Abstract
The ELM constructed based on the least squares loss function and ±1 label has poor generalization in the classification of data containing noise. The introduction of square pinball loss function can improve the robustness of ELM. However, the algorithm based on the squared loss function and the ±1 label imposes a margin of 1 for all training samples. At the same time, due to the unbounded nature of the loss function, the generalization of the algorithm in the classification problem is reduced. This paper proposes a soft threshold square pinball loss (SSP-Loss) function. This function can set more flexible thresholds for training samples while maintaining the robustness of the square pinball loss function. The soft-threshold square pinball loss function can approximate the bounded loss function in stages to further improve the classification performance of the algorithm. The performance of ELM based on the soft pinball loss function on several benchmark data sets proves the effectiveness of our proposed algorithm. More importantly, the excellent robustness and classification performance of the algorithm is very suitable for aeroengine gas path fault diagnosis, and is expected to become its candidate technology.
Highlights
Due to the harsh working environment, large number of parts and complicated internal structure of the aeroengine, performance degradation inevitably occurs during operation, so it’s important to take some measures to get these signs of degradation in advance to get the rest of the engine’s life, the field of engine performance parameter prediction appeared
In order to improve the limitations of Extreme learning machine (ELM) robustness and versatility, we propose an ELM based on the soft pinball loss function (SSPELM)
In order to improve the robustness of ELM, we introduce the pinball loss (P-loss) function and correntropy-induced loss (C-loss) function to improve ELM
Summary
Due to the harsh working environment, large number of parts and complicated internal structure of the aeroengine, performance degradation inevitably occurs during operation, so it’s important to take some measures to get these signs of degradation in advance to get the rest of the engine’s life, the field of engine performance parameter prediction appeared. When the value in parentheses of equation (13) is not less than 0, f (x) = +1, otherwise it’s −1, As for the loss function of ELM mentioned above, we can find that: in the classification problem with ±1 label, if the algorithm is based on the square loss function, the square of the network output of all samples will approach 1. We take the value calculated in equation (17) as the classification standard, and update δ according to certain rules [32]: (1) If ski +1 > 1,this situation indicates that the i-th training sample has been correctly classified and the output of the network is greater than 1, which far meets the margin requirement of equation (13), the threshold corresponding to the i-th sample of the iteration can be set as: δik+1 = ski +1.
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