Multi-way Array Decomposition on Acoustic Source Separation for Fault Diagnosis of a Motor-Pump System

In this study, we propose a multi-way array decomposition approach to solve the complexity of approximate joint diagonalization process for fault diagnosis of a motor-pump system. Sources used in this study came from  drive end-motor, nondrive end-motor , drive end pump , and nondrive end pump. An approximate joint diagonalization is a common approach to resolving an underdetermined cases in blind source separation. However, it has quite heavy computation and requires more complexity. In this study, we use an acoustic emission to detect faults based on multi-way array decomposition approach. Based on the obtained results, the difference types of machinery fault such as misalignment and outer bearing fault can be detected by vibration spectrum and estimated acoustic spectrum. The performance of proposed method is evaluated using MSE and LSD. Based on the results of the separation, the estimated signal of the nondrive end pump is the closest to the baseline signal compared to other signals with  LSD is 1.914 and MSE is 0.0707. The instantaneous frequency of the estimated source signal will also be compared with the vibration signal in frequency spectrum to test the effectiveness of the proposed method

On blind separability based on the temporal predictability method

This letter discusses blind separability based on temporal predictability (Stone, 2001; Xie, He, & Fu, 2005). Our results show that the sources are separable using the temporal predictability method if and only if they have different temporal structures (i.e., autocorrelations). Consequently, the applicability and limitations of the temporal predictability method are clarified. In addition, instead of using generalized eigendecomposition, we suggest using joint approximate diagonalization algorithms to improve the robustness of the method. A new criterion is presented to evaluate the separation results. Numerical simulations are performed to demonstrate the validity of the theoretical results

Blind identification of mixtures of quasi-stationary sources.

由於在盲語音分離的應用，線性準平穩源訊號混合的盲識別獲得了巨大的研究興趣。在這個問題上，我們利用準穩態源訊號的時變特性來識別未知的混合系統系數。傳統的方法有二：i)基於張量分解的平行因子分析(PARAFAC);ii)基於對多個矩陣的聯合對角化的聯合對角化算法(JD)。一般來說，PARAFAC和JD 都採用了源聯合的提取方法；即是說，對應所有訊號源的系統係數在升法上是用時進行識別的。在這篇論文中，我利用Khati-Rao(KR)子空間來設計一種新的盲識別算法。在我設計的算法中提出一種與傳統的方法不同的提法。在我設計的算法中，盲識別問題被分解成數個結構上相對簡單的子問題，分別對應不同的源。在超定混合模型，我們提出了一個專門的交替投影算法(AP)。由此產生的算法，不但能從經驗發現是非常有競爭力的，而且更有理論上的利落收斂保證。另外，作為一個有趣的延伸，該算法可循一個簡單的方式應用於欠混合模型。對於欠定混合模型，我們提出啟發式的秩最小化算法從而提高算法的速度。Blind identification of linear instantaneous mixtures of quasi-stationary sources (BI-QSS) has received great research interest over the past few decades, motivated by its application in blind speech separation. In this problem, we identify the unknown mixing system coefcients by exploiting the time-varying characteristics of quasi-stationary sources. Traditional BI-QSS methods fall into two main categories: i) Parallel Factor Analysis (PARAFAC), which is based on tensor decomposition; ii) Joint Diagonalization (JD), which is based on approximate joint diagonalization of multiple matrices. In both PARAFAC and JD, the joint-source formulation is used in general; i.e., the algorithms are designed to identify the whole mixing system simultaneously.In this thesis, I devise a novel blind identification framework using a Khatri-Rao (KR) subspace formulation. The proposed formulation is different from the traditional formulations in that it decomposes the blind identication problem into a number of