CN117009784A - Cloud-to-ground flash characteristic signal identification method for distributed cut space mapping - Google Patents
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Abstract
The invention provides a method for identifying cloud-to-ground flash characteristic signals of distributed tangential space mapping, and belongs to the technical field of lightning electric field signal analysis. The method solves the problem that the lightning low-frequency electric field signal is very easy to be interfered by environmental noise, so that the acquired data cannot embody real characteristic information. The technical proposal is as follows: the method comprises the following steps: step one, framing processing of lightning electric field signals; step two, extracting arrangement entropy features of lightning electric field signals based on distributed local mean decomposition; step three, a local tangential space arrangement reconstruction ELM lightning electric field signal processing method; and step four, fitting the lightning electric field signals through the model, so that a cloud-to-ground flash type identification result is obtained by using the distributed signal acquisition device. The beneficial effects of the invention are as follows: the invention can effectively improve the filtering capability of the lightning electric field signal and extract the lightning characteristic information.
Description
Technical Field
The invention relates to the technical field of lightning electric field signal analysis, in particular to a cloud-to-ground flash characteristic signal identification method for distributed tangential space mapping.
Background
Lightning is one of the serious main natural disasters, can cause forest and oil depot fires, cause power supply and communication information system faults or damages, and has great threat to aerospace, mines, some important and sensitive high-technology equipment and the like. After eighties, the damage caused by lightning is significantly increased, and particularly in the fields with close relation with high and new technologies, such as aerospace, national defense, communication, electric power, computer, electronic industry and the like, the probability of being struck by lightning is greatly increased due to wide application of large-scale and ultra-large-scale integrated circuits extremely sensitive to lightning electromagnetic interference.
Compared with cloud flash, the ground flash has larger damage to the personal and property safety of the ground. And distinguishing cloud flash from ground flash is important to physical research of lightning, thunderstorm prediction and improvement of lightning protection technology. Research on lightning discharge characteristics is continuously carried out by scientific research teams, different lightning initial positions, charge structures and lightning transmission forms can influence the subsequent discharge types of lightning, and whether the lightning finally develops into ground flash or cloud flash is limited by a plurality of conditions is difficult to predict.
Ground flash and cloud flash have different discharge characteristics in the development process. For example, ground flash, the leading in the cloud-out direction goes through the processes of pre-breakdown, leading step development, back striking and the like, and all the processes have unique discharge characteristics. The characteristics of the electric field waveform of the discharge in these processes can be analyzed to distinguish cloud-to-ground flashovers, such as literature lightning electric field variation waveform time domain characteristic analysis and discharge type identification (weather, that is, cloud-to-ground flashovers are identified by the characteristics of the electric field waveform (pulse waveform rise time, width, etc.), but the identification is only performed by individual pulse waveform characteristics, which is not efficient.
The document EMD and fractal theory-based lightning electric field signal identification research (university of northwest university (2019)) researches the fractal characteristics of the lightning electric field signal, and the support vector machine is used for extracting and identifying the characteristics of the lightning electric field signal. This gives a new idea of identifying cloud-to-earth flash signals, but there are still problems: if only single-station data is adopted for signal analysis, the accuracy of the signals is very dependent, and lightning low-frequency electric field signals are very easy to be interfered by environmental noise, the environmental noise can be white noise, and the environmental noise can also be noise with wider frequency band and can not confirm sources, so that the acquired data can not embody real characteristic information.
How to solve the technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a method for identifying lightning characteristic signals of distributed cut-space mapping; the space-slicing lightning electric field signal processing method based on the distributed local mean decomposition entropy can obtain relatively real lightning electric field characteristic information, so that a precise cloud-to-ground flash type identification result is provided.
In order to achieve the aim of the invention, the invention adopts the technical scheme that:
a method of identifying lightning signature signals for distributed cut-space mapping, the method comprising the steps of:
step one, framing processing of lightning electric field signals;
step two, extracting arrangement entropy features of lightning electric field signals based on distributed local mean decomposition;
step three, a local tangential space arrangement reconstruction ELM lightning electric field signal processing method;
and step four, fitting the lightning electric field signals through the model, so that a cloud-to-ground flash type identification result is obtained by using the distributed signal acquisition device.
