CN108051018A - Distributed fiber grating transducing signal peak-seeking control system based on FPGA - Google Patents

Distributed fiber grating transducing signal peak-seeking control system based on FPGA Download PDF

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CN108051018A
CN108051018A CN201711289598.0A CN201711289598A CN108051018A CN 108051018 A CN108051018 A CN 108051018A CN 201711289598 A CN201711289598 A CN 201711289598A CN 108051018 A CN108051018 A CN 108051018A
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mrow
msub
peak
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msup
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闫旭
刘宪阳
王鹏程
崔鹤
侯旭涛
李晓飞
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Beijing Institute of Satellite Information Engineering
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Beijing Institute of Satellite Information Engineering
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    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/26Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light

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Abstract

The invention discloses a kind of distributed fiber grating transducing signal peak-seeking control systems based on FPGA, by the influence of noise being mingled in external environment and signal acquisition process, so that the peak point of reflectance spectrum shifts, largely affect the precision of peak-seeking, so peak-seeking again after being first filtered to the discrete data collected, to the digital signal filter collected, preprocessing part is completed;Then by the conversion of FPGA internal state machines, the Wave data after denoising is adjusted into threshold value and is split, rough estimate peak value position scope;Pretreated data are handled again based on FPGA state machines, then peak-seeking.It not only increases speed and compensates for previous common peak-seeking algorithm and ignore problem for asymmetric waveform, improve the precision of algorithm.Algorithm mainly splits acquisition module, peak-data detection module composition by peak region.

