CN116127409A - Non-invasive load identification method based on Gram angle difference field feature fusion - Google Patents

Non-invasive load identification method based on Gram angle difference field feature fusion Download PDF

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CN116127409A
CN116127409A CN202310178005.2A CN202310178005A CN116127409A CN 116127409 A CN116127409 A CN 116127409A CN 202310178005 A CN202310178005 A CN 202310178005A CN 116127409 A CN116127409 A CN 116127409A
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load
steady
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段斌
符明
蔡令仪
柯其聪
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Xiangtan University
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Abstract

The invention discloses a non-invasive load identification method based on the fusion of characteristics of a gram angle difference field, which comprises the following steps: preprocessing high-frequency steady-state data acquired by equipment to obtain a complete fundamental wave period current and voltage signal; encoding the one-dimensional voltage and current signals by using the Graham angle difference field respectively to generate a corresponding two-dimensional characteristic diagram; and (3) inputting the superposition fusion into a neural network based on a convolution block attention module, and constructing a load identification model to finish load identification. According to the invention, the gram angle difference field theory is applied to load imprinting construction, so that the representation capability of one-dimensional voltage and current signals is enhanced, and the identification degree between different load characteristics is further improved. In addition, a convolution block attention module is introduced into the load identification model, so that the model is helped to acquire more useful information required by load identification from the load imprinting, other useless information is restrained, and the load identification capacity is further improved.

Description

Non-invasive load identification method based on Gram angle difference field feature fusion
Technical Field
The invention relates to a non-invasive load identification method based on the fusion of characteristics of a gram angle difference field.
Background
Under the driving of the double carbon target, the power industry is newly and revolutionized, and the transformation to green low-carbonization is complete. The most important way of transformation is to strengthen the fine management of the demand side, and non-invasive load monitoring (non-intrusive load monitoring, NILM) is used as one of the key technologies of the fine management of the demand side of the smart grid, and can monitor information such as the type, running state and energy consumption condition of each electric appliance of a user in real time through data collected by a smart electric meter, so as to provide decision basis for the user to optimize the self electricity consumption mode, guide the user to reasonably reduce the household electricity consumption, improve the household electricity consumption efficiency, promote energy conservation and emission reduction, and realize ' carbon peak and ' carbon neutralization ' by assistance.
Non-invasive load identification is one of the important subtasks of NILM, comprising two key steps: feature extraction and load classification. Early home and abroad scholars mainly adopt mathematical optimization or traditional machine learning algorithm to extract characteristics and classification. The document [ non-invasive load identification method based on DTW algorithm and steady-state current waveform ] calculates the distance between the load steady-state waveform and template library waveform by Dynamic Time Warping (DTW) algorithm to realize load identification, and the algorithm utilizes the additivity of the steady-state current waveform to effectively reduce the phase error generated during steady-state current extraction and improve the load identification capability. Document [ Modern development of an Adaptive Non-Intrusive Appliance Load Monitoring system in electricity energy conservation ] proposes two load identification methods based on a k nearest neighbor algorithm and a BP neural network, and improves the identification accuracy by adaptively adjusting model parameters through an Artificial Immune Algorithm (AIA) with Fisher criteria. The document [ non-invasive load monitoring method based on k-NN combined kernel Fisher discrimination ] constructs a feature library taking the odd harmonic of load current as a feature, screens effective features through an AdaBoost algorithm to obtain a more simplified load feature library, and finally combines a k nearest neighbor algorithm with kernel Fisher discrimination to realize household load identification. The method mainly realizes load identification by extracting the frequency, the phase or other statistical characteristics of the sampled data, and the calculated amount is not high, but the identification accuracy is difficult to reach a high level.
With the continuous development of deep learning technology and the decrease of the difficulty of acquiring high frequency data, the research of extracting fine-grained features from steady-state or transient data for non-invasive load identification is increasing. Some scholars explore the use of V-I trajectories to describe the characteristics of appliances, literature [ Electric Load Classification by Binary Voltage-Current Trajectory Mapping ] explains in detail the physical characteristics that can be described by V-I trajectories, and verifies that different types of loads can characterize their unique shape characteristics via V-I trajectories, achieving better load recognition results. The literature [ non-invasive load identification algorithm based on feature fusion and deep learning ] provides a load identification method based on feature fusion and deep learning, and the problem that the V-I track cannot embody the power of equipment is solved by fusing power features into the V-I track, so that the multi-state load identification capability is improved. The literature [ non-invasive load identification method based on V-I track color coding ] firstly utilizes a K-means clustering algorithm to carry out preliminary classification, and then the V-I track characteristics after color coding are input into an AlexNet neural network to carry out load refined classification. The above study shows that the V-I trajectory and its two-dimensional image representation can be effectively used for non-invasive load recognition tasks, and deeper features can be extracted by using a deep learning algorithm to enhance the overall performance of load recognition.
Although the method has successfully applied the V-I track to the non-invasive load identification task, the V-I track is mainly obtained by drawing normalized voltage and current, and the working voltage and current of partial electric appliances are similar, so that the V-I track has overlapping phenomenon and is difficult to effectively identify.
Disclosure of Invention
In order to solve the technical problems, the invention provides a non-invasive load identification method based on the fusion of the characteristics of the gram angle difference field, which is simple in algorithm and high in identification precision.
The technical scheme for solving the problems is as follows: a non-invasive load identification method based on the fusion of the characteristics of a gram angle difference field comprises the following steps:
step one: preprocessing high-frequency steady-state data acquired by equipment to obtain a complete fundamental wave period current and voltage signal;
step two: encoding the one-dimensional voltage and current signals by using the Graham angle difference field respectively to generate a corresponding two-dimensional characteristic diagram;
step three: and (3) inputting the superposition fusion into a neural network based on a convolution block attention module, and constructing a load identification model to finish load identification.
