CN113343877B - Electrical appliance fingerprint feature extraction method based on different Prony methods - Google Patents

Electrical appliance fingerprint feature extraction method based on different Prony methods Download PDF

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CN113343877B
CN113343877B CN202110679440.4A CN202110679440A CN113343877B CN 113343877 B CN113343877 B CN 113343877B CN 202110679440 A CN202110679440 A CN 202110679440A CN 113343877 B CN113343877 B CN 113343877B
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CN113343877A (en
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张珊珊
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Shanghai Mengxiang Intelligent Technology Co ltd
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    • G06F2218/12—Classification; Matching
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Abstract

The invention belongs to the technical field of non-invasive load monitoring, and particularly relates to an electrical appliance fingerprint feature extraction method based on different Prony methods. The invention utilizes some characteristic quantities which present unique characteristics when the equipment runs as the electrical fingerprint of the equipment to describe different modes presented by the current or voltage waveform of the equipment. Extracting aggregated load information obtained by non-invasive load monitoring, extracting electrical appliance fingerprints by adopting five Prony methods so as to obtain transient (exponential damping) and steady (harmonic information) characteristics of circuit loads, and separating the electrical appliance fingerprints of each load by adopting a load decomposition method; the individual energy consumption of a device connected to a certain power bus is determined and the change in electrical energy at a single point of the bus is measured. The invention can help better process circuit load information and realize better energy scheduling and management of equipment in the circuit.

Description

Electrical appliance fingerprint feature extraction method based on different Prony methods
Technical Field
The invention belongs to the technical field of non-invasive load monitoring, and particularly relates to an electrical appliance fingerprint feature extraction method based on different Prony methods.
Background
The non-invasive load monitoring is applied to the power grid, so that various load curves can be predicted, the power grid can be scheduled, and unnecessary resource waste is reduced; the household user can know the power utilization condition of the household appliance, so that better household power utilization management and more energy-saving means are realized.
Non-intrusive load monitoring determines the individual consumption of energy by devices connected to a certain power bus, mainly through characteristics at the power inlet (such as current, voltage, etc.), measures the variation of the electrical energy at a single point of the bus, defines the load or appliance fingerprint of the device and how to extract the two most critical phases of non-intrusive load monitoring. In order to correctly extract the appliance fingerprint, it is necessary to extract a set of general characteristic quantities that can be obtained by conventional measurements to characterize the appliance fingerprint of the device, and the currently obtained load information of the device is aggregate information, so how to separate the power signal of each load, one of the problems that should be solved is to extract the characteristic.
The method for extracting the electrical appliance fingerprint of the circuit equipment can be divided into a steady state method, a transient state method or two methods, the steady state extraction method is not easily influenced by noise, and the transient state characteristics of the load can carry more identification information, so that the accuracy of classification and identification is improved.
Disclosure of Invention
The invention provides an electric power fingerprint feature extraction method based on different Prony methods, aiming at the problems that the prior art has more feature quantity for representing electric appliance fingerprints, is difficult to model data, and how to combine extraction methods of two states to separate and extract circuit load features.
The invention utilizes some characteristic quantities which present unique characteristics when the equipment runs as the electrical fingerprint of the equipment to describe different modes presented by the current or voltage waveform of the equipment. The method comprises the steps of extracting aggregated load information obtained by non-intrusive load monitoring, extracting electrical appliance fingerprints by adopting five Prony methods, thus obtaining transient (exponential damping) and steady (harmonic information) characteristics of circuit loads, and separating the electrical appliance fingerprints of each load by adopting a load decomposition method.
The method is characterized in that components in the Prony method, such as exponential damping, frequency, phase and amplitude, are used as characteristic quantities, and the linear composition of the exponential damping is used for modeling input data, and the method is mainly divided into three basic steps: the method comprises the steps of determining linear prediction parameters for fitting available data, estimating exponential damping and sinusoidal frequency, estimating exponential amplitude and sinusoidal initial phase, and realizing five different extraction methods based on transient (exponential damping) and steady-state (harmonic information) characteristics, thereby solving the difficulties in the technology. The method is based on the Prony method, and can fit equidistant sampling data by linear combination of a group of exponential terms, so that the information of amplitude, phase, damping factor, frequency and the like of a signal can be analyzed to realize the extraction of the fingerprint of the electric appliance.
