setting a threshold delta and comparingAnd->If->The loop is terminated to obtain parameter estimatesOtherwise, increasing m by 1, and updating the system parameters again.
As a preferred embodiment of the preconditioning method for a distributed network system according to the present application, wherein: and when the system parameters are unchanged for two times, the system parameters are the optimal estimated parameters.
The application has the beneficial effects that: the application designs a method for solving the conditions of the distributed network system, which can avoid solving the solution of the derivative function equation and further expand the application range; the speed is superior to that of the original gradient algorithm, and when the original information matrix has pathological characteristics, the method can be obtainedFaster convergence speed due to the precondition matrix P k The condition number of the matrix is reduced, and the parameter convergence speed can be remarkably improved by designing the optimal step length gamma.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is a schematic diagram of a basic flow of a preconditioning method for a distributed network system according to one embodiment of the present application;
FIG. 2 is a basic system diagram of a preconditioning methodology for a distributed network system, in accordance with one embodiment of the present application;
FIG. 3 is a system diagram of a continuous stirred tank heating system for a preconditioning approach to a distributed network system, in accordance with one embodiment of the present application;
FIG. 4 is a graph of the convergence of the parameter errors of the present application and a conventional gradient algorithm (T-GD) and a least squares algorithm (LS) for a preconditioning method for a distributed network system according to an embodiment of the present application.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present application can be understood in detail, a more particular description of the application, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, but the present application may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present application is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the application. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
While the embodiments of the present application have been illustrated and described in detail in the drawings, the cross-sectional view of the device structure is not to scale in the general sense for ease of illustration, and the drawings are merely exemplary and should not be construed as limiting the scope of the application. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
Also in the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper, lower, inner and outer", etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present application. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected, and coupled" should be construed broadly in this disclosure unless otherwise specifically indicated and defined, such as: can be fixed connection, detachable connection or integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be a communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
Example 1
Referring to fig. 1-2, for one embodiment of the present application, a preconditioning method for a distributed network system is provided, comprising:
s1: and acquiring system control data to construct an original information matrix. It should be noted that:
the original information matrix comprises a matrix of information,
setting the information vector asFor L sets of data, the vector is constructed as +.>Information vectorThe original information matrix Φ (L) of (b) is:
H(L)＝Φ T (L)Φ(L)
wherein Φ (L) ∈R L×n N is the number of unknowns, and<l, H (L) represents an information matrix, H (L) ∈R n×n T is the rank of the matrix.
S2: and according to the original information matrix, solving an approximation value of the inverse of the information matrix by utilizing a Newton secondary iteration method, and constructing a new information matrix. It should be noted that:
inverse P of information matrix k Comprising the steps of (a) a step of,
P k ＝2P k-1 -P k-1 H(L)P k-1
P 0 ＝rI,
where k represents the number of iterations, P 0 Initial value representing the inverse of the information matrix, I represents and P 0 Identity matrix lambda with same dimension max [H(L)]Representing the maximum eigenvalue of matrix H (L), r represents the step size of the algorithm during the update.
S3: and solving the maximum eigenvalue and the minimum eigenvalue of the new information matrix by using a power method, and constructing an optimal step length based on the maximum eigenvalue and the minimum eigenvalue. It should be noted that:
in the L groups of data, the input and output of the system control are respectively: u (1), …, u (L) and Y (1), …, Y (L), based on the output of the system control, the constructed data vector Y (L) is:
Y(L)＝[y(1),…,y(L)] T 。
using power method to determine new information matrix P k The maximum eigenvalue of H (L),
ν m ＝P k H(L)ν m-1
wherein lambda is max [P k H(L)]Representing a new information matrix P k Maximum characteristic value of H (L), max (v) m ) Representing vector v m The element with the largest absolute value in m represents the iteration number, and m=0 and v in the initial state 0 Representing an arbitrary non-zero vector.
New information matrix P using error power method k The minimum eigenvalue of H (L),
d＝||P k H(L)|| 1
D＝dI-P k H(L)
λ min [P k H(L)]＝d-λ max [D]
wherein d represents a value of 1 norm, ||P k H(L)|| 1 Representation matrix P k H (L) 1 norm, D is the adjusted information matrix, I represents and matrix P k H (L) same-dimensional identity matrix lambda max [D]Representing the maximum eigenvalue, lambda, of matrix D min [P k H(L)]Representing a new information matrix P k Minimum eigenvalue of H (L).
According to the new information matrix P k Maximum eigenvalue λ of H (L) max [P k H(L)]And a minimum eigenvalue lambda min [P k H(L)]An optimal step length gamma is obtained,
s4: updating system parameters based on the new information matrix and the optimal step length to obtain new parameters according to the precondition matrix and the optimal step length
Wherein,for the estimated value of the parameter after the mth iteration, the initial parameter vector +.>
Setting a threshold delta and comparingAnd->If->The loop is terminated to obtain parameter estimatesOtherwise, increasing m by 1 and updating the parameters again.
