CN110490659A - A kind of customer charge curve generation method based on GAN - Google Patents
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Abstract
The customer charge curve generation method based on GAN that the present invention relates to a kind of, belongs to electric system Demand Side Response field.This method comprises: load curve normalizes, builds generation network, builds differentiation network, alternately training generation network, load curve generation.This method is based on GAN (Generative Adversarial Network, generate confrontation network), the implicit statistical nature of truthful data is captured using GAN, and mass users load is generated based on statistical nature, so that the intrinsic distribution characteristics and diversity of user can be followed by generating load data.Magnanimity virtual load data can be generated in the insufficient situation of truthful data using this method, generation data are able to reflect user and really use electrical feature, embody the statistical nature of true load, it is capable of the electricity consumption behavior of analog subscriber multiplicity simultaneously, to substitute simulation of the truthful data for distribution system analysis and Demand Side Response technology.
Description
Technical field
The customer charge curve generation method based on GAN that the present invention relates to a kind of belongs to electric system Demand Side Response neck
Domain.
Background technique
At this stage, power grid is towards intelligence, and distributed, the direction cleaned is developed, along with the deep change of power grid
Leather, for the analysis and research object of electric system, also terminad distribution, terminal user extend since system layer, busbar laminate.
Important component of the customer charge as end distribution is obtaining more and more concerns, many distribution system analysis methods
The support of customer charge data is be unable to do without with the deployment of Demand Side Response technology.However, due to by secret protection law and intelligence
The limitation of energy ammeter popularity, the true load data wretched insufficiency of currently available user, this seriously inhibits phases in field
Close the propulsion of research.
It is, therefore, desirable to provide a kind of customer charge generation method, it is virtual can to generate magnanimity in the case where data deficiencies
Load data, generation data are able to reflect user and really use electrical feature, embody the statistical nature of true load, while being capable of mould
The electricity consumption behavior of quasi- user's multiplicity, to substitute simulation of the truthful data for distribution system analysis and Demand Side Response technology.
Summary of the invention
The purpose of the present invention is to propose to one kind, and based on GAN, (Generative Adversarial Network generates confrontation
Network) customer charge curve generation method supplemented by way of generating data in the insufficient situation of true load data
Data set.
Customer charge curve generation method proposed by the present invention based on GAN the following steps are included:
Step 1: load normalization:
Remember the existing historical load collection of curves of userWherein, every load curve is denoted as:Wherein, T is load length of curve, finds the maxima and minima of user's history load first:
Load value is adjusted between section [- 1,1] according to very big load and minimum load, as follows:
Step 2: build generation network:
It is G that note, which generates network, and the input for generating network is the noise vector z of Gaussian distributed, generates the output of network
It is the simulation load curve x generatedg, it is denoted as:
xg=G (z；θg)
Wherein, θgFor the parameter to be asked in G；
Since load curve is one-dimensional vector, what generation network was actually accomplished is from fixed length one-dimensional vector to fixed length
Mapping between one-dimensional vector, the characteristics of according to neural network, the hidden layer for generating network directly selects full articulamentum, tool
Body is as follows:
The dimension of curve to be generated is 1 × N, therefore the noise vector z length for inputting Gaussian Profile is also 1 × N, wherein z
In each element Normal Distribution, i.e. zi~N (0,1)；
The first layer for generating network is the full articulamentum f containing 2N neuron1, remember that its output is p1, then this layer of operation is fixed
Justice are as follows:
p1=f1(z), wherein z ∈ R1×N, p1∈R1×2N
f1Z is mapped to a twice original higher dimensional space；