The invention provides a method for extracting electrical appliance fingerprints based on different Prony methods, which comprises the following specific steps:
step 1: acquiring aggregated load information, and performing data preprocessing;
step 2: modeling the input data using an exponentially damped linear composition according to the Prony method;
and step 3: determining linear prediction parameters for fitting available data, and calculating the coefficient a [ m ] to be utilized subsequently]And a basic parameter set bak；
And 4, step 4: calculating the damping of exponential level, sinusoidal frequency index, amplitude, sinusoidal initial phase and other data;
and 5: and classifying different waveforms, and extracting the fingerprints of the electric appliance.
Each step is further described below
Step 1, data preprocessing is carried out
The non-intrusive load monitoring is applied to an electric power inlet, aggregated load information can be obtained, electric appliance fingerprints are extracted from the load information of electric power equipment at the present stage, and the adopted method can be mainly divided into a steady state method, a transient state method and a combination of the two methods.
The steady-state load information data is more stable and is less susceptible to noise, and the transient load information data can carry more identification information, so that the accuracy of classification and identification is improved. Modeling and information extraction are carried out on data according to a Prony method, and the data are subjected to a data preprocessing process before being finally input into a set classifier, specifically, the data such as amplitudes and initial phases of sinusoids calculated by different Prony methods are subjected to standardization processing in a (0, 1) range.
Step 2. modeling input data using linear components of exponential damping according to Prony's method
The Prony method uses an exponentially damped linear component to model the input data, and is mainly divided into three basic steps:
determining linear prediction parameters fitting available data;
estimating the damping and sine frequency of exponential order;
(III) estimating exponential amplitude and sine initial phase;
if there are N data samples, the Prony method uses p complex exponentials to estimate the final result x [ N ]:
Figure BDA0003122294200000021
wherein, TsFor the sampling period, the index k is from 1 to p, representing the current complex exponential of the kth term, AkIs amplitude, αkIs a damping factor, fkIs the frequency, thetakIs the initial phase;
the Prony method specifically comprises the following steps:
(1) polynomial method
The p-exponential discrete time function is represented by the following form:
Figure BDA0003122294200000022
wherein the complex constant amplitude set amkAnd a basic set bakIs represented as follows:
Figure BDA0003122294200000023
the function (2) is written in the form of a matrix multiplication, ZH ═ x:
Figure BDA0003122294200000031
wherein the matrix Z is a basic set bakIs a complex constant amplitude set amkA matrix representation of (a);
the Prony method of polynomials defines a polynomial
Figure BDA0003122294200000032
Figure BDA0003122294200000033
The expression (5) can also be rewritten in the form of matrix by Ta-x, where the elements x p of the matrix T]Expressed is an exponential parameter bapThe matrix a is the coefficient a [ m ]]Matrix representation of (m from 1 to p):
Figure BDA0003122294200000034
(2) least square method (Least Squares)
In the Prony classical polynomial method, the number of samples must be equal to 2p, i.e. N ═ 2p, so that the signal can be obtained without reconstruction errors. However, the idea of the invention is to reduce the order of the models, which results in N > 2p, in which case the linear system is over-determined (the equation is larger than the unknowns) and therefore the values need to be approximated using a least squares based approach. Least squares solution x for an overdetermined linear system, i.e. a general linear system Ax ═ b associated with Zh ═ x and Ta ═ x when N > 2pLSThe following were used:
xLS＝(AHA)-1AHb， (7)
wherein A isHThe least squares problem can also be solved by using Singular Value Decomposition (SVD) instead of the original equation, corresponding to hermitian conjugation of the matrix a.