The non-invasive load identification method based on the Graham angle difference field feature fusion comprises the following specific steps:
the premise of realizing load identification is that firstly, load characteristics are extracted from high-frequency aggregate signals; assuming that only one electrical equipment generates a switching event at the same moment, the load characteristics of the single electrical equipment can be extracted by calculating the steady-state aggregate signal difference in a short time window before and after the switching event; the active power change difference delta P is used as a judgment basis for detecting switching events of the electrical equipment, and steady-state voltage and current signals of the electrical equipment are extracted from the aggregated voltage and current signals to serve as load characteristics; for easy calculation, v is used respectively off 、i off And v on 、i on The method is characterized in that the method comprises the steps of representing steady-state aggregation voltage and current before an electrical equipment switching event and steady-state aggregation voltage and current after the switching event, and taking an average value of the steady-state aggregation voltage before and after the switching event by the voltage v of single electrical equipment, namely:
Figure BDA0004101617360000031
in contrast, the steady-state aggregate current signal changes due to the occurrence of switching events of the electrical equipment, and the current i of the single electrical equipment is obtained by calculating the difference value of the steady-state aggregate current before and after the switching events, namely:
i＝i on -i off (2)
due to v off And v on And i off And i on The addition and subtraction operation is needed in the same voltage phase, and the waveform of the steady-state voltage signal approximates to a sine wave, so that the voltage positive zero crossing points are selected to be aligned; in addition, steady-state voltage and current signals periodically change, so that the steady-state voltage and current signals with a single fundamental wave period are used for representing the load characteristics of the electrical equipment, but the state of the electrical equipment still changes when the electrical equipment stably works, and continuous N is extracted for better representing the load characteristics of the electrical equipment t The steady-state voltage and current signals of each fundamental wave period are averaged to obtain the steady-state voltage and current signals of a complete fundamental wave period, N t ＞1；
Firstly, assume that the sampling frequency of steady-state voltage and current signals of electrical equipment is f s The fundamental frequency is f, the number of samples per fundamental period is N s ＝f s /f，N t The number of samples of each fundamental period is N ts ＝N t ×N s N of electrical equipment k t Steady-state voltage signal with single fundamental wave period
Figure BDA0004101617360000041
And steady state current signal>
Figure BDA0004101617360000042
Then let v k 、i k At v k Each fundamental wave period is aligned at the positive zero crossing point to obtain an aligned steady-state voltage signal +.>
Figure BDA0004101617360000043
And steady state current signal>
Figure BDA0004101617360000044
The following are provided: />
Figure BDA0004101617360000045
Figure BDA0004101617360000046
Wherein:
Figure BDA0004101617360000047
representing electrical equipment k N ts Steady state voltage values after alignment, +.>
Figure BDA0004101617360000048
Representing electrical equipment k N ts A plurality of aligned steady state current values;
finally, to
Figure BDA0004101617360000049
And->
Figure BDA00041016173600000410
To obtain steady-state voltage signal and current signal one-dimensional vector of a complete fundamental wave period>
Figure BDA00041016173600000411
And->
Figure BDA00041016173600000412
In the second step, the gladhand field is an encoding method for converting one-dimensional time sequence signals into two-dimensional images, and the specific encoding steps are as follows:
first, for a composition containing N s Voltage of electrical equipment k obtained by preprocessing of individual time stamps
Figure BDA0004101617360000051
Or current->
Figure BDA0004101617360000052
Normalization processing is performed to normalize the time sequence signal to [ -1,1]In the range, the formula is as follows:
Figure BDA0004101617360000053
wherein: x is x p Representation of
Figure BDA0004101617360000054
Or->
Figure BDA0004101617360000055
P-th value of>
Figure BDA0004101617360000056
Represents x p Normalized value, max represents maximum function, min represents minimum function;
then, the normalized product is
Figure BDA0004101617360000057
Converting from a Cartesian coordinate system to a polar coordinate system, namely converting the numerical value thereof to an angular cosine phi in the polar coordinate system, converting the timestamp to a radius r in the polar coordinate system, and converting the formula as follows:
Figure BDA0004101617360000058
wherein: phi (phi) p An angular cosine representing the p-th value in the polar coordinate system, r p Radius, t, representing the p-th value in a polar coordinate system p A timestamp representing the p-th value; n represents a constant factor generated by regularized polar coordinate system,
Figure BDA0004101617360000059
the representation comprises N s A normalized time sequence signal->
Figure BDA00041016173600000510
The method for representing the time sequence signals in the polar coordinate system provides a new idea for understanding the time sequence signals, after the time sequence signals are converted into the polar coordinate system, the time sequence signals of each time stamp are used as one-dimensional measurement space, and the amplitude of the time sequence signals generates bending between different angular points crossing a circle along with the time;
finally, angle difference is carried out on points converted to a polar coordinate system through a sine function to obtain a gram angle difference field characteristic diagram, and time correlation in different time intervals is identified through angle change; the gram angle difference field GADF is defined as follows:
Figure BDA0004101617360000061
wherein:
Figure BDA0004101617360000062
representing the N-th in a polar coordinate system s The angle cosine of the individual values, I representing the unit row vector,/->
Figure BDA0004101617360000063
Representation->
Figure BDA0004101617360000064
Is a transpose of (a).
The non-invasive load identification method based on the Graham angle difference field feature fusion comprises the following specific steps:
first, the one-dimensional voltage signal obtained by preprocessing
Figure BDA0004101617360000065
And current signal->
Figure BDA0004101617360000066
Normalized to interval [ -1, 1] according to formula (5)]；
Then, the normalized voltage and current signals are respectively converted into a polar coordinate system by a formula (6), and the angle in the polar coordinate system is used
Figure BDA0004101617360000067
And radius r characterizes its amplitude and timestamp;
then, GADF matrix transformation is performed by the formula (7) to generate 2N-sized products s ×N s Is a two-dimensional feature map of (1);
finally, the two components are overlapped and fused to generate a composite material with the size of 2 XN s ×N s As a load signature; to enhance the feature expression capability of the three-dimensional feature map, each pixel value of the feature map is multiplied by 256 and subjected to a downward rounding process so that the gray value of the feature map ranges from [0,1]The interval becomes 0,255]Between them.
