Application of differential evolution to multi-objective tuning of vibration spectrum analyzers based on microelectromechanical systems

Abstract

The vibration spectrum is a feature used in several monitoring systems designed to diagnose many mechanical systems. The most usual way to obtain this feature is to input the time domain vibration data into a processor programmed with algorithms, such as the Fast Fourier Transform. Alternatively, this feature can be obtained more directly by using twin-microaccelerometers data and a simple electronic circuit. When compared to the spectrum calculation using the Fast Fourier Transform, the second strategy presents advantages related to the possibility to design microsensors with reduced size and low power consumption. However, the manufacturing process results into different physical parameters between the twin-accelerometers, and these differences raise the spectrum distortion. To overcome this drawback, in this work the tuning of the spectrum analyzer microdevice based on twin-microaccelerometers is proposed by adjusting the accelerometers actuation voltages amplitudes. To perform the tuning, three different variations of the Generalized Differential Evolution algorithm—an extension of Differential Evolution to solve multi-objective problems—with four boundary-handling strategies are used and their results are compared. The objective functions and constraints are based on the Fourier series composition of the spectrum analyzer system closed-loop gain—which depends on the actuation voltages. The advantages and disadvantages of applying this strategy are discussed in detail, as well as the results obtained for the Pareto-set approximation. The results obtained in MATLAB® simulations—specially the distortion-sensitivity compromise—are demonstrated, discussed, and validated.