(3) Total Least square method (Total Least Squares)
The total least squares method can be considered as a generalization of the LS solution of the linear system Ax ═ b, designed mainly for the problem of numerical conditioning, since Zh ═ x and Ta ═ x are composed of measured signals (noisy), the TLS algorithm should include applying the Singular Value Decomposition (SVD) of the matrix C:
C＝[A][b]＝U∑VH， (8)
where | corresponds to the column expansion of matrix a with vector b, U and V are rotation matrices, and Σ is a scale matrix of single values in matrix C, the resulting TLS solution is:
Figure BDA0003122294200000035
(4) matrix Pencil (Matrix Pencil) method
The matrix bundling method is to define the basic parameter set of characteristic polynomial by solving the generalized eigenvalue problem, and first two matrixes Y are given1、Y2∈C(N-p)×(p-1)：
Figure BDA0003122294200000041
Figure BDA0003122294200000042
By Y2-λY1The determined matrix is used as a matrix bundle to obtain a basic parameter set bakComprises the following steps:
Figure BDA0003122294200000043
(5) IIR (IIR-Based) Based method
Parameters are estimated using an Infinite Impulse Response (IIR) filter transfer function, using the following equation model:
Figure BDA0003122294200000044
the above equation represents a convolution, which can be rewritten as a matrix multiplication, and thus can be defined as:
Figure BDA0003122294200000045
using the parameters of the first K +1 subscript of the impulse response, the following matrix relationship can be written:
Figure BDA0003122294200000046
it can also be expressed in the form of a matrix multiplication:
Figure BDA0003122294200000047
wherein b is a numerical vector of dimension M +1, and a is set as a0N-dimensional vector of values, h, 11Is a (M +1) × (N +1) -dimensional matrix of the last K-M impulse responses, H2Is a (K-M) x N dimensional matrix of another impulse response, H is the Toeplitz matrix T of the input signal x1Then vector H1And b can be expressed as:
h1＝-H2a， (17)
b＝-H1a， (18)
a is given for the above formula and gives b.
The invention can obtain the basic parameter z by a polynomial method according to the following stepskAmplitude amkAnd corresponding parametric damping factor alphakFrequency fkAmplitude AkAnd an initial phase thetak。
Step 3, determining linear prediction parameters for fitting available data, and calculating a coefficient a [ m ]]And a basic parameter set bak；
From the modeling results above, the solution of Prony basically comprises 3 steps:
firstly, processing an equation Ta ═ x to obtain a coefficient a [ m ] which needs to be utilized subsequently;
the second step, the basic parameter ba of van der Mond matrix in formula ZH ═ x is obtainedk；
Thirdly, calculating the amplitude set am by the equations to obtain the amplitude set amk。
Step 4, calculating the exponential damping and sine frequency index, and calculating the data such as amplitude and sine initial phase, and the like, wherein the data comprises the following specific steps:
wherein the damping factor alphakAnd frequency fkCan be calculated from the basic parameter ba in the van der Mond matrixkObtained by the following equation:
αk＝ln|bak|/Ts， (19)
fk＝tan-1(Im[bak]/Re[bak])/(2πTs)， (20)
wherein the amplitude AkAnd an initial phase thetakCan be assembled by amplitude amkIs obtained by the following equation:
Ak＝|amk|， (21)
θk＝tan-1(Im[amk]/Re[amk])， (22)
step 5, classifying different waveforms, and extracting the electrical appliance fingerprint, wherein the method comprises the following steps:
(1) classifying different waveforms by adopting set classifier
The set classifier consists of a set of classifiers whose individual decisions are combined in some way (usually an averaging result) to classify new sample data. In classification methods, the results of an ensemble classifier, which incorporates a set of trained weak learning models, are typically much more accurate than the results of the individual classifiers that make up them. It obtains the final classification result by averaging the prediction results of each weak learning classifier. The method can use different algorithms for sequential learning (weaker learning models), such as adaboost m1, adaboost m2 Bag, GentleBoost, LogitBoost, LPBoost, LSBoost, RobustBoost, RUSBoost, Subspace, and TotalBoost.
(2) Classified extraction of electric appliance fingerprints
The method adopts different Prony methods to extract the electrical appliance fingerprint according to specific scenes, can also be used by a plurality of methods simultaneously, each method has advantages and disadvantages, the extraction result of each method is combined (usually averaged), components in the Prony method, including exponential damping, frequency, phase and amplitude, are adopted as characteristics, the related data obtained by calculation according to the steps are extracted, the unique current and voltage waveforms of the equipment in the aggregated load information are found, and then the data can be classified to obtain the corresponding electrical appliance fingerprint.
