CN101216512A - Non-sine periodic signal real time high precision detection method - Google Patents

Non-sine periodic signal real time high precision detection method Download PDF

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CN101216512A
CN101216512A CNA2007103034616A CN200710303461A CN101216512A CN 101216512 A CN101216512 A CN 101216512A CN A2007103034616 A CNA2007103034616 A CN A2007103034616A CN 200710303461 A CN200710303461 A CN 200710303461A CN 101216512 A CN101216512 A CN 101216512A
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何怡刚
王小华
刘美容
李庆国
肖迎群
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Hunan University
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Abstract

The invention discloses a realtime high-accuracy non-sinusoidal periodic signal detection method, which comprises the following steps of: sampling non-sinusoidal periodic signals to be detected; calculating frequency, amplitude and phase of fundamental wave and harmonic of each order by using neural network based on triangular base function; and correcting the frequency of the fundamental wave of the non-sinusoidal periodic signal calculated by the neutral network by using windowed interpolation algorithm. By improving the neural network algorithm, the invention can execute high-accuracy analysis of frequency of the fundamental wave and amplitudes and phases of the fundamental wave and the harmonic of each order for asynchronous sampling and non-integer-period truncation, and high-accuracy harmonic analysis result of non-sinusoidal periodical signal can be obtained when the neutral network is convergent. The invention has the advantages of high speed, realtime operation, high accuracy, etc., and has wide application prospect in fields of mechanical engineering, motor testing, electric system stability analysis, signal processing, instrument and apparatus, industrial control, etc.

Description

A kind of non-sine periodic signal real time high precision detection method
Technical field
The present invention relates to a kind of non-sine periodic signal real time high precision detection method in signal Processing field.
Background technology
Usually need non-sine periodic signal is detected in fields such as mechanical engineering, electromechanical testing, stability of power system analysis, signal Processing, instrument and meter, Industry Control, and this detection all requires to have high precision and property real-time.Yet present method is difficult to accomplish this point.As adopt the fast Fourier transform (FFT) method to detect, and often there are blue effect of grid and leakage phenomenon, make the signal parameter that calculates, promptly frequency, amplitude, phase place are forbidden, and especially phase error is very big, can't satisfy the harmonic measure requirement.Adopt interpolation algorithm can eliminate the error that the blue effect of grid causes, adopt the method for windowed function to eliminate the error that spectrum leakage causes, algorithm has higher precision, but frequency, amplitude and phase place to each harmonic wave all will be proofreaied and correct separately, calculated amount is bigger, can't satisfy modern industry to the harmonic wave requirement of monitoring in real time.
In recent years, artificial neural network has obtained using energetically in the non-sine periodic signal context of detection.Yet the accurate fundamental frequency that the self-adaptation artificial neural network must known system just can be carried out accurate frequency analysis; And multilayer feedforward self-adaptation artificial neural network training process is uncertain, generally needed a large amount of training before using, and this network neuron is too much, and calculated amount is excessive, bad adaptability.
Summary of the invention
The existing real-time detection computations amount of non-sine periodic signal is excessive in order to solve, the technical matters of low precision, the invention provides a kind of non-sine periodic signal real time high precision detection method, calculated amount of the present invention is little, has high precision and property real-time, can satisfy the demand of modern industry.
The technical scheme that the present invention solves above-mentioned technical matters may further comprise the steps:
Non-sine periodic signal to be detected is sampled;
Utilization is based on the first-harmonic of the neural network calculating sampling signal of triangular basis function and frequency, amplitude and the phase place of each harmonic;
The fundamental frequency that adopts window function and interpolation algorithm correction neural network to calculate.
In the above-mentioned non-sine periodic signal real time high precision detection method, non-synchronous sampling, non-integer-period are blocked situation, adopt and improve amplitude and the phase analysis that carries out high precision non-sine periodic signal fundamental frequency, first-harmonic and each harmonic based on the neural network of triangular basis function, when neural network restrains, can obtain high-precision frequency analysis result.
