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The electromechanical brake system is leading the latest development trend in railway braking technology. The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder. The tolerance leads to imprecise brake control, so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system. This paper aims to present improved variational mode decomposition (VMD) algorithm, which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.

The VMD algorithm plays a pivotal role in the preliminary phase, employing mode decomposition techniques to decompose the motor speed signals. Afterward, the error energy algorithm precision is utilized to extract abnormal features, leveraging the practical intrinsic mode functions, eliminating extraneous noise and enhancing the signal’s fidelity. This refined signal then becomes the basis for fault analysis. In the analytical step, the cepstrum is employed to calculate the formant and envelope of the reconstructed signal. By scrutinizing the formant and envelope, the fault point within the electromechanical brake system is precisely identified, contributing to a sophisticated and accurate fault diagnosis.

This paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake (EMB) motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction. The signal is reconstructed according to the effective intrinsic mode functions (IMFS) component of removing noise, and the formant and envelope are calculated by cepstrum to locate the fault point. Experiments show that the empirical mode decomposition (EMD) algorithm can effectively decompose the original speed signal. After feature extraction, signal enhancement and fault identification, the motor mechanical fault point can be accurately located. This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.

By using this improved VMD algorithm, the electromechanical brake system can precisely identify the rotational anomaly of the motor. This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled. Compared with the conventional motor diagnosis method, this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs. Moreover, the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.

Due to the continuous and rapid evolution of telecommunication equipment, the demand for more efficient and noise-robust detection of dual-tone multi-frequency (DTMF) signals is most significant.

A novel machine learning-based approach to detect DTMF tones affected by noise, frequency and time variations by employing the k-nearest neighbour (KNN) algorithm is proposed. The features required for training the proposed KNN classifier are extracted using Goertzel's algorithm that estimates the absolute discrete Fourier transform (DFT) coefficient values for the fundamental DTMF frequencies with or without considering their second harmonic frequencies. The proposed KNN classifier model is configured in four different manners which differ in being trained with or without augmented data, as well as, with or without the inclusion of second harmonic frequency DFT coefficient values as features.

It is found that the model which is trained using the augmented data set and additionally includes the absolute DFT values of the second harmonic frequency values for the eight fundamental DTMF frequencies as the features, achieved the best performance with a macro classification F1 score of 0.980835, a five-fold stratified cross-validation accuracy of 98.47% and test data set detection accuracy of 98.1053%.

The generated DTMF signal has been classified and detected using the proposed KNN classifier which utilizes the DFT coefficient along with second harmonic frequencies for better classification. Additionally, the proposed KNN classifier has been compared with existing models to ascertain its superiority and proclaim its state-of-the-art performance.