Demodulation Accuracy Research Articles

High-precision IFM receiver based on random forest algorithm

Abstract The six-port network-based Instantaneous Frequency Measurement (IFM) receiver is widely utilized in industrial applications for signal frequency demodulation. However, current IFM receivers face the issue of low algorithmic demodulation accuracy (ACC). According to the four-channel output characteristics of the IFM receiver, we use the Random Forest algorithm to extract features, train and test the output voltage data set, and recognize frequency labels. The experimental results show that the ACC of the proposed algorithm reaches 0.9583, which is 13.99% higher than that of the traditional polynomial fitting algorithm. To evaluate the noise reduction performance of the algorithm, we add Gaussian white noise to the original data and demodulate the signal with noise. Comparative tests prove the advantages of the algorithm in high stability and flexibility. Finally, multiple model evaluation indicators demonstrate that the algorithm features strong applicability and robustness to the experimental data with IFM receiver.

Research on a signal demodulation algorithm for fiber optic acoustic sensors based on the amplitude ratio of harmonic components

Fiber optic sensing technology's performance is crucially influenced by the choice of demodulation algorithms. Traditional intensity demodulation methods rely on precisely controlling the working point to the quadrature point (Q point) by adjusting the laser wavelength. However, issues like laser wavelength adjustment accuracy and laser power variations with wavelength affect demodulation accuracy, limiting its application in complex scenarios. Additionally, this method requires sensitivity calibration and has a limited dynamic range. To address these limitations, this paper proposes an amplitude ratio of harmonic components (ARHC) demodulation algorithm. It analyzes the harmonic components of the interference light intensity output by the sensor to calculate Fabry-Perot cavity length changes, achieving real-time demodulation of dynamic signals. Compared to traditional methods, the ARHC algorithm simplifies system adjustment, has a larger demodulation range and higher accuracy, and is more adaptable to environmental changes. Simulations and experiments demonstrate its effectiveness and high-precision, large-dynamic-range signal demodulation capabilities under different interference conditions. The EFPI ultrasonic sensitivity based on the ARHC algorithm is 2.5 nm/Pa@23kHz, and it can linearly demodulate up to a vibration amplitude of 372.8 nm for the sensitive diaphragm, with a demodulation error of less than or equal to 0.8 nm.

Research on ELoran Demodulation Algorithm Based on Multiclass Support Vector Machine

Demodulation and decoding are pivotal for the eLoran system’s timing and information transmission capabilities. This paper proposes a novel demodulation algorithm leveraging a multiclass support vector machine (MSVM) for pulse position modulation (PPM) of eLoran signals. Firstly, the existing demodulation method based on envelope phase detection (EPD) technology is reviewed, highlighting its limitations. Secondly, a detailed exposition of the MSVM algorithm is presented, demonstrating its theoretical foundations and comparative advantages over the traditional method and several other methods proposed in this study. Subsequently, through comprehensive experiments, the algorithm parameters are optimized, and the parallel comparison of different demodulation methods is carried out in various complex environments. The test results show that the MSVM algorithm is significantly superior to traditional methods and other kinds of machine learning algorithms in demodulation accuracy and stability, particularly in high-noise and -interference scenarios. This innovative algorithm not only broadens the design approach for eLoran receivers but also fully meets the high-precision timing service requirements of the eLoran system.

3D reconstruction with single-frame two-step phase-shift method based on orthogonal composite fringe pattern projection

Abstract In order to realize single-frame three-dimensional (3D) reconstruction, a single-frame two-step phase-shift method based on orthogonal composite pattern projection is proposed to solve the problem that the traditional N-step phase-shift profilometry needs multiple projections for 3D reconstruction. The orthogonal composite pattern uses only two carrier channels to reduce the spectrum overlapping influence on the demodulation accuracy of carrier and modulated fringes. A two-dimensional variational mode decomposition method is adopted to remove the background DC component of the sinusoidal fringe to overcome the mode overlap problem by controlling the size of the bandwidth. Thus, the two-step phase-shift method is applied to calculate the phases for 3D reconstruction. The experimental results show that, compared with the typical Fourier transform profilometry method, 3-step composite method and 2 + 1 composite method, the 3D reconstruction accuracy of the proposed method is improved by 49.1%,31.4% and 23.2% respectively according to mean absolute error, and by 73.0%, 58.4% and 56.8% respectively according to mean squared error as the evaluation index. Finally, the dynamic 3D reconstruction experiment demonstrates the good adaptability of dynamic 3D reconstruction.