Technique effect of the present invention is: utilize the neural network of triangular basis function to carry out the amplitude and the phase analysis of non-sine periodic signal fundamental frequency, first-harmonic and each harmonic, when neural network restrains, neural network is output as the amplitude and the phase place of first-harmonic and each harmonic, relatively near truth, this moment, relative difference on frequency was less than 2.5 * 10 -5, amplitude relative error<3 * 10 -2, phase place relative error<2 * 10 -2Degree, and computing velocity is soon less than 5 seconds; When having white noise to disturb in the actual signal, when utilizing the neural network of triangular basis function to carry out the amplitude of non-sine periodic signal fundamental frequency, first-harmonic and each harmonic and phase analysis, the fundamental frequency that adopts window function and interpolation algorithm correction neural network to calculate obtains above-mentioned identical precision.
Non-synchronous sampling, non-integer-period are blocked situation, adopt and improve amplitude and the phase analysis that carries out non-sine periodic signal fundamental frequency, first-harmonic and each harmonic based on the neural network of triangular basis function, when neural network restrains, the output of neural network approaches truth very much, at this moment amplitude error | Δ A n|<2 * 10 -13, phase error | Δ  n|<4 * 10 -11Degree, and computing velocity is very soon less than 1 second.Therefore say characteristics such as non-sine periodic signal detection method of the present invention has fast, real-time, high precision, have wide application prospect in fields such as mechanical engineering, electromechanical testing, stability of power system analysis, signal Processing, instrument and meters.
The present invention is further illustrated below in conjunction with drawings and the specific embodiments.
Description of drawings
Fig. 1 is for the present invention is based on triangular basis function neural network model.
Fig. 2 is that the fundamental frequency that the present invention is based on different learning rate β is estimated the sensitivity signal.
Graph of errors when Fig. 3 asks the actual fundamental frequency of analysis nonsinusoidal signal to be 60Hz for the inventive method.
Embodiment
The step that the present invention detects non-sine periodic signal is as follows:
Non-sine periodic signal to be detected is sampled;
Utilization is based on the first-harmonic of the neural network calculating sampling signal of triangular basis function and frequency, amplitude and the phase place of each harmonic, and referring to Fig. 1, non-sine periodic signal is as follows based on the neural network model of triangular basis function:
y ( m ) = w 0 + Σ j = 1 N w j cos ( jω 0 mT s ) + Σ j = N + 1 2 N w j sin [ ( j - N ) ω 0 mT s ] - - - ( 1 )
W in the formula jBe neural network weight, c jBe triangular basis function, c j=cos (j ω 0MT s) (j=0,1,2 ... N), c j=sin[(j-N) ω 0MT s], j=N+1, N+2 ... 2N; ω 0Be signal first-harmonic angular frequency, ω 0=2 π f 0, j is an overtone order, m is a m sampled point, T sBe the sampling period, N is higher hamonic wave number of times.
The amplitude of the fundamental frequency of non-sine periodic signal, first-harmonic and each harmonic and phase place are:
Figure S2007103034616D00032
F in the formula nBe the nth harmonic frequency, A n,  nBe respectively nth harmonic amplitude and phase place.
Neural network output: y d ( m ) = Σ j = 0 2 N w j c j ( ω 0 ) = W T C
Error function: e (m)=y (m)-y d(m), m=0,1,2 ... M-1
Performance index: J = 1 2 Σ m = 0 M e 2 ( m )
Weights are adjusted: W ( m + 1 ) = W ( m ) - η ∂ J ∂ W = W ( m ) + ηe ( m ) C ( m )
Weight matrix is in the formula: W=[w 0, w 1... w 2N] T, excitation matrix is: C=[c 0, c 10) ... c 2N0)] T, η is a learning rate, and 0<η<1.
Particularly be noted that the selection of learning rate η, in order to guarantee the neural network algorithm convergence, theory and substantive test and experiment draw necessary 0<η<2/ (N+1), and wherein 2N+1 is the hidden neuron number.