The second layer for generating network is the full articulamentum f containing 4N neuron2, remember that its output is p2, then this layer of operation is fixed
Justice are as follows:
p2=f2(p1), wherein p1∈R1×2N, p2∈R1×4N
f2Further by p1It is mapped to a twice original higher dimensional space；
The last layer for generating network is the full articulamentum f containing N number of neuron3, output is formation curve xg, then originally
Layer operation definition are as follows:
xg=f3(p2), wherein p2∈R1×4N, xg∈R1×N
f3Abstract characteristics in higher dimensional space are mapped to real space；
f1、f2、f3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is respectivelyI.e. full articulamentum f1、f2、f3Corresponding mapping mode are as follows:
p1=zA1、p2=p1A2、xg=p2A3
But only introduce affine transformation and model is made to be still linear, and include a large amount of non-thread in load curve
Property, it is therefore desirable to it makes a living into network and non-linear elements is added, so that it is had the ability for establishing nonlinear model, by each time
Can be non-linear for model addition using nonlinear activation function after affine transformation, i.e., in first time and second of affine transformation
Afterwards, as follows using relu activation primitive:
p′1=relu (p1), p'2=relu (p2)
Wherein, relu activation primitive are as follows:
After last time affine transformation, tanh activation primitive is used, it may be assumed that
x'g=tanh (xg)
Wherein, tanh activation primitive are as follows:
By tanh activation primitive by formation curve xgCodomain adjust between section [- 1,1], it is identical as real curve；
It generates in network G, the element in affine matrix is network parameter θg, need to obtain by training；
Step 3: build differentiation network:
Note differentiates that network is D, differentiates that the input of network is load curve x, differentiates that the output of network is that load curve comes from
The probability P of authentic specimen collection, when differentiating that network thinks that load curve is that true probability is bigger, then its output tends to 1, when thinking
Load curve is that the probability of generation is bigger, then its output tends to 0, is denoted as:
P=D (x；θd)
Wherein, θdFor the parameter to be asked in D；
Since load curve is one-dimensional vector, what differentiation network was actually accomplished is from fixed length one-dimensional vector to numerical value
Mapping between section [0,1] the characteristics of according to neural network, differentiates that the hidden layer of network directly selects full articulamentum,
It is specific as follows:
The dimension of curve to be discriminated is 1 × N, differentiates that the first layer of network is the full articulamentum d containing 4N neuron1,
Remember that its output is q1, then this layer of operation definition are as follows:
q1=d1(x), wherein x ∈ R1×N, q1∈R1×4N
d1X is mapped to one and is four times in original higher dimensional space；
The second layer for differentiating network is the full articulamentum d containing 2N neuron2, remember that its output is q2, then this layer of operation is fixed
Justice are as follows:
q2=d2(q1), wherein q1∈R1×4N, q2∈R1×2N
d2By q1A half is mapped in original lower dimensional space；
The last layer for differentiating network is the full articulamentum d containing N number of neuron3, output is to sentence to curve source
Other probability P, then this layer of operation definition are as follows:
P=d3(q2), wherein q2∈R1×2N, P ∈ [0,1]
d1、d2、d3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is B respectively1∈RN×4N、B2∈
R4N×2N、B3∈R2N×N, i.e., full articulamentum d1、d2、d3Corresponding mapping mode are as follows:
q1=xB1、q2=q1B2, P=q2B3
It is similarly and differentiates that nonlinear element is added in network, i.e., for the first time and after second of affine transformation, use leaky-
Relu activation primitive, as follows:
q′1=leaky-relu (q1), q'2=leaky-relu (q2)
Wherein, leaky-relu activation primitive are as follows:
After last time affine transformation, Sigmoid activation primitive is used, it may be assumed that
P'=Sigmoid (P)
Wherein, Sigmoid activation primitive are as follows:
The codomain of P is adjusted between section [0,1] by Sigmoid activation primitive, it is made to have probability attribute；
Differentiate in network D, the element in affine matrix is network parameter θd, need to obtain by training；
Step 4: network training:
Neural network obtains the optimal estimation of parameter by gradient descent algorithm, and this method model includes two networks, and two
A network is alternately trained, and another party fixes when a side trains, therefore also using the optimization algorithm declined based on gradient；