Description

Distributed fiber grating transducing signal peak-seeking control system based on FPGA
Technical field
The invention belongs to optical data acquisition fields more particularly to a kind of distributed fiber grating based on FPGA to sense letter Number peak-seeking control system.
Background technology
Fiber Bragg Grating FBG has passivity, corrosion-resistant, high temperature resistant, transmission range as a kind of New Sensing Technology Far, the features such as strong antijamming capability, distribution array, in oil exploration, bridge, tunnel, the isostructural health monitoring of building with And it is used widely in the device structure status monitoring of aero-engine, big machinery.In sensing demodulating system, according to solution Principle is adjusted to understand that the shift amount of reflectance spectrum centre wavelength corresponds to fiber grating reflection configuration peak point position, is reflected in FBG Compose in demodulating system it is measured all centered on wavelength minor shifts amount.So how quickly, accurately navigate to peak It is worth point, is the key content studied herein.And among the process handled in gathered data and data transmission, often by To the interference of many factors, such as:The variation of external environment, electronic device wait caused influence of noise in itself so that peak-seeking knot Fruit generates larger error, and demodulation accuracy is caused to be greatly affected, so the key of demodulating system then for filtering and noise reduction and is sought Peak.
Peak-seeking algorithm is the algorithm for finding peak point, and the key that this algorithm is not only in demodulating system is also in system A difficulties.The purpose of peak-seeking algorithm is to look for peak point to a large amount of discrete discrete dates collected, Among practical application, peak-seeking algorithm will not only meet accuracy height, also meet fireballing requirement.In practice process In, it is primarily present following both sides problem:(1) precision influences, during the gathered data of optical fiber grating regulating system, device Part, which also has in itself inside external environment and system hardware, is all easily introduced substantial amounts of noise, and these noises can cause light work( The variation of rate so that the centre wavelength of FBG reflectance spectrums is deformed upon and shaken, and causes the reduction of follow-up peak-seeking precision, and error increases Greatly, largely the applicability of peak-seeking algorithm is had an impact.(2) speed influences, since optical fiber grating regulating system is to want It is used among practical engineering project, so be also higher for rate request, and the calculating processing of peak-seeking algorithm is fast Degree is the key factor for influencing the whole system speed of service, if Algorithms of Selecting needs to carry out substantial amounts of interative computation, it will cause whole The delay of a system running speed has again resulted in demodulating system and has been a greater impact in terms of real-time.
At present, peak-seeking algorithm is broadly divided into common traditional peak-seeking algorithm, classical fitting peak-seeking algorithm and improves new peak-seeking Algorithm.Common tradition peak-seeking algorithm is the algorithm under a kind of ideal conditions, easy to operate, easy to implement, but in practical application In, generated error is larger;Classics fitting peak-seeking algorithm, it is contemplated that gathered data wavy curve meets Gaussian curve, still For condition for will be in strict conformity with Standard Symmetric Multivariate Gaussian, practicability be bad;New peak-seeking algorithm is improved, is that preceding two classes algorithm is changed Into, it is contemplated that the factor that preceding two classes algorithm is not considered for the precision of peak-seeking algorithm, there is promotion.Although there is improvement The appearance of algorithm, but promotion further is stilled need in precision, and among high-speed demodulating system, for wanting for speed It asks, also needs the promotion of bigger.
The content of the invention
It is an object of the invention to realize the high speed to grating fibers transducing signal, high-precision peak-seeking, one kind is provided and is based on The distributed fiber grating transducing signal Peak Search Method of FPGA, this method be based on FPGA state machines to pretreated data again Secondary to be handled, then peak-seeking, not only increases speed and compensates for previous common peak-seeking algorithm for asymmetric waveform Ignore problem, improve the precision of algorithm.Algorithm mainly splits acquisition module, peak-data detection module group by peak region Into.
The purpose of the present invention is what is be achieved by following technical solution:
A kind of distributed fiber grating transducing signal peak-seeking control system based on FPGA is split comprising peak region and is gathered Preprocessing module, peak data acquisition module, peak-seeking fitting module,
Peak region segmentation acquisition preprocessing module, for gathering filtered valid data;
Peak-seeking Value Data acquisition module, for gathering the data at peak value;
Peak-seeking fitting module, for obtaining the peak point of Gaussian function.
As the further preferred of the distributed fiber grating transducing signal peak-seeking control system based on FPGA of the invention Scheme, peak-seeking fitting module uses asymmetric Gauss model, for being compensated and corrected to the obtained peak value of Gauss curve fitting.
As the further preferred of the distributed fiber grating transducing signal peak-seeking control system based on FPGA of the invention Scheme, the work step of peak-seeking fitting module are specific as follows:
Step 1, after grating fibers signal is by A/D chip, there is the digital signal that analog quantity switchs to digital quantity;In FPGA After portion's state machine conversion process, one group of discrete data has been obtained, Gauss curve fitting has been carried out, obtains the peak point of Gaussian function, be denoted as A′;
Step 2, the FBG signal wavelengths gathered by A/D chip are in practical situations to be asymmetric, so herein will be non-right Gauss model f (t) is claimed to introduce, verification compensation is carried out to the peak value that Gaussian function fitting obtains;
Step 3, the judgement of asymmetric Gaussian function is 2 second order parameters based on left and right varianceWith
As the further preferred of the distributed fiber grating transducing signal peak-seeking control system based on FPGA of the invention Scheme in step 2, it is as follows to carry out the peak value that Gaussian function fitting obtains the specific formula of verification compensation:
G (x)=A'+f (t) (1-1)
Wherein,
Wherein, μ is the time point corresponding to peak point, σ obtained by Gauss curve fitting function1For Gauss curve fitting function left part Time point hits, σ2For the time point hits of Gauss curve fitting function right part.
As the further preferred of the distributed fiber grating transducing signal peak-seeking control system based on FPGA of the invention Scheme, in step 3, the judgement of asymmetric Gaussian function is 2 second order parameters based on left and right varianceWithIt is specific to calculate It is as follows:
As the further preferred of the distributed fiber grating transducing signal peak-seeking control system based on FPGA of the invention Scheme can derive that the peak A after verification compensation is by the judgement of variance and by formula (1-2):
Compared with the prior art, the invention has the advantages that:
(1) pretreated data are handled again based on FPGA state machines, then peak-seeking.Improve processing speed And it compensates for previous common peak-seeking algorithm and ignores problem for asymmetric waveform, improve the precision of algorithm;
(2) use the grating fibers Peak Search Method of the design, accuracy of detection can be controlled within 0.5pm, and speed with Stability all has significant advantage compared with above-mentioned algorithm;
(3) by the transfer process of FPGA internal state machines, corresponding high speed filtering algorithm is designed and Implemented, is following The Data Management Analysis carried out provides reliable relatively accurate wavelength data.Algorithm had both avoided the waste of memory space, Simultaneously promotion is obtained in speed and precision again.
Description of the drawings
Fig. 1 (a) is original waveform schematic diagram of the present invention;
Fig. 1 (b) is the present invention using the waveform diagram after low-pass filtering;
Fig. 2 is peak ranges determination process flow chart of the present invention;
Fig. 3 is grating fibers sensing acquisition of the present invention each Algorithm Error figure under alternating temperature;
Fig. 4 is grating fibers sensing acquisition of the present invention each Algorithm Error figure under different noises.
Specific embodiment
Further similar description is carried out to the specific embodiment of the present invention below in conjunction with the accompanying drawings.
Original FBG waveforms as shown in Fig. 1 (a) and Fig. 1 (b) with after Butterworth low pass ripple of the present invention Comparison of wave shape figure, Fig. 1 (a) are original waveform schematic diagram of the present invention;Fig. 1 (b) is that the present invention is shown using the waveform after low-pass filtering It is intended to;
It is described below:
By the influence of noise being mingled in external environment and signal acquisition process so that the peak point of reflectance spectrum occurs inclined It moves, largely affects the precision of peak-seeking, so filtering process is to carry out the step first of peak-seeking algorithm, it be first to acquisition Peak-seeking again after obtained discrete data is filtered.For digital filtering, digital filtering is the filtering algorithm that the present invention uses Without the cost that other hardware straps come, and resistance matching problem is not present, only in a kind of filtering algorithm realized by software algorithm Filtering characteristic can easily be changed by suitably filter being improved, boostfiltering effect.
The Butterworth low pass ripple that the present invention uses, setup measures are passband maximum attenuation αp=3dB, stopband minimum decline Subtract αs=20dB.After experiment, SNR=30.081, MSE=1.725 × 10-2 are obtained.
Pass through the signal-to-noise ratio (SNR) and the data result of mean square deviation (MSE) and the scope of application of each algorithm of above-mentioned algorithm Comprehensive analysis compares, it is known that Butterworth low pass ripple has preferable performance, by Butterworth low pass ripple, after processing Data be passed to FPGA and carry out subsequent processing.
It is peak ranges determination process flow chart as shown in Figure 2, is described below:
The data acting as at acquisition peak value of peak data acquisition module, provide more reliable for peak-seeking algorithm hereafter Effective data message.Detailed process is mutually converted between up and down, mistake tri-state, and is divided in FPGA system It does not devise to record and keeps stablizing the data with state, rise the start position data of state and decline state final position number According to register, be deposited into array a [n], as shown in Figure 2.
It is compared one by one with pretreated data first, if current data is more than the threshold value set and last data is small In threshold value, this data is included in home location register, is transferred to next data;If current data is more than threshold value and more than previous Data initially enter condition adjudgement, if not declining state, then initially enter the rising state of waveform, otherwise by current data with it is upper One data carry out difference comparsion, and difference range is set as K (K values are identified value after lot of experimental data comparison), if difference Less than or equal to K, then same state is kept at this time, if difference is more than K, switch to mistake state;If current data is more than threshold value and is less than Equal to last data, into difference comparsion, if difference is less than or equal to K, is converted to one and judges flow, otherwise it is assumed that ripple at this time Shape fluctuates, and carries out next step judgement:If state is declines state, NextState is wrong state, is otherwise maintained the original state.If Current data is less than threshold value and last data is more than threshold value, judges difference between the two, if less than or equal to K, is transferred to next Data;If more than K, then process terminates, and a upper data are included in end position register.
It is grating fibers sensing acquisition each Algorithm Error figure under alternating temperature as shown in Figure 3, is described below:
Peak-seeking algorithm chooses direct comparison method, Gauss curve fitting method, adaptive half-peak peak-seeking method, Steger peak-seeking algorithms respectively And the asymmetric Gauss algorithm proposed by the present invention based on FPGA state machines is contrast experiment, passes through MATLAB emulation experiments pair Ratio error and speed verify the validity set forth herein algorithm.
Sensor is put into 0 DEG C~50 DEG C of temperature control chamber, and guarantee is identical with having in above-mentioned isothermal experiments Parameter, spectrum (FBG) demodulator gather 10 times at a temperature of distinguishing 5 DEG C, 10 DEG C, 15 DEG C, 20 DEG C, 25 DEG C, 30 DEG C, 35 DEG C, 40 DEG C, 45 DEG C Data take its average value, and with above-mentioned algorithm equally gather 10 times at different temperatures and obtain average peak data and be compared, As shown in Figure 3.
It can be drawn by the analysis to Fig. 3, no matter for error or stability, effect is not direct comparison method It is highly desirable;Situation of the Gauss curve fitting method due to not considering asymmetrical peak dissymmetric peak spectrum, so being affected, stability and peak-seeking precision need It is promoted;Adaptive half-peak detection method peak-seeking and Gauss curve fitting method is better than based on Steger peak-seeking arithmetic accuracies and is affected by temperature It is small;Algorithm proposed by the present invention, precision is compared with other algorithms, and mean error is between 0.40pm-0.55pm, and stability It is good.
It is grating fibers sensing acquisition each Algorithm Error figure under different noises as shown in Figure 4, is described below:
Temperature is held constant at 25 DEG C, adds in white Gaussian noise so that the noise magnitude of addition accounts for the model of signal amplitude It encloses between 0.001-0.1, measurement takes its average value for 10 times, calculation error, as shown in Figure 4.
By analyzing Fig. 4, with the increasing of noise magnitude, the precision of algorithm can all be affected.Directly relatively Method influences maximum, and Gauss curve fitting method is taken second place, and adaptive half-peak peak-seeking method mean error is based in respectively 4.21pm, 3.94pm Steger peak-seekings algorithm and algorithm proposed by the present invention be affected generation error all in below 1.8pm, antijamming capability compared with By force.