The neural network convergence is that performance index, error function meet the demands when stablizing, and the first-harmonic of non-sine periodic signal and the amplitude of each harmonic and phase place are calculated by following formula:
Fundamental voltage amplitude A 1 = w 1 2 + w N + 1 2 ; Fundamental phase  1=arctg (w 1/ w N+1)
The nth harmonic amplitude A n = w n 2 + w N + n 2 ; Nth harmonic phase place  n=arctg (w n/ w N+n)
Fundamental frequency computation process is as follows among the present invention:
Δ ω 0 ( m ) = - η ∂ J ∂ ω 0 ( m ) = ηe ( m ) m T s { - Σ j = 1 N jw j sin ( jω 0 mT s ) + Σ j = N + 1 2 N ( j - N ) w j cos [ ( j - N ) ω 0 mT s ] }
Make I=[1,2 ... N] T, A=[w 1, w 2... w N] T, B=[w N+1, w N+2... w 2N] T, P=[c 10), c 20) ... c N0)] T, Q=[c N+10), c N+20) ... c 2N0)] T, then the first-harmonic angular frequency is pressed the following formula adjustment
ω 0(m+1)=ω 0(m)+ηe(m)mT s×sum(I·*B·*P-I·*A·*Q)
In the formula, symbol sum is for asking rectangular array element and computing, and .* is expressed as the matrix element band multiplication computing in the MATLAB environment, and neural network weight W, learning rate η still determine in a manner described.
In order further to improve the accuracy of the fundamental frequency of being tried to achieve by above-mentioned neural network algorithm, utilization of the present invention adds rectangular window or the Hanning window interpolation algorithm is revised: f 0=(K 0+ Δ K 0) f s/ M, sample frequency is f in the formula s, fundamental frequency is f 0, K 0Be integer, Δ K 0Be decimal, M is a sampled point.
The updating formula that adds the fundamental frequency of rectangular window
&Delta; K 0 = Y ( K 0 + 1 ) Y ( K 0 ) + Y ( K 0 + 1 ) , Y ( K 0 + 1 ) &GreaterEqual; Y ( K 0 - 1 ) Y ( K 0 - 1 ) Y ( K ) + Y ( K - 1 ) , Y ( K 0 + 1 ) < Y ( K 0 - 1 )
The updating formula that adds the fundamental frequency of Hanning window is
&Delta; K 0 = 2 Y w ( K 0 + 1 ) - Y w ( K 0 ) Y w ( K 0 ) + Y w ( K 0 + 1 ) , Y w ( K 0 + 1 ) &GreaterEqual; Y w ( K 0 - 1 ) Y w ( K 0 ) - 2 Y w ( K 0 - 1 ) Y w ( K ) + Y w ( K - 1 ) , Y w ( K 0 + 1 ) < Y w ( K 0 - 1 )
Non-synchronous sampling, non-integer-period are blocked situation, utilize above-mentioned neural network algorithm to ask the amplitude and the phase analysis precision of non-sine periodic signal fundamental frequency, first-harmonic and each harmonic for further improving, the present invention proposes improved neural network algorithm based on the triangular basis function, step is as follows:
1) initial value setting: produce initial weight vector a and b at random, make initial first-harmonic angular frequency 0=100 π specify sample frequency f sAnd the sampled data length M, energy error minimum value ε selects suitable learning rate η and β;
2) produce a=[a in the neural network output vector y:y=aC+bS formula by following formula 1, a 2... a N], b=[b 1, b 2... b N], a n=A nSin θ n, b n=A nCos θ n
C = cos [ &omega; 0 T s ] cos [ &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ &omega; 0 MT s ] cos [ 2 &omega; 0 T s ] cos [ 2 &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ 2 &omega; 0 MT s ] &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; cos [ N&omega; 0 T s ] cos [ N&omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ N&omega; 0 MT s ]
S = sin [ &omega; 0 T s ] sin [ &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ &omega; 0 M T s ] sin [ 2 &omega; 0 T s ] sin [ 2 &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ 2 &omega; 0 M T s ] &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; sin [ N&omega; 0 T s ] sin [ N&omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ N&omega; 0 M T s ]
3) difference error of calculation vector e:e=x-y and energy error function J: J = 1 2 &Sigma; m = 1 M e 2 ( m ) Value,
X is the discrete sample vector of actual continuous signal in the formula, and y is the output vector of neural network;
4) difference refreshing weight vector a, b and scalar ω 0:
a k + 1 = a k - &eta; &PartialD; J &PartialD; a k = a k + &eta; e k C T b k + 1 = b k - &eta; &PartialD; J &PartialD; b k = b k + &eta; e k S T
&omega; 0 ( k + 1 ) = &omega; 0 ( k ) - &beta; &PartialD; J &PartialD; &omega; 0 ( k ) = &omega; 0 ( k ) + &beta;T s e { P T &CenterDot; * C T * b k T - P T &CenterDot; * S T * a k T }
β in the formula>0 is ω 0Learning rate, and " .* " is groups of elements computing, i.e. P.*C=[P IjC Ij] N * M,
P = 1 2 &CenterDot; &CenterDot; &CenterDot; M 2 4 &CenterDot; &CenterDot; &CenterDot; 2 M &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; N 2 N &CenterDot; &CenterDot; &CenterDot; NM .