Interference correction for polarization spectral intensity modulation (PSIM) with spatial heterodyne spectroscopy (SHS)

Spectropolarimetry, capable of measuring both the polarization parameters and spectral information of light, is widely utilized in astrophysical research and atmospheric remote sensing. Spatial Static Polarization Modulation Interferometric Spectroscopy merges polarization spectral intensity modulation (PSIM) with spatial heterodyne spectroscopy to achieve high spectral resolution and static synchronous measurement of continuous band polarization spectral information. This article is based on spatial static polarization modulation interferometric spectroscopy principles and describes correction techniques for non-uniform response and phase errors observed in interferograms. A quantitative relationship was established through simulation between the non-uniform response, phase errors in the interferograms, and the demodulation accuracy of polarization parameters. An experimental setup based on these principles was constructed to validate the effectiveness of the correction. The experimental results demonstrated that by using the reported data processing workflow the error in the degree of polarization was reduced from 0.1354 to 0.0095.

Wavelength detection of serial WDM ultra-short fiber Bragg grating sensor networks based on a CCD interrogator using deep belief networks and sparrow search algorithm

In this paper, in order to make fiber Bragg grating spectra easier to overlap, it is proposed to use ultra-short fiber Bragg grating to build a sensor network, and for serial wavelength division multiplexing (WDM) fiber Bragg grating (FBG) sensor networks using charge-coupled device (CCD) interrogator as data acquisition devices, an efficient method for measuring strain sensor signals is presented, which combines a deep belief network (DBN) with the sparrow search algorithm (SSA). The FBG sensor network uses serial WDM connectivity, negating the need for optical switches and reducing latency of the whole sensor system. The application of a low-precision, low-resolution CCD interrogator as the data acquisition device enhances the model's generalizability and facilitates its implementation in real-world projects. DBN, a generative graphical model in machine learning, for learning features from overlapping spectra of FBGs and build the center wavelength detection model. SSA is a swarm intelligence algorithm, for optimizing the hyperparameters of the DBN model. Experimental results show that even using spectral data collected by a CCD interrogator, the DBN-SSA model can achieve good demodulation accuracy and speed, with an optimal root mean square error of 1.68pm and a single inference time of 1.4 ms. In summary, the demodulation system offers a dependable and effective solution for FBG sensor networks with limited data precision.

Temperature prediction based on long short‐term memory convolutional neural network Bragg grating sensing

AbstractTo address the constraints associated with conventional fitting techniques for temperature demodulation in the context of subway tunnel fires, a new method of demodulation grating sensing spectrum using long short‐term memory convolutional neural network (LSTM‐CNN) is proposed in this paper. Build the monitoring platform based on LSTM‐CNN ultra‐weak fiber grating temperature measurement system, predict its sensing signals by LSTM‐CNN algorithm, select 18000 spectra as sample data for training, use AdamW stochastic optimization algorithm for training, and carry out the temperature calibration and demodulation error analysis of the Fiber Bragg Grating within the temperature range of 25–75°C. Compared with GRU algorithm, LSTM algorithm and traditional maximum peak method, the algorithm of this paper is good and can effectively improve the measurement accuracy, the experimental results show that: the demodulation accuracy of temperature wavelength prediction in this paper can be up to 99.27%, and the root mean square deviation is 0.08528°C, through the experiments, it is verified that the method proposed in this paper has a certain reference and support in terms of theories and technology significance. It is suitable for the identification and monitoring of fire hazards in underground tunnels, and also has application value in the signal processing of grating array sensing demodulation system.