In the above non-invasive load identification method based on the fusion of the gram angle difference field features, in the third step, the convolution block attention module CBAM is composed of a channel attention sub-module and a space attention sub-module;
given a feature map F.epsilon.R C×H×W As input, the CBAM sequentially extrapolates the one-dimensional channel attention pattern M c ∈R C ×1×1 And two-dimensional space attention to figure M s ∈R 1×H×W The overall attentiveness process is summarized as follows:
Figure BDA0004101617360000068
Figure BDA0004101617360000069
wherein:
Figure BDA0004101617360000071
representing multiplication of corresponding elements one by one, during the multiplication operation, the channel attention value is broadcast along the spatial dimension, the spatial attention value is broadcast along the channel dimension, F' represents the channel attention weight, F "represents the final output attention weight, R represents the real space, C represents the channel number of the feature map, H represents the length of the feature map, and W represents the width of the feature mapA degree;
in the channel attention module, firstly, the input feature images are respectively compressed in the space dimension through maximum pooling and average pooling, and two different space feature descriptors are obtained through aggregation:
Figure BDA0004101617360000072
and->
Figure BDA0004101617360000073
The two space feature descriptors are then transferred to a shared network composed of multiple layers of perceptrons to generate a channel attention map M c ∈R C×1×1 The method comprises the steps of carrying out a first treatment on the surface of the To reduce the parameter overhead, the hidden activation size of the multi-layer perceptron is set to R C/r×1×1 R is the compression ratio, and the channel attention calculation formula is as follows:
Figure BDA0004101617360000074
wherein: sigma denotes sigmoid function, MLP denotes multi-layer perceptron, avgPool denotes average pooling, maxPool denotes maximum pooling, W 0 ∈R C/r×C And W is 1 ∈R C×C/r Representing the weight of the multi-layer perceptron;
similarly, the spatial attention module first compresses the feature map in the channel dimension using maximum pooling and average pooling to generate two-dimensional feature maps
Figure BDA0004101617360000075
And->
Figure BDA0004101617360000076
Then will->
Figure BDA0004101617360000077
And->
Figure BDA0004101617360000078
The two feature maps are spliced to obtain a three-dimensional feature map containing 2 channel numbers +.>
Figure BDA0004101617360000079
Then the feature map is ++7 with convolution layer of convolution kernel size 7×7>
Figure BDA00041016173600000710
Performing convolution operation to obtain a two-dimensional characteristic diagram +.>
Figure BDA00041016173600000711
Finally, inputting the two-dimensional space attention feature map M into sigmoid function to generate two-dimensional space attention feature map M s ∈R H×W The method comprises the steps of carrying out a first treatment on the surface of the The calculation process of the spatial attention is as follows:
Figure BDA00041016173600000712
wherein: f (f) 7×7 The convolution kernel representing the convolution layer is 7 x 7 in size.
In the non-invasive load identification method based on the Graham angle difference field feature fusion, the structure of the constructed load identification model comprises an input unit, a residual unit, a CBAM unit and an output unit;
in the input unit, a size of 2 XN is input through an input layer s ×N s The method comprises the steps of (1) carrying out preliminary feature extraction on the load marks by utilizing a convolution layer, enabling features extracted by the convolution layer to have zero mean and unit variance in order to reduce influence caused by data distribution, adding a batch normalization layer after the convolution layer, and finally reducing feature dimension by 1 maximum pooling layer, so that the calculated amount of a subsequent unit is reduced, and the model training speed is improved; the calculation formula of the input unit convolution layer is as follows:
Figure BDA0004101617360000081
Figure BDA0004101617360000082
wherein:
Figure BDA0004101617360000085
representing a convolution operation; />
Figure BDA0004101617360000083
Represents the omega weight on the tau convolution kernel; />
Figure BDA0004101617360000084
Representing the omega input value of the convolution operation; b represents bias; reLu denotes the ReLu activation function; x is x l Representing the features obtained by the convolution operation;
the residual unit consists of an identity mapping part and a residual part, and deep feature extraction is carried out on the basis of the input unit, and the expression is as follows:
x l+1 ＝h(x l )+F(xl,W l ) (13)
wherein: h (x) l )＝W′ l x l Wherein W' l Representing a 1 x 1 convolution operation in an identity map, which is used to adjust the number of channels of the input and output; f (x) l ,W l ) A mapping function representing the residual portion; x is x l+1 Representing the characteristics obtained after the residual error unit is processed;
the residual part in the residual unit comprises 13 multiplied by 3 convolution layer and 2 1 multiplied by 1 convolution layers, and each convolution layer is connected with 1 batch normalization layer and 1 ReLu activation function; the residual unit is firstly connected with a 1 multiplied by 1 convolution layer, and the channel number is set to 128; then connecting 3×3 convolution layers, setting the channel number to 128, and finally connecting another 1×1 convolution layer, setting the channel number to 512; the feature images extracted by the identity mapping part and the residual part are fused through pixel-by-pixel addition operation; the CBAM unit is accessed to the last layer 1 multiplied by 1 convolution layer of the residual part, so that the whole neural network is focused on important area information of the load imprinting image in the process of extracting the load characteristics, irrelevant area information is ignored, the characteristic learning capacity of the whole network is enhanced, and the performance of a load identification task is further improved;
the output unit consists of 2 full connection layers, is the last unit of the whole neural network and is connected with the residual error unit; the number of the neurons of the two full-connection layers is 128 and K, the activation functions are a Relu function and a softmax function, and K is determined by the number of the types of electrical equipment; to train the entire neural network to obtain optimal parameters, a multi-class cross entropy loss function defined in the back propagation optimization equation (14) is used:
Figure BDA0004101617360000091
/>
in the method, in the process of the invention,
Figure BDA0004101617360000092
a true class one-hot vector representing sample ζ; />
Figure BDA0004101617360000093
A prediction class one-hot vector representing sample ζ; num represents the number of samples; k represents the class to which the sample belongs.
The invention has the beneficial effects that: according to the invention, the gram angle difference field theory is applied to load imprinting construction, so that the representation capability of one-dimensional voltage and current signals is enhanced, and the identification degree between different load characteristics is further improved. In addition, a convolution block attention module is introduced into the load identification model, so that the model is helped to acquire more useful information required by load identification from the load imprinting, other useless information is restrained, and the load identification capacity is further improved. Through the verification of an example, the average recognition accuracy of the method reaches 98.36 percent, the average F1 fraction reaches 98.46 percent, and the method has better recognition capability through the deep discussion and analysis of a comparison experiment.
Drawings
Fig. 1 is an overall flow chart of the present invention.
FIG. 2 is a schematic diagram of load imprinting construction.
FIG. 3 is a block diagram of a convolutionally constructed attention model.
Fig. 4 is a diagram of an attention sub-model structure.
Fig. 5 is a structural diagram of the load recognition model.
Fig. 6 is a statistical chart of sample data amounts of respective electrical devices in the PLAID 2018 dataset.
Fig. 7 is a schematic diagram of a training process of a CBAM-based neural network on a PLAID dataset.
Fig. 8 is a confusion matrix diagram of the final test result in the example.
FIG. 9 shows a different N t Experimental results of the values.
FIG. 10 is a diagram of a ResNet-18 network architecture.
FIG. 11 is a diagram of a LeNet-5 network architecture.
Detailed Description
The invention is further described below with reference to the drawings and examples.