5) if J>ε got back to for (2) step, otherwise, neural metwork training finished.
The present invention uses example:
Example 1: signal to be analyzed:
Figure S2007103034616D00058
Wherein, fundamental frequency f 1Be 50.1Hz, the frequency of other each harmonics is the integral multiple of fundamental frequency, and sample frequency is 1000Hz, and sampling number is 80 points, and amplitude of first-harmonic and each harmonic (for no unit amount) and phase place are as shown in table 1.Send neural metwork training with specified power frequency 50Hz and the sampled value that samples, can disposable acquisition first-harmonic and survey frequency, amplitude and the phase place of each harmonic.Table 2 is for the harmonic frequency that adopts neural network algorithm of the present invention to obtain, amplitude, phase place and with respect to the error of true value.By the simulation analysis result as can be seen, the harmonic measuring method that the present invention proposes has excellent adaptability to frequency jitter, and is high to the computational accuracy of the amplitude of each harmonic and phase angle.Document [Zhang Fusheng, Geng Zhonghang, Ge Yaozhong, Proceedings of the CSEE, 1999,19 (3)] sample frequency is 3000Hz, and sampling number is 1024 points, adopt respectively to add Hanning window and Blackman window interpolation correction algorithm carries out frequency analysis to same signal, also all the analysis result precision than the present invention algorithm is low for income analysis result.
In order to check white noise signal to disturb the size of actual analysis signal, having added amplitude in simulate signal is the random white noise signal of fundamental voltage amplitude 1%.Obtain fundamental frequency according to window function and interpolation algorithm of the present invention (add rectangular window or add Hanning window), and the fundamental frequency of this fundamental frequency as the neural network algorithm use, the sampled value of the previous primitive period that will sample (80 points) is sent neural metwork training again, neural network convergence after 6 iteration, the first-harmonic that can disposable acquisition obtains as stated above and the measurement amplitude and the phase place of each harmonic with same precision.As seen, the non-sine periodic signal harmonic detecting method that the present invention proposes has adaptability preferably to frequency jitter, and it is little disturbed by white noise signal, to the amplitude of each harmonic and the computational accuracy height of phase angle.
