An Azimuth Signal-Reconstruction Method Based on Two-Step Projection Technology for Spaceborne Azimuth Multi-Channel High-Resolution and Wide-Swath SAR

Azimuth non-uniform signal-reconstruction is a critical step for azimuth multi-channel high-resolution wide-swath (HRWS) synthetic aperture radar (SAR) data processing. However, the received non-uniform signal has noise in the actual azimuth multi-channel SAR (MCSAR) operation, which leads to the serious reduction in the signal-to-noise ratio (SNR) of the results processed by a traditional reconstruction algorithm. Aiming to address the problem of reducing the SNR of the traditional reconstruction algorithm in the reconstruction of non-uniform signal with noise, a novel signal-reconstruction algorithm based on two-step projection technology (TSPT) for the MCSAR system is proposed in this paper. The key part of the TSPT algorithm consists of a two-step projection. The first projection is to project the given signal into the selected intermediate subspace, spanned by the integer conversion of the compact support kernel function. This process generates a set of sparse equations, which can be solved efficiently by using the sparse equation solver. The second key projection is to project the first projection result into the subspace of the known sampled signal. The secondary projection can be achieved with a digital linear translation invariant (LSI) filter and generate a uniformly spaced signal. As a result, compared with the traditional azimuth MCSAR signal-reconstruction algorithm, the proposed algorithm can improve SNR and reduce the azimuth ambiguity-signal-ratio (AASR). The processing results of simulated data and real raw data verify the effectiveness of the proposed algorithm.

A Lightweight Framework for Intelligent Fault Diagnosis Acceleration in Complex Industrial Systems

<p>With the acquisition of massive condition monitoring data, how to realize real-time and efficient intelligent fault diagnosis is the focus of current research. Inspired by the ideas of compressed sensing (CS) and deep extreme learning machines (DELM), a data-driven lightweight framework is proposed to accelerate intelligent fault diagnosis. The integrated framework contains two modules: data sampling and fault diagnosis. Data sampling module projects the intensive original monitoring data into lightweight compressed sampling data non-linearly, which can effectively reduce the pressure of transmission, storage and calculation. Fault diagnosis module digs deeply into the inner connection between the compressed sampled signal and the fault types to realize accurate fault diagnosis. This work has three meaningful points. First, we believe that the bearing vibration signal is not strictly sparse in the transform domain. Second, we verified that the sparse signal after compressed sampling can be directly used for fault diagnosis without being reconstructed. Third, adding a kernel function to the DELM can perfectly map the low-dimensional inseparable features after compressed sampling to the high-dimensional space non-linearly to make it linearly separable and thus improve the classification accuracy</p>

A Lightweight Framework for Intelligent Fault Diagnosis Acceleration in Complex Industrial Systems

<p>With the acquisition of massive condition monitoring data, how to realize real-time and efficient intelligent fault diagnosis is the focus of current research. Inspired by the ideas of compressed sensing (CS) and deep extreme learning machines (DELM), a data-driven lightweight framework is proposed to accelerate intelligent fault diagnosis. The integrated framework contains two modules: data sampling and fault diagnosis. Data sampling module projects the intensive original monitoring data into lightweight compressed sampling data non-linearly, which can effectively reduce the pressure of transmission, storage and calculation. Fault diagnosis module digs deeply into the inner connection between the compressed sampled signal and the fault types to realize accurate fault diagnosis. This work has three meaningful points. First, we believe that the bearing vibration signal is not strictly sparse in the transform domain. Second, we verified that the sparse signal after compressed sampling can be directly used for fault diagnosis without being reconstructed. Third, adding a kernel function to the DELM can perfectly map the low-dimensional inseparable features after compressed sampling to the high-dimensional space non-linearly to make it linearly separable and thus improve the classification accuracy</p>

A Novel Sub-Image Local Area Minimum Entropy Reconstruction Method for HRWS SAR Adaptive Unambiguous Imaging

Multichannel high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) is a vital technique for modern remote sensing. As multichannel SAR systems usually face the problem of azimuth nonuniform sampling resulting in azimuth ambiguity, the conventional reconstruction methods are adopted to obtain the uniformly sampled signal. However, various errors, especially amplitude, phase, and baseline errors, always significantly degrade the performance of the reconstruction methods. To solve this problem, in this paper, a novel sub-image local area minimum entropy reconstruction method (SILAMER) is proposed, which has favorable adaptability to the HRWS SAR system with various errors. First, according to the idea of image domain reconstruction, the sub-images are generated by employing the back-projection algorithm. Then, we proposed an estimation algorithm based on sub-image local area minimum entropy to obtain the optimal reconstruction coefficient and the compensation phase, which can greatly improve the estimation efficiency by using a local area of the sub-image as the input for estimation. Finally, the sub-images are weighted by the optimal estimated reconstruction coefficient and calibrated by the compensation phase to obtain the unambiguous reconstruction image. The experimental results verify the effectiveness of the proposed method. Noticeably, the proposed algorithm has two additional advantages, i.e., (1) it can perform well under the condition of low signal-to-noise ratio (SNR), and (2) it is suitable for the curved trajectory SAR reconstruction. The simulations verify these advantages of the proposed method.

Noise Processes in Discrete Communication Systems

This chapter focuses on noise processes in discrete communication systems. The problem with white Gaussian noise process discretization is that a strict definition implies that the noise has theoretically infinite power. Thus, it would be impossible to generate discrete noise, because the sampling theorem requires that the sampled signal must be physically realizable, that is, the sampled noise needs to have a finite power. To overcome this problem, noise entropy is defined as an additional measure of noise properties, and a truncated Gaussian probability density function is used. Adding entropy and truncated density to the definition of the noise autocorrelation and power spectral density functions allows mathematical modelling of the discrete noise source for both baseband and bandpass noise generators and regenerators. Noise theory and noise generators are essential for a theoretical explanation of the operation of digital and discrete communications systems and their design, simulation, emulation, and testing.