In the first step, N sampling points of each acquisition station are selected as standard length of time-frequency processing, a data segment formed by the N sampling points is called a frame, and in order to avoid the occurrence of a lightning electric field signal between two frames and influence analysis and feature extraction of the signal, each frame comprises M sampling points of the previous frame; wherein, N and M are constants, and the value of N is larger than the sampling point number contained in the lightning process period.
In the second step, the second step is to carry out the process,
the traditional method for acquiring information by a single station has limited information quantity, and for increasingly complex space environments, signal detection data are extremely easy to be interfered by environmental noise, more space diversity is acquired through distributed observation, and more information beneficial to lightning electric fields is acquired. By combining an information theory method and through partial mean decomposition-arrangement entropy characteristics, a signal space and a noise space can be effectively separated, and entropy characteristics capable of representing cloud-to-ground flash signals are obtained.
The lightning electric field signal of a single acquisition station is x p (t), wherein p is the acquisition station number and t is time; calculating a local mean function m ji (t) and envelope estimation function a ji (t)：
Wherein m is ji (t) is a local mean Function of an ith PF component (Product Function component, PF component for short), which is a Product Function of physical significance of a plurality of instantaneous frequencies decomposed by lightning electric field signals, of the jth acquisition station; a, a ji (t) is the j-thAn envelope estimation function of an ith PF component of the acquisition station; n is n i Is x p (t) at t i Extreme points of time;
all extreme points are connected and smooth treatment is carried out; will local mean function m ji (t) from the original signal x p Separating and dividing the envelope estimation function in (t) to obtain:
where x (t) is the original lightning signal acquired by the first acquisition station. s is(s) 11 (t) is the PF component.
If s 11 (t) the satisfying range is [ -1,1]And a 11 (t) =1, then s 11 (t) is the first PF component, and let x (t) =x (t) -s 11 (t) continuing to calculate a second PF component according to equations (1) (2) (3); if the condition is not satisfied, repeating the formulas (1), (2) and (3) until the signal is iterated:
multiplying all the iterated envelope estimation functions to obtain an envelope signal of the first iteration:
signal s 1n (t) and envelope signal a 1 (t) multiplying to obtain a first PF component:
PF 1 (t)＝a 1 (t)s 1n (t) (6)
PF is set to 1 (t) separating from the original signal x (t), the remainder being:
u 1 (t)＝x(t)-PF 1 (t) (7)
will u 1 (t) repeating the above steps as an original signal to obtain a subsequent PF component; the following holds in the iteration process:
then, for each calculated PF component (PF i (t), i=1, 2, …, k) performing phase space reconstruction, with an embedding dimension of m and a time delay of t; then k subsequences are obtained:
k＝n-(m-1)t (9)
and arranging the sequences according to the size relations, and calculating the probability P of each size relation arrangement:
P＝Z/k (10)
wherein Z is the number of times of arrangement occurrence; each PF component information entropy is:
wherein m is the number of arrangement possibilities of the arrangement relation;
then the jth PF component of the ith base station signal is characterized byThe total feature PF is:
in the third step
The information obtained by the distributed observation station contains more information, but the fitting difficulty of the high-dimensional characteristics to the lightning location function is higher. By adopting the method of local cut space arrangement, the high-dimensional features can be effectively mapped and reconstructed, and the influence of the redundancy of the high-dimensional features on function fitting is reduced.
