CN109040002B - Real-time reconstruction method of smart meter data based on compressed sensing - Google Patents

Real-time reconstruction method of smart meter data based on compressed sensing Download PDF

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CN109040002B
CN109040002B CN201810520192.7A CN201810520192A CN109040002B CN 109040002 B CN109040002 B CN 109040002B CN 201810520192 A CN201810520192 A CN 201810520192A CN 109040002 B CN109040002 B CN 109040002B
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meter data
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CN109040002A (en
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唐穗谷
许银亮
但唐也
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Foshan Shunde Sun Yat-Sen University Research Institute
Sun Yat Sen University
SYSU CMU Shunde International Joint Research Institute
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Foshan Shunde Sun Yat-Sen University Research Institute
Sun Yat Sen University
SYSU CMU Shunde International Joint Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L69/00—Network arrangements, protocols or services independent of the application payload and not provided for in the other groups of this subclass
    • H04L69/04—Protocols for data compression, e.g. ROHC
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Abstract

The invention discloses a real-time reconstruction method of intelligent electric meter data based on compressive sensing, which comprises the following steps: s1: the transmission model of the electric meter data based on real-time compressed sensing mainly comprises three parts: smart meter, access point and control center S2: the compressed sensor-auto-encoder proposed herein mainly consists of two parts: compression encoding and reconstruction encoding, S3: in the compression coding part of the signal, data is mainly compressed, and circuit communication links are reduced. S4: when the signal is reconstructed and coded. The time consumed by the intelligent electric meter is very short, and the intelligent electric meter data transmission method is very suitable for transmission of intelligent electric meter data with high real-time requirements.

Description

Real-time reconstruction method of smart meter data based on compressed sensing
Technical Field
The invention relates to the field of smart power grids, in particular to a real-time reconstruction method of smart meter data based on compressive sensing.
Background
Along with the construction of the smart grid, more and more smart meters are installed. It is reported that the data of smart meters around the world in 2022 is expected to reach 11 hundred million. Typically, a smart meter collects data every 30 minutes or more frequently, so a large number of smart meters will generate a large amount of data. However, the smart meter data is transmitted over the power line communication link. Whereas a power line communication link is a bandwidth limited communication link. Therefore, the problem of transmission delay and data packet loss is caused when a large amount of intelligent electric meter data is transmitted. This brings huge challenges to real-time transmission and monitoring of the smart grid.
In recent years, Donoho, cans, Tao et al have proposed Compressive Sensing (CS) and demonstrated that when the signal is a sparse signal or can be converted to a sparse vector at some sparse transform basis, the signal can be reconstructed below the nyquist rate. Compressive sensing breaks through the nyquist-shannon sampling theorem and is therefore of great interest.
Sparse representation of signals, measurement matrix design and reconstruction algorithm are three major core contents of compressed sensing. A good sparse transform base can enable the signal to have high sparsity in a transform domain, a good measurement matrix can enable the compression rate of the signal to be lower, and a good reconstruction algorithm enables the signal to be accurately reconstructed under the condition that the compression rate is low or the measured value is mixed with noise. Therefore, the design of a sparse transformation base, a measurement matrix and a reconstruction algorithm is very important for the reconstruction accuracy of the electric meter data.
Although compressive sensing can reduce transmission pressure and storage costs of the communication network. However, many researchers use the method in the fields of magnetic resonance imaging, face recognition and the like at present, but the compressive sensing still has the larger time delay when the compressive sensing reconstructs signals in the fields, and the method is not very suitable for the engineering with high real-time requirement. Therefore, more and more scholars are paying attention to research on the real-time performance of compressed sensing and widening the application field of the CS. Current research literature on real-time compressive sensing is:
[1]S.Tang,Y.Xu,and X.Tang,“Real-time reconstruction of multi-area power system signals based on compressed sensing”2017International Electrical and Energy Conference(CIEEC2017),pp.389-394,2017.
[2]Y.Xu,Z.Y,J.Zhang,Z.Fei and W.Liu,“Real-time compressive sensing based control strategy for a multi-area power system,”IEEE Trans.Smart Grid,2017.