The harmonic components of table 1 example 1 signal
Simulate signal Overtone order/time
First-harmonic 2 3 4 5 6 7 8 9 10 11
Amplitude A iPhase place  (°) 240 0 0.1 10 12 20 0.1 30 2.7 40 0.05 50 2.1 60 0 - 0.3 80 0 - 0.6 100
The example 1 frequency analysis result that the neural network algorithm that table 2 proposes with the present invention obtains
Overtone order Harmonic frequency Humorous wave amplitude Harmonic phase
Frequency (Hz) Relative error (%) Amplitude Relative error (%) Phase place (°) Relative error (%)
1 2 3 4 5 6 7 9 11 50.099991 100.199982 150.299973 200.399964 250.499955 300.599946 350.699937 450.899919 551.099901 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 239.999937 0.099945 11.999964 0.099969 2.699976 0.049979 2.099982 0.299978 0.600030 -0.000026 -0.055000 -0.000300 -0.031000 -0.000889 -0.021000 -0.000857 -0.007333 0.005000 0.0002294 10.001377 20.0007044 30.003245 40.001252 50.007723 60.001777 80.014041 100.006906 0.000064 0.013770 0.003520 0.010817 0.003130 0.015446 0.002962 0.017551 0.006906
Example 2:, establish fundamental frequency and change from 40 to 60Hz for the analytic signal of example 1.In order to check the improved non-sine periodic signal of the present invention to detect the validity of analysis of neural network method to the non-synchronous sampling discrete signal, we specify sample frequency is 1510Hz, and discrete data length is 40 sampled points.The fundamental frequency of now considering actual signal is 3 kinds of situations such as 40Hz, 50Hz, 60Hz, and under these actual 3 kinds of fundamental frequency situations, sample frequency and data length with appointment obviously are in non-synchronous sampling, non-integer-period blocks situation.If ε=10 -29, η=0.0227, first-harmonic initial angle frequencies omega 0=100 π.At first analyze respectively under above-mentioned 3 kinds of actual fundamental frequencies learning rate β as shown in Figure 2 to the sensitivity of fundamental frequency estimated value.As we know from the figure, when β=230 are neighbouring, its estimated frequency error minimum, we get β=230 for this reason, above-mentioned 3 kinds of different actual fundamental frequency situations are carried out frequency analysis, through 550 times, 443 times, 421 times training, be respectively 0.265 second, 0.218 second, 0.204 second neural network convergence (amplitude and the phase error of gained frequency analysis when Fig. 3 is 60Hz for fundamental frequency) respectively computing time.In addition, when actual fundamental frequency was 40Hz, gained fundamental frequency evaluated error was Δ f 0=2.132 * 10 -14Hz, and when actual fundamental frequency be 50 and during 60Hz, gained fundamental frequency evaluated error is Δ f 0=-1.421 * 10 -14Hz.Know by analysis result, when actual fundamental frequency when 40Hz to 60Hz changes, gained fundamental frequency error | Δ f 0|<3 * 10 -14Hz, amplitude error | Δ A n|<1.2 * 10 -13, phase error | Δ  n|<3.5 * 10 -11Degree.And document [Zhang F, Geng Z, Yuan W.IEEE Trans.PowerDelivery, 2001,16 (2): 160] adopts windowing FFT interpolation algorithm to carry out frequency analysis to same signal, and actual fundamental frequency is f 0=50Hz, sample frequency are that 3000Hz, data length are 1024 sampled points, promptly block under the situation gained fundamental frequency error at synchronized sampling, non-integer-period | Δ f 0|>10 -7Hz; Document [Serna J A..IEEE Trans.Instrum.Meas.2001,50 (6): 1556-1562] signal that contains 4 subharmonic is carried out frequency analysis, sample frequency is 6400Hz, and data length is 4096 sampled points, the fundamental frequency variation range is 49.5 to 50.5Hz, the gained amplitude error | Δ A n|>10 -4, phase error | Δ  n|>10 -7Degree (estimated frequency error does not provide).Obviously, the neural network frequency analysis precision of the present invention's introduction will be far above windowing FFT interpolation algorithm.The result shows once more at non-synchronous sampling, non-integer-period and blocks under the situation, detects the analysis of neural network method with non-sine periodic signal that the present invention chats frequency analysis has been obtained very high precision.

Claims (9)

1. non-sine periodic signal real time high precision detection method may further comprise the steps:
Non-sine periodic signal to be detected is sampled;
Utilization is based on the first-harmonic of the neural network calculating sampling signal of triangular basis function and frequency, amplitude and the phase place of each harmonic;
The fundamental frequency that adopts window function and interpolation algorithm correction neural network to calculate.