Compared with the prior art, the invention has the following excellent effects:
the invention provides five Prony methods to separate the electrical appliance fingerprint of each device by adopting a load decomposition method for the transient state (exponential damping) and the steady state (harmonic information) characteristics of a circuit load. Five methods have small performance difference in aggregate information processing, a lower MSE value is obtained based on an IIR filter method, a matrix bundle method has optimal classification accuracy, different Prony methods are adopted to extract electrical appliance fingerprints according to specific scenes, so that individual energy consumption of equipment connected to a certain power bus is determined, electric energy change on a single point of the bus is measured, better processing of circuit load information can be facilitated, and better energy scheduling and management of equipment in the circuit are realized.
Drawings
FIG. 1 is a simplified flow chart of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following by combining the drawings and the embodiment.
Example (b):
the invention provides a method for extracting electrical appliance fingerprints based on different Prony methods, a flow chart of which is shown in figure 1 and can be divided into the following steps:
step 1: acquiring aggregated load information, and performing data preprocessing;
step 2: modeling the input data using an exponentially damped linear composition according to the Prony method;
and step 3: determining linear prediction parameters for fitting available data, and calculating the coefficient a [ m ] to be utilized subsequently]And a basic parameter set bak；
And 4, step 4: calculating the data of damping, sine frequency index, amplitude, sine initial phase and the like of an exponential level;
and 5: and classifying different waveforms and extracting the fingerprints of the electric appliance.
1. Data pre-processing
The non-intrusive load monitoring is applied to an electric power inlet, aggregated load information can be obtained, electric appliance fingerprints are extracted from the load information of electric power equipment at the present stage, and the adopted method can be mainly divided into a steady state method, a transient state method and a combination of the two methods.
The steady-state load information data is more stable and is less susceptible to noise, and the transient load information data can carry more identification information, so that the accuracy of classification and identification is improved. Modeling and information extraction are carried out on data according to a Prony method, the data are subjected to a data preprocessing process before being finally input into a set classifier, and all features are subjected to standardization processing according to the range (0, 1) corresponding to the model.
2. Prony method modeling
The Prony method uses an exponentially damped linear component to model the input data, and is mainly divided into three basic steps: determining linear prediction parameters for fitting available data; estimating the damping and sine frequency of the exponential order; estimating exponential amplitude and sine initial phase, if N data samples exist, estimating final result x [ N ] by using p-term complex exponential by using Prony method]Wherein T issFor a sampling period, AkIs amplitude, αkIs a damping factor, fkIs the frequency, thetakInitial phase:
Figure BDA0003122294200000061
(1) polynomial/traditional (Polynomial/classic) method
The p-exponential discrete time function in the polynomial method can be compactly represented by the following form:
Figure BDA0003122294200000062
wherein the complex constant amk(amplitude set, amplitude) and bak(basis set, basicagregate) is expressed as follows:
Figure BDA0003122294200000071
the p-exponential discrete-time function can also be written in the form of a matrix multiplied by ZH ═ x:
Figure BDA0003122294200000072
wherein the matrix Z is a basic set bakIs a complex constant amplitude set amkA matrix representation of (a);
the Prony method of polynomials defines a polynomial
Figure BDA0003122294200000073
Figure BDA0003122294200000074
This expression can be rewritten in the form of a matrix by Ta-x, where the elements x p of the matrix T]Expressed is an exponential parameter bapThe matrix a is the coefficient a [ m ]](m is from 1 to p) matrix representation
Figure BDA0003122294200000075
(2) Least square method (Least Squares)
In the Prony classical polynomial method, the number of samples must be equal to 2p, i.e. N ═ 2p, so that the signal can be obtained without reconstruction errors. However, the idea of the invention is to reduce the order of the models, which results in N > 2p, in which case the linear system is over-determined (the equation is larger than the unknowns) and therefore the values need to be approximated using a least squares based approach. Least squares solution x for an overdetermined linear system, i.e. a general linear system Ax ═ b associated with Zh ═ x and Ta ═ x when N > 2pLSThe following were used:
xLS＝(AHA)-1AHb
wherein A isHThe least squares problem can also be solved by using Singular Value Decomposition (SVD) instead of the original equation, corresponding to hermitian conjugation of the matrix a.