Firstly, mapping high-dimensional characteristics (data with dimension more than 3) PE of a lightning electric field signal by utilizing principal component analysis PCA (Principal Component Analysis, PCA) to obtain a main body subspace; let the conversion matrix be A pca Obtaining low-dimensional characteristics (data with dimensions less than or equal to 3 and greater than 0) C= [ C ] 1 ,c 2 ,…,c N ]；
Secondly, constructing Euclidean distances among data points by using a K nearest neighbor algorithm; and calculate C i H k Singular eigenvectors corresponding to q maximum right singular values, solving a local low-dimensional space matrix V, and calculating W i ＝H k (I-V i V i T ) The method comprises the steps of carrying out a first treatment on the surface of the Where H is a centralised matrix, i.e. h=i-ee T N, I is the identity matrix, e is the N-dimensional column vector with element 1, N is the number of features. q is a set dimension value, and samples are generally estimated by maximum likelihood value estimation, so as to obtain a latitude value. i is the class of the sample, k is the sample centering matrix corresponding to the class i
Then, let the initial arrangement matrix b=0, and calculate B (I i ,I i )＝B(I i ,I i )+W i W i T The method comprises the steps of carrying out a first treatment on the surface of the Calculating the characteristic value and the characteristic vector of the generalized characteristic problem:
XH N BH N C T α＝λXH N C T α (13)
eigenvalue lambda 1 ＜λ 2 …＜λ q The corresponding feature vector is alpha 1 ,α 2 …α q Then A lltsa ＝(α 1 ,α 2 …α q ) The method comprises the steps of carrying out a first treatment on the surface of the The transformation matrix a=a pca A lltsa The lightning low-dimensional characteristic coordinate is Y=A T CH N ；
Setting the number of hidden layer neurons to L, the activation function to g (), the mathematical description of the extreme learning machine (Extreme Learning Machine, ELM) is expressed as:
where j=1, 2, …, N, ω i For the connection weight of the input node and the ith hidden layer neuron, beta i Connection weight for i-th hidden neuron and output node, b i Bias for the ith hidden layer neuron.
Approximation with zero errorN samples (X) i ,t i ) And meet the followingWherein O is j The actual output value of ELM algorithm for the jth sample, t j Is the actual value of the j-th sample. Beta is then i ，ω i ，b i The method meets the following conditions:
the above can be abbreviated as:
wherein the method comprises the steps ofBeta is an output weight matrix, and T is a desired output matrix; then the output weight β=h + T；
H + The Moore-Penrose generalized inverse of the matrix H is output for the hidden layer.
Compared with the prior art, the invention has the beneficial effects that:
1. compared with the traditional single-station sensor signal processing method, more information capable of representing cloud-to-ground flash type characteristics can be obtained through distributed information acquisition.
2. The local mean decomposition-permutation entropy features can effectively separate signal space and noise space information, and feature information capable of effectively representing cloud-to-ground flash types is obtained by combining an information theory method.
3. The local cut space reconstruction ELM lightning electric field signal processing method reduces the influence of multi-base high-dimensional information on the fitting of the lightning electric field signal function, avoids the restriction of invalid characteristics on ELM classification performance, and ensures the identification precision of a distributed system on cloud-to-ground flash types.
4. In summary, compared with the traditional method, the invention has new improvements and innovations in the aspects of noise separation, feature extraction, positioning method and the like, and can effectively improve the lightning electric field signal filtering capability and extract lightning feature information.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a schematic flow chart of the method of the invention.
FIG. 2 is a graph of the three-dimensional entropy values before the partial cut space arrangement mapping according to the present invention.
FIG. 3 is a graph showing the characteristics of the three-dimensional entropy values after the partial cut space arrangement mapping according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Example 1:
FIG. 1 illustrates the implementation and calculation process of the proposed method; 8 lightning observation stations with average distance of 15 km are adopted to synchronously collect lightning electric field signals of one thunderstorm. Each station is provided with a fast antenna and mainly comprises a sensing plate, an amplifier and an RC charge-discharge circuit. When lightning in the atmosphere breaks down and discharges, the ambient electric field around the fast antenna sensing plate causes an induced current. By adjusting the parameters of the RC-circuit, different time constants (τ) can be obtained. The effective band range of the fast antenna is 1.5kHz to 2MHz, and the time constant is 100 mus. And carrying out local mean decomposition on the collected lightning electric field signals, and extracting corresponding permutation entropy to form a high-dimensional entropy characteristic. Thereby constituting a Gao Weishang value feature. And then reconstructing the high-dimensional features through partial cut space arrangement to remove feature redundancy. And finally, establishing an ELM cloud-to-ground flash identification model by using the reconstructed feature set, and identifying the cloud-to-ground flash type.
Fig. 2 shows a spatial distribution of the front three-dimensional features of the Gao Weishang value feature. As can be seen from the figure, in the high-dimensional feature, the two types of distribution are close, and cloud-to-ground flash is difficult to distinguish by the distribution distance between the different types.