S5: and repeating the iteration S2-S4 to obtain the optimal estimation parameters. It should be noted that:
and when the system parameters are unchanged for two times, the system parameters are the optimal estimated parameters.
The application designs a method for solving the conditions of the distributed network system, which can avoid solving the solution of the derivative function equation and further expand the application range; the speed is superior to the original gradient algorithm, and when the original information matrix has pathological characteristics, the method can obtain higher convergence speed as well, and the precondition matrix P k The condition number of the matrix is reduced, and the parameter convergence speed can be remarkably improved by designing the optimal step length gamma.
Example 2
Referring to fig. 3 to 4, a second embodiment of the present application is different from the first embodiment in that a verification test of a precondition method for a distributed network system is provided, and in order to verify and explain the technical effects adopted in the method, the present embodiment adopts a conventional technical scheme to perform a comparison test with the method of the present application, and the test results are compared by means of scientific proof to verify the true effects of the method.
FIG. 3 is a graph showing the modeling of a distributed continuous stirred tank heating system in this example, with experimental conditions set forth in Table 1, at which the system reached a steady state condition.
Table 1: the continuous stirred tank heating system specification table of the preconditioning process.
Variable Value
Level 12mA(20.48cm)
Cold value 12.96mA(9.0383×10 -5 m 3 /s)
Steam Value 12.57mA
Temperature 10.5Ma(42.52℃)
Wherein Level represents the liquid Level, cold valve represents the Cold water injection rate, stem valve represents the Steam valve, and Temperature represents the water Temperature.
The stirred tank heating system model has 4 parameters, namely θ= [ a ] 1 ,a 2 ,a 3 ,a 4 ] T ＝[0.06012,0.05390,0.04832,0.04332] T The steam temperature, namely the input of a heating system, is used for heating a heating wire, cold water is injected into the heating system, the purpose of heating is achieved through the heating wire, a valve is arranged under the system and is used for discharging water to achieve the temperature in a heating chamber, a sensor is arranged under a container and is used for measuring the temperature of hot water, the collected temperature is transmitted to a control center through a wireless network and is used as output, the temperature of the heating wire is regulated according to the steam temperature (input u) and the water temperature display value (output y) of the control center, and then the relation between the steam temperature (input u) and the water temperature display value (output y) of the control center is found out through a corresponding algorithm, so that the mathematical model establishment of the continuous stirring tank heating system is achieved.
In the model, the input u (t) is steam temperature, the control center displays temperature as output y (t), when the temperature y (t) of hot water is lower than an ideal value, the power of the heating wire is increased, namely, the power of the heating wire is increased, and when y (t) is higher than the ideal value, the power of the heating wire is decreased; the temperature sensor is placed at the bottom of the water tank, the real hot water temperature acquired by the sensor is transmitted to the control center through a network, and v (t) is used for representing measurement errors, namely, the measured value y (t) is formed by the temperature measured by the water tank sensor and the noise v (t).
During the experiment, when y (T) is stabilized near the ideal value, it can be considered that the hot water reaches the ideal temperature, i.e. the continuous stirred tank heating system reaches the steady state, at which time the input data u (1), …, u (L) are collected, the corresponding output display values collected by the sensors and transmitted to the control center are y (1), …, y (L), and the corresponding measurement errors v (1), …, v (L), the continuous stirred tank heating system is modeled by using the conventional gradient algorithm (T-GD), the least squares algorithm (LS) and the method (P-GD) of the patent, and the effectiveness of the application is verified in terms of algorithm speed, as shown in fig. 4.
Fig. 4 is a graph showing the effect of the preconditioning method (P-GD) algorithm and the conventional gradient algorithm (T-GD) and least squares algorithm (LS) in the present application, the preconditioning method can quickly identify the parameters of the continuous stirred tank heating system, the error is lower than 2% only by 4 iterations, and the conventional T-GD method is lower than 2% only by 9 iterations, so that the convergence speed of the T-GD algorithm is slowest in terms of speed, LS is fastest, but the matrix inversion operation is performed, and the solution is performed in the derivative function equation of the cost function.
It should be noted that the above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present application may be modified or substituted without departing from the spirit and scope of the technical solution of the present application, which is intended to be covered in the scope of the claims of the present application.

