CN112911530B - Method for establishing small and micro intelligent sensor network congestion identification model - Google Patents

Method for establishing small and micro intelligent sensor network congestion identification model Download PDF

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CN112911530B
CN112911530B CN202011446595.5A CN202011446595A CN112911530B CN 112911530 B CN112911530 B CN 112911530B CN 202011446595 A CN202011446595 A CN 202011446595A CN 112911530 B CN112911530 B CN 112911530B
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CN112911530A (en
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周柯
王晓明
巫聪云
林翔宇
吴敏
张炜
丘晓茵
彭博雅
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Electric Power Research Institute of Guangxi Power Grid Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30Services specially adapted for particular environments, situations or purposes
    • H04W4/38Services specially adapted for particular environments, situations or purposes for collecting sensor information
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/02Traffic management, e.g. flow control or congestion control
    • H04W28/0289Congestion control

Abstract

The invention relates to a network congestion identification model, in particular to a method for establishing a network congestion identification model of a small and micro intelligent sensor, which comprises the steps of establishing a small and micro intelligent sensor network system data set by utilizing Koopman operator theory analysis, selecting a basis function to carry out dimensionality enhancement on the data set, enhancing the dimensionality of an original system to a high-dimensional observable function space, establishing a small and micro intelligent sensor network Koopman high-dimensional linear model, solving Koopman operator finite dimension approximation by utilizing the obtained enhanced dimensionality data set, and training by utilizing a neural network to obtain a final high-dimensional linear model; the technical scheme provided by the invention can effectively overcome the defect that the global linearization model with universality can not be established in the prior art.

Description

Method for establishing small and micro intelligent sensor network congestion identification model
Technical Field
The invention relates to a network congestion identification model, in particular to a method for establishing a network congestion identification model of a small intelligent sensor.
Background
In a transparent power grid, large-scale data streams in a wireless sensor network consisting of small and micro intelligent sensors are input to sensor nodes to possibly cause network congestion, and the network congestion seriously affects the performance of the network. The small intelligent sensor network system has strong nonlinearity, which increases difficulty for further analyzing and designing the network congestion controller, so that the establishment of a small intelligent sensor network congestion system linearization model is one of the key research directions of small intelligent sensors.
The congestion control directly influences the service quality of the network, and most scholars focus on local linearization at a balance point and then design a subsequent network congestion controller aiming at the problem that a network congestion model has strong nonlinearity.
Researchers at home and abroad carry out a great deal of research, and a university scholars at Shandong adopts a congestion degree threshold value as a basis for congestion adjustment, and provides a congestion avoidance strategy based on RED. (periodical: computer simulation, author: Li Luwei, Yang Hongyong; published New year month: 2012; article title: congestion control of RED-based wireless sensor network; page number: 168-
A scholars of Beijing university of science and technology proposes a controller based on a PID type neural network control queue, which solves the problem of online setting of algorithm parameters when the network changes in real time by utilizing the self-learning capability of an RBF neural network, so that the queue length in the router cache is stabilized at a set value. (periodical: small-sized microcomputer system; author: exemplary of Tang Dynasty, Muzhi Chun, Zhaoshi, Zhongdafu; published New year and moon: 2010; article topic: wireless sensor network congestion algorithm based on RBF prediction neural network controller; page number: 32-35)
Scholars at taiwan, zhongxing university propose a robust congestion controller based on a non-linear interference observer, which focuses on suppressing queue oscillation and compensating for time lag. (journal: IFAC Proceedings Volumes; authors: Hsu P, Lin C; published New year and month: 2014; article title: Active queue management in wireless networks by using nonlinearly extended network disturbance; page number: 1613-
Scholars of the combined fertilizer industry university adopt a sliding mode learning control method, which can relieve congestion, reduce packet loss and keep queue length. (meeting: 2014International Conference on Wireless Communication and Sensor Network; author: Jiang K W, Wang J P, Sun W, Qi yue Li; year of publication: 2015; article title: Sliding model learning control for controlling of Wireless Sensor Network; page number: 291-
The university scholars of Islam, Azader, proposed a fuzzy PID control method to control buffer queue length. (journal: Wireless Personal Communications; Rezaee AA, Pasandndeh F; published New year month: 2017; article title: A fuzzy control protocol based active request management in Wireless sensor network with media applications; page: 816-842)
Most of the existing methods focus on local linearization of a network congestion system and then control law design. Due to incompleteness of the mathematical model considered by the methods, the conclusion is difficult to be generalized to the general case.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects in the prior art, the invention provides a method for establishing a congestion identification model of a small micro intelligent sensor network, which can effectively overcome the defect that a global linearization model with universality cannot be established in the prior art.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for establishing a congestion identification model of a small and micro intelligent sensor network is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a small and micro intelligent sensor network system data set by utilizing Koopman operator theory analysis;
s2, selecting a basis function to upgrade the dimension of the data set, and upgrading the dimension of the original system to a high-dimensional observable function space;
s3, establishing a Koopman high-dimensional linear model of the small micro intelligent sensor network;
and S4, solving the Koopman operator finite dimension approximation by using the obtained ascending dimension data set, and training by using a neural network to obtain a final high-dimensional linear model.