(3) Total Least square method (Total Least Squares)
The total least squares method can be considered as a generalization of the LS solution of the linear system Ax ═ b, designed mainly for the problem of numerical conditioning, since Zh ═ x and Ta ═ x are composed of measured signals (noisy), the TLS algorithm should include applying the Singular Value Decomposition (SVD) of the matrix C:
C＝[A][b]＝U∑VH
where | corresponds to the column expansion of matrix a with vector b, U and V are rotation matrices, and Σ is a scale matrix of single values in matrix C, the resulting TLS solution is:
Figure BDA0003122294200000076
(4) matrix Pencil (Matrix Pencil) method
The matrix bundle method defines the basic parameter set of the eigen-polynomial by solving the generalized eigenvalue problem, first giving two matrices Y1、Y2∈C(N-p)×(p-1)：
Figure BDA0003122294200000081
Figure BDA0003122294200000082
By Y2-λY1The determined matrix is used as a matrix bundle to obtain a basic parameter set bakComprises the following steps:
Figure BDA0003122294200000083
(5) IIR (IIR-Based) Based method
Parameters are estimated using an Infinite Impulse Response (IIR) filter transfer function, using the following equation model:
Figure BDA0003122294200000084
the above formula represents a convolution, which can be rewritten as a matrix multiplication and thus can be defined as
Figure BDA0003122294200000085
Using the parameters of the first K +1 subscript of the impulse response, the following matrix relationship can be written:
Figure BDA0003122294200000086
also can be expressed in the form of matrix multiplication
Figure BDA0003122294200000087
Wherein b is a numerical vector of dimension M +1, and a is set to a0N-dimensional vector of values, h, 11Is a (M +1) × (N +1) -dimensional matrix of the last K-M impulse responses, H2Is a (K-M) x N dimensional matrix of another impulse response, H is the Toeplitz matrix T of the input signal x1Then vector H1And b can be expressed as:
h1＝-H2a
b＝-H1a
given a and b of the above formula, the present invention can obtain the basic parameter z by a polynomial method through the following stepskAmplitude amkAnd corresponding parametric damping factor alphakFrequency fkAmplitude AkAnd an initial phase thetak。
3. Calculating the coefficient a [ m ]]And a basic parameter set bakFrom the modeling results, it can be seen that the solution of Prony basically includesComprises 3 steps:
firstly, processing an equation Ta ═ -x to obtain a coefficient a [ m ] which needs to be utilized subsequently;
the second step, the basic parameter ba of van der Mond matrix in formula ZH ═ x is obtainedk；
Thirdly, calculating the amplitude set am by the equations to obtain the amplitude set amk。
4. Estimating characteristic quantity
Wherein the damping factor alphakAnd frequency fkCan be calculated from the basic parameter ba in the van der Mond matrixkObtained by the following equation:
αk＝ln|bak|/Ts
fk＝tan-1(Im[bak]/Re[bak])/(2πTs)
wherein the amplitude AkAnd an initial phase thetakCan be assembled by amplitude amkIs determined by the following equation:
Ak＝|amk|
θk＝tan-1(Im[amk]/Re[amk])。
5. extracting electric appliance fingerprint
(1) Set classifier
The aggregation method consists of a set of classifiers whose individual decisions are combined in some way (usually an averaging result) to classify new sample data. In classification methods, the results of an ensemble classifier, which incorporates a set of trained weak learning models, are typically much more accurate than the results of the individual classifiers that make up them. It obtains the final classification result by averaging the prediction results of each weak learning classifier. The method can use different algorithms for sequential learning (weaker learning models), such as adaboost m1, adaboost m2 Bag, GentleBoost, LogitBoost, LPBoost, LSBoost, RobustBoost, RUSBoost, Subspace, and TotalBoost.