[3]H.Palangi,R.Ward,and L.Deng,“Distributed compressive sensing:a deep learning approach,”IEEE Trans.Signal Processing,vol.64,no.17,pp.4504-4518,Sep.2016.
[4]W.Yu,C.Chen,T.He,B.Yang and X.Guan,“Adaptive compressive engine for real-time electrocardiogram monitoring under unreliable wireless channels,”IET Commun.,vol.10,no.6,pp.607-615,2016.
[5]B.Sun,and H.Feng,“Efficient compressed sensing for wireless neural recording:a deep learning approach,”IEEE Signal Processing Letters,vol.24,no.6,pp.863-867,2017.
[6]Z.Zhang,T.P.Jung,S.Makeig,Z.Pi,and B.D.Rao,“Spatiotemporal sparse Bayesian learning with applications to compressed sensing of multichannel physiological signals.”IEEE Trans.on Neural System and Rehabilitation Engineering,vol.22,no.6,pp.1186-1197,2014.
the literature [ 1 ] provides a multi-region dictionary learning algorithm for training multi-region power signals, meanwhile, a sparse Bayesian learning reconstruction algorithm is used for reconstructing the power signals, and experimental results show that the method uses real-time reconstruction of the power signals. Document [ 2 ] applies real-time compressive sensing to multi-regional power control systems, enabling the systems to transmit with fewer signals and recover the original signals through a suitable reconstruction algorithm. Document [ 3 ] proposes to use a deep learning method to solve the problem of reconstructing sparse vectors by multi-task measurement vectors in compressive sensing. The long and short term memory network is used to capture the characteristic information among the sparse vectors of different channels, and then the sparse vectors are reconstructed by using the characteristic information during signal reconstruction, so that signals are reconstructed. Document [ 4 ] proposes a self-adaptive compression sensing method, which is mainly used for self-adaptively adjusting the dimension of a measurement matrix required to be used when data is transmitted next time through a loss rate sparse error and an output error of the data in the transmission process, so as to reduce the reconstruction error of a signal. The document [ 5 ] provides a method for reconstructing a neural recording signal by using a binary automatic encoder, and simulation results show that the reconstruction speed of the method is higher than that of other methods and the signal-to-noise ratio and the classification accuracy are also higher. The document [ 6 ] provides a space-time sparse Bayesian learning algorithm to solve the problem of multi-task measurement vector reconstruction. Therefore, the application of the sparse Bayesian learning in compressed sensing is widened.
Disclosure of Invention
The invention aims to provide a method for reconstructing smart meter data in real time based on compressive sensing, so as to solve the problems in the background technology.
The technical scheme adopted by the invention for realizing the aim is as follows:
a method for transmitting data of an intelligent electric meter based on real-time compression sensing mainly comprises the following steps:
s1: the transmission model of the electric meter data based on real-time compressed sensing mainly comprises three parts: the system comprises a smart meter, an Access Point (AP) and a control center. The intelligent electric meter compresses the collected data, transmits the measured value to the AP through a power line communication link, transmits the collected measured value to the control center through the wireless communication network, and reconstructs the measured value at the control center.
S2: the compression and reconstruction of signals based on the principle of an automatic encoder mainly consists of two parts: compression coding and reconstruction coding, wherein the compression coding mainly comprises an input layer and a compression layer. The reconstruction coding is mainly composed of a reconstruction layer and an output layer.
S3: in the compression encoding portion of the signal: the compression encoding process of the compression sensing mainly utilizes a measurement matrix phi to carry out compression encoding on signals. Firstly, the data x belonging to the original input layer belongs to RN×1The compression layer is the measured value y ∈ RM×1Wherein the measurement of the compressed layer can be obtained from the input layer by:
y＝Φx(1)
where Φ is the measurement matrix and Φ ∈ RM×N(M<N). Currently, commonly used measurement matrices are: random gaussian matrices, random bernoulli matrices, simple binary matrices, and the like.
