Improved FastICA algorithm based on symmetic orthogonalization

For mechanical compound fault, it is of great significance to employ the vibration signal of a single-channel compound fault to analyze and realize the separation of multiple fault sources, which is essentially the problem of single-channel blind source separation. Shift invariant K-means singular value decomposition (shift invariant K-SVD) dictionary learning is suitable to extract the periodic and repeated fault features of a rotating machinery fault, hence in this article a single-channel compound fault analysis method is put forward which combines shift invariant K-SVD with improved fast independent component analysis (improved FastICA) algorithm. Firstly, based on single-channel compound fault signal, the shift invariant K-SVD algorithm can be used for learning multiple latent components that can be constructed as a virtual multi-channel signal. Then the improved FastICA algorithm is utilized to realize the separation of multiple fault source signals. With regard to the FastICA algorithm, the third-order convergence Newton iteration method is adopted to improve convergence speed. Moreover, in order to address the problem that FastICA is very sensitive to initialization, a steepest descent method can be applied. The experimental analysis of the compound fault of rolling bearing verifies that the presented method is effective to separate multiple fault source signals and the improved FastICA algorithm can increase convergence rate and overcome the problem of sensitivity to initialization.

Combined the improved fast independent component analysis (FastICA) algorithm with the singular value decomposition algorithm, a single-channel fetal electrocardiogram (fECG) extraction method is proposed. First, the improved FastICA algorithm is used to estimate the maternal ECG component from a single-channel abdominal signal of pregnant women using an overrelaxation factor. Then, a preliminary estimate of the fECG signal is obtained by subtracting from the single-channel abdominal signal. Subsequently, the singular value decomposition algorithm is used to denoise the preliminarily estimated fECG signal to obtain a high signal-to-noise ratio. In addition, in the singular value decomposition algorithm for fetal arrhythmia, an improved method for constructing the ECG signal reconstruction matrix is proposed. Finally, the fECG extraction experiments on synthetic abdominal signals and actual abdominal signals (data from 49 abdominal channels sourced from DAISY database and the non-invasive fECG database in PhysioNet) are carried out. The experimental results show that the method in this paper can effectively improve the signal-to-noise ratio and the accuracy of fECG signal extraction, and is suitable for maternal or fetal arrhythmias. Compared with the FastICA algorithm, the signal-to-noise ratio of the fECG signal extracted by the method in this paper is improved by about 5 dB, and the accuracy of fECG extraction in the PhysioNet database can reach 96.54%.

A method based on a sparse auto-encoder (SAE) network for the estimation of spreading sequences in long-code direct-sequence code-division multiple access (LC-DS-CDMA) signals is proposed. First, a network classification model based on SAE and softmax classifier is established. Next, the effectiveness of the proposed method is verified by estimating Walsh sequences and m sequences. To estimate the spreading sequences, the LC-DS-CDMA signal is divided into fragments. Then, each user’s spreading sequence is separated by the fast independent component analysis (Fast-ICA) algorithm, and the amplitude fuzziness is eliminated by the delay-and-multiply method. Finally, the spreading sequences are estimated by the SAE model. Experimental results showed that the proposed algorithm could effectively estimate the spreading sequences of LC-DS-CDMA signals. Compared to the existing matching algorithm and Fast-ICA algorithm, the estimation time required by the proposed algorithm was shorter, and its estimation performance at low signal-to-noise ratios was superior.

To solve the problem that vibration signal is easily affected by noise, which leads to the difficulty of fault feature extraction. This paper proposes a method for rolling bearing fault feature extraction which based on Cubic spline interpolation Intrinsic Time-scale Decomposition (CITD) algorithm and Fast Independent Component Analysis (FastICA) algorithm. Firstly, CITD method was used to decompose the original fault vibration signal, and a series of Proper Rotation (PR) components were obtained. Then the components with abundant fault information are selected by kurtosis criterion to reconstruct the observed signal, and the remaining components are reconstructed to obtain the virtual noise channel signal. FastICA algorithm is used to reduce the noise of reconstructed signal. The Teager-Kaiser Energy Operator (TKEO) is used to demodulate the signal after noise reduction. Finally, FFT transform is applied to the demodulated signal, the fault feature information of the original signal is extracted. Through comparative experiments, the results show that the proposed method can extract the fundamental frequency and frequency doubling characteristic information of rolling bearing faults more clearly and effectively.