As shown in fig. 1, a non-invasive load identification method based on the fusion of the characteristics of a glamer angle difference field comprises the following steps:
step one: preprocessing high-frequency steady-state data acquired by the equipment to obtain a complete fundamental wave period current and voltage signal.
Load identification is a key step in non-invasive load monitoring (non-intrusive load monitoring, NILM) and its main objective is to identify the appliances in operation from the aggregate signal. Thus, the premise of realizing load identification is to extract load characteristics from the high-frequency aggregate signal; assuming that only one electrical equipment generates a switching event at the same moment, the load characteristics of the single electrical equipment can be extracted by calculating the steady-state aggregate signal difference in a short time window before and after the switching event; the active power change difference delta P is used as a judgment basis for detecting switching events of the electrical equipment, and steady-state voltage and current signals of the electrical equipment are extracted from the aggregated voltage and current signals to serve as load characteristics; for easy calculation, v is used respectively off 、i off And v on 、i on The method is characterized in that the method comprises the steps of representing steady-state aggregation voltage and current before an electrical equipment switching event and steady-state aggregation voltage and current after the switching event, and taking an average value of the steady-state aggregation voltage before and after the switching event by the voltage v of single electrical equipment, namely:
Figure BDA0004101617360000111
in contrast, the steady-state aggregate current signal changes due to the occurrence of switching events of the electrical equipment, and the current i of the single electrical equipment is obtained by calculating the difference value of the steady-state aggregate current before and after the switching events, namely:
i＝i on -i off (2)
due to v off And v on And i off And i on The addition and subtraction operation is needed in the same voltage phase, and the waveform of the steady-state voltage signal approximates to a sine wave, so that the voltage positive zero crossing points are selected to be aligned; in addition, steady-state voltage and current signals periodically change, so that the steady-state voltage and current signals with a single fundamental wave period are used for representing the load characteristics of the electrical equipment, but the state of the electrical equipment still changes when the electrical equipment stably works, and continuous N is extracted for better representing the load characteristics of the electrical equipment t The steady-state voltage and current signals of each fundamental wave period are averaged to obtain the steady-state voltage and current signals of a complete fundamental wave period, N t ＞1；
Firstly, assume that the sampling frequency of steady-state voltage and current signals of electrical equipment is f s The fundamental frequency is f, the number of samples per fundamental period is N s ＝f s /f，N t The number of samples of each fundamental period is N ts ＝N t ×N s N of electrical equipment k t Steady-state voltage signal with single fundamental wave period
Figure BDA0004101617360000112
And steady state current signal>
Figure BDA0004101617360000113
Then let v k 、i k At v k Each fundamental wave period is aligned at the positive zero crossing point to obtain an aligned steady-state voltage signal +.>
Figure BDA0004101617360000114
And steady state current signal>
Figure BDA0004101617360000115
The following are provided:
Figure BDA0004101617360000116
Figure BDA0004101617360000117
finally, to
Figure BDA0004101617360000118
And->
Figure BDA0004101617360000119
To obtain steady-state voltage signal and current signal one-dimensional vector of a complete fundamental wave period>
Figure BDA0004101617360000121
And->
Figure BDA0004101617360000122
Step two: and respectively encoding the one-dimensional voltage and current signals by using the gram angle difference field to generate a corresponding two-dimensional characteristic diagram. The unique load signature is then constructed by superposition fusion, and the overall load signature construction flow is shown in FIG. 2.
The gladhand field (Gramian Angular Field, GAF) is a coding method for converting a one-dimensional time sequence signal into a two-dimensional image, and the specific coding steps are as follows:
first, for a voltage or current timing signal x= { X containing n time stamps 1 ,x 2 ,x 3 ,…,x n Normalized to [ -1,1 }, time series signal]In the range, the formula is as follows:
Figure BDA0004101617360000123
wherein: x is x i Representing the original time-series signal,
Figure BDA0004101617360000124
representing the normalized time sequence signal, max representing the maximum function, and min representing the minimum function;
then, the normalized time sequence signal is converted from a Cartesian coordinate system to a polar coordinate system, namely, the numerical value of the time sequence signal is converted into an angular cosine phi in the polar coordinate system, and the time stamp is converted into a radius r in the polar coordinate system, wherein the conversion formula is as follows:
Figure BDA0004101617360000125
wherein: phi (phi) i Representing the angular cosine in a polar coordinate system, r i Representing radius in polar coordinate system, t i Representing a time stamp; n represents the space constant generated by the regularized polar coordinate system,
Figure BDA0004101617360000126
representing a sequence comprising n normalized timing signals +.>
Figure BDA0004101617360000127
The method for representing the time sequence signals in the polar coordinate system provides a new idea for understanding the time sequence signals, after the time sequence signals are converted into the polar coordinate system, the time sequence signals of each time stamp are used as one-dimensional measurement space, and the amplitude of the time sequence signals generates bending between different angular points crossing a circle along with the time;
finally, angle difference is carried out on points converted to a polar coordinate system through a sine function to obtain a gram angle difference field characteristic diagram, and time correlation in different time intervals is identified through angle change; the gram angle difference field GADF is defined as follows:
Figure BDA0004101617360000131
wherein: i represents a unit row vector and,
Figure BDA0004101617360000132
representation->
Figure BDA0004101617360000133
Is a transpose of (a).
The specific process of the second step is as follows:
first, the one-dimensional voltage signal obtained by preprocessing
Figure BDA0004101617360000134
And current signal->
Figure BDA0004101617360000135
Normalized to interval [ -1, 1] according to formula (5)]；
Then, the normalized voltage and current signals are respectively converted into a polar coordinate system by a formula (6), and the angle in the polar coordinate system is used
Figure BDA0004101617360000136
And radius r characterizes its amplitude and timestamp;
then, GADF matrix transformation is performed by the formula (7) to generate 2N-sized products s ×N s Is a two-dimensional feature map of (1);
finally, the two components are overlapped and fused to generate a composite material with the size of 2 XN s ×N s As a load signature; to enhance the feature expression capability of the three-dimensional feature map, each pixel value of the feature map is multiplied by 256 and subjected to a downward rounding process so that the gray value of the feature map ranges from [0,1]The interval becomes 0,255]Between them.
Step three: and (3) inputting the superposition fusion into a neural network based on a convolution block attention module, and constructing a load identification model to finish load identification.
The convolution block attention module CBAM consists of a channel attention sub-module and a space attention sub-module; which can extract important features from both the space and channel dimensions, suppress unnecessary features, and the structure is shown in fig. 3.