In order to better compress the electric meter data and obtain lower compression rate, the invention improves the measurement matrix as follows:
the singular value decomposition of the measurement matrix Φ yields:
Figure BDA0001674611830000061
wherein U and V are unitary matrices,
Figure BDA0001674611830000062
multiply both sides of equation (15) to the left
Figure BDA0001674611830000063
Wherein
Figure BDA0001674611830000064
Equation (15) is thus converted to:
t＝Ψx (3)
wherein:
Figure BDA0001674611830000065
s4: signal reconstruction and coding: after the measured value t is obtained, the measured value is transmitted to the control center through the communication network, and the measured value needs to be restored to the original data of the smart meter in the control center. The problems can be summarized as follows:
Figure BDA0001674611830000066
where v is a sparse vector, ACSΨ D is the perceptual matrix. D is a sparse transformation base of the electric meter data x.
Since equation (18) is an NP problem, it is difficult to solve in actual engineering. Thus, one solution is to combine l0Norm to l1Norm solvers, such as Orthogonal Matching Pursuit (OMP), Sparse Adaptive Matching Pursuit (SAMP), and Regularized Orthogonal Matching Pursuit (ROMP). Other solutions include sparse bayesian learning algorithms, combinatorial algorithms, and the like.
In order to better reconstruct the electric meter data, the invention provides a reconstruction algorithm of a compressed sensing-automatic encoder, which comprises the following steps:
(1) before the layer is reformed, the measured value t is normalized, i.e.
Figure BDA0001674611830000071
Wherein t isminIs the minimum value of the measured value t, tmaxIs the maximum value of the measured value t.
(2) Assuming the reconstruction layer is L, the dimension of each reconstruction layer is
Figure BDA0001674611830000073
Wherein
Figure BDA0001674611830000074
Given a weight matrix W for each reconstructed layerlAnd an offset vector bl. Then the firstthThe activation function of the reconstruction layer can be expressed by the following equation:
zl＝f(Wlzl-1+bl) (6)
wherein z is0T. f (α) is the activation function of α. Generally, a sigmoid function, a tanh function, a ReLU function, etc. are commonly used as the activation function f (α), and the activation function used in the present invention is sigmoid, which is defined as follows:
Figure BDA0001674611830000072
(3) the output layer is reconstructed electric meter data, and the expression of the reconstructed electric meter data is as follows:
Figure BDA0001674611830000081
wherein xminIs the minimum value of the meter data x, xmaxThe maximum value of the meter data x.
(4) To better capture the features of the meter data and thus better reconstruct the meter data, the weighting matrix W is neededlAnd an offset vector blFine tuning is performed. The present invention uses a directional propagation algorithm to fine tune the parameters. The method comprises the following specific steps:
Figure BDA0001674611830000082
Figure BDA0001674611830000083
Figure BDA0001674611830000084
Δbl＝ηδl (12)
δl-1＝(Wl Tδl)⊙f'(Wl-1zl-2+bl-1) (13)
Wl＝Wl-ΔWl (14)
bl＝bl-Δbl (15)
where η is the learning rate, and indicates multiplication by element.
S4: the invention measures the performance index of compressive sensing from the following three aspects:
(1) compression ratio:
Figure BDA0001674611830000085
where M represents the dimension of the measured value after compression is used and N represents the dimension of the signal itself.
(2) Signal-to-noise ratio:
Figure BDA0001674611830000091
wherein the content of the first and second substances,xwhich represents the original signal or signals of the original signal,
Figure BDA0001674611830000092
representing the reconstructed signal.
(3) Relative error:
Figure BDA0001674611830000093
compared with the prior art, the invention has the beneficial effects that: the method has the advantages that the reconstruction time is very short, the method is very suitable for the transmission of the data of the intelligent electric meter with high real-time requirement, the dimensionality of the transmitted data is greatly reduced, and the transmission cost is reduced.
Drawings
Fig. 1 is a diagram of a real-time propagation model of smart meter data based on real-time compressive sensing according to the present invention.
Fig. 2 is a data compression coding diagram of the smart meter according to the present invention.
Fig. 3 is a data graph of a week collected by the smart meter according to the present invention.
FIG. 4 is a schematic diagram of a compressed sensor-auto-encoder according to the present invention.
Fig. 5 is a graph of original smart meter data and reconstructed data with a compression ratio ρ 12/48 when no noise is mixed in the measured value according to the present invention.
Fig. 6 is a graph of original smart meter data and reconstructed data with a compression ratio ρ 12/48 when the measured value is mixed with noise according to the present invention.