A new blind image source separation algorithm based on feedback sparse component analysis

The economic and environmental losses due to serious leakage in the urban water supply network have increased the effort to control the water leakage. However, current methods for leakage estimation are inaccurate leading to the development of ineffective leakage controls. Therefore, this study proposes a method based on the blind source separation theory (BSS) to calculate the leakage of water supply network. The method uses fast independent component analysis (FastICA) algorithm to separate flow signal of laboratory and practical measuring area, adopts trend similarity to solve the uncertainty of separation sequence to get hourly change curve of user usage and physical leakage, and embeds the leakage model into amplitude optimization model to solve amplitude uncertainty to obtain physical leakage value. The study found that the estimation of leakage level using the blind source separation is reasonably accurate and facilitates the identification of the subsequent reduction in water leakage. This can provide scientific evidence for leakage reduction and the investment of pressure relief devices in the next stage.

The multicarrier code division multiple access (MC-CDMA) technique has received considerable interest for its potential application to future wireless communication systems due to its high data rate. A common problem regarding the blind multiuser detectors used in MC-CDMA systems is that they are extremely sensitive to the complex channel environment. Besides, the perturbation of colored noise may negatively affect the performance of the system. In this paper, a new coherent detection method will be proposed, which utilizes the modified fast independent component analysis (FastICA) algorithm, based on approximate negentropy maximization that is subject to the second-order cone programming (SOCP) constraint. The aim of the proposed coherent detection is to provide robustness against small-to-medium channel estimation mismatch (CEM) that may arise from channel frequency response estimation error in the MC-CDMA system, which is modulated by downlink binary phase-shift keying (BPSK) under colored noise. Noncoherent demodulation schemes are preferable to coherent demodulation schemes, as the latter are difficult to implement over time-varying fading channels. Differential phase-shift keying (DPSK) is therefore the natural choice for an alternative modulation scheme. Furthermore, the new blind differential SOCP-based ICA (SOCP-ICA) detection without channel estimation and compensation will be proposed to combat Doppler spread caused by time-varying fading channels in the DPSK-modulated MC-CDMA system under colored noise. In this paper, numerical simulations are used to illustrate the robustness of the proposed blind coherent SOCP-ICA detector against small-to-medium CEM and to emphasize the advantage of the blind differential SOCP-ICA detector in overcoming Doppler spread.

The impact of outliers on signal separation performance of an independent component analysis (ICA) algorithm is an important factor when selecting an ICA algorithm. If an ICA estimator has the property of B-robustness, the influence of an extreme point is bounded, leading to good separation performance in the presence of outliers. Since this property is binary, it does not give the degree of influence an outlier has on the separation performance. To address this issue, a Mamdani-type fuzzy inference, based on the location of a potential outlier and on the skewness of the data set, has been developed. It creates an outlier sensitivity map for an ICA algorithm. The implication of this work is a criterion to switch from one ICA algorithm to another in real time, as determined by the algorithms sensitivity to the data set under consideration. This paper describes estimation of the outlier impact on the separation performance of the non-B-robust FastICA algorithm using a Mamdani-type fuzzy inference. In simulations with data sets contaminated by outliers, the FastICA sensitivity map resembles the separation performance measured by the Amari performance index.

The separation of independent components from an array of mixtures is an interesting but difficult problem in signal processing. This paper re-examine the fastICA algorithm proposed by Hyvarinen and Oja for independent component analysis. The ways needed in fastICA algorithm for decorrelation the separating matrix can be deflationary or symmetric orthogonalization. Using the one-unit fastICA algorithm, this paper proposes a method to choose a suitable initial separating matrix of the fastICA algorithm with symmetric orthonormalization. The formed new algorithm can get faster speed without losing the intrinsic advantage of the original symmetric fastICA algorithm. Simulation results confirm the validity of the new algorithm.