Interference fading suppression with fault-tolerant Kalman filter in phase-sensitive OTDR

A multi-sensor information fusion algorithm based on fault-tolerant Kalman filter is proposed in phase-sensitive optical time-domain reflectometer (Φ-OTDR) system, for achieving fading-free distributed vibration sensing. Firstly, a fault-tolerant dual-core complementary array model is designed. The Rayleigh scattering signal denoising, and vibration existence judgment of localization points are carried out to obtain the differentiated frequency demodulation results of the sensing points of the dual-core fiber array. Then a fault-tolerant control strategy is used to determine the sensor weight coefficients and vibration judgment coefficients during data fusion processing, and array data fusion is carried out based on time series data using Kalman filter to realize error value identification and filling. The advantage of this method is the combination of redundant data in a complementary way to improve the system stability. The frequency response ranges from 10 Hz to 2400 Hz and the localization accuracy is 98.33%. The influence of key parameters on the frequency demodulation performance of fault-tolerant Kalman filter is discussed, and a standard deviation of 14.6 Hz and an average error of 7.6 Hz are obtained. The demodulation frequency data matrix obtained by the classical demodulation method has a demodulation error probability of 89.18%, which proves the widespread existence of demodulation errors in vibration signals. The fusion error of demodulation frequency is reduced to 0.25 Hz, the frequency demodulation accuracy reaches 100%, and the demodulation error caused by interference attenuation can be completely eliminated. This system based on fault-tolerant Kalman filter has the characteristics of simple multiplexing structure, interference fading resistance and stable demodulation performance.

ZPW-2000 frequency-shift signal detection algorithm based on nonlinear least squares method

Aiming at the problems of spectrum leakage, difficulty in guaranteeing demodulation accuracy, and endangering driving safety in signal detection algorithm based on periodogram with limited sampling duration, this paper proposes for the first time a kind of ZPW-20000 frequency-shift signal detection algorithm based on nonlinear least squares, so as to improve the detection performance of ZPW-2000 frequency-shift signal, to ensure the safe operation of trains, and to improve the operational efficiency. The mathematical model of ZPW-2000 frequency-shift signal is established, the Cramér-Rao bound (CRB) for carrier-frequency and low-frequency estimation are derived, and a nonlinear least squares algorithm containing three processes, namely, the coarse estimation, the grid search based on Fast Fourier Transform (FFT), and the exact search, is designed, which is applied to the detection of ZPW-2000 frequency-shift signal. The research results show that the accuracy of carrier-frequency and low-frequency estimation of the proposed algorithm is better than that of the periodogram method for different sampling durations, and the number of decoding errors of the proposed algorithm and the periodogram method is reduced to zero when the sampling durations are greater than or equal to 0.11 s and 0.19 s, respectively, and the proposed algorithm reduces the limitation on the sampling durations. As the signal-to-noise ratio (SNR) increases, the root mean square error (RMSE) of carrier-frequency and low-frequency estimation of the proposed algorithm can approach the CRB. when the SNR of −2 dB, the number of decoding errors of the proposed algorithm is reduced to zero, while the periodogram method requires the SNR of 2 dB to achieve the same effect. The proposed algorithm performs well in detection accuracy, real-time and anti-interference ability, which is of great significance for ensuring driving safety and improving the reliability of the vehicle-ground communication mode based on ZPW-2000 track circuit.

Acceleration of the frequency-shift demodulation in phase-sensitive OTDR

Abstract The frequency-shift demodulation is a primary demodulation method in phase-sensitive optical time domain reflectometry (Φ-OTDR) with intrinsic resistance to interference fading. So far, the least mean squares (LMS) estimation method has the optimal demodulation accuracy and robustness. However, it takes much processing time due to the step-by-step sliding operation. In this work, we propose a fast LMS estimation method based on cross-correlation calculation to accelerate the demodulation while maintaining accuracy. Experiments are performed along a 9 km sensing fiber with a 4 m spatial resolution. The performance of the fast LMS, LMS, and cross-correlation methods are compared by using the same parameters. Compared with the LMS method, the fast LMS achieves a 12-time improvement in processing speed while remaining the same demodulation accuracy. Although the proposed fast LMS method takes slightly more time than the cross-correlation method (1.6 times), it improves the demodulation accuracy ∼6 dB for the vibration signal and ∼2.1 dB for the overall demodulation accuracy.