The CBAM belongs to a lightweight attention module, can be seamlessly fused with the CNN, improves the feature extraction capability of the CNN, guides the CNN to better capture key areas in an image, suppresses background and unnecessary attention areas, and improves the image recognition capability. Given a feature map F.epsilon.R C×H×W As input, the CBAM sequentially extrapolates the one-dimensional channel attention pattern M c ∈R C×1×1 And two-dimensional space attention to figure M s ∈R 1×H×W The overall attentiveness process is summarized as follows:
Figure BDA0004101617360000141
Figure BDA0004101617360000142
wherein:
Figure BDA0004101617360000143
representing multiplication of corresponding elements one by one, wherein during multiplication operation, a channel attention value is broadcast along a space dimension, a space attention value is broadcast along the channel dimension, F 'represents a channel attention weight, F' represents a final output attention weight, R represents a real space, C represents the channel number of the feature map, H represents the length of the feature map, and W represents the width of the feature map;
the specific calculation process of the channel attention module and the spatial attention module of the CBAM is shown in figure 4;
in the channel attention module, firstly, the input feature images are respectively compressed in the space dimension through maximum pooling and average pooling, and two different space feature descriptors are obtained through aggregation:
Figure BDA0004101617360000144
and->
Figure BDA0004101617360000145
The two space feature descriptors are then transferred to a shared network composed of multiple layers of perceptrons to generate a channel attention map M c ∈R C×1×1 The method comprises the steps of carrying out a first treatment on the surface of the To reduce the parameter overhead, the hidden activation size of the multi-layer perceptron is set to R C/r×1×1 R is the compression ratio, and the channel attention calculation formula is as follows: />
Figure BDA0004101617360000146
Wherein: sigma denotes sigmoid function, MLP denotes multi-layer perceptron, avgPool denotes average pooling, maxPool denotes maximum pooling, W 0 ∈R C/r×C And W is 1 ∈R C×C/r Representing the weight of the multi-layer perceptron;
similarly, the spatial attention module first compresses the feature map in the channel dimension using maximum pooling and average pooling to generate two-dimensional feature maps
Figure BDA0004101617360000147
And->
Figure BDA0004101617360000148
Then will->
Figure BDA0004101617360000149
And->
Figure BDA00041016173600001410
The two feature maps are spliced to obtain a three-dimensional feature map containing 2 channel numbers +.>
Figure BDA00041016173600001411
Then the feature map is ++7 with convolution layer of convolution kernel size 7×7>
Figure BDA00041016173600001412
Performing convolution operation to obtain a two-dimensional characteristic diagram +.>
Figure BDA00041016173600001413
Finally, inputting the two-dimensional space attention feature map M into sigmoid function to generate two-dimensional space attention feature map M s ∈R H×W The method comprises the steps of carrying out a first treatment on the surface of the The calculation process of the spatial attention is as follows:
Figure BDA0004101617360000151
wherein: f (f) 7×7 The convolution kernel representing the convolution layer is 7 x 7 in size.
As shown in fig. 5, the structure of the constructed load recognition model includes an input unit, a residual unit, a CBAM unit, and an output unit;
in the input unit, a size N is input through an input layer s ×N s The method comprises the steps of (1) carrying out primary feature extraction on load marks by using a convolution layer, enabling features extracted by the convolution layer to have zero mean and unit variance in order to reduce influence caused by data distribution, adding a batch normalization layer after the convolution layer, and finally reducing feature dimension by 1 maximum pooling layer, so that the calculated amount of a subsequent unit is reduced, and the model training speed is improved; the calculation formula of the input unit convolution layer is as follows:
Figure BDA0004101617360000152
wherein:
Figure BDA0004101617360000153
representing a convolution operation; />
Figure BDA0004101617360000154
Representing the ith weight on the jth convolution kernel; b represents bias; reLu denotes the ReLu activation function; x is x l Representing the features obtained by the convolution operation;
the residual unit consists of an identity mapping part and a residual part, and deep feature extraction is carried out on the basis of the input unit, and the expression is as follows:
x l+1 ＝h(x l )+F(x l ,W l ) (13)
wherein: h (x) l )＝W′ l x l Wherein W' l Representing a 1 x 1 convolution operation in an identity map, which is used to adjust the number of channels of the input and output; f (x) l ,W l ) A mapping function representing the residual portion; x is x l+1 Representing the characteristics obtained after the residual error unit is processed;
the residual part in the residual unit comprises 13 multiplied by 3 convolution layer and 2 1 multiplied by 1 convolution layers, and each convolution layer is connected with 1 batch normalization layer and 1 ReLu activation function; the residual unit is firstly connected with a 1 multiplied by 1 convolution layer, and the channel number is set to 128; then connecting 3×3 convolution layers, setting the channel number to 128, and finally connecting another 1×1 convolution layer, setting the channel number to 512; the feature images extracted by the identity mapping part and the residual part are fused through pixel-by-pixel addition operation; the CBAM unit is accessed to the last layer 1 multiplied by 1 convolution layer of the residual part, so that the whole neural network is focused on important area information of the load imprinting image in the process of extracting the load characteristics, irrelevant area information is ignored, the characteristic learning capacity of the whole network is enhanced, and the performance of a load identification task is further improved;
the output unit consists of 2 full connection layers, is the last unit of the whole neural network and is connected with the residual error unit; the number of neurons of the full-connection layer is 128 and K, the activation function is a Relu function and a softmax function, and K is determined by the number of types of electrical equipment; to train the entire neural network to obtain optimal parameters, a multi-class cross entropy loss function defined in the back propagation optimization equation (14) is used:
Figure BDA0004101617360000161
in the method, in the process of the invention,
Figure BDA0004101617360000162
a true class one-hot vector representing sample i; />
Figure BDA0004101617360000163
A prediction class one-hot vector representing sample i; n represents the number of samples.
Calculation case analysis
In order to verify the validity and feasibility of the proposed method, the invention chooses to perform an example analysis on the public dataset PLAID. The PLAID dataset records electricity usage data for a number of households, pittsburgh 60, pa.S., 3 versions, PLAID 2014, PLAID 2017 and PLAID 2018, respectively, have been updated. The invention selects the PLAID 2018 of the latest version for example verification, which comprises 1876 groups of voltage and current data of 17 different electrical equipment, and the fundamental wave frequency and the sampling frequency of the 1876 groups of voltage and current data are respectively 60Hz and 30kHz. The calculation hardware platform of the invention is a computer with CPU Intel i7-9700K, GPU NVIDIA RTX2028Ti and memory 64GB, and the software platform is a Windows 10 operating system, python3.8 programming language, deep learning framework Keras 3.4.2 and Tensorflow 2.4.0.