Fetal electrocardiograms (FECGs) provide important clinical information for early diagnosis and intervention. However, FECG signals are extremely weak and are greatly influenced by noises. FECG signal extraction and detection are still challenging. In this work, we combined the fast independent component analysis (FastICA) algorithm with singular value decomposition (SVD) to extract FECG signals. The improved wavelet mode maximum method was applied to detect QRS waves and ST segments of FECG signals. We used the abdominal and direct fetal ECG database (ADFECGDB) and the Cardiology Challenge Database (PhysioNet2013) to verify the proposed algorithm. The signal-to-noise ratio of the best channel signal reached 45.028 dB and the issue of missing waveforms was addressed. The sensitivity, positive predictive value and F1 score of fetal QRS wave detection were 96.90%, 98.23%, and 95.24%, respectively. The proposed algorithm may be used as a new method for FECG signal extraction and detection.

As one of the main optical wireless communication technologies, visible light communication (VLC) is considered a promising supplement in 5G/6G and the internet of things (IoT) networks. The multiple-input–multiple-output (MIMO) multiplexing scheme can significantly enhance a VLC system’s performance. To handle the blind MIMO demultiplexing, geometric vector extraction (GVE) algorithms are used in a mixture space (MS), which has not been presented in the extant literature. In a 2 × 2 VLC MIMO scenario, the singular value decomposition of an arbitrary MIMO channel matrix is introduced to discuss the one-to-one relationship between channel-matrix elements and the outline-shape conversion starting from the transmitted rectangular-shaped points in the MS. By extracting the vector features of the adjacent sides of the received parallelogram-shaped constellation points, we can obtain the elements of an unknown channel matrix and recover the superposed signals transmitted by two light-emitting diodes (LED). To obtain a vector from these constellation points, clustering is required to obtain the scattered points’ centroids in advance. To avoid falling into a local minimum, we present a clustering algorithm with an initial-position-expansion pre-processing stage to place the initial centroids with the greatest accumulated distance. To enhance the computational efficiency, we enhance the clustering algorithm via a single iteration to obtain the centroids, which we named the GVE-for-iteration-once (GVE–IO) algorithm. The enhanced algorithm has an equivalent or better MIMO demultiplexing performance and quick convergence performance compared to the fast independent component analysis (FastICA) algorithm. Moreover, the GVE–IO algorithm’s computational complexity and measured running time is reduced to 29% and 23%, respectively, of the FastICA algorithm’ time costs. Finally, the experimental investigation shows that the proposed scheme exhibits a significantly reduced computational complexity in all discussed voltage peak-to-peak (Vpp) cases of LED and a Q-value enhancement in two-thirds of the Vpp combination regions for 50 input points.

The complex fast independent component analysis (c-FastICA) algorithm is one of the most popular methods for solving the ICA problem with complex-valued data. In this study, we extend the work of Bingham and Hyvarinen [1] by deriving conditions for local stability for the more general case of noncircular sources. We use the results of the analysis to quantify the effects of noncircularity on the performance of the algorithm using various nonlinearities and source distributions. Simulations are presented to demonstrate the results of our analysis.

Musical Instrument Sound Signal Separation from Mixture using DWT and Fast ICA Based Algorithm in Noisy Environment

This paper presents a blind multi-user detection technique for multi-antenna quadrature amplitude modulation (QAM) receivers with Inphase/Quadrature phase (I/Q) imbalances. The estimation of multiple users in the presence of I/Q imbalances is performed by Blind Source Separation (BSS) methods. While the complex-valued signal model for multi-antenna QAM receivers does not lend itself to BSS due to the effect of I/Q imbalances, reformulating the signal model to a real-valued equivalent form enables the application of BSS. The proposed method enables multiple users to share the same bandwidth simultaneously in different geographical locations, and avoids the need for the knowledge of the channel state information. In addition, despite of the presence of I/Q imbalances in all receiver branches, the number of antenna required in the receiver is equal to the number of users. Computer simulations are conducted using the popular Fast-ICA (Independent Component Analysis) algorithm, and the simulation results confirmed the effectiveness of the proposed technique.

Constrained independent component analysis (ICA) is an effective method for solving the blind source separation with a prior knowledge. However, most constrained ICA algorithms are proposed for the real-valued sources. In this paper, a novel constrained noncircular complex fast independent component analysis (c-ncFastICA) algorithm based on the fixed-point learning is proposed to address the complex-valued sources. The c-ncFastICA algorithm uses the augmented Lagrangian method to obtain a new cost function and then utilizes the quasi-Newton method to search its optimal solution. Compared with other ICA and constrained ICA algorithms, c-ncFastICA has better separation performance. Simulations confirm the effectiveness and superiority of the c-ncFastICA algorithm.