Fig. 3 shows a spatial distribution of the front three-dimensional features of low-dimensional entropy features (features after partial cut spatial arrangement). According to the graph, through the characteristics of the local cut space arrangement, the space distribution of the two cloud-to-ground flash types has obvious difference, and the performance and the accuracy of the cloud-to-ground flash type identification model are improved.
Referring to fig. 1 and 2, the technical scheme provided by the invention is as follows: a method of identifying lightning signature signals for distributed cut-space mapping, the method comprising the steps of:
step one, framing processing of lightning electric field signals;
step two, extracting arrangement entropy features of lightning electric field signals based on distributed local mean decomposition;
step three, a local tangential space arrangement reconstruction ELM lightning electric field signal processing method;
and step four, fitting the lightning electric field signals through the model, so that a cloud-to-ground flash type identification result is obtained by using the distributed signal acquisition device.
In the first step, N sampling points of each acquisition station are selected as standard length of time-frequency processing, a data segment formed by the N sampling points is called a frame, and in order to avoid the occurrence of a lightning electric field signal between two frames and influence analysis and feature extraction of the signal, each frame comprises M sampling points of the previous frame; wherein N and M are constants, the value of N is larger than the sampling point number contained in the lightning process period, and N is set to 2 in the embodiment 23 M takes half of the value of N.
In the second step, the second step is to carry out the process,
the traditional method for acquiring information by a single station has limited information quantity, and for increasingly complex space environments, signal detection data are extremely easy to be interfered by environmental noise, more space diversity is acquired through distributed observation, and more information beneficial to lightning electric fields is acquired. By combining an information theory method and through partial mean decomposition-arrangement entropy characteristics, a signal space and a noise space can be effectively separated, and entropy characteristics capable of representing cloud-to-ground flash signals are obtained.
The lightning electric field signal of a single acquisition station is x p (t), wherein p is the acquisition station number and t is time; calculating a local mean function m ji (t) and envelope estimation function a ji (t)：
Wherein m is ji (t) is a local mean Function of an ith PF component (Product Function component, PF component for short), which is a Product Function of physical significance of a plurality of instantaneous frequencies decomposed by lightning electric field signals, of the jth acquisition station; a, a ji (t) an envelope estimation function for the ith PF component of the jth acquisition station; n is n i Is x p (t) at t i Extreme points of time;
all extreme points are connected and smooth treatment is carried out; will local mean function m ji (t) from the original signal x p Separating and dividing the envelope estimation function in (t) to obtain:
where x (t) is the original lightning signal acquired by the first acquisition station. s is(s) 11 (t) is the PF component.
If s 11 (t) the satisfying range is [ -1,1]And a 11 (t) =1, then s 11 (t) is the first PF component, and let x (t) =x (t) -s 11 (t) continuing to calculate a second PF component according to equations (1) (2) (3); if the condition is not satisfied, repeating the formulas (1), (2) and (3) until the signal is iterated:
multiplying all the iterated envelope estimation functions to obtain an envelope signal of the first iteration:
signal s 1n (t) and envelope signal a 1 (t) multiplying to obtain a first PF component:
PF 1 (t)＝a 1 (t)s 1n (t) (6)
PF is set to 1 (t) separating from the original signal x (t), the remainder being:
u 1 (t)＝x(t)-PF 1 (t) (7)
will u 1 (t) repeating the above steps as an original signal to obtain a subsequent PF component; the following holds in the iteration process:
then, for each calculated PF component (PF i (t), i=1, 2, …, k) performing phase space reconstruction, with an embedding dimension of m and a time delay of t; then k subsequences are obtained:
k＝n-(m-1)t (9)
and arranging the sequences according to the size relations, and calculating the probability P of each size relation arrangement:
P＝Z/k (10)
wherein Z is the number of times of arrangement occurrence; each PF component information entropy is:
wherein m is the number of arrangement possibilities of the arrangement relation;
then the jth PF component of the ith base station signal is characterized byThe total feature PF is:
in the third step
The information obtained by the distributed observation station contains more information, but the fitting difficulty of the high-dimensional characteristics to the lightning location function is higher. By adopting the method of local cut space arrangement, the high-dimensional features can be effectively mapped and reconstructed, and the influence of the redundancy of the high-dimensional features on function fitting is reduced.