FIG. 7 is a graph showing the relationship between the compression rate and the signal-to-noise ratio of the data of the smart meter when no noise is mixed in the measured value according to the present invention.
FIG. 8 is a graph showing the relationship between the compression rate and the signal-to-noise ratio of the data of the smart meter when the measured value is mixed with noise according to the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used only for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention. Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first," "second," etc. may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art through specific situations.
The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
Referring to fig. 1 to 8, in an embodiment of the present invention, a method for reconstructing smart meter data in real time based on compressive sensing includes the following steps:
s1: the transmission model of the electric meter data based on real-time compressed sensing mainly comprises three parts: the system comprises a smart meter, an Access Point (AP) and a control center. The intelligent electric meter compresses the collected data, transmits the measured value to the AP through a power line communication link, transmits the collected measured value to the control center through the wireless communication network, and reconstructs the measured value at the control center.
S2: the compression and reconstruction of signals based on the principle of an automatic encoder mainly consists of two parts: compression coding and reconstruction coding, wherein the compression coding mainly comprises an input layer and a compression layer. The reconstruction coding is mainly composed of a reconstruction layer and an output layer.
S3: in the compression encoding portion of the signal: the compression encoding process of the compression sensing mainly utilizes a measurement matrix phi to carry out compression encoding on signals. Firstly, the data x belonging to the original input layer belongs to RN×1The compression layer is the measured value y ∈ RM×1Wherein the measurement of the compressed layer can be obtained from the input layer by:
y＝Φx (19)
where Φ is the measurement matrix and Φ ∈ RM×N(M<N). Currently, commonly used measurement matrices are: random gaussian matrices, random bernoulli matrices, simple binary matrices, and the like.
In order to better compress the electric meter data and obtain a lower compression rate, the invention improves the measurement matrix as follows:
the singular value decomposition of the measurement matrix Φ yields:
Figure BDA0001674611830000121
wherein U and V are unitary matrices,
Figure BDA0001674611830000122
multiply both sides of equation (15) to the left
Figure BDA0001674611830000123
Wherein
Figure BDA0001674611830000124
Equation (15) is thus converted to:
t＝Ψx (21)
wherein:
Figure BDA0001674611830000125
s4: signal reconstruction and coding: after the measured value t is obtained, the measured value is transmitted to the control center through the communication network, and the measured value needs to be restored to the original data of the smart meter in the control center. The problems can be summarized as follows:
Figure BDA0001674611830000131
where v is a sparse vector, ACSΨ D is the perceptual matrix. D is a sparse transformation base of the electric meter data x.
Since equation (18) is an NP problem, it is difficult to solve in actual engineering. Thus, one solution is to combine l0Norm to l1Norm solvers, such as Orthogonal Matching Pursuit (OMP), Sparse Adaptive Matching Pursuit (SAMP), and Regularized Orthogonal Matching Pursuit (ROMP). Other solutions include sparse bayesian learning algorithms, combinatorial algorithms, and the like.
In order to better reconstruct the electric meter data, the invention provides a reconstruction algorithm of a compressed sensing-automatic encoder, which comprises the following steps:
(1) before the layer is reformed, the measured value t is normalized, i.e.
Figure BDA0001674611830000132
Wherein t isminIs the minimum value of the measured value t, tmaxIs the maximum value of the measured value t.
(2) Assuming the reconstruction layer is L, the dimension of each reconstruction layer is
Figure BDA0001674611830000133
Wherein
Figure BDA0001674611830000134
Given a weight matrix W for each reconstructed layerlAnd an offset vector bl. Then the firstthThe activation function of the reconstruction layer can be expressed by the following equation:
zl＝f(Wlzl-1+bl) (24)
wherein z is0T. f (α) is the activation function of α. In general, a sigmoid function, a tanh function, a ReLU function, etc. are commonly used as an activation function for f (α), and the activation function used in the present invention is a sigmoid, which is defined as follows:
Figure BDA0001674611830000141
(3) the output layer is reconstructed electric meter data, and the expression of the reconstructed electric meter data is as follows:
Figure BDA0001674611830000142
wherein xminIs the minimum value of the meter data x, xmaxThe maximum value of the meter data x.