Preferably, the establishing of the small micro intelligent sensor network system data set by using Koopman operator theory analysis comprises:
the method comprises the following steps of utilizing control input capable of exciting network characteristics of the small micro intelligent sensor to collect input and output data, and utilizing the generated output data and the control input data to establish a data set:
Figure GDA0003717432120000031
wherein, U is an input sequence, X is a current state sequence, Y is a next state sequence, n represents the total sampling times of each control, k represents the collection of k groups of data, i.e. open-loop control is carried out under k different random input sequences by k different initial states, p is the packet discarding probability,
Figure GDA0003717432120000041
for the current state, w is the window size, q is the queue length, x n Is the next state value.
Preferably, the selecting a basis function to perform dimension raising on the data set includes the following steps:
s21, defining a group of basis functions
Figure GDA0003717432120000042
S22, selecting a simple neural network as an approximator of the basis function, and setting the form as follows:
Figure GDA0003717432120000043
h=tanh(W x +b); (1)
wherein W is equal to R16 multiplied by 2, W out ∈R40×16,b∈R16×1,b out E R40 × 1, and the parameter set to be trained is θ ═ W, b, W out ,b out };
S23, bringing the data set into a neural network for dimensionality improvement to obtain a dimensionality-improved data set X lift 、Y lift
Preferably, the establishing of the Koopman high-dimensional linear model of the small micro intelligent sensor network comprises the following steps:
based on the combination of Koopman operator theory and extended dynamics modal decomposition algorithm, the small micro intelligent sensor network is expressed as a high-dimensional linear model:
z(k+1)=A Z (k)+BU(k),
Figure GDA0003717432120000044
wherein z is a state after the dimension is raised,
Figure GDA0003717432120000045
the state of an original space obtained based on a Koopman operator theory is represented, A belongs to RM multiplied by N, B belongs to RN multiplied by 1, C belongs to R2 multiplied by N and is a linear constant matrix, N is a state dimension after dimension rising, and an expression (2) is a global linearization model.
Preferably, the obtaining of the Koopman operator finite-dimensional approximation by using the obtained ascending-dimension dataset and the training by using the neural network to obtain the final high-dimensional linear model includes:
using the obtained ascending data set X lift 、Y lift And (3) solving the Koopman operator finite dimension approximation by an extended dynamic modal decomposition algorithm, namely solving the following minimization problem to obtain a matrix A, B, C in the high-dimensional linear model:
Figure GDA0003717432120000051
Figure GDA0003717432120000052
the analytical formula for solving the minimum value is:
[A,B]=Y lift [X lift ,U]
Figure GDA0003717432120000053
obtaining the preliminary analysis of the high-dimensional linear model (2) by the formulas (1) and (4), and training the obtained matrix A, B, C and the neural network parameter set by using the automatic training capability of the neural network to obtain a model closer to the real model, wherein the defined loss function is expressed as:
Figure GDA0003717432120000054
continuously training the equations (1), (4) and the loss function (5) through a neural network until
Figure GDA0003717432120000055
And reducing the state error with the real data set to be below 0.0001, and stopping training to obtain the final high-dimensional linear model.