Firstly, definition differentiates the training objective function of network, differentiate that network should make it become the output of real curve
In 1,0 is tended to the output of formation curve, two classification is introduced herein and intersects entropy function:
Wherein,For predicted value, y true value, the correlated variables to real curve, in above formula are as follows:
Correlated variables to formation curve, in above formula are as follows:
The correlated variables of the above real curve and formation curve is substituted into two classification respectively and intersects entropy function, the friendship that will be obtained
It pitches entropy function to be added, then has:
lossD=-ln (D (xi；θd))-ln(1-D(xg；θd))
The training objective for differentiating network is so that loss function reaches minimum, it is contemplated that the second part derivation of above formula right end
Difficulty, by its further abbreviation are as follows:
lossD=-ln (D (xi；θd))+ln(D(xg；θd))
Wherein, xg=G (z；θg), therefore have:
lossD=-ln (D (xi；θd))+ln(D(G(z；θg)；θd))
Meanwhile needing to make a living into network objective function, the target of generating function is that formation curve is passed through
The detection for differentiating network is thought to generate net when differentiating that network can not differentiate the difference between formation curve and real curve
Network training finishes, and real curve can be replaced to be used as subsequent analysis with formation curve, therefore generating network should to differentiate network
1 is tended to the output of formation curve, it is same to introduce two classification intersection entropy functions, have at this time:
lossG=-ln (D (xg；θd))=- ln (D (G (z；θg)；θd))
Differentiate that network replaces training with network is generated, target is so that respective loss function lossDAnd lossGIt minimizes,
When a network training, the parameter of another network is fixed；
When training starts, remember that training round is 0, sampling to obtain according to normal distribution N (0,0.01) generates network and differentiation
The parameter of network is denoted asWithWhen t takes turns training beginning previous existence into network and differentiates that the parameter of network is denoted asWithThis
When generation network and differentiate network loss function be denoted asWithThe parameter of network at the end of then t wheel is trained
Are as follows:
Wherein:
α is learning rate, is arranged between 0.0002~0.0001；
The judge index ε that training completion is arranged is 0.0001, if meeting after T wheel training:
Then think to train completion, save current network parameter, be denoted as:
At this point, magnanimity Virtual User curve can be generated with network is generated:
Wherein, z ∈ R1×NAnd zi~N (0,1),For the optimized parameter that training obtains, the curve that generation network is exported
Normalization is carried out to get formation curve is arrived:
The beneficial effects of the present invention are:
This method is realized based on GAN, captures the implicit statistical nature of truthful data using GAN, and raw based on statistical nature
At mass users load, so that the intrinsic distribution characteristics and diversity of user can be followed by generating load data.Utilize this
Method can generate magnanimity virtual load data in the insufficient situation of truthful data, and it is true that generation data are able to reflect user
With electrical feature, the statistical nature of true load is embodied, while capableing of the electricity consumption behavior of analog subscriber multiplicity, thus the true number of substitution
According to the simulation for distribution system analysis and Demand Side Response technology.
Specific embodiment
Embodiment 1:
Customer charge curve generation method proposed by the present invention based on GAN the following steps are included:
Step 1: load normalization:
Remember the existing historical load collection of curves of userWherein, every load curve is denoted as:Wherein, T is load length of curve, finds the maxima and minima of user's history load first:
Load value is adjusted between section [- 1,1] according to very big load and minimum load, as follows:
Step 2: build generation network:
It is G that note, which generates network, and the input for generating network is the noise vector z of Gaussian distributed, generates the output of network
It is the simulation load curve x generatedg, it is denoted as:
xg=G (z；θg)
Wherein, θgFor the parameter to be asked in G；
Since load curve is one-dimensional vector, what generation network was actually accomplished is from fixed length one-dimensional vector to fixed length