Claims (6)

1. a kind of distributed fiber grating transducing signal peak-seeking control system based on FPGA, it is characterised in that:Include peak region Regional partition acquisition preprocessing module, peak data acquisition module, peak-seeking fitting module,
Peak region segmentation acquisition preprocessing module, for gathering filtered valid data;
Peak-seeking Value Data acquisition module, for gathering the data at peak value;
Peak-seeking fitting module, for obtaining the peak point of Gaussian function.
2. the distributed fiber grating transducing signal peak-seeking control system according to claim 1 based on FPGA, feature It is, peak-seeking fitting module uses asymmetric Gauss model, for being compensated and corrected to the obtained peak value of Gauss curve fitting.
3. the distributed fiber grating transducing signal peak-seeking control system according to claim 1 based on FPGA, feature It is, the work step of peak-seeking fitting module is specific as follows:
Step 1, after grating fibers signal is by A/D chip, there is the digital signal that analog quantity switchs to digital quantity;The shape inside FPGA After state machine conversion process, one group of discrete data has been obtained, Gauss curve fitting has been carried out, obtains the peak point of Gaussian function, be denoted as A ';
Step 2, the FBG signal wavelengths gathered by A/D chip are in practical situations to be asymmetric, so herein by asymmetric height This model f (t) is introduced, and verification compensation is carried out to the peak value that Gaussian function fitting obtains;
Step 3, the judgement of asymmetric Gaussian function is 2 second order parameters based on left and right varianceWith
4. the distributed fiber grating transducing signal peak-seeking control system according to claim 1 based on FPGA, feature It is:In step 2, it is as follows that the specific formula of verification compensation is carried out to the peak value that Gaussian function fitting obtains:
G (x)=A'+f (t) (1-1)
Wherein,
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;mu;</mi> <mo>-</mo> <mi>t</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&amp;le;</mo> <mi>&amp;mu;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&gt;</mo> <mi>&amp;mu;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, μ is the time point corresponding to peak point, σ obtained by Gauss curve fitting function1For Gauss curve fitting function left part when Between point sampling number, σ2For the time point hits of Gauss curve fitting function right part.
5. the distributed fiber grating transducing signal peak-seeking control system according to claim 4 based on FPGA, feature It is:In step 3, the judgement of asymmetric Gaussian function is 2 second order parameters based on left and right varianceWithIt is specific to calculate It is as follows:
<mrow> <msubsup> <mi>&amp;delta;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>&lt;</mo> <mi>&amp;mu;</mi> </mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>&amp;delta;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>&gt;</mo> <mi>&amp;mu;</mi> </mrow> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
6. the distributed fiber grating transducing signal peak-seeking control system according to claim 5 based on FPGA, feature It is:It can derive that the peak A after verification compensation is by the judgement of variance and by formula (1-2):
<mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>A</mi> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;mu;</mi> <mo>-</mo> <mi>t</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;delta;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>&lt;</mo> <msubsup> <mi>&amp;delta;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mi>A</mi> <mo>&amp;prime;</mo> </msup> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;delta;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;delta;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>A</mi> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>t</mi> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;delta;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>&gt;</mo> <msubsup> <mi>&amp;delta;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
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CN108549023A (en) * 2018-06-21 2018-09-18 厦门大学 A kind of relay secondary pick-up voltage detection device and method based on peak-seeking algorithm
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CN110542441B (en) * 2019-10-10 2021-08-27 华北电力大学(保定) Signal demodulation method of optical fiber Bragg grating sensing system
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Application publication date: 20180518