The bicrossed products of H4H_4 and H8H_8

Let $H_4$ and $H_8$ be the Sweedler's and Kac-Paljutkin Hopf algebras, respectively. In this paper we prove that any Hopf algebra which factorizes through $H_8$ and $H_4$ (equivalently, any bicrossed product between the Hopf algebras $H_8$ and $H_4$) must be isomorphic to one of the following four Hopf algebras: $H_8 \otimes H_4, H_{32,1}, H_{32,2}, H_{32,3}$. The set of all matched pair $(H_8, H_4, \triangleright, \triangleleft)$ is explicitly described, and then the associated bicrossed products is given by generators and relations

Frequency Demodulation-Aided Condition Monitoring for Drivetrain Gearboxes

Condition monitoring and fault diagnosis (CMFD) of drivetrain gearboxes has become a prominent challenge in assorted industries. Current-based diagnostic techniques have significant advantages over traditional vibration-based techniques in terms of accessibility, cost, implementation and reliability. This paper proposes a current-based, frequency demodulation-aided CMFD method for drivetrain gearboxes. A mathematical model is developed for a drivetrain consisting of a two-stage gearbox and a permanent magnet synchronous generator (PMSG), from which the characteristic frequencies of gearbox faults in the PMSG stator current are derived. An adaptive signal resampling method is proposed to convert the variable fault characteristic frequencies to constant values for the drivetrain running at variable speed conditions. A demodulation method, combining the Hilbert transform, a finite impulse response (FIR) differentiator, and a phase unwrapping algorithm, is developed to extract the instantaneous frequency (IF) patterns that are related to the faultinduced gearbox vibration. A fault detector is proposed for diagnosis of gearbox faults using statistical analysis on the extracted fault signatures. Experimental studies are carried out to validate the effectiveness of the proposed method

Current-Based Fault Detection for Wind Turbine Systems via Hilbert-Huang Transform

Mechanical failures of wind turbines represent a significant cost in both repairs and downtime. Detecting incipient faults of wind turbine components permits maintenance to be scheduled and failed parts to be repaired or replaced before causing failures of other components or catastrophic failure of the system. This paper proposes a Hilbert-Huang transform (HHT)-based algorithm to effectively extract fault signatures in generator current signals for wind turbine fault diagnosis by using the HHT’s capability of accurately representing the instantaneous amplitude and frequency of nonlinear and nonstationary signals. A phase-lock-loop (PLL) method is integrated to estimate wind turbine rotating speed, which is then used to facilitate the fault detection. The proposed method is validated by a real direct-drive wind turbine with different types of faults. The experimental results demonstrate that the proposed method is effective to detect various faults in wind turbine systems as well as to reveal the severities of the faults

Limb-girdle muscular dystrophy due to GMPPB mutations: A case report and comprehensive literature review

Mutations in the guanosine diphosphate mannose (GDP-mannose) pyrophosphorylase B (GMPPB) gene are rare. To date, 72 cases with GMPPB gene mutations have been reported. Herein, we reported a case of a 29-year-old Chinese male presenting with limb-girdle muscular dystrophy (LGMD) who was found to have two heterozygous GMPPB mutations. The patient had a progressive limb weakness for 19 years. His parents and elder brother were normal. On examination he had a waddling gait, and absent tendon reflexes in all four limbs. Electromyography showed myogenic damage. Muscle magnetic resonance imaging (MRI) showed fatty degeneration in the bilateral medial thigh muscles. High throughput gene panel sequencing revealed that the patient carried compound heterozygous mutations in the GMPPB gene, c.553C>T (p.R185C, maternal inheritance) and c.346C>T (p.P116S, paternal inheritance). This case provides additional information regarding the phenotypic spectrum of GMPPB mutations in the Chinese population

Adaptive Feature Extraction and SVM Classification for Real-Time Fault Diagnosis of Drivetrain Gearboxes

Drivetrain gearboxes play an important role in many modern industrial applications. This paper presents a novel method consisting of adaptive feature extraction and support vector machine (SVM)-based classification for condition monitoring and fault diagnosis of drivetrain gearboxes operating in variable-speed conditions. An adaptive signal resampling algorithm, a frequency tracker, and a feature generation algorithm are integrated in the proposed method for effective extraction of the features of gearbox faults from the stator current signal of the AC electric machine connected to the gearbox. A radial basis function kernel-SVM classifier is designed to identify the fault in the gearbox according to the fault features extracted. Experimental studies are performed for a drivetrain gearbox with a gear crack fault connected with a permanent magnet synchronous machine. Results show that the fault can be effectively identified by the proposed method

A GA-SVM Hybrid Classifier for Multiclass Fault Identification of Drivetrain Gearboxes

This paper presents a genetic algorithm (GA)- support vector machine (SVM) hybrid classifier for multiclass fault identification of drivetrain gearboxes in variable-speed operational conditions. An adaptive feature extraction algorithm is employed to effectively extract the features of gearbox faults from the stator current signal of an AC machine connected to the gearbox. The multiclass GA-SVM classifier is used to identify the faults in the gearbox according to the fault features extracted. A GA is designed to find the optimal parameters of the SVM to obtain the best classification accuracy. The proposed hybrid classifier is validated on a gearbox connected with a permanent-magnet synchronous machine with three different faults. Experimental results show that the multiple types of gearbox faults can be effectively identified and classified by the proposed hybrid classifier with better accuracy than the traditional SVM classifier

Fault Diagnosis for Drivetrain Gearboxes Using PSO-Optimized Multiclass SVM Classifier

A novel method consisting of an adaptive feature extraction scheme and a particle swarm optimization (PSO)- optimized multiclass support vector machine (SVM) classifier is proposed for condition monitoring and fault diagnosis of drivetrain gearboxes in variable-speed operational conditions. The adaptive feature extraction scheme consists of an adaptive signal resampling algorithm, a frequency tracker, and a feature generation algorithm for effective extraction of the features of gearbox faults from the stator current signal of the AC electric machine connected to the gearbox. The multiclass SVM classifier is designed to identify different faults in the gearbox according to the fault features extracted. The PSO algorithm is utilized to optimize the parameter setting of the SVM classifier to obtain the best classification accuracy. The proposed method is testified on a drivetrain gearbox connected with a permanent-magnet synchronous machine with three different faults. Experimental results show that the faults can be effectively classified by the proposed method

A Survey on Wind Turbine Condition Monitoring and Fault Diagnosis−Part I: Components and Subsystems

This paper provides a comprehensive survey on the state-of-the-art condition monitoring and fault diagnostic technologies for wind turbines. The Part I of this survey briefly reviews the existing literature surveys on the subject, discusses the common failure modes in the major wind turbine components and subsystems, briefly reviews the condition monitoring and fault diagnostic techniques for these components and subsystems, and specifically discusses the issues of condition monitoring and fault diagnosis for offshore wind turbines