(4) To better capture the features of the meter data and thus better reconstruct the meter data, the weighting matrix W is neededlAnd an offset vector blFine tuning is performed. The present invention uses a directional propagation algorithm to fine tune the parameters. The method comprises the following specific steps:
Figure BDA0001674611830000143
Figure BDA0001674611830000144
Figure BDA0001674611830000145
Δbl＝ηδl (30)
δl-1＝(Wl Tδl)⊙f'(Wl-1zl-2+bl-1) (31)
Wl＝Wl-ΔWl (32)
bl＝bl-Δbl (33)
where η is the learning rate, and indicates multiplication by element.
S4: the invention measures the performance index of compressive sensing from the following three aspects:
(1) compression ratio:
Figure BDA0001674611830000151
where M represents the dimension of the measured value after compression is used and N represents the dimension of the signal itself.
(2) Signal-to-noise ratio:
Figure BDA0001674611830000152
wherein the content of the first and second substances,xwhich represents the original signal or signals of the original signal,
Figure BDA0001674611830000153
representing the reconstructed signal.
(3) Relative error:
Figure BDA0001674611830000154
the method has the advantages that the reconstruction time is very short, the method is very suitable for the transmission of the data of the intelligent electric meter with high real-time requirement, the dimensionality of the transmitted data is greatly reduced, and the transmission cost is reduced.
Fig. 3 shows real data of the smart meter, and the smart meter collects data every 30 minutes. The data of the intelligent electric meter shows that the consumed electric quantity is mainly concentrated in 8 morning: 00 to 6 pm: 00.
the first step is as follows: the compression ratio p is set to 12/48, i.e. the dimension of the measurement t is 12, and the measurement matrix Φ ∈ RM×NA measuring matrix is designed, wherein only 5 elements are 1, the rest elements are 0, and the positions of the measuring matrix are random. The measurement matrix is then transformed by equation (16) to obtain the newThe matrix Ψ is measured.
The second step is that: partitioning a test set of compressed sensor-autoencoder { x }testAnd training set xtrain}. Then, the number of decoding process layers is set to be L equal to 3, the learning rate eta is 0.1, the number of iterations is 5000, and the reconstruction layer multiple is set
Figure BDA0001674611830000162
Initializing the weight matrix WlAnd an offset vector bl，Wl＝rand-0.5，bl＝rand-0.5。
The third step: training set { x) according to equation (21) and equations (23) - (33)trainAnd (5) training a compressed sensing-automatic encoder algorithm. The compressed sensor-autoencoder algorithm flow is shown in fig. 4.
The fourth step: using the measurement set { xtestTest is carried out. The simulation process is discussed in several cases, with no noise mixed in the measurement values and noise mixed in the measurement values. The following are discussed in turn for each case:
1) the measured values are free from noise. Firstly, a test set is compressed by using a measurement matrix psi designed in the first step to obtain ttest＝ΨxtestThen, after normalization is carried out by using the formula (23), finally, the reconstructed data is obtained by reconstruction by using the third step of trained compressed sensor-automatic encoder algorithm
Figure BDA0001674611830000161
The results of the raw data and the reconstructed data of the smart meter are shown in fig. 5.
2) The measured value was mixed with noise, and the noise was 0.1 × randn (M, 1). Firstly, the measurement matrix psi mentioned in the first step is used to compress the test set
Figure BDA0001674611830000171
Then after normalization, reconstruction is carried out by using a compressed sensing-automatic encoder to obtain reconstruction data
Figure BDA0001674611830000172
The results of the raw data and the reconstructed data of the smart meter are shown in fig. 6.
The fifth step: fig. 7-8 show the compression ratio versus the signal-to-noise ratio, with lower compression ratios indicating smaller dimensions of the measured values. As can be seen from the figure, the signal-to-noise ratio is higher as the compression ratio is higher, i.e., the dimension of the measurement value t is larger, regardless of whether the measurement value is mixed with noise or not. In addition, the signal-to-noise ratio can be affected by noise.