Mapping between one-dimensional vector, the characteristics of according to neural network, the hidden layer for generating network directly selects full articulamentum, tool
Body is as follows:
The dimension of curve to be generated is 1 × N, therefore the noise vector z length for inputting Gaussian Profile is also 1 × N, wherein z
In each element Normal Distribution, i.e. zi~N (0,1)；
The first layer for generating network is the full articulamentum f containing 2N neuron1, remember that its output is p1, then this layer of operation is fixed
Justice are as follows:
p1=f1(z), wherein z ∈ R1×N, p1∈R1×2N
f1Z is mapped to a twice original higher dimensional space；
The second layer for generating network is the full articulamentum f containing 4N neuron2, remember that its output is p2, then this layer of operation is fixed
Justice are as follows:
p2=f2(p1), wherein p1∈R1×2N, p2∈R1×4N
f2Further by p1It is mapped to a twice original higher dimensional space；
The last layer for generating network is the full articulamentum f containing N number of neuron3, output is formation curve xg, then originally
Layer operation definition are as follows:
xg=f3(p2), wherein p2∈R1×4N, xg∈R1×N
f3Abstract characteristics in higher dimensional space are mapped to real space；
f1、f2、f3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is A respectively1∈RN×2N、A2∈
R2N×4N、A3∈R4N×N, therefore the three-decker generated in network can be summarized as following table:
| Full articulamentum | Affine matrix | Input vector | Output vector | Mapping mode |
| f1 | A1∈RN×2N | z∈R1×N | p1∈R1×2N | p1=zA1 |
| f2 | A2∈R2N×4N | p1∈R1×2N | p2∈R1×4N | p2=p1A2 |
| f3 | A3∈R4N×N | p2∈R1×4N | xg∈R1×N | xg=p2A3 |
It can see full articulamentum f1、f2、f3Corresponding mapping mode are as follows:
p1=zA1、p2=p1A2、xg=p2A3
But only introduce affine transformation and model is made to be still linear, and include a large amount of non-thread in load curve
Property, it is therefore desirable to it makes a living into network and non-linear elements is added, so that it is had the ability for establishing nonlinear model, by each time
Can be non-linear for model addition using nonlinear activation function after affine transformation, i.e., in first time and second of affine transformation
Afterwards, as follows using relu activation primitive:
p′1=relu (p1), p'2=relu (p2)
Wherein, relu activation primitive are as follows:
After last time affine transformation, tanh activation primitive is used, it may be assumed that
x'g=tanh (xg)
Wherein, tanh activation primitive are as follows:
By tanh activation primitive by formation curve xgCodomain adjust between section [- 1,1], it is identical as real curve；
It generates in network G, the element in affine matrix is network parameter θg, need to obtain by training；
Step 3: build differentiation network:
Note differentiates that network is D, differentiates that the input of network is load curve x, differentiates that the output of network is that load curve comes from
The probability P of authentic specimen collection, when differentiating that network thinks that load curve is that true probability is bigger, then its output tends to 1, when thinking
Load curve is that the probability of generation is bigger, then its output tends to 0, is denoted as:
P=D (x；θd)
Wherein, θdFor the parameter to be asked in D；
Since load curve is one-dimensional vector, what differentiation network was actually accomplished is from fixed length one-dimensional vector to numerical value
Mapping between section [0,1] the characteristics of according to neural network, differentiates that the hidden layer of network directly selects full articulamentum,
It is specific as follows:
The dimension of curve to be discriminated is 1 × N, differentiates that the first layer of network is the full articulamentum d containing 4N neuron1,
Remember that its output is q1, then this layer of operation definition are as follows:
q1=d1(x), wherein x ∈ R1×N, q1∈R1×4N
d1X is mapped to one and is four times in original higher dimensional space；
The second layer for differentiating network is the full articulamentum d containing 2N neuron2, remember that its output is q2, then this layer of operation is fixed
Justice are as follows:
q2=d2(q1), wherein q1∈R1×4N, q2∈R1×2N
d2By q1A half is mapped in original lower dimensional space；
The last layer for differentiating network is the full articulamentum d containing N number of neuron3, output is to sentence to curve source
Other probability P, then this layer of operation definition are as follows:
P=d3(q2), wherein q2∈R1×2N, P ∈ [0,1]
d1、d2、d3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is B respectively1∈RN×4N、B2∈
R4N×2N、B3∈R2N×N, therefore differentiate that the three-decker in network can be summarized as following table:
| Full articulamentum | Affine matrix | Input vector | Output vector | Mapping mode |
| d1 | B1∈RN×4N | x∈R1×N | q1∈R1×4N | q1=xB1 |
| d2 | B2∈R4N×2N | q1∈R1×4N | q2∈R1×2N | q2=q1B2 |
| d3 | B3∈R2N×N | q2∈R1×2N | P∈[0,1] | P=q2B3 |
It can see full articulamentum d1、d2、d3Corresponding mapping mode are as follows:
q1=xB1、q2=q1B2, P=q2B3
It is similarly and differentiates that nonlinear element is added in network, i.e., for the first time and after second of affine transformation, use leaky-
Relu activation primitive, as follows:
q′1=leaky-relu (q1), q'2=leaky-relu (q2)
Wherein, leaky-relu activation primitive are as follows:
After last time affine transformation, Sigmoid activation primitive is used, it may be assumed that
P'=Sigmoid (P)
Wherein, Sigmoid activation primitive are as follows:
The codomain of P is adjusted between section [0,1] by Sigmoid activation primitive, it is made to have probability attribute；
Differentiate in network D, the element in affine matrix is network parameter θd, need to obtain by training；
Step 4: network training:
Neural network obtains the optimal estimation of parameter by gradient descent algorithm, and this method model includes two networks, and two
A network is alternately trained, and another party fixes when a side trains, therefore also using the optimization algorithm declined based on gradient；
Firstly, definition differentiates the training objective function of network, differentiate that network should make it become the output of real curve
In 1,0 is tended to the output of formation curve, two classification is introduced herein and intersects entropy function:
Wherein,For predicted value, y true value, the correlated variables to real curve, in above formula are as follows:
Correlated variables to formation curve, in above formula are as follows:
The correlated variables of the above real curve and formation curve is substituted into two classification respectively and intersects entropy function, the friendship that will be obtained
It pitches entropy function to be added, then has:
lossD=-ln (D (xi；θd))-ln(1-D(xg；θd))
The training objective for differentiating network is so that loss function reaches minimum, it is contemplated that the second part derivation of above formula right end
Difficulty, by its further abbreviation are as follows:
lossD=-ln (D (xi；θd))+ln(D(xg；θd))
Wherein, xg=G (z；θg), therefore have:
lossD=-ln (D (xi；θd))+ln(D(G(z；θg)；θd))
Meanwhile needing to make a living into network objective function, the target of generating function is that formation curve is passed through
The detection for differentiating network is thought to generate net when differentiating that network can not differentiate the difference between formation curve and real curve
Network training finishes, and real curve can be replaced to be used as subsequent analysis with formation curve, therefore generating network should to differentiate network
1 is tended to the output of formation curve, it is same to introduce two classification intersection entropy functions, have at this time:
lossG=-ln (D (xg；θd))=- ln (D (G (z；θg)；θd))
Differentiate that network replaces training with network is generated, target is so that respective loss function lossDAnd lossGIt minimizes,
When a network training, the parameter of another network is fixed；
When training starts, remember that training round is 0, sampling to obtain according to normal distribution N (0,0.01) generates network and differentiation
The parameter of network is denoted asWithWhen t takes turns training beginning previous existence into network and differentiates that the parameter of network is denoted asWithThis
When generation network and differentiate network loss function be denoted asWithThe parameter of network at the end of then t wheel is trained
Are as follows:
Wherein:
α is learning rate, is arranged between 0.0002~0.0001；
The judge index ε that training completion is arranged is 0.0001, if meeting after T wheel training:
Then think to train completion, save current network parameter, be denoted as:
At this point, magnanimity Virtual User curve can be generated with network is generated:
Wherein, z ∈ R1×NAnd zi~N (0,1),For the obtained optimized parameter of training, to generate the curve of network output into
Row goes normalization to get formation curve is arrived:
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention.For those of ordinary skill in the art, may be used also on the basis of the above description
To make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.It is all this
Made any modifications, equivalent replacements, and improvements etc., should be included in the claims in the present invention within the spirit and principle of invention
Protection scope within.