2. non-sine periodic signal real time high precision detection method according to claim 1, the neural network model of described triangular basis function is:
y ( m ) = w 0 + &Sigma; j = 1 N w j cos ( j&omega; 0 mT s ) + &Sigma; j = N + 1 2 N w j sin [ ( j - N ) &omega; 0 mT s ]
W in the following formula jBe neural network weight, c jBe triangular basis function, c j=cos (j ω 0MT s) (j=0,1,2 ... N), c j=sin[(j-N) ω 0MT s], j=N+1, N+2 ... 2N, ω 0Be signal first-harmonic angular frequency, ω 0=2 π f 0, j is an overtone order, m is a m sampled point, T sBe the sampling period, N is higher hamonic wave number of times.
3. non-sine periodic signal real time high precision detection method according to claim 2, the adjustment of described triangular basis function neural network weight is undertaken by following formula:
W ( m + 1 ) = W ( m ) - &eta; &PartialD; J &PartialD; W = W ( m ) + &eta;e ( m ) C ( m )
Weight matrix is in the formula: W=[w 0, w 1... w 2N] T, excitation matrix is: C=[c 0, c 10) ... c 2N0)] T, η is a learning rate, and 0<η<1.
4. according to claim 1,2,3 described non-sine periodic signal real time high precision detection methods, the amplitude and the phase place of the fundamental frequency of described non-sine periodic signal and first-harmonic and each harmonic are calculated by following formula:
Fundamental voltage amplitude A 1 = w 1 2 + w N + 1 2 ; Fundamental phase  1=arctg (w 1/ w N+1);
The nth harmonic amplitude A n = w n 2 + w N + n 2 ; Nth harmonic phase place  n=arctg (w n/ w N+n).
5. a kind of non-sine periodic signal real time high precision detection method according to claim 1, the described fundamental frequency of utilizing rectangular window or Haining interpolation algorithm correction to try to achieve by neural network algorithm.
6. a kind of non-sine periodic signal real time high precision detection method according to claim 1 is characterized in that utilizing improved amplitude and the phase analysis precision that improves non-sine periodic signal fundamental frequency, first-harmonic and each harmonic based on the neural network algorithm of triangular basis function.
7. according to claim 1,6 described improved neural network algorithms, it is characterized in that neural network parameter ω based on the triangular basis function 0Adjust by following formula:
&omega; 0 ( k + 1 ) = &omega; 0 ( k ) - &beta; &PartialD; J &PartialD; &omega; 0 ( k )
= &omega; 0 ( k ) + &beta; T s e { P T &CenterDot; * C T * b k T - P T &CenterDot; S T * a k T }
In the formula P = 1 2 &CenterDot; &CenterDot; &CenterDot; M 2 4 &CenterDot; &CenterDot; &CenterDot; 2 M &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; N 2 N &CenterDot; &CenterDot; &CenterDot; NM , β>0 is ω 0Learning rate, and " .* " is groups of elements computing, i.e. P.*C=[P IjC Ij] N * M
8. non-sine periodic signal real time high precision detection method according to claim 3, described learning rate η is chosen as 0<η<2/ (N+1), and wherein 2N+1 is the hidden neuron number.
