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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.

The environmental deterioration has become one of the most economically consequential and charged topics. Numerous scholars have examined the driving factors failing to consider the structural breaks. This study aims to explore sustainability using the per capita ecological footprints (EF) as an indicator of environmental adversities and controlling the resources rent [(natural resources (NR)], labor capital (LC), urbanization (UR) and per capita economic growth [gross domestic product (GDP)] of China.

Through the analysis of the long- and short-run effects with an autoregressive distributed lag model (ARDL), structural break based on BP test and Granger causality test based on vector error correction model (VECM), empirical evidence is provided for the policies formulation of sustainable development.

The long-run equilibrium between the EF and GDP, NR, UR and LC is proved. In the long run, an environmental Kuznets curve (EKC) relationship existed, but China is still in the rising stage of the curve; there is a positive relationship between the EF and NR, indicating a resource curse; the UR is also unsustainable. The LC is the most favorable factor for sustainable development. In the short term, only the lagged GDP has an inhibitory effect on the EF. Besides, all explanatory variables are Granger causes of the EF.

A novel attempt is made to examine the long-term equilibrium and short-term dynamics under the prerequisites that the structural break points with its time and frequencies were examined by BP test and ARDL and VECM framework and the validity of the EKC hypothesis is tested.