IESMGCFFOgram: A new method for multicomponent vibration signal demodulation and rolling bearing fault diagnosis

Resonance demodulation of vibration signals is an essential strategy for rolling bearing fault diagnosis. However, most resonance demodulation methods focus on searching for only one optimal informative frequency band, which is only valid for single-component signal analysis. In industrial applications, many interfering components are included in the monitored signal because of the complex equipment composition and running environment. Therefore, multicomponent vibration signal demodulation methods are more practical for bearing fault diagnosis. Although decomposition methods are commonly used to extract multiple components from a mixed signal, they are not accurate enough because they are implemented based on empirical statistical indicators rather than fault-related information with physical meaning. To achieve accurate multicomponent vibration signal demodulation, the improved envelope spectrums via multigroup candidate fault frequency optimization-gram (IESMGCFFOgram) is proposed. Firstly, the candidate fault frequencies (CFFs) are identified based on the local maxima distribution of the Spectral coherence (SCoh). Secondly, multigroup CFFs (MGCFFs) are extracted from the original CFFs according to the multiple relationship. Thirdly, the MGCFFs are optimized by redundant group elimination, significance ranking, and homologous group fusion. Finally, several IESMGCFFOgrams and corresponding improved envelope spectrums (IESs) are respectively obtained by using different diagnostic indicators and the classical 1/3-binary tree filter structure, where the diagnostic indicators are adaptively designed based on each group of CFFs in the final MGCFFs. It is worth noting that the noise benchmark of all IESs will be unified by subtracting the minimum before constructing each IESMGCFFOgram. The effectiveness and superiority of the proposed method are validated by simulated and experimental data. Results show that the proposed IESMGCFFOgram has higher demodulation accuracy and computational efficiency compared with three state-of-the-art methods.

Location deviation correction method based oncross-correlation spectrum in OFDR.

A location deviation compensation algorithm based on cross-correlation spectrum is proposed for optical frequency domain reflection (OFDR) measurement. The strain and the imperfect repeatability of the laser source may cause a location deviation of the OFDR measurement system, resulting in a demodulation error. This paper proposes to use the peak-to-average ratio (PAR) to measure the quality of the correlation results and achieve compensation, which achieves efficient compensation for location deviation. Compared to other compensation methods, this algorithm can deal with the complex location deviation with better demodulation accuracy and stability. Through a strain measurement experiment, we demonstrate that the demodulation error caused by location deviation is largely eliminated. As a result, the spatial resolution of the system is improved from 8cm to 2cm, and the maximum measurement range is expanded to 5000µε.

The performance analysis of the laser heterodyne ultra-high frequency detection based on the optical phase-locked loop

The performance of the laser heterodyne ultra-high frequency detection based on the optical phase-locked loop is analyzed through theoretical calculations and numerical simulations, considering the residual phase error and carrier stability. Appling the Wiener–Khinchin theorem, a general expression of the residual phase variance with essential affecting factors is derived. Furthermore, we define the error gain factor based on the ultra-high frequency carrier stability, which consists of the amplitude deviation and frequency deviation. Then the model of the demodulation output with the amplitude deviation and frequency deviation is presented. According to numerical simulation results, we acquired the variation curve of the residual phase variance with the loop bandwidth and the performance of the carrier signal stability. For the residual phase variance expression, the minimum variance corresponding to the optimal parameters can be obtained through the numerical simulation. The simulation experiment proves that the numerical results are consistent with the theoretical analysis. Our model for evaluating the influence of the carrier stability on the heterodyne ultra-high frequency detection can provide powerful support for improving the demodulation accuracy. The quantitative analysis of the paper will be available for theoretical basis and guidance for laser heterodyne detection based on optical phase-locked loops.