per-source, structurally less complex subproblems. For the over determined mixing models, a specialized alternating projections algorithm is proposed for the KR subspace for¬mulation. The resulting algorithm is not only empirically found to be very competitive, but also has a theoretically neat convergence guarantee. Even better, the proposed algorithm can be applied to the underdetermined mixing models in a straightforward manner. Rank minimization heuristics are proposed to speed up the algorithm for the underdetermined mixing model. The advantages on employing the rank minimization heuristics are demonstrated by simulations.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Lee, Ka Kit.Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 72-76).Abstracts also in Chinese.Abstract --- p.iAcknowledgement --- p.iiChapter 1 --- Introduction --- p.1Chapter 2 --- Settings of Quasi-Stationary Signals based Blind Identification --- p.4Chapter 2.1 --- Signal Model --- p.4Chapter 2.2 --- Assumptions --- p.5Chapter 2.3 --- Local Covariance Model --- p.7Chapter 2.4 --- Noise Covariance Removal --- p.8Chapter 2.5 --- Prewhitening --- p.9Chapter 2.6 --- Summary --- p.10Chapter 3 --- Review on Some Existing BI-QSS Algorithms --- p.11Chapter 3.1 --- Joint Diagonalization --- p.11Chapter 3.1.1 --- Fast Frobenius Diagonalization [4] --- p.12Chapter 3.1.2 --- Pham’s JD [5, 6] --- p.14Chapter 3.2 --- Parallel Factor Analysis --- p.16Chapter 3.2.1 --- Tensor Decomposition [37] --- p.17Chapter 3.2.2 --- Alternating-Columns Diagonal-Centers [12] --- p.21Chapter 3.2.3 --- Trilinear Alternating Least-Squares [10, 11] --- p.23Chapter 3.3 --- Summary --- p.25Chapter 4 --- Proposed Algorithms --- p.26Chapter 4.1 --- KR Subspace Criterion --- p.27Chapter 4.2 --- Blind Identification using Alternating Projections --- p.29Chapter 4.2.1 --- All-Columns Identification --- p.31Chapter 4.3 --- Overdetermined Mixing Models (N > K): Prewhitened Alternating Projection Algorithm (PAPA) --- p.32Chapter 4.4 --- Underdetermined Mixing Models (N <K) --- p.34Chapter 4.4.1 --- Rank Minimization Heuristic --- p.34Chapter 4.4.2 --- Alternating Projections Algorithm with Huber Function Regularization --- p.37Chapter 4.5 --- Robust KR Subspace Extraction --- p.40Chapter 4.6 --- Summary --- p.44Chapter 5 --- Simulation Results --- p.47Chapter 5.1 --- General Settings --- p.47Chapter 5.2 --- Overdetermined Mixing Models --- p.49Chapter 5.2.1 --- Simulation 1 - Performance w.r.t. SNR --- p.49Chapter 5.2.2 --- Simulation 2 - Performance w.r.t. the Number of Available Frames M --- p.49Chapter 5.2.3 --- Simulation 3 - Performance w.r.t. the Number of Sources K --- p.50Chapter 5.3 --- Underdetermined Mixing Models --- p.52Chapter 5.3.1 --- Simulation 1 - Success Rate of KR Huber --- p.53Chapter 5.3.2 --- Simulation 2 - Performance w.r.t. SNR --- p.54Chapter 5.3.3 --- Simulation 3 - Performance w.r.t. M --- p.54Chapter 5.3.4 --- Simulation 4 - Performance w.r.t. N --- p.56Chapter 5.4 --- Summary --- p.56Chapter 6 --- Conclusion and Future Works --- p.58Chapter A --- Convolutive Mixing Model --- p.60Chapter B --- Proofs --- p.63Chapter B.1 --- Proof of Theorem 4.1 --- p.63Chapter B.2 --- Proof of Theorem 4.2 --- p.65Chapter B.3 --- Proof of Observation 4.1 --- p.65Chapter B.4 --- Proof of Proposition 4.1 --- p.66Chapter C --- Singular Value Thresholding --- p.67Chapter D --- Categories of Speech Sounds and Their Impact on SOSs-based BI-QSS Algorithms --- p.69Chapter D.1 --- Vowels --- p.69Chapter D.2 --- Consonants --- p.69Chapter D.1 --- Silent Pauses --- p.70Bibliography --- p.7

