A novel framework, named intra-class variation reduced features-based manifold regularisation dictionary pair learning model, is presented for solving facial expression recognition (FER) tasks. Since a query face and its corresponding image with intra-class variations (e.g. identity and illumination) are similar in appearance, the authors generate intra-class variation reduced features (IVRF) from the difference between a query face image and its corresponding estimated image of each expression class. IVRF can reduce negative influence from the intra-class variations and make their model robust to intraclass variations. Furthermore, a manifold regularisation term is incorporated into the dictionary pair learning model, which leads to a smoothly varying sparse representation. Their model fully takes advantage of the geometrical structure of data, which benefits the FER task. The experimental results on two public databases verify the effectiveness and superiority of their method and indicate its promising capability in expression discrimination.

Chatter is a self-excited and unstable vibration phenomenon during machining operations, which affects the workpiece surface quality and the production efficiency. Active chatter control has been intensively studied to mitigate chatter and expand the boundary of machining stability. This paper presents a discrete time-delay optimal control method for chatter suppression. A dynamical model incorporating the time-periodic and time-delayed characteristic of active chatter suppression during the milling process is first formulated. Next, the milling system is represented as a discrete linear time-invariant (LTI) system with state-space description through averaging and discretization. An optimal control strategy is then formulated to stabilize unstable cutting states, where the balanced realization method is applied to determine the weighting matrix without trial and error. Finally, a closed-loop stability lobe diagram (CLSLD) is proposed to evaluate the performance of the designed controller based on the proposed method. The CLSLD can provide the stability lobe diagram with control and evaluate the performance and robustness of the controller cross the tested spindle speeds. Through many numerical simulations and experimental studies, it demonstrates that the proposed control method can make the unstable cutting parameters stable with control on, reduce the control force to 21% of traditional weighting matrix selection method by trial and error in simulation, and reduce the amplitude of chatter frequency up to 78.6% in experiment. Hence, the designed controller reduces the performance requirements of actuators during active chatter suppression.

Real-time frequency information is extremely important in many fields of mechanical engineering, such as fault diagnosis, noise and vibration control, underwater acoustic detection, vehicle communication, etc. However, sometimes frequencies cannot be directly detected, making it important to quickly and accurately estimate the frequencies from contaminated signals of a mechanical system. An adaptive notch filter (ANF) is one of the most popular methods for online frequency estimation due to its simple structure and low computational complexity. However, ANF is a biased estimation if the signal contains uncorrelated noise. An enhanced adaptive notch filtering (EANF) method, which is able to reduce the frequency estimation bias and improve the estimation speed from contaminated signals, is proposed in this paper. Firstly, the limitations of the traditional ANF method are theoretically and numerically analyzed. Then, the principles of the proposed EANF method are formulated, including key parameter optimization and uncorrelated noise compensation in the update process. Afterwards, a multiple extension of the proposed EANF method is constructed using the adaptive simultaneous structure. The results of the numerical simulation show that the proposed method is superior to traditional ones. Finally, a two-stage vibration isolation system is established for experimental validation. The experimental results also demonstrate the effectiveness of the proposed method.

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