Firstly, mapping high-dimensional characteristics (data with dimension more than 3) PE of a lightning electric field signal by utilizing principal component analysis PCA (Principal Component Analysis, PCA) to obtain a main body subspace; let the conversion matrix be A pca Obtaining low-dimensional characteristics (data with dimensions less than or equal to 3 and greater than 0) C= [ C ] 1 ,c 2 ,…,c N ]；
Secondly, constructing Euclidean distances among data points by using a K nearest neighbor algorithm; and calculate C i H k Singular eigenvectors corresponding to q maximum right singular values, solving a local low-dimensional space matrix V, and calculating W i ＝H k (I-V i V i T ) The method comprises the steps of carrying out a first treatment on the surface of the Where H is a centralised matrix, i.e. h=i-ee T N, I is the identity matrix, e is the N-dimensional column vector with element 1, N is the number of features. q is a set dimension value, and samples are generally estimated by maximum likelihood value estimation, so as to obtain a latitude value. i is the class of the sample, k is the sample centering matrix corresponding to the class i
Then, let the initial arrangement matrix b=0, and calculate B (I i ,I i )＝B(I i ,I i )+W i W i T The method comprises the steps of carrying out a first treatment on the surface of the Calculating the characteristic value and the characteristic vector of the generalized characteristic problem:
XH N BH N C T α＝λXH N C T α (13)
eigenvalue lambda 1 ＜λ 2 …＜λ q The corresponding feature vector is alpha 1 ,α 2 …α q Then A lltsa ＝(α 1 ,α 2 …α q ) The method comprises the steps of carrying out a first treatment on the surface of the The transformation matrix a=a pca A lltsa The lightning low-dimensional characteristic coordinate is Y=A T CH N ；
Setting the number of hidden layer neurons to L, the activation function to g (), the mathematical description of the extreme learning machine (Extreme Learning Machine, ELM) is expressed as:
where j=1, 2, …, N, ω i For the connection weight of the input node and the ith hidden layer neuron, beta i Connection weight for i-th hidden neuron and output node, b i Bias for the ith hidden layer neuron.
Approximation of N samples (X) with zero error i ,t i ) And meet the followingWherein O is j The actual output value of ELM algorithm for the jth sample, t j Is the actual value of the j-th sample. Beta is then i ，ω i ，b i The method meets the following conditions:
the above can be abbreviated as:
wherein the method comprises the steps ofBeta is an output weight matrix, and T is a desired output matrix; then the output weight β=h + T；
H + The Moore-Penrose generalized inverse of the matrix H is output for the hidden layer.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (4)
1. The method for identifying the cloud-to-earth flash characteristic signals of the distributed cut space mapping is characterized by comprising the following steps of:
step one, framing processing of lightning electric field signals;
step two, extracting arrangement entropy features of lightning electric field signals based on distributed local mean decomposition;
step three, a local tangential space arrangement reconstruction ELM lightning electric field signal processing method;
and step four, fitting the lightning electric field signals through the model, so that a cloud-to-ground flash type identification result is obtained by using the distributed signal acquisition device.
2. The method for identifying cloud-to-ground flash characteristic signals mapped by distributed space-cutting according to claim 1, wherein in the first step, N sampling points of each acquisition station are selected as standard lengths of time-frequency processing, a data segment formed by the N sampling points is called a frame, and each frame comprises M sampling points of a previous frame; wherein, N and M are constants, and the value of N is larger than the sampling point number contained in the lightning process period.