(III) advantageous effects
Compared with the prior art, the method for establishing the small and micro intelligent sensor network congestion identification model provided by the invention obtains the global linearization model of the small and micro intelligent sensor network system by utilizing the Koopman operator theory, utilizes the neural network form as a basis function, and improves the precision of the global linearization model through automatic training, thereby effectively solving the problems that the prior art only carries out local linearization at a balance point, and the considered mathematical model has incompleteness, so that the model is difficult to popularize to the general condition, and the global linearization model is simple in design, thereby providing convenience for subsequent analysis and design of small and micro intelligent sensor network congestion control.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a schematic flow chart of a small micro intelligent sensor network congestion identification model establishment according to the invention;
FIG. 2 is a graph of accuracy verification for a Koopman high-dimensional linear model under a sine input designed in accordance with the present invention;
FIG. 3 is a graph of the accuracy verification of the Koopman high-dimensional linear model under the square wave input designed by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The Koopman operator is an infinite dimensional linear operator which transforms the system from the original state space to another space for approximation purposes, and is a powerful tool for nonlinear dynamical system analysis and decomposition. The role of Koopman operator K is as follows: kg (x) k )=gof(x k );
Where o is a function-conforming operator, x k The state of the system is f, which is a function of state evolution in a state space, and g which is a real-valued observation function and is an element of an infinite dimension Hilbert space. Koopman operator K is an infinite dimensional linear operator acting on the observation function, in other words, the original system can be upscaled to an infinite dimensional observable function space, and Koopman operator will be likeObservation of State g (x) k ) Advancing to the next time step: kg (x) k )=g(x k+1 )。
The Koopman operator captures the dynamics of the underlying system over the observable space, and the original system evolves linearly under the new coordinate system. Theoretically, an infinite space can completely restore a nonlinear system, but in practical application, finite-dimension approximation of an infinite model is adopted, and the finite-dimension approximation of a Koopman operator is solved by adopting an extended dynamic modal decomposition algorithm. To obtain a finite-dimensional approximation of the Koopamn operator, a set of basis functions is first defined:
Figure GDA0003717432120000071
and obtaining an observation function linearly combined by the basis functions:
Figure GDA0003717432120000072
wherein, a is the weight matrix, and the following formula holds:
Figure GDA0003717432120000073
where r (x) is a residual term. The approximate Koopamn operator K can be calculated by the least squares method f :K f =EG
Wherein the content of the first and second substances,
Figure GDA0003717432120000074
Figure GDA0003717432120000075
a method for establishing a congestion identification model of a small smart sensor network is disclosed, as shown in FIG. 1, and comprises the following steps:
s1, establishing a small and micro intelligent sensor network system data set by utilizing Koopman operator theory analysis;
s2, selecting a basis function to upgrade the dimension of the data set, and upgrading the dimension of the original system to a high-dimensional observable function space;
s3, establishing a Koopman high-dimensional linear model of the small micro intelligent sensor network;
and S4, solving the Koopman operator finite dimension approximation by using the obtained ascending dimension data set, and training by using a neural network to obtain a final high-dimensional linear model.
A small and micro intelligent sensor network system data set is established by utilizing Koopman operator theory analysis, and in order to facilitate subsequent network congestion control analysis and design, the window size and the queue length (w, q) are used as states, the packet drop probability p is used as input, and the queue length q is used as output.
The method comprises the following steps of utilizing control input capable of exciting network characteristics of the small micro intelligent sensor to collect input and output data, and utilizing the generated output data and the control input data to establish a data set:
Figure GDA0003717432120000081
wherein, U is an input sequence, X is a current state sequence, Y is a next state sequence, n represents the total sampling times of each control, k represents the collection of k groups of data, i.e. open-loop control is carried out under k different random input sequences by k different initial states, p is the packet discarding probability,
Figure GDA0003717432120000082
for the current state, w is the window size, q is the queue length, x n Is the next state value.