Claims (1)
1. a kind of customer charge curve generation method based on GAN, which comprises the following steps:
Step 1: load normalization:
Remember the existing historical load collection of curves of userWherein, every load curve is denoted as:Wherein, T is load length of curve, finds the maxima and minima of user's history load first:
Load value is adjusted between section [- 1,1] according to very big load and minimum load, as follows:
Step 2: build generation network:
It is G that note, which generates network, and the input for generating network is the noise vector z of Gaussian distributed, and it is raw for generating the output of network
At simulation load curve xg, it is denoted as:
xg=G (z；θg)
Wherein, θgFor the parameter to be asked in G；
Since load curve is one-dimensional vector, what generation network was actually accomplished is one-dimensional from fixed length one-dimensional vector to fixed length
Mapping between vector, the hidden layer for generating network directly selects full articulamentum, specific as follows:
The dimension of curve to be generated is 1 × N, therefore the noise vector z length for inputting Gaussian Profile is also 1 × N, wherein in z
Each element Normal Distribution, i.e. zi~N (0,1)；
The first layer for generating network is the full articulamentum f containing 2N neuron1, remember that its output is p1, then this layer of operation definition
Are as follows:
p1=f1(z), wherein z ∈ R1×N, p1∈R1×2N
f1Z is mapped to a twice original higher dimensional space；
The second layer for generating network is the full articulamentum f containing 4N neuron2, remember that its output is p2, then this layer of operation definition
Are as follows:
p2=f2(p1), wherein p1∈R1×2N, p2∈R1×4N
f2Further by p1It is mapped to a twice original higher dimensional space；
The last layer for generating network is the full articulamentum f containing N number of neuron3, output is formation curve xg, then this layer is transported
It calculates is defined as:
xg=f3(p2), wherein p2∈R1×4N, xg∈R1×N
f3Abstract characteristics in higher dimensional space are mapped to real space；
f1、f2、f3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is A respectively1∈RN×2N、A2∈R2N ×4N、A3∈R4N×N, i.e., full articulamentum f1、f2、f3Corresponding mapping mode are as follows:
p1=zA1、p2=p1A2、xg=p2A3
But introduce affine transformation and model made to be still linear, and include in load curve it is a large amount of non-linear, therefore
It needs to make a living into network and non-linear elements is added, so that it is had the ability for establishing nonlinear model, by affine change each time
Can be non-linear for model addition using nonlinear activation function after changing, i.e., for the first time and after second of affine transformation, use
Relu activation primitive, as follows:
p'1=relu (p1), p'2=relu (p2)
Wherein, relu activation primitive are as follows:
After last time affine transformation, tanh activation primitive is used, it may be assumed that
x'g=tanh (xg)
Wherein, tanh activation primitive are as follows:
By tanh activation primitive by formation curve xgCodomain adjust between section [- 1,1], it is identical as real curve；
It generates in network G, the element in affine matrix is network parameter θg, need to obtain by training；
Step 3: build differentiation network:
Note differentiates that network is D, differentiates that the input of network is load curve x, and the output for differentiating network is load curve from true
The probability P of sample set, when differentiating that network thinks that load curve is that true probability is bigger, then its output tends to 1, when thinking load
Curve is that the probability of generation is bigger, then its output tends to 0, is denoted as:
P=D (x；θd)
Wherein, θdFor the parameter to be asked in D；
Since load curve is one-dimensional vector, what differentiation network was actually accomplished is from fixed length one-dimensional vector to numerical intervals
Mapping between [0,1] differentiates that the hidden layer of network directly selects full articulamentum, specific as follows:
The dimension of curve to be discriminated is 1 × N, differentiates that the first layer of network is the full articulamentum d containing 4N neuron1, remember that its is defeated
It is out q1, then this layer of operation definition are as follows:
q1=d1(x), wherein x ∈ R1×N, q1∈R1×4N
d1X is mapped to one and is four times in original higher dimensional space；
The second layer for differentiating network is the full articulamentum d containing 2N neuron2, remember that its output is q2, then this layer of operation definition
Are as follows:
q2=d2(q1), wherein q1∈R1×4N, q2∈R1×2N
d2By q1A half is mapped in original lower dimensional space；
The last layer for differentiating network is the full articulamentum d containing N number of neuron3, output is the differentiation probability to curve source
P, then this layer of operation definition are as follows:
P=d3(q2), wherein q2∈R1×2N, P ∈ [0,1]
d1、d2、d3It is substantially linear affine operation, the corresponding parameter matrix of every step operation is B respectively1∈RN×4N、B2∈R4N ×2N、B3∈R2N×N, i.e., full articulamentum d1、d2、d3Corresponding mapping mode are as follows:
q1=xB1、q2=q1B2, P=q2B3
It is similarly and differentiates that nonlinear element is added in network, i.e., for the first time and after second of affine transformation, use leaky-relu
Activation primitive, as follows:
q'1=leaky-relu (q1), q'2=leaky-relu (q2)
Wherein, leaky-relu activation primitive are as follows:
After last time affine transformation, Sigmoid activation primitive is used, it may be assumed that
P'=Sigmoid (P)
Wherein, Sigmoid activation primitive are as follows:
The codomain of P is adjusted between section [0,1] by Sigmoid activation primitive, it is made to have probability attribute；
Differentiate in network D, the element in affine matrix is network parameter θd, need to obtain by training；
Step 4: network training:
Neural network obtains the optimal estimation of parameter by gradient descent algorithm, and this method model includes two networks, two nets
Network is alternately trained, and another party fixes when a side trains, therefore also using the optimization algorithm declined based on gradient；
Firstly, definition differentiates the training objective function of network, differentiate that network should make it tend to 1 to the output of real curve,
0 is tended to the output of formation curve, two classification is introduced herein and intersects entropy function:
Wherein,For predicted value, y true value, the correlated variables to real curve, in above formula are as follows:
Correlated variables to formation curve, in above formula are as follows:
The correlated variables of the above real curve and formation curve is substituted into two classification respectively and intersects entropy function, the cross entropy that will be obtained
Function is added, then is had:
lossD=-ln (D (xi；θd))-ln(1-D(xg；θd))
Differentiating the training objective of network is so that loss function reaches minimum, it is contemplated that the second part derivation of above formula right end is tired
Difficulty, by its further abbreviation are as follows:
lossD=-ln (D (xi；θd))+ln(D(xg；θd))
Wherein, xg=G (z；θg), therefore have:
lossD=-ln (D (xi；θd))+ln(D(G(z；θg)；θd))
Meanwhile needing to make a living into network objective function, the target of generating function is that formation curve is enabled to pass through differentiation
The detection of network is thought to generate network instruction when differentiating that network can not differentiate the difference between formation curve and real curve
White silk finishes, and real curve can be replaced to be used as subsequent analysis with formation curve, therefore generating network should to differentiate network to life
Tend to 1 at the output of curve, it is same to introduce two classification intersection entropy functions, have at this time:
lossG=-ln (D (xg；θd))=- ln (D (G (z；θg)；θd))
Differentiate that network replaces training with network is generated, target is so that respective loss function lossDAnd lossGIt minimizes, when one
When a network training, the parameter of another network is fixed；
When training starts, remember that training round is 0, sampling to obtain according to normal distribution N (0,0.01) generates network and differentiation network
Parameter be denoted asWithWhen t takes turns training beginning previous existence into network and differentiates that the parameter of network is denoted asWithAt this time
Generation network and differentiate network loss function be denoted asWithThe parameter of network at the end of then t wheel is trained
Are as follows:
Wherein:
α is learning rate, is arranged between 0.0002~0.0001；
The judge index ε that training completion is arranged is 0.0001, if meeting after T wheel training:
Then think to train completion, save current network parameter, be denoted as:
At this point, generating magnanimity Virtual User curve with network is generated:
Wherein, z ∈ R1×NAnd zi~N (0,1),For the optimized parameter that training obtains, the curve for generating network output is gone
It normalizes to get formation curve is arrived:
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