In order to evaluate the load identification method more comprehensively, the load identification result is evaluated by adopting 3 evaluation indexes of confusion matrix, accuracy and F1 score. The confusion matrix is used for evaluating the overall effect of load identification, the identification results of the load identification model on various categories can be intuitively displayed, each row represents the real category of the load, each row represents the predicted category of the load, the values of diagonal cells represent the result of the correct identification of the load, and the values of non-diagonal cells represent the result of the incorrect identification of the load. The accuracy is used for evaluating the overall effect of load identification, the value of the accuracy is the ratio of the number of the correct load identification examples to the total number of the load examples, and the calculation formula is as follows:
Figure BDA0004101617360000171
wherein: n is n true Representing the number of correctly identified instances, n total Representing the total number of instances of the load.
F1 fraction F 1 For evaluating the recognition effect of each load category, the accuracy rate P and the recall rate R can be balanced and the load recognition method can be comprehensively evaluated by the formulas (16) - (18)And (5) calculating.
Figure BDA0004101617360000172
Figure BDA0004101617360000173
Figure BDA0004101617360000174
Wherein: t (T) P Representing a real case, i.e. the load is actually a positive class, and is predicted as the number of positive classes; f (F) P Representing a false positive example, i.e. the load is actually a negative class, but is predicted as the number of positive classes; f (F) N Representing true counterexamples, i.e. the load is actually a positive class, but is predicted as the number of negative classes.
The present invention first visualizes the number of samples for each appliance type of PLAID 2018 dataset, as shown in FIG. 6. From fig. 6, it can be found that the number of samples of 5 electrical appliances of the electric iron, the coffee machine, the water kettle, the electric iron and the stirrer is small, so that the samples of the 5 electrical appliances are removed in the verification process of the embodiment of the invention, and the samples of 11 electrical appliance types shown in fig. 6 are selected. The PLAID dataset is then preprocessed to obtain 1824 sets of sample instances, each set of sample instances containing 500 preprocessed steady state voltage and current values. Finally, 1824 groups of load marks are generated by using a load mark construction method, and the training set and the test set are randomly divided according to the ratio of 4:1. And randomly extracting 85% of samples for model common parameter optimization in a training set, and taking the remaining 15% of samples as a verification set for model super parameter optimization. The test set is used to evaluate the overall performance of the model. Based on the constructed training set and verification set, the invention trains a model by using an Adam optimizer. In the training process, the batch_size is set to be 32, the training times are 50, and an Early-stop mechanism is introduced to obtain an optimal load recognition model, wherein the training process is shown in fig. 7. The test set is input into the optimal load recognition model obtained through training for testing, and a final test result is obtained, namely the average accuracy is 98.36%, the average F1 score is 98.45%, and the confusion matrix is shown in FIG. 8. As can be seen from fig. 8, the recognition accuracy of the other electrical devices is 100% except that the recognition rate of the two electrical devices of the refrigerator and the air conditioner is lower than the average accuracy.
In order to further explore factors influencing the load identification performance, the invention aims at the key element design comparison experiment in the load identification model to carry out deep analysis and discussion.
In the process of acquiring and preprocessing load identification data, N needs to be extracted first t Steady-state voltage and current signals of each fundamental wave period, so N t The setting of the value size affects the load identification final performance. For this purpose, the invention designs comparative experiment discussion N t Influence of the value on the load recognition effect. The invention uses N t Set as {5,10,15,20,25}, respectively, and then construct corresponding load marks to complete a comparative experiment, the experimental results are shown in fig. 9. As can be seen from FIG. 9, when N t When the value is low, the load detail information contained in the load mark is insufficient, the load characteristic cannot be fully reflected, and the load identification accuracy and the F1 score are relatively low. When N is t When the value is high, load detail information contained in the load marks is excessive, noise in the load data is amplified, and the load identification effect is poor. When N is t When the load identification effect is optimal in the case of being=20, the identification accuracy and the F1 fraction respectively reach 98.36 percent and 98.45 percent, so that the invention finally uses N t The value is set to 20.
The invention realizes voltage and current characteristic coding and superposition fusion by using the gram angle difference field, and completes load identification through a neural network based on CBAM. Accordingly, it is necessary to discuss the effectiveness of analyzing feature codes and fusion and the load identification capabilities of different neural networks. In the aspect of load characteristics, the invention introduces a V-I track for comparison experiments, and the resolution of the V-I track image is 128 multiplied by 128; in the aspect of neural network, the invention introduces two classical convolutional neural networks ResNet-18 and LeNet-5 for comparison experiments, the network structures of which are shown in FIG. 10 and FIG. 11, and the experimental results are shown in Table 1. As can be seen from Table 1, the load imprinting based on the fusion of the characteristics of the gram angle difference field has better recognition effect compared with the V-I track, and has certain advantages of recognition accuracy and F1 fraction.
Table 1 results of comparative experiments
Figure BDA0004101617360000191
In order to verify the superiority of the method of the invention, the invention is selected to be compared with other literature advanced load identification methods. All literature experiments were performed on PLAID datasets, where literature [11] fused V-I trajectory images with power numerical features and realized load identification through BP neural networks. Document [12] non-invasive load recognition method based on V-I track color coding, using color coded V-I tracks, and using K-means clustering algorithm and AlexNet neural network for recognition. Document [13] a non-invasive load fine granularity recognition method based on color coding, which constructs a load identifier by using RGB color coding fusion characteristics and realizes load recognition by using VGG16 convolutional neural network. The accuracy of each load recognition method is compared with the results shown in table 2.
Table 2 accuracy comparison with other load identification methods
Figure BDA0004101617360000201
As can be seen from Table 2, the method of the present invention is superior to the other 3 advanced load recognition methods in the recognition accuracy of each electrical apparatus as a whole.

Claims (6)

1. A non-invasive load identification method based on the fusion of the characteristics of a gram angle difference field is characterized by comprising the following steps:
step one: preprocessing high-frequency steady-state data acquired by equipment to obtain a complete fundamental wave period current and voltage signal;
step two: encoding the one-dimensional voltage and current signals by using the Graham angle difference field respectively to generate a corresponding two-dimensional characteristic diagram;
step three: and (3) inputting the superposition fusion into a neural network based on a convolution block attention module, and constructing a load identification model to finish load identification.