(2) Classified extraction
The method adopts different Prony methods to extract the electric appliance fingerprint according to specific scenes, can also be used by a plurality of methods simultaneously, each method has advantages and disadvantages, the extraction result of each method is combined (usually averaged), components in the Prony method, including exponential damping, frequency, phase and amplitude, are adopted as characteristics, the characteristic extraction is carried out according to the related data obtained by the calculation of the steps, the unique current and voltage waveforms of the equipment in the aggregated load information are found, and then the data can be classified to obtain the corresponding electric appliance fingerprint.
The invention provides five Prony methods to separate the electrical appliance fingerprint of each device by adopting a load decomposition method for the transient state (exponential damping) and the steady state (harmonic information) characteristics of a circuit load. Five methods have little difference in aggregate information processing, a low MSE value is provided based on an IIR filter method, a matrix bundle method has optimal classification precision, different Prony methods are adopted for electrical appliance fingerprint extraction according to specific scenes, a plurality of methods can be simultaneously used, each method has advantages and disadvantages, the extraction result of each method is combined (generally averaged), so that the individual energy consumption of equipment connected to a certain power bus is determined, the electric energy change on a single point of the bus is measured, better processing of circuit load information can be facilitated, and better energy scheduling and management of the equipment in the circuit are realized.

Claims (4)

1. A method for extracting electrical appliance fingerprints based on different Prony methods is characterized in that some characteristic quantities which present unique characteristics when equipment runs are used as electrical appliance fingerprints of the equipment and are used for describing different modes presented by current or voltage waveforms of the equipment; extracting aggregated load information obtained by non-invasive load monitoring, extracting electrical appliance fingerprints by adopting five Prony methods so as to obtain the transient state, namely exponential damping, and the steady state, namely harmonic information characteristics of the circuit load, and separating the electrical appliance fingerprints of each load by adopting a load decomposition means; the method comprises the following specific steps:
step 1: acquiring aggregated load information, and performing data preprocessing;
step 2: modeling the input data using an exponentially damped linear composition according to the Prony method;
and step 3: determining linear prediction parameters for fitting available data, and calculating the coefficient a [ m ] to be utilized subsequently]And a basic parameter set bak；
And 4, step 4: calculating the damping and sine frequency index of an exponential level, and calculating amplitude and sine initial phase data;
and 5: classifying different waveforms, and extracting fingerprints of the electric appliance;
in step 2, the Prony method uses the linear component of exponential damping to model the input data, and is mainly divided into three basic steps:
determining linear prediction parameters fitting available data;
estimating the damping and sine frequency of exponential order;
(III) estimating exponential amplitude and sine initial phase;
if there are N data samples, the Prony method uses p complex exponentials to estimate the final result
Figure FDA0003411237460000014
Figure FDA0003411237460000011
Wherein, TsFor the sampling period, the index k is from 1 to p, representing the current complex exponential of the kth term, AkIs amplitude, αkIs a damping factor, fkIs the frequency, thetakIs the initial phase;
the Prony method specifically comprises the following steps:
(1) polynomial method
The p-exponential discrete time function is represented by the following form:
Figure FDA0003411237460000012
wherein the complex constant amplitude set amkAnd a base set bakIs represented as follows:
Figure FDA0003411237460000013
the function (2) is written in the form of a matrix multiplication, Zh ═ x:
Figure FDA0003411237460000021
wherein the matrix Z is a basic set bakIs a complex constant amplitude set amkA matrix representation of (a);
the Prony method of polynomials defines a polynomial
Figure FDA0003411237460000022
Figure FDA0003411237460000023
The expression (5) can also be rewritten in the form of matrix by Ta-x, where the elements x p of the matrix T]Expressed is an exponential parameter bapThe matrix a is the coefficient a [ m ]]M is from 1 to p:
Figure FDA0003411237460000024
(2) least square method