Five-Step Phase-Shift-Based Multiwavelength Averaging for Extrinsic Fabry–Perot Interferometric Sensors

In order to address issues such as low demodulation accuracy, large demodulation errors, small dynamic range, and complex algorithms for the extrinsic Fabry–Perot interferometric (EFPI) sensor, a five-step phase-shift algorithm based on a multiwavelength (MW)-averaging method is proposed to improve demodulation speed, noise stability, dynamic range, and noise suppression. The proposed demodulation method utilizes white-light interferometry (WLI) technology to acquire the reflection spectra and extract the five-step phase-shift signals at Ns consecutive operating points. The demodulation results of Ns sets of five-step phase-shift signals are averaged to obtain the average demodulated phase and cavity length variation. Theoretical analysis demonstrates the significant effects of the MW demodulation method on demodulation parameter errors and noise suppression. Particularly, when the demodulation parameter θ = π/2 rad, the method exhibits excellent stability against demodulation parameter error-induced instability. Moreover, it greatly improves noise suppression and reduces noise fluctuations. Numerical simulations are conducted to validate the performance of the proposed demodulation method. Compared with the traditional single-wavelength (SW) five-step phase-shifting demodulation method, the MW demodulation method exhibits stronger noise- and harmonic-suppression capabilities as the number of averaging wavelengths Ns increases. The harmonic distortion of the MW demodulation method with Ns = 128 is 20 dB lower than that of the SW demodulation method, and the noise is 15 dB lower. Furthermore, the proposed method effectively suppresses the influence of demodulation parameter errors on signal demodulation. This proposed demodulation method has the potential for fast real-time dynamic demodulation. It has great significance and application in the field of weak signal detection in fiber-optic sensors with interferometer structures and has enormous advantages in noise-suppression in complex environments.

Demodulation of the overlapping reflection spectrum of serial FBGs based on a weighted differential evolution algorithm.

This study addresses the wavelength demodulation problem of the overlapping reflection spectrum of serial fiber Bragg gratings (FBGs) with nearly-identical wavelength. Specifically, a novel demodulation model for the overlapping reflection spectrum was presented based on spectrum similarity, and this model encodes FBGs through reflectivity. Subsequently, a weighted differential evolution algorithm was employed to calculate the FBG wavelengths. And the factors affecting the demodulation accuracy of the proposed method were simulated and analyzed. Finally, the proposed method was applied to demodulate the overlapping reflection spectra of serial FBGs. The experiment results indicate that the proposed method is suitable for completely overlapping, partially overlapping, and non-overlapping reflection spectra of serial FBGs. The wavelength demodulation accuracy demonstrated here in fully overlapping situations for two, three, and four FBGs was only 4.5, 14.9, and 24.6 pm, respectively.

Dense ultraweak fiber Bragg grating temperature detection method based on minimal gating unit demodulation

To solve the problems encountered by fiber Bragg grating temperature sensing technology, such as slow response speed and low detection accuracy in small heat source monitoring, a dense ultraweak fiber Bragg grating (UWFBG) temperature detection method based on minimal gating unit (MGU) demodulation is proposed and experimentally demonstrated. This method utilizes a dense UWFBG array with a spatial distance of 10 cm for linear temperature sensing, which is approximate in size to the heat source. Field programmable gate array/advanced RISC machine-embedded circuitry implements data transfer, analog-to-digital conversion, and 1 GSPS high-speed sampling. The MGU network is trained using a mixture of real and simulated data for the demodulation of the central wavelength. Parameters, such as batch size and hidden units, are explored to optimize the demodulation speed and accuracy of the overlapping spectra. Results show that the UWFBG detection temperature method based on the MGU network can demodulate 1000 sets of wavelength data in 2.7 s and obtains a root mean square error of less than 0.923 pm, thereby achieving a fast response to heat sources of 10 cm size and a detection temperature accuracy better than 0.34 °C.

High-performance transient SBS-based microwave measurement using high-chirp-rate modulation and advanced algorithms.