Claims (7)

1. A preconditioning method for a distributed network system, comprising:
acquiring system control data to construct an original information matrix, comprising:
the original information matrix: setting the information vector asFor L sets of data, the vector is built asSaid information vector->The original information matrix Φ (L) of (b) is:
H(L)＝Φ T (L)Φ(L)
wherein Φ (L) ∈R L×n N is the number of unknowns, and n < L, H (L) represents the information matrix, H (L) εR n×n T is the conversion rank of the matrix;
according to the original information matrix, a Newton secondary iteration method is utilized to calculate the approximate value of the inverse of the information matrix, and a new information matrix is constructed, and the method comprises the following steps:
inverse P of the information matrix k ：
P k ＝2P k-1 -P k-1 H(L)P k-1
P 0 ＝rI，
Where k represents the number of iterations, P 0 Initial value representing the inverse of the information matrix, I represents and P 0 Identity matrix lambda with same dimension max [H(L)]Representing the maximum eigenvalue of matrix H (L), r representing the step size of the algorithm in the updating process;
solving a maximum eigenvalue and a minimum eigenvalue of the new information matrix by using a power method, and constructing an optimal step length based on the maximum eigenvalue and the minimum eigenvalue, wherein the method comprises the following steps:
in the L groups of data, the input and output of the system control are respectively: u (1), …, u (L) and Y (1), …, Y (L), based on the output of the system control, a constructed data vector Y (L) is:
Y(L)＝[y(1)，…，y(L)] T ；
when the continuous stirring tank heating system reaches a stable state, input data u (1), … and u (L) are acquired, and output display values acquired by corresponding sensors and transmitted to a control center are y (1), … and y (L);
updating system parameters based on the new information matrix and the optimal step length;
repeating the iteration to obtain the optimal estimation parameters.
2. The preconditioning method for a distributed network system as recited in claim 1, wherein: the new information matrix P is obtained by exponentiation k The maximum eigenvalue of H (L),
v m ＝P k H(L)v m-1
wherein lambda is max [P k H(L)]Representing the new information matrix P k Maximum characteristic value of H (L), max (v m ) Representing vector v m The element with the largest absolute value in m represents the iteration number, and m=0 and v in the initial state 0 Representing an arbitrary non-zero vector.
3. The preconditioning method for a distributed network system as recited in claim 2, wherein: solving the new information matrix P by using error power method k The minimum eigenvalue of H (L),
d＝||P k H(L)|| 1
D＝dI-P k H(L)
λ min [P k H(L)]＝d-λ max [D]
wherein d represents a value of 1 norm, ||P k H(L)|| 1 Representation matrix P k H (L) 1 norm, D is the adjusted information matrix, I represents and matrix P k H (L) same-dimensional identity matrix lambda max [D]Representing the maximum eigenvalue, lambda, of matrix D min [P k H(L)]Representing the new information matrix P k Minimum eigenvalue of H (L).
4. A method as claimed in any one of claims 1, 2 and 3A preconditioning method for a distributed network system, characterized by: according to the new information matrix P k Maximum eigenvalue λ of H (L) max [P k H(L)]And a minimum eigenvalue lambda min [P k H(L)]The optimal step length gamma is obtained,
5. the preconditioning method for a distributed network system as recited in claim 4, wherein: according to the precondition matrix and the optimal step length, obtaining new parameters
Wherein,for the estimated value of the parameter after the mth iteration, the initial parameter vector +.>
6. The preconditioning method for a distributed network system as recited in claim 5, wherein: the step of updating the system parameters includes,
setting a threshold delta and comparingAnd->If->Then the loop is terminated to obtain the parameter estimate +.>Otherwise, increasing m by 1, and updating the system parameters again.
7. The preconditioning method for a distributed network system as recited in claim 6, wherein: and when the system parameters are unchanged for two times, the system parameters are the optimal estimated parameters.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015192696A1 (en) * 2014-06-20 2015-12-23 深圳大学 Gossip algorithm based multiple target doa estimating system and estimating method in distributed network
CN106788644A (en) * 2016-12-30 2017-05-31 东南大学 A kind of extensive MIMO method for precoding based on improved Newton iteration method
WO2018068629A1 (en) * 2016-10-10 2018-04-19 深圳超级数据链技术有限公司 Signal sampling and recovery method and apparatus applicable to ovxdm system and ovxdm system
CN109685400A (en) * 2018-02-24 2019-04-26 山东大学 Time-lag power system stability method of discrimination based on time integral IGD
CN112989275A (en) * 2021-03-10 2021-06-18 江南大学 Multidirectional method for network large-scale control system

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015192696A1 (en) * 2014-06-20 2015-12-23 深圳大学 Gossip algorithm based multiple target doa estimating system and estimating method in distributed network
WO2018068629A1 (en) * 2016-10-10 2018-04-19 深圳超级数据链技术有限公司 Signal sampling and recovery method and apparatus applicable to ovxdm system and ovxdm system
CN106788644A (en) * 2016-12-30 2017-05-31 东南大学 A kind of extensive MIMO method for precoding based on improved Newton iteration method
CN109685400A (en) * 2018-02-24 2019-04-26 山东大学 Time-lag power system stability method of discrimination based on time integral IGD
CN112989275A (en) * 2021-03-10 2021-06-18 江南大学 Multidirectional method for network large-scale control system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
求解逆特征值问题的牛顿类方法的收敛判据;魏婷婷;沈卫平;;高等学校计算数学学报(04);312-323 *

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