For over-determined linear systems, i.e. when the number of samples N>In the case of 2p, the least squares solution x of the general linear system Ax ═ b associated with Zh ═ x and Ta ═ xLSThe following were used:
xLS＝(AHA)-1AHb， (7)
wherein A isHCorresponding to Hermite conjugation of the matrix A, the original equation can be replaced by Singular Value Decomposition (SVD)Thereby solving the least squares problem;
(3) total least square method
The total least squares method is a generalization of the LS solution of the linear system Ax ═ b, and is mainly designed for the problem of numerical conditioning, and since Zh ═ x and Ta ═ x are composed of measured signals, the TLS algorithm includes applying the singular value decomposition SVD of the matrix C:
C＝[A][b]＝UΣVH， (8)
where [ a ] [ b ] corresponds to the column expansion of matrix a with vector b, U and V are rotation matrices, Σ is a scale matrix of a single value in matrix C, the resulting TLS solution is:
Figure FDA0003411237460000025
(4) matrix bundling method
The method is to define the basic parameter set of characteristic polynomial by solving the generalized eigenvalue problem, and firstly, two matrixes Y are given1、Y2∈C(N-p)×(p-1)：
Figure FDA0003411237460000026
Figure FDA0003411237460000031
By Y2-λY1The determined matrix is used as a matrix bundle to obtain a basic parameter set bakComprises the following steps:
Figure FDA0003411237460000032
(5) IIR-based method
Parameters are estimated using an infinite impulse response, IIR, filter transfer function, using the following equation model:
Figure FDA0003411237460000033
the above equation represents a convolution, rewritten as a matrix multiplication, defined as:
Figure FDA0003411237460000034
using the parameters of the first K +1 subscript of the impulse response, a matrix relationship is obtained:
Figure FDA0003411237460000035
also expressed in matrix multiplication form:
Figure FDA0003411237460000036
wherein b is a numerical vector of dimension M +1, and a is set as a0N-dimensional vector of values, h, 11Is a (M +1) × (N +1) -dimensional matrix of the last K-M impulse responses, H2Is a (K-M) x N dimensional matrix of another impulse response, H is the Toeplitz matrix T of the input signal x1Then vector H1And b is expressed as:
h1＝-H2a， (17)
b＝-H1a， (18)
a is given for the above formula and gives b.
2. The method for extracting appliance fingerprint based on different Prony methods as claimed in claim 1, wherein the step 3 of determining linear prediction parameters for fitting available data calculates coefficient a [ m [ ] m [ ] m]And a basic parameter set bakThe method comprises 3 steps:
firstly, processing an equation Ta ═ x to obtain a coefficient a [ m ] which needs to be utilized subsequently;
the second step, the basic parameter ba of van der Mond matrix in formula Zh ═ x is obtainedk；
Thirdly, calculating the amplitude set am by the equations to obtain the amplitude set amk。
3. The method for extracting fingerprints of electric appliances based on different Prony methods as claimed in claim 2, wherein the step 4 of calculating the damping of exponential order, the sine frequency index, and the amplitude and the sine initial phase data comprises the following steps:
wherein the damping factor alphakAnd frequency fkFrom the basic parameters ba in the van der Mond matrixkObtained by the following equation:
αk＝ln|bak|/Ts， (19)
fk＝tan-1(Im[bak]/Re[bak])/(2πTs)， (20)
wherein the amplitude AkAnd an initial phase thetakBy amplitude set amkIs obtained by the following equation:
Ak＝|amk|， (21)
θk＝tan-1(Im[amk]/Re[amk])， (22)。
4. the method for extracting the fingerprint of the electric appliance based on the different Prony methods as claimed in claim 2, wherein the classifying the different waveforms in step 5 to extract the fingerprint of the electric appliance comprises:
(1) classifying different waveforms by adopting set classifier
The set classifier is composed of a group of classifiers, the individual decisions of the set classifier are combined in a certain mode to classify new sample data, and the set classifier is combined with a group of trained weak learning models to obtain a final classification result by averaging the prediction result of each weak learning classifier;
(2) classified extraction of electric appliance fingerprints
Adopting different Prony methods in the step 2 to extract the electrical appliance fingerprint according to specific scenes, or simultaneously using a plurality of methods, and taking a combined result of the extraction result of each method; and extracting the components in the Prony method, including exponential damping, frequency, phase and amplitude, according to the related data obtained by calculation in the steps, finding out the unique current and voltage waveforms of the equipment in the aggregated load information, and classifying the data to obtain the corresponding electrical appliance fingerprint.
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