Correction: Fault diagnosis and prediction of industrial hydraulic pumps based on KOA-CNN-BILSTM model

Equation 4 in 2.2 Section was erroneously given as y k l = ReLU ∑ i = 1 K c ω k , j · x l + i − 1 + b k. The correct equation is y k l = ReLU ∑ i = 1 K c ω k , i · x l + i − 1 + b k.

Among them, Please revise the sentence. The sentence in Line 383 of Section 2.2 was erroneously given as “In Equation 4, ω k , j is the weight of the ith conv kernel”. The correct sentence is “In Equation 4, ω k , i is the weight of the ith conv kernel”.

Equation 6 in 2.2 Section was erroneously given as f t = S i g m o i d W f · h t − 1 , x t + b f d t = S i g m o i d W d · h t − 1 , x t + b d C t ∼ = tanh W c · h t − 1 , x t + b c C t = f t ⊙ C t − 1 + i i ⊙ C t ∼ o t = S i g m o i d W o · h t − 1 , x t + b o h t = o t ⊙ tanh C t.

The correct equation isf t = S i g m o i d W f · h t − 1 , x t + b f i t = S i g m o i d W d · h t − 1 , x t + b d C t ∼ = tanh W c · h t − 1 , x t + b c C t = f t ⊙ C t − 1 + i t ⊙ C t ∼ o t = S i g m o i d W o · h t − 1 , x t + b o h t = o t ⊙ tanh C t.

Among them, Please revise the sentence. The sentence in Line 400 of Section 2.2 was erroneously given as “input gate d t”. The correct sentence is “input gate i t”.

Equation 8 in 2.2 Section was erroneously given as y j ∼ = exp W j + b j ∑ k = 1 k exp W k + b k. The correct equation is y j ∼ = exp W j · v + b j ∑ k = 1 k exp W k + b k.

Equation 12 in 2.2 Section was erroneously given as Q i t + 1 = Q i t + α r 3 ⊙ Q s u n − Q i t + 1. The correct equation is Q i t + 1 = Q i t + α r 3 ⊙ Q s u n − Q i t.

The original version of this article has been updated.

There was a mistake in Table 1 as published. The corrected Table 1 appears below.

TABLE 1. Parameter settings of the KOA-CNN-BILSTM.

There was a mistake in Figure 9 as published. The corrected Figure 9 appears below.

There was a mistake in the caption of Figure 5 as published. The corrected caption of Figure 5 appears below.

“Figure 5 Comparison of accuracy and precision curves. (a) Accuracy; (b) Precision”.

There was a mistake in the caption of Figure 7 as published. The corrected caption of Figure 7 appears below.

“Figure 7 Comparison of training time, inference time and the GFLOPs (a) Training time; (b) Inference time; (c) GFLOPs”.

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Footnotes

Edited and reviewed by: Donato Perfetto, Università della Campania Luigi Vanvitelli, Italy