Selecting a basis function to carry out dimension increasing on the data set, and the method comprises the following steps:
s21, defining a group of basis functions
Figure GDA0003717432120000083
S22, selecting a simple neural network as an approximator of the basis function, and setting the form as follows:
Figure GDA0003717432120000091
h=tanh(W x +b); (1)
wherein W is equal to R16 multiplied by 2, W out ∈R40×16,b∈R16×1,b out E R40 × 1, and the parameter set to be trained is θ ═ W, b, W out ,b out };
S23, bringing the data set into a neural network for dimensionality improvement to obtain a dimensionality-improved data set X lift 、Y lift
Establishing a Koopman high-dimensional linear model of a small and micro intelligent sensor network, which comprises the following steps:
based on the combination of Koopman operator theory and extended dynamics modal decomposition algorithm, the small micro intelligent sensor network is expressed as a high-dimensional linear model:
z(k+1)=A Z (k)+BU(k),
Figure GDA0003717432120000092
wherein z is a state after the dimension is raised,
Figure GDA0003717432120000093
and the state of an original space obtained based on a Koopman operator theory is shown, A belongs to RM multiplied by N, B belongs to RN multiplied by 1, C belongs to R2 multiplied by N and is a linear constant matrix, N is a state dimension after dimension rising, and the formula (2) is a global linearization model.
Using the obtained ascending dimension data set to obtain a Koopman operator finite dimension approximation, and using a neural network to train to obtain a final high-dimensional linear model, wherein the method comprises the following steps:
using the resulting upscaled dataset X lift 、Y lift And (3) solving the Koopman operator finite dimension approximation by an extended dynamic modal decomposition algorithm, namely solving the following minimization problem to obtain a matrix A, B, C in the high-dimensional linear model:
Figure GDA0003717432120000094
Figure GDA0003717432120000095
the analytical formula for solving the minimum value is:
[A,B]=Y lift [X lift ,U]
Figure GDA0003717432120000101
obtaining the preliminary analysis of the high-dimensional linear model (2) by the formulas (1) and (4), and training the obtained matrix A, B, C and the neural network parameter set by using the automatic training capability of the neural network to obtain a model closer to the real model, wherein the defined loss function is expressed as:
Figure GDA0003717432120000102
continuously training the equations (1), (4) and the loss function (5) through a neural network until
Figure GDA0003717432120000103
And reducing the state error with the real data set to be below 0.0001, and stopping training to obtain the final high-dimensional linear model.
In FIG. 2, (a) is a system given sinusoidal control input variation curve; (b) is a comparison curve of the Koopman high-dimensional model queue length and the real model queue length under sine input; (c) is a comparison curve of the Koopman high-dimensional model window size and the real model window size under sine input.
In fig. 3, (a) is a given square wave control input variation curve of the system; (b) is a comparison curve of the length of the Koopman high-dimensional model queue and the length of the real model queue under sine input; (c) is a comparison curve of the Koopman high-dimensional model window size and the real model window size under sine input.
In order to verify the performance of the identification model designed by the invention, the identification model designed by the invention is verified by taking the traditional small and micro intelligent sensor network congestion mathematical model as a real model. Wherein, the simulation parameters of the network environment of the small and micro intelligent sensor are set as follows: the number of active TCP links is 60, the link capacity is 300 packets, the round trip delay is 3.2 seconds, and the fixed broadcast delay is 0.2 seconds.
The method of the invention comprises the following steps of acquiring a state initial value and an open loop input value range: the packet discarding probability p is randomly valued in 0-1, the queue length q is randomly valued in 100-300, the window size w is randomly valued in 0-10, and the expected queue length is set to be 200 packets by simulation. The simulation time was 100 seconds and the sampling frequency was 200 hz.
It can be seen from fig. 2 that the two states of queue length and window size under the Koopman model designed by the present invention fit the real case well given the sinusoidal open loop input. To avoid chance, the different input validation models of a given system fit the effect graph as shown in FIG. 3. As can be seen from fig. 3, the Koopman model still fits well to the variations in queue length and window size with a square wave input.