9. non-sine periodic signal real time high precision detection method according to claim 1, adopt the neural network algorithm of improved triangular basis function to carry out the amplitude and the phase analysis of high precision non-sine periodic signal fundamental frequency, first-harmonic and each harmonic, when neural network restrains, can obtain high-precision frequency analysis result, its step is as follows:
1) initial value setting: produce initial weight vector a and b at random, make initial first-harmonic angular frequency 0=100 π specify sample frequency f sAnd the sampled data length M, energy error minimum value ε selects suitable learning rate η and β;
2) produce a=[a in the neural network output vector y:y=aC+bS formula by following formula 1, a 2..., a N], b=[b 1, b 2..., b N], a n=A nSin θ n, b n=A nCos θ n
C = cos [ &omega; 0 T s ] cos [ &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ &omega; 0 M T s ] cos [ 2 &omega; 0 T s ] cos [ 2 &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ 2 &omega; 0 M T s ] &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; cos [ N&omega; 0 T s ] cos [ N&omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; cos [ N&omega; 0 M T s ]
S = sin [ &omega; 0 T s ] sin [ &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ &omega; 0 M T s ] sin [ 2 &omega; 0 T s ] sin [ 2 &omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ 2 &omega; 0 M T s ] &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; sin [ N&omega; 0 T s ] sin [ N&omega; 0 2 T s ] &CenterDot; &CenterDot; &CenterDot; sin [ N&omega; 0 M T s ]
3) difference error of calculation vector e:e=x-y and energy error function J: J = 1 2 &Sigma; m = 1 M e 2 ( m ) Value, x is the discrete sample vector of actual continuous signal in the formula, y is the output vector of neural network;
4) difference refreshing weight vector a, b and scalar ω 0:
a k + 1 = a k - &eta; &PartialD; J &PartialD; a k = a k + &eta; e k C T b k + 1 = b k - &eta; &PartialD; J &PartialD; b k = b k + &eta; e k S T
&omega; 0 ( k + 1 ) = &omega; 0 ( k ) - &beta; &PartialD; J &PartialD; &omega; 0 ( k ) = &omega; 0 ( k ) + &beta; T s e { P T &CenterDot; * C T * b k T - P T &CenterDot; * S T * a k T }
β in the formula>0 is ω 0Learning rate, and " .* " is groups of elements computing, i.e. P.*C=[P IjC Ij] N * M,
P = 1 2 &CenterDot; &CenterDot; &CenterDot; M 2 4 &CenterDot; &CenterDot; &CenterDot; 2 M &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; &CenterDot; N 2 N &CenterDot; &CenterDot; &CenterDot; NM .
5) if J>ε got back to for (2) step, otherwise, neural metwork training finished.
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CN104569569A (en) * 2015-01-20 2015-04-29 天津市英贝特航天科技有限公司 Electrical characteristic determination method for any fixed-frequency AC
CN104655928A (en) * 2013-11-21 2015-05-27 国家电网公司 Method for detecting inter-harmonics of input voltage of electric automobile charger
CN104777356A (en) * 2015-03-10 2015-07-15 三峡大学 Neural-network-based real-time high-accuracy harmonic detection method
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CN102393488A (en) * 2011-08-24 2012-03-28 江苏技术师范学院 Harmonic analysis method
CN102393488B (en) * 2011-08-24 2013-12-11 江苏理工学院 Harmonic analysis method
CN103091563A (en) * 2013-01-15 2013-05-08 广西电网公司电力科学研究院 Calculation method of dielectric power factors of high-voltage electrical equipment
CN103091563B (en) * 2013-01-15 2015-04-22 广西电网公司电力科学研究院 Calculation method of dielectric power factors of high-voltage electrical equipment
CN104655928A (en) * 2013-11-21 2015-05-27 国家电网公司 Method for detecting inter-harmonics of input voltage of electric automobile charger
CN104569569A (en) * 2015-01-20 2015-04-29 天津市英贝特航天科技有限公司 Electrical characteristic determination method for any fixed-frequency AC
CN104569569B (en) * 2015-01-20 2019-03-01 天津市英贝特航天科技有限公司 Arbitrarily determine the electrical characteristic measuring method of frequency alternating current
CN104777356A (en) * 2015-03-10 2015-07-15 三峡大学 Neural-network-based real-time high-accuracy harmonic detection method
CN107167658A (en) * 2017-05-11 2017-09-15 南京国电南自电网自动化有限公司 A kind of jamproof power system fundamental frequency of high accuracy and Method for Phase Difference Measurement
CN107167658B (en) * 2017-05-11 2019-06-28 南京国电南自电网自动化有限公司 A kind of jamproof electric system fundamental frequency of high-precision and Method for Phase Difference Measurement
CN108152584A (en) * 2017-12-21 2018-06-12 中南大学 A kind of high ferro tractive power supply system harmonic wave Multi-path synchronous rapid detection method
CN108663570A (en) * 2018-03-15 2018-10-16 杭州市电力设计院有限公司 Current harmonics analysis method based on trigonometric function neural network
CN108663570B (en) * 2018-03-15 2023-05-23 杭州市电力设计院有限公司 Current harmonic analysis method based on trigonometric function neural network

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