The engine in-cylinder pressure is a very important parameter for the optimization of internal combustion engines. This paper proposes an alternative recursive Kalman filter-based engine cylinder pressure reconstruction approach using sensor-fused engine speed. In the proposed approach, the fused engine speed is first obtained using the centralized sensor fusion technique, which synthesizes the information from the engine vibration sensor and engine flywheel angular speed sensor. Afterwards, with the fused speed, the engine cylinder pressure signal can be reconstructed by inverse filtering of the engine structural vibration signal. The cylinder pressure reconstruction results of the proposed approach are validated by two combustion indicators, which are pressure peak $P_{\max }$ and peak location $P_{\mathrm{loc}}$. Meanwhile, the reconstruction results are compared with the results obtained by the cylinder pressure reconstruction approach using the calculated engine speed. The results of sensor fusion can indicate that the fused speed is smoother when the vibration signal is trusted more. Furthermore, the cylinder pressure reconstruction results can display the relationship between the sensor-fused speed and the cylinder pressure reconstruction accuracy, and with more belief in the vibration signal, the reconstructed results will become better.

Order tracking is a crucial method for time-frequency analysis of vibration signals which can provide important information for fault diagnosis in rotating machines. Several existing techniques such as the short-time Fourier transform (STFT) and the Vold-Kalman filter (VKF) can be used for time-frequency analysis under both stationary and non-stationary operating conditions. However, the problems of frequency components overlapping and interference from other frequencies are still not solved well. In this paper, we propose two alternative order tracking filters to handle these two problems. The results of numerical studies illustrate the effectiveness of the proposed methods.

The inverse system identification toolbox named INVSID 1.0 for MATLAB, which is used to identify the inversion of single-input single-output systems, is developed. The complete process of developing the toolbox is demonstrated. Afterwards, a numerical example is illustrated to describe how the toolbox can be used to solve inverse identification problems. Simulation results demonstrate the effectiveness of the toolbox.