The transient stimulated Brillouin scattering (SBS) effect, enabled by optical chirp chain (OCC) technology, has already been proposed and demonstrated for microwave frequency identification with high temporal resolution. Through increasing the OCC chirp rate, the instantaneous bandwidth can be effectively extended without loss of the temporal resolution. However, the higher chirp rate results in more asymmetric transient Brillouin spectra, which worsens the demodulation accuracy when using the traditional fitting method. In this Letter, advanced algorithms, including image processing and artificial neural network, are employed to improve the measurement accuracy and demodulation efficiency. A microwave frequency measurement scheme is implemented with 4 GHz instantaneous bandwidth and 100 ns temporal resolution. Through the proposed algorithms, the demodulation accuracy of transient Brillouin spectra under 50 MHz/ns high chirp rate is improved from 9.85 MHz to 1.17 MHz. Moreover, owing to the matrix computations of the proposed algorithm, the time consumption is reduced by two orders of magnitude compared with the fitting method. The proposed method allows a high-performance OCC transient SBS-based microwave measurement, which provides new possibilities to realize real-time microwave tracking for diverse application fields.

A high accuracy measurement method based on vortex polar axis rotation phase-shifting interferometry (VPAR-PSI)

For higher precision phase shift measurement, based on the characteristics of vortex beam, the manuscript introduces phase shift directly through the polar axis rotation of the vortex beam. Compared to traditional grey-scale modulation, the proposed VPAR-PSI method introduces a phase-shifting directly instead of changing the grey-scale, which not only can largely reduce the deviation caused by traditional PSI phase modulation via grey-scale change, but also can effectively avoid the non-linearity between grey-scale and phase of traditional PSI. For verifying the effectiveness of the method proposed in this manuscript, a simulation experiment, sample experiment, and VPAR-PSI and PSI comparison experiment were conducted. The results show that the proposed VPAR-PSI has a high phase-shifting and demodulation accuracy, and can be well implemented to measurement of optical components. The comparative experimental show that compared to conventional PSI, the measurement results of VPAR-PSI have smaller envelope values (mean envelope reduction of 1.4202λ), smaller RMS and standard deviation (the values decreased by 0.3515, 0.3067, and the percentage decreases were 59.69%, 59.71% respectively), proving that the VPAR-PSI technique are more accurate and stable.© 2020 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Global Science and Technology Forum Pte Ltd.

The Impact of Rayleigh Scattering in UWFBG Array-Based Φ-OTDR and Its Suppression Method.

Ultra-weak fiber Bragg grating (UWFBG) array-based phase-sensitive optical time-domain reflectometry (Φ-OTDR) utilizes the interference interaction between the reference light and the reflected light from the broadband gratings for sensing. It significantly improves the performance of the distributed acoustic sensing system (DAS) because the intensity of the reflected signal is much higher than that of the Rayleigh backscattering. This paper shows that Rayleigh backscattering (RBS) has become one of the primary noise sources in the UWFBG array-based Φ-OTDR system. We reveal the impact of the Rayleigh backscattering signal on the intensity of the reflective signal and the precision of the demodulated signal, and we suggest reducing the pulse duration to improve the demodulation accuracy. Experimental results demonstrate that using light with a 100 ns pulse duration can improve the measurement precision by three times compared with the use of a 300 ns pulse duration.

Simultaneous distributed acoustic and temperature sensing system based on ultra-weak chirped fiber Bragg grating array.

The quasi-static temperature and dynamic acoustic signals based on ultra-weak chirped fiber Bragg grating (CFBG) array is proposed and experimentally demonstrated, which can be employed to detect distributed acoustic and temperature signals simultaneously. Distributed temperature sensing (DTS) was realized by cross-correlation operation to measure the spectral drift of each CFBG, and distributed acoustic sensing (DAS) was achieved by gauging the phase difference between adjacent CFBG. Using CFBG as the sensor unit can protect acoustic signals from the fluctuations and drifts induced by temperature change without deterioration of signal-to-noise ratio (SNR). Applying least square mean adaptive filter (AF) can enhance harmonic frequency suppression ratio and increase the SNR of system. In the proof-of-concept experiment the SNR of acoustic signal is higher than 100 dB after the digital filter and frequency response is from 2 Hz to 1.25 kHz with repetition frequency of laser pulses of 10 kHz. Temperature measurement from 30°C to 100°C is achieved with demodulation accuracy of ±0.8°C. The spatial resolution (SR) of two-parameter sensing is 5 m.