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A new on-board turbo-fan engine modeling method based on a batch normalize (BN) minibatch gradient descent (MGD) deep neural network (NN) is proposed. This new method adopts BN algorithm, which accelerates the network training speed and overcomes the gradient vanish problem. Hence, using the BN algorithm, the neural network adopts the deeper structure, which means the network has a stronger representation capacity. This mini-batch gradient descent (MGD-NN) algorithm that consumes much less time to update the NN parameters is adopted. Therefore, it is more suitable for training big dataset and establishing a high-accuracy engine model in a large flight envelope. Finally, to verify whether the proposed method could be applied to larger flight envelope, the conventional NN also adopts MGD (called MGD-NN). The turbo-fan engine models based on these two modeling methods are both conducted within a sub-sonic cruise envelope. The simulation results show that the proposed modeling method has much higher accuracy than the MGD-NN. Moreover, the proposed method has the characteristics of less data storage, low computation complexity, and good real-time performance, which are the most importance indices for model realize on-board. INDEX TERMS Aero-engine model, batch normalize, deep neural network, turbo-fan on-board model, mini-batch gradient descent, data storage.

A novel performance seeking control) method based on Beetle Antennae Search algorithm is proposed to improve the real-time performance of performance seeking control. The Beetle Antennae Search imitates the function of antennae of beetle. The Beetle Antennae Search has better real-time performance because of the objective function only calculated twice in Beetle Antennae Search at each iteration. Moreover, the Beetle Antennae Search has global search ability. The performance seeking control simulations based on Beetle Antennae Search, Genetic Algorithm and particle swarm optimization are carried out. The simulations show that the Beetle Antennae Search has much better real-time performance than the conventional probability-based algorithms Genetic Algorithm and particle swarm optimization. The simulations also show that these three probability-based algorithms can get better engine performance, such as more thrust, less specific fuel consumption and less turbine inlet temperature.