3. The method for identifying cloud-to-ground flash characteristic signals mapped in distributed space-cutting manner according to claim 2, wherein in the second step, the lightning electric field signal of a single acquisition station is x p (t), wherein p is the acquisition station number and t is time; calculating a local mean function m ji (t) and envelope estimation function a ji (t)：
Wherein m is ji (t) is a local mean function of the ith PF component of the jth acquisition station; a, a ji (t) an envelope estimation function for the ith PF component of the jth acquisition station; n is n i Is x p (t) at t i Extreme points of time;
all extreme points are connected and smooth treatment is carried out; will local mean function m ji (t) from the original signal x p Separating and dividing the envelope estimation function in (t) to obtain:
wherein x (t) is the lightning original signal collected by the first collecting station; s is(s) 11 (t) is the PF component;
if s 11 (t) the satisfying range is [ -1,1]And a 11 (t) =1, then s 11 (t) is the first PF component, and let x (t) =x (t) -s 11 (t) continuing to calculate a second PF component according to equations (1) (2) (3); if the condition is not satisfied, repeating the formulas (1), (2) and (3) until the signal is iterated:
multiplying all the iterated envelope estimation functions to obtain an envelope signal of the first iteration:
signal s 1n (t) and envelope signal a 1 (t) multiplying to obtain a firstThe PF components:
PF 1 (t)＝a 1 (t)s 1n (t) (6)
PF is set to 1 (t) separating from the original signal x (t), the remainder being:
u 1 (t)＝x(t)-PF 1 (t) (7)
will u 1 (t) repeating the above steps as an original signal to obtain a subsequent PF component; the following holds in the iteration process:
for each calculated PF component PF i (t), i=1, 2, k; reconstructing a phase space, wherein the embedding dimension is m, and the time delay is t; then k subsequences are obtained:
k＝n-(m-1)t (9)
and arranging the sequences according to the size relations, and calculating the probability P of each size relation arrangement:
P＝Z/k (10)
wherein Z is the number of times of arrangement occurrence; each PF component information entropy is:
wherein m is the number of arrangement possibilities of the arrangement relation;
then the jth PF component of the ith base station signal is characterized byThe characteristic PE is as follows:
4. the method for identifying cloud-to-ground flash characteristic signals mapped by distributed space-cutting as recited in claim 3, wherein in step three
Mapping the high-dimensional characteristic PE of the lightning electric field signal by utilizing principal component analysis to obtain a main subspace; let the conversion matrix of principal component analysis be A pca Obtaining the low-dimensional feature C= [ C ] 1 ,c 2 ,…,c N ]；
Constructing Euclidean distances among data points by using a K nearest neighbor algorithm; and calculate C i H k Singular eigenvectors corresponding to q maximum right singular values, solving a local low-dimensional space matrix V, and calculating W i ＝H k (I-V i V i T )；
Where H is a centralised matrix, i.e. h=i-ee T N, I is an identity matrix, e is an N-dimensional column vector with elements of 1, and N is the number of features; q is a set dimension value, and the sample is estimated through maximum likelihood value estimation, so that a latitude value is obtained; i is the class of the sample, and k is a sample centering matrix corresponding to the class i;
let the initial arrangement matrix b=0, and calculate B (I i ,I i )＝B(I i ,I i )+W i W i T The method comprises the steps of carrying out a first treatment on the surface of the Calculating a characteristic value X and a characteristic vector alpha of the generalized characteristic problem:
XH N BH N C T α＝λXH N C T α (13)
eigenvalue lambda 1 ＜λ 2 …＜λ q The corresponding feature vector is alpha 1 ,α 2 …α q Intermediate conversion matrix a lltsa ＝(α 1 ,α 2 …α q ) The method comprises the steps of carrying out a first treatment on the surface of the The overall transformation matrix a=a pca A lltsa The lightning low-dimensional characteristic coordinate is Y=A T CH N ；
Setting the number of neurons of a hidden layer as L, an activation function as g (·), and expressing the mathematical description of the extreme learning machine as:
where j=1, 2, …, N, ω i For the connection weight of the input node and the ith hidden layer neuron, beta i Connection weight for i-th hidden neuron and output node, b i Bias for the ith hidden layer neuron;
approximation of N samples (X) with zero error i ,t i ) And meet the followingWherein O is j The actual output value of ELM algorithm for the jth sample, t j The actual value of the j-th sample; x is X i For the ith sample feature value, t i An actual value for the i-th sample;
beta is then i ，ω i ，b i The method meets the following conditions:
the above can be abbreviated as
Wherein the method comprises the steps ofBeta is an output weight matrix, and T is a desired output matrix; then the output weight β=h + T；
H + The Moore-Penrose generalized inverse of the matrix H is output for the hidden layer.
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