And a sixth step: the simulation environment and the machine configuration of the invention are as follows:
(1) and a processor: intel (R) core (TM) i7-6700CPU @3.40GHz3.41GHz
(2) And installing a memory: 16.0GB
(3) And the system type: windows 10(64 bit operating system)
(4) And simulation conditions: MATLAB R2016b
TABLE 1 relative error and reconstruction time comparison for different compression ratios
Figure BDA0001674611830000173
Figure BDA0001674611830000181
Table 1 shows the comparison of different compression ratios, relative errors, reconstruction times. As the compression rate increases, the error gradually decreases and the reconstruction time gradually increases. But the reconstruction time is very short each time, so that the method is very suitable for the transmission of the data of the intelligent electric meter with high real-time requirement, the dimensionality of the transmitted data is greatly reduced, and the transmission cost is reduced.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (2)

1. A real-time reconstruction method of smart meter data based on compressed sensing is characterized by comprising the following steps:
s1: the transmission model of the electric meter data based on real-time compressed sensing comprises three parts: the intelligent electric meter compresses data after collecting the data, transmits a measured value to the access point through a power line communication link, transmits the collected measured value to the control center by using a wireless communication network through the access point, and reconstructs the measured value in the control center;
s2: the compression and reconstruction of signals based on the principle of an automatic encoder consists of two parts: the method comprises the steps of compression coding and reconstruction coding, wherein the compression coding consists of an input layer and a compression layer, and the reconstruction coding consists of a reconstruction layer and an output layer;
s3: in the compression encoding portion of the signal: firstly, the data x belonging to the original input layer belongs to RN×1The compression layer is the measured value y ∈ RM×1The measured value of the compression layer can be obtained from the input layer by:
y＝Φx (1)
wherein, phi is a measurement matrix and phi is epsilon to RM×N(M<N), the measurement matrix may be: random gaussian matrices, random bernoulli matrices and simple binary matrices;
in step S3: the singular value decomposition of the measurement matrix Φ yields:
Figure FDA0003463444440000011
wherein U and V are unitary matrices,
Figure FDA0003463444440000012
multiply the left sides of both sides of equation (1)
Figure FDA0003463444440000013
Wherein
Figure FDA0003463444440000021
Thus, equation (1) is converted to:
t＝Ψx (3)
wherein:
Figure FDA0003463444440000022
s4: signal reconstruction and coding: after the measured value t is obtained, the measured value is transmitted to the control center through the communication network, the control center restores the measured value to original intelligent electric meter data, and the measured value t is obtained through the following formula:
Figure FDA0003463444440000023
where v is a sparse vector, ACSΨ D is the perceptual matrix, D is the sparse transformation basis of the meter data x.
2. The method for real-time reconstruction of smart meter data based on compressive sensing as claimed in claim 1, wherein in the step S3, the reconstruction of the meter data specifically includes the following steps:
the method comprises the following steps: before the layer is reformed, the measured value t is normalized, i.e.
Figure FDA0003463444440000024
Wherein, tminIs the minimum value of the measured value t, tmaxIs the maximum value of the measured value t;
step two: the number of reconstruction layers is L, and the dimension of each reconstruction layer is
Figure FDA0003463444440000025
Wherein the content of the first and second substances,
Figure FDA0003463444440000026
given a weight matrix W for each reconstructed layerlAnd an offset vector blThen the activation function of the l-th reconstruction layer can be expressed by:
zl＝f(Wlzl-1+bl) (5)
wherein z is0T, f (α) is an activation function of α, which is defined as follows:
Figure FDA0003463444440000031
step three: the output layer is reconstructed electric meter data, and the expression of the output layer is as follows:
Figure FDA0003463444440000032
wherein x isminIs the minimum value of the meter data x, xmaxThe maximum value of the electric meter data x is obtained;
step four: before step two, the weight matrix W needs to be alignedlAnd an offset vector blFine tuning is carried out, and parameters are fine tuned by using a direction propagation algorithm, which specifically comprises the following steps:
Figure FDA0003463444440000033
Figure FDA0003463444440000034
Figure FDA0003463444440000035
Δbl＝ηδl (11)
Figure FDA0003463444440000036
Wl＝Wl-ΔWl (13)
bl＝bl-Δbl (14)
wherein η is the learning rate, "" indicates multiplication by element, and the current weight matrix WlAnd an offset vector blAfter the update is completed, a reconstructed signal can be obtained by equation (7).
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