Discrete sampling theorem to Shannon’s sampling theorem using the hyperreal numbers R

Shannon’s sampling theorem is one of the most important results of modern signal theory. It describes the reconstruction of any band-limited signal from a finite number of its samples. On the other hand, although less well known, there is the discrete sampling theorem, proved by Cooley while he was working on the development of an algorithm to speed up the calculations of the discrete Fourier transform. Cooley showed that a sampled signal can be resampled by selecting a smaller number of samples, which reduces computational cost. Then it is possible to reconstruct the original sampled signal using a reverse process. In principle, the two theorems are not related. However, in this paper we will show that in the context of Non Standard Mathematical Analysis (NSA) and Hyperreal Numerical System R, the two theorems are equivalent. The difference between them becomes a matter of scale. With the scale changes that the hyperreal number system allows, the discrete variables and functions become continuous, and Shannon’s sampling theorem emerges from the discrete sampling theorem.

Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram

We present a set of three fundamental methods for electrocardiogram (ECG) diagnostic interpretation adapted to process non-uniformly sampled signal. The growing volume of ECGs recorded daily all over the world (roughly estimated to be 600 TB) and the expectance of long persistence of these data (on the order of 40 years) motivated us to challenge the feasibility of medical-grade diagnostics directly based on arbitrary non-uniform (i.e., storage-efficient) ECG representation. We used a refined time-independent QRS detection method based on a moving shape matching technique. We applied a graph data representation to quantify the similarity of asynchronously sampled heartbeats. Finally, we applied a correlation-based non-uniform to time-scale transform to get a multiresolution ECG representation on a regular dyadic grid and to find precise P, QRS and T wave delimitation points. The whole processing chain was implemented and tested with MIT-BIH Database (probably the most referenced cardiac database) and CSE Multilead Database (used for conformance testing of medical instruments) signals arbitrarily sampled accordingly to a perceptual model (set for variable sampling frequency of 100–500 Hz, compression ratio 3.1). The QRS detection shows an accuracy of 99.93% with false detection ratio of only 0.18%. The classification shows an accuracy of 99.27% for 14 most frequent MIT-BIH beat types and 99.37% according to AAMI beat labels. The wave delineation shows cumulative (i.e., sampling model and non-uniform processing) errors of: 9.7 ms for P wave duration, 3.4 ms for QRS, 6.7 ms for P-Q segment and 17.7 ms for Q-T segment, all the values being acceptable for medical-grade interpretive software.

The Application of K Value Adaptive VMD Method in Pipeline Leakage Location

The research about online monitoring and leakage automatic location of water distribution networks (WDN) has a wide range of applications that include water resource protection, monitoring, and allocation. Variational mode decomposition (VMD) and cross-correlation (CC) based leakage location is a popular and effective method in WDN. However, the value of K intrinsic mode functions (IMFs) based on VMD decomposition needs to be determined artificially, which affects the separation effect of signal frequency band characteristics directly. Hence, this work proposes an adaptive method to determine the parameter K of leakage vibration signal’s IMFs, which will be applied to automatic leakage location in WDN. Firstly, the number of saddle points in the frequency domain envelope of the sampled signal in different step sizes is calculated. The parameter K is determined according to the curvature change of the number of saddle points and the sampled signal. Finally, the selective IMFs are reconstituted into a new signal, which can determine a leak position using CC based time-delay estimation (TDE). To verify the effectiveness of the proposed algorithm, the different methods based on EMD and Fast ICA are compared. The experimental results demonstrate that the proposed parameter K value adaptive VMD (KVA-VMD) decomposition method is more suitable for leakage location in WDN.

Low-Frequency Signal Sampling Method Implemented in a PLC Controller Dedicated to Applications in the Monitoring of Selected Electrical Devices

High requirements for power systems, and hence for electrical devices used in industrial processes, make it necessary to ensure adequate power quality. The main parameters of the power system include the rms-values of the current, voltage, and active and reactive power consumed by the loads. In previous articles, the authors investigated the use of low-frequency sampling to measure these parameters of the power system, showing that the method can be easily implemented in simple microcontrollers and PLCs. This article discusses the methods of measuring electrical quantities by devices with low computational efficiency and low sampling frequency up to 1 kHz. It is not obvious that the signal of 50–500 Hz can be processed using the sampling frequency of fs = 47.619 Hz because it defies the Nyquist–Shannon sampling theorem. This theorem states that a reconstruction of a sampled signal is only guaranteed possible for a bandlimit fmax < fs, where fmax is the maximum frequency of a sampled signal. Therefore, theoretically, neither 50 nor 500 Hz can be identified by such a low-frequency sampling. Although, it turns out that if we have a longer period of a stable multi-harmonic signal, which is band-limited (from the bottom and top), it allows us to map this band to the lower frequencies, thus it is possible to use the lower sampling ratio and still get enough precise information of its harmonics and rms value. The use of aliasing for measurement purposes is not often used because it is considered a harmful phenomenon. In our work, it has been used for measurement purposes with good results. The main advantage of this new method is that it achieves a balance between PLC processing power (which is moderate or low) and accuracy in calculating the most important electrical signal indicators such as power, RMS value and sinusoidal-signal distortion factor (e.g., THD). It can be achieved despite an aliasing effect that causes different frequencies to become indistinguishable. The result of the research is a proposal of error reduction in the low-frequency measurement method implemented on compact PLCs. Laboratory tests carried out on a Mitsubishi FX5 compact PLC controller confirmed the correctness of the proposed method of reducing the measurement error.