2. The non-invasive load identification method based on the fusion of the characteristics of the angular difference between the gladhand fields according to claim 1, wherein the specific process of the step one is as follows:
the premise of realizing load identification is that firstly, load characteristics are extracted from high-frequency aggregate signals; assuming that only one electrical equipment generates a switching event at the same moment, the load characteristics of the single electrical equipment can be extracted by calculating the steady-state aggregate signal difference in a short time window before and after the switching event; the active power change difference delta P is used as a judgment basis for detecting switching events of the electrical equipment, and steady-state voltage and current signals of the electrical equipment are extracted from the aggregated voltage and current signals to serve as load characteristics; for easy calculation, v is used respectively off 、i off And v on 、i on The method is characterized in that the method comprises the steps of representing steady-state aggregation voltage and current before an electrical equipment switching event and steady-state aggregation voltage and current after the switching event, and taking an average value of the steady-state aggregation voltage before and after the switching event by the voltage v of single electrical equipment, namely:
Figure FDA0004101617350000011
in contrast, the steady-state aggregate current signal changes due to the occurrence of switching events of the electrical equipment, and the current i of the single electrical equipment is obtained by calculating the difference value of the steady-state aggregate current before and after the switching events, namely:
i＝i on -i off (2)
due to v off And v on And i off And i on The addition and subtraction operation is needed in the same voltage phase, and the waveform of the steady-state voltage signal approximates to a sine wave, so that the voltage positive zero crossing points are selected to be aligned; in addition, the steady-state voltage and current signals change periodicallyThe steady-state voltage and current signals with a single fundamental wave period are used for representing the load characteristics of the electrical equipment, but the state of the electrical equipment is still changed when the electrical equipment stably works, and in order to better represent the load characteristics of the electrical equipment, continuous N is extracted t The steady-state voltage and current signals of each fundamental wave period are averaged to obtain the steady-state voltage and current signals of a complete fundamental wave period, N t ＞1；
Firstly, assume that the sampling frequency of steady-state voltage and current signals of electrical equipment is f s The fundamental frequency is f, the number of samples per fundamental period is N s ＝f s /f，N t The number of samples of each fundamental period is N ts ＝N t ×N s N of electrical equipment k t Steady-state voltage signal with single fundamental wave period
Figure FDA0004101617350000021
And steady state current signal>
Figure FDA0004101617350000022
Then let v k 、i k At v k Each fundamental wave period is aligned at the positive zero crossing point to obtain an aligned steady-state voltage signal +.>
Figure FDA0004101617350000023
And steady state current signal>
Figure FDA0004101617350000024
The following are provided:
Figure FDA0004101617350000025
/>
Figure FDA0004101617350000026
wherein:
Figure FDA0004101617350000027
representing electrical equipment k N ts Steady state voltage values after alignment, +.>
Figure FDA00041016173500000212
Representing electrical equipment k N ts A plurality of aligned steady state current values;
finally, to
Figure FDA0004101617350000028
And->
Figure FDA0004101617350000029
To obtain steady-state voltage signal and current signal one-dimensional vector of a complete fundamental wave period>
Figure FDA00041016173500000210
And->
Figure FDA00041016173500000211
3. The non-invasive load identification method based on the fusion of the characteristics of the gram angle difference field according to claim 2, wherein in the second step, the gram angle difference field is an encoding method for converting a one-dimensional time sequence signal into a two-dimensional image, and the specific encoding steps are as follows:
first, for a composition containing N s Voltage of electrical equipment k obtained by preprocessing of individual time stamps
Figure FDA0004101617350000039
Or current->
Figure FDA00041016173500000310
Normalization processing is performed to normalize the time sequence signal to [ -1,1]In the range, the formula is as follows:
Figure FDA0004101617350000031
wherein: x is x p Representation of
Figure FDA0004101617350000032
Or->
Figure FDA0004101617350000033
P-th value of>
Figure FDA0004101617350000034
Represents x p Normalized value, max represents maximum function, min represents minimum function;
then, the normalized product is
Figure FDA0004101617350000035
Converting from a Cartesian coordinate system to a polar coordinate system, namely converting the numerical value thereof to an angular cosine phi in the polar coordinate system, converting the timestamp to a radius r in the polar coordinate system, and converting the formula as follows:
Figure FDA0004101617350000036
wherein: phi (phi) p An angular cosine representing the p-th value in the polar coordinate system, r p Radius, t, representing the p-th value in a polar coordinate system p A timestamp representing the p-th value; n represents a constant factor generated by regularized polar coordinate system,
Figure FDA0004101617350000037
the representation comprises N s A normalized time sequence signal->
Figure FDA0004101617350000038
This way of representing the timing signal in the polar coordinate system provides a new idea for understanding the timing signal, converting the timing signal to polar coordinatesAfter that, the time sequence signal of each time stamp is used as a one-dimensional measurement space, and the amplitude of the time sequence signal generates bending between different corner points crossing a circle along with the time;
finally, angle difference is carried out on points converted to a polar coordinate system through a sine function to obtain a gram angle difference field characteristic diagram, and time correlation in different time intervals is identified through angle change; the gram angle difference field GADF is defined as follows:
Figure FDA0004101617350000041
wherein:
Figure FDA0004101617350000042
representing the N-th in a polar coordinate system s The angle cosine of the individual values, I representing the unit row vector,/->
Figure FDA0004101617350000043
Representation->
Figure FDA0004101617350000044
Is a transpose of (a).
4. The non-invasive load identification method based on the fusion of the characteristics of the gram angle difference field according to claim 3, wherein the specific process of the step two is as follows:
first, the one-dimensional voltage signal obtained by preprocessing
Figure FDA0004101617350000045
And current signal->
Figure FDA0004101617350000046
Normalized to interval [ -1, 1] according to formula (5)]；
Then, the normalized voltage and current signals are respectively converted into a polar coordinate system by a formula (6), and the angle in the polar coordinate system is used
Figure FDA0004101617350000047
And radius r characterizes its amplitude and timestamp;
then, GADF matrix transformation is performed by the formula (7) to generate 2N-sized products s ×N s Is a two-dimensional feature map of (1);
finally, the two components are overlapped and fused to generate a composite material with the size of 2 XN s ×N s As a load signature; to enhance the feature expression capability of the three-dimensional feature map, each pixel value of the feature map is multiplied by 256 and subjected to a downward rounding process so that the gray value of the feature map ranges from [0,1]The interval becomes 0,255]Between them.