Therefore, the Koopman operator can restore the nonlinear small and micro intelligent sensor network system, can well predict the original system, realizes global linearization on the original system model, and provides convenience for subsequent analysis and design of the small and micro intelligent sensor network congestion controller. In a word, the method adopted by the invention can carry out global linearization on the original nonlinear system, overcomes the defect that the network congestion system is only locally linearized at a balance point in the prior art, can popularize the conclusion to a general condition, and provides convenience for analyzing the small and micro intelligent sensor network system.
The effectiveness of the algorithm is proved through the analysis.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions.

Claims (1)

1. A method for establishing a congestion identification model of a small and micro intelligent sensor network is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a small and micro intelligent sensor network system data set by utilizing Koopman operator theory analysis;
s2, selecting a basis function to upgrade the dimension of the data set, and upgrading the dimension of the original system to a high-dimensional observable function space;
s3, establishing a Koopman high-dimensional linear model of the small micro intelligent sensor network;
s4, solving a Koopman operator finite dimension approximation by using the obtained ascending dimension data set, and training by using a neural network to obtain a final high-dimensional linear model;
the method for establishing the small and micro intelligent sensor network system data set by utilizing Koopman operator theory analysis comprises the following steps:
the method comprises the following steps of utilizing control input capable of exciting network characteristics of the small micro intelligent sensor to collect input and output data, and utilizing the generated output data and the control input data to establish a data set:
Figure FDA0003708702020000011
wherein, U is an input sequence, X is a current state sequence, Y is a next state sequence, n represents the total sampling times of each control, k represents the collection of k groups of data, i.e. open loop control is carried out under k different random input sequences by k different initial states, p is the packet discarding probability,
Figure FDA0003708702020000012
for the current state, w is the window size, qIs queue length, x n Is the next state value;
the method for selecting the basis function to carry out dimension increasing on the data set comprises the following steps:
s21, defining a group of basis functions
Figure FDA0003708702020000021
S22, selecting a simple neural network as an approximator of the basis function, and setting the form as follows:
Figure FDA0003708702020000022
h=tanh(W x +b); (1)
wherein W is equal to R16 multiplied by 2, W out ∈R40×16,b∈R16×1,b out E R40 × 1, and the parameter set to be trained is θ ═ W, b, W out ,b out };
S23, bringing the data set into a neural network for dimensionality improvement to obtain a dimensionality-improved data set X lift 、Y lift
The establishment of the Koopman high-dimensional linear model of the small and micro intelligent sensor network comprises the following steps:
based on the combination of a Koopman operator theory and an extended dynamics modal decomposition algorithm, a small micro intelligent sensor network is represented as a high-dimensional linear model;
z(k+1)=A Z (k)+BU(k),
Figure FDA0003708702020000023
wherein z is a state after the dimension is raised,
Figure FDA0003708702020000025
representing the state of an original space obtained based on a Koopman operator theory, wherein A belongs to RM multiplied by N, B belongs to RN multiplied by 1, C belongs to R2 multiplied by N and is a linear constant matrix, N is a state dimension after dimension rising, and a formula (2) is a global linearization model;
the method comprises the steps of solving the Koopman operator finite dimension approximation by using the obtained ascending dimension data set, and training by using a neural network to obtain a final high-dimensional linear model, wherein the method comprises the following steps:
using the obtained ascending data set X lift 、Y lift And (3) solving the Koopman operator finite dimension approximation by an extended dynamic modal decomposition algorithm, namely solving the following minimization problem to obtain a matrix A, B, C in the high-dimensional linear model:
Figure FDA0003708702020000024
Figure FDA0003708702020000031
the analytical formula for solving the minimum value is:
[A,B]=Y lift [X lift ,U]
Figure FDA0003708702020000032
obtaining the preliminary analysis of the high-dimensional linear model (2) through the formula (1) and the formula (4), and training the obtained matrix A, B, C and a neural network parameter set by utilizing the automatic training capability of a neural network in order to obtain a model which is closer to a real model, wherein a defined loss function is expressed as;
Figure FDA0003708702020000033
continuously training the equations (1), (4) and the loss function (5) through a neural network until
Figure FDA0003708702020000034
Reducing the state error with the real data set to be below 0.0001, stopping training and obtaining the bestFinal high-dimensional linear model.
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