Analisis Pemisahan Sinyal Tercampur di Bawah Air Menggunakan Metode Blind Source Separation (BSS) pada Tangki Uji Mini Semi-Tanpa Gaung (Semi-Anechoic)

Thesis ini berisi laporan eksperimen perekaman suara tercampur di bawah air berkonfigurasi overdetermined dengan jumlah sensor tiga buah dan jumlah sumber dua buah menggunakan tiga skenario keadaan untuk kemudian diurai kembali sehingga didapatkan sinyal penyusunnya menggunakan teknik Blind Source Separation (BSS) algoritma joint diagonalization time-frequency blind source separation (TFBSS) dan alternating least squares (ALS). Algoritma Time-Frequency Blind Source Separation (TFBSS) dalam memisahkan suara mendapatkan sistem pengurai (demixing matrix) dari eigenvalue dan eigenvector autokorelasi sinyal observasi, sedangkan algoritma Alternating Least Squres (ALS) mendapatkan sistem pengurai (demixing matrix) dari cross spectral density dan korelasi dari sinyal observasi. Perbedaan kedua algoritma tersebut berada pada adanya algoritma adjusting permutation pada ALS sedangkan pada TFBSS tidak. Hasil eksperimen menunjukkan bahwa unjuk kerja algoritma ALS konsisten lebih baik pada variasi suhu maupun salinitas serta kedua parameter eror yaitu MSE dan SIR dibandingkan dengan algoritma TFBSS ketika digunakan untuk memisahkan sinyal observasi yang direkam dari tangki uji mini semi-tanpa gaung. Skenario pertama yaitu variasi suhu, nilai MSE terkecil berada pada variasi sinyal observasi tipe I, penggunaan metode ALS pada suhu 21℃ yaitu sebesar 0.0966. Berdasarkan rata-rata nilai MSE metode ALS juga memiliki nilai lebih kecil yaitu sebesar 0.55 dibanding nilai rata-rata MSE TFBSS yaitu 0.6. Konsisten dengan skenario pertama, skenario kedua yaitu variasi salinitas memiliki nilai MSE terkecil pada variasi sinyal observasi tipe I, penggunaan metode ALS pada salinitas 3.1% yaitu sebesar 0.044 serta nilai rata-rata MSE metode ALS memiliki nilai lebih kecil yaitu sebesar 0.42 dibanding nilai rata-rata MSE TFBSS yaitu 0.56. Sedangkan dalam analisis nilai SIR baik pada variasi suhu maupun variasi salinitas hasil pemisahan suara menggunakan metode ALS memiliki nilai rata-rata SIR 21 dB sehingga antara sinyal estimasi satu dengan sinyal estimasi lainnya memiliki perbedaan 4 kali lebih keras ketika diterima oleh telinga, berbeda jauh dengan nilai rata-rata SIR metode TFBSS yang sebesar 3 dB. Skenario ketiga dimana perekaman percampuran suara di bawah air dilakukan pada tangki uji besar berdimensi 200×10×5.5 m tanpa variasi pada medium airnya menunjukkan adanya anomali pada hasil unjuk kerja teknik BSS kedua algoritma ALS dan TFBSS baik dari segi nilai MSE maupun SIR. Hasil skenario ketiga menunjukkan hal yang berkebalikan dari yang terjadi pada skenario pertama dan kedua yaitu nilai rata-rata MSE algoritma TFBSS yang memiliki nilai rata-rata MSE lebih kecil yaitu 0.013 dibanding rata-rata nilai MSE algoritma ALS sebesar 0.34. Hasil nilai rata-rata absolut selisih desibel dari SIR metode ALS yaitu 5.8 dB lebih besar dibandingkan nilai rata-rata absolut selisih desibel dari SIR metode TFBSS yaitu 2.5 dB. Didapatkan kesimpulan bahwa dimensi dan kondisi tempat percampuran suara memiliki pengaruh lebih signifikan dalam keberhasilan proses pemisahan suara tercampur di bawah air dibandingkan dengan variasi suhu dan salinitas pada medium air. ==================================================================================================================In this thesis, we report the sound mixed recording in underwater overdetermined configured with the number of sensors three and the number of sources two using three scenarios, then we separate again using Blind Source Separation (BSS) method with specific algorithm joint diagonalization time-frequency blind Source separation (TFBSS) and alternating least squares (ALS). When separating the mixtures, Time-Frequency Blind Source Separation (TFBSS) algorithm gets demixing matrix from the eigenvalue and eigenvector autocorrelation observation signal, while the Alternating Least Squares (ALS) algorithm gets a demixing matrix from cross spectral density and correlation the observation signal. The difference between the two algorithms is in the presence of adjusting permutation algorithm in ALS whereas in TFBSS it is not. The experimental results show that the performance of the ALS algorithm is consistently better on both temperature and salinity variations as well as the two error parametere MSE and SIR compared with the TFBSS algorithm when used to separate the observed signals recorded from mini semi-anechoic test tank. For the first scenario temperature variation, the smallest MSE value is in variation of type I observation signal, using ALS method at temperature 21℃ that is equal to 0.0966. Based on the average value, MSE ALS method also has a smaller value that is equal to 0.55 compared to the mean value of MSE TFBSS is 0.6. Consistent with the first scenario, the second scenario of salinity variation has the smallest MSE value on the variation of type I observation signal, using ALS method on salinity 3.1% which is equal to 0.044 and the average value of MSE ALS method has a smaller value that is 0.42 compared to the average value of MSE TFBSS is 0.56. While in SIR value analysis both in temperature variation and variation of salinity results using ALS method have mean value of SIR 21 dB so that between estimation signal one with other estimation signal have difference 4 times louder when received by ear, far different with average value of SIR from TFBSS method that is equal to 3 dB. For a third scenario where the recording of sound mixing is performed on a large dimension test tank 200×10×5.5 m without variation on the water medium indicates an anomaly in the results of the BSS technique's performance for both ALS and TFBSS algorithms in terms of MSE and SIR values. In this third scenario occurs the opposite of what happens in the first scenario and the second where the average value of MSE TFBSS algorithm is 0.013 smaller when compared to the average value of MSE ALS algorithm that is equal to 0.34. While for the absolute average value of the decibel difference of SIR the ALS method have value 5.8 dB greater when compared with the absolute average value of the decibel difference of SIR of TFBSS method that is equal to 2.5 dB. It is concluded that the dimensions and conditions of the mixing sound have a more significant influence in the success of the sound separation process from underwater than the variations in temperature and salinity on the water medium