5. The non-invasive load recognition method based on the fusion of the angular difference field features of the gram according to claim 4, wherein in the third step, the convolution block attention module CBAM is composed of a channel attention sub-module and a spatial attention sub-module;
given a feature map F.epsilon.R C×H×W As input, the CBAM sequentially extrapolates the one-dimensional channel attention pattern M c ∈R C×1×1 And two-dimensional space attention to figure M s ∈R 1×H×W The overall attentiveness process is summarized as follows:
Figure FDA0004101617350000048
Figure FDA0004101617350000051
wherein:
Figure FDA0004101617350000052
representing multiplication of corresponding elements one by one, during which the channel attention value is broadcast along the spatial dimension, the spatial attention value is broadcast along the channel dimension, F' represents the channel attention weight, F "represents the most significantThe final output attention weight, R represents real space, C represents the channel number of the feature map, H represents the length of the feature map, and W represents the width of the feature map;
in the channel attention module, firstly, the input feature images are respectively compressed in the space dimension through maximum pooling and average pooling, and two different space feature descriptors are obtained through aggregation:
Figure FDA0004101617350000053
and->
Figure FDA0004101617350000054
The two space feature descriptors are then transferred to a shared network composed of multiple layers of perceptrons to generate a channel attention map M c ∈R C×1×1 The method comprises the steps of carrying out a first treatment on the surface of the To reduce the parameter overhead, the hidden activation size of the multi-layer perceptron is set to R C/β×1×1 Beta is the compression ratio, and the channel attention calculation formula is as follows:
Figure FDA0004101617350000055
wherein: sigma denotes sigmoid function, MLP denotes multi-layer perceptron, avgPool denotes average pooling, maxPool denotes maximum pooling, W 0 ∈R C/r×C And W is 1 ∈R C×C/r Representing the weight of the multi-layer perceptron;
similarly, the spatial attention module first compresses the feature map in the channel dimension using maximum pooling and average pooling to generate two-dimensional feature maps
Figure FDA0004101617350000056
And->
Figure FDA0004101617350000057
Then will->
Figure FDA0004101617350000058
And->
Figure FDA0004101617350000059
The two feature maps are spliced to obtain a three-dimensional feature map containing 2 channel numbers +.>
Figure FDA00041016173500000510
Then the feature map is ++7 with convolution layer of convolution kernel size 7×7>
Figure FDA00041016173500000511
Performing convolution operation to obtain a two-dimensional characteristic diagram +.>
Figure FDA00041016173500000512
Finally, inputting the two-dimensional space attention feature map M into sigmoid function to generate two-dimensional space attention feature map M s ∈R H×W The method comprises the steps of carrying out a first treatment on the surface of the The calculation process of the spatial attention is as follows:
Figure FDA00041016173500000513
wherein: f (f) 7×7 The convolution kernel representing the convolution layer is 7 x 7 in size.
6. The non-invasive load identification method based on the fusion of the characteristics of the gram angle difference field according to claim 5, wherein in the third step, the structure of the constructed load identification model comprises an input unit, a residual unit, a CBAM unit and an output unit;
in the input unit, a size of 2 XN is input through an input layer s ×N s The method comprises the steps of (1) carrying out preliminary feature extraction on the load marks by utilizing a convolution layer, enabling features extracted by the convolution layer to have zero mean and unit variance in order to reduce influence caused by data distribution, adding a batch normalization layer after the convolution layer, and finally reducing feature dimension by 1 maximum pooling layer, so that the calculated amount of a subsequent unit is reduced, and the model training speed is improved; calculation formula of input unit convolution layerThe following are provided:
Figure FDA0004101617350000061
wherein:
Figure FDA0004101617350000062
representing a convolution operation; />
Figure FDA0004101617350000063
Represents the omega weight on the tau convolution kernel; />
Figure FDA0004101617350000064
Representing the omega input value of the convolution operation; b represents bias; reLu denotes the ReLu activation function; x is x l Representing the features obtained by the convolution operation;
the residual unit consists of an identity mapping part and a residual part, and deep feature extraction is carried out on the basis of the input unit, and the expression is as follows:
x l+1 ＝h(x l )+F(x l ,W l ) (13)
wherein: h (x) l )＝W l ′x l Wherein W is l ' represents a 1 x 1 convolution operation in an identity map, which is used to adjust the number of channels of the input and output; f (x) l ,W l ) A mapping function representing the residual portion; x is x l+1 Representing the characteristics obtained after the residual error unit is processed;
the residual part in the residual unit comprises 13 multiplied by 3 convolution layer and 2 1 multiplied by 1 convolution layers, and each convolution layer is connected with 1 batch normalization layer and 1 ReLu activation function; the residual unit is firstly connected with a 1 multiplied by 1 convolution layer, and the channel number is set to 128; then connecting 3×3 convolution layers, setting the channel number to 128, and finally connecting another 1×1 convolution layer, setting the channel number to 512; the feature images extracted by the identity mapping part and the residual part are fused through pixel-by-pixel addition operation; the CBAM unit is accessed to the last layer 1 multiplied by 1 convolution layer of the residual part, so that the whole neural network is focused on important area information of the load imprinting image in the process of extracting the load characteristics, irrelevant area information is ignored, the characteristic learning capacity of the whole network is enhanced, and the performance of a load identification task is further improved;
the output unit consists of 2 full connection layers, is the last unit of the whole neural network and is connected with the residual error unit; the number of the neurons of the two full-connection layers is 128 and K, the activation functions are a Relu function and a softmax function, and K is determined by the number of the types of electrical equipment; to train the entire neural network to obtain optimal parameters, a multi-class cross entropy loss function defined in the back propagation optimization equation (14) is used:
Figure FDA0004101617350000071
in the method, in the process of the invention,
Figure FDA0004101617350000072
a true class one-hot vector representing sample ζ; />
Figure FDA0004101617350000073
A prediction class one-hot vector representing sample ζ; num represents the number of samples; k represents the class to which the sample belongs. />
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CN117093918A (en) * 2023-10-18 2023-11-21 成都信息工程大学 Overlapping spike identification method based on Gellam angle, field and CBAM-Resnet34
CN117132808A (en) * 2023-08-07 2023-11-28 中南民族大学 Multi-load identification method and system based on wavelet mixed convolution

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CN117132808A (en) * 2023-08-07 2023-11-28 中南民族大学 Multi-load identification method and system based on wavelet mixed convolution
CN117132808B (en) * 2023-08-07 2024-02-06 中南民族大学 Multi-load identification method and system based on wavelet mixed convolution
CN117093918A (en) * 2023-10-18 2023-11-21 成都信息工程大学 Overlapping spike identification method based on Gellam angle, field and CBAM-Resnet34

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