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Extreme learning machine and genetic algorithm in quantitative analysis of sulfur hexafluoride by infrared spectroscopy: erratum

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Abstract

This erratum reports corrections for the original publication, Appl. Opt. 61, 2834 (2022) [CrossRef]  .

© 2023 Optica Publishing Group

 figure: Fig. 7.

Fig. 7. Imitative effects of the prediction sets of the extreme learning machine (ELM), genetic algorithm joint extreme learning machine (GA-ELM), genetic algorithm joint backpropagation (GA-BP), and partial least squares (PLS) algorithm.

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Since the unit of gas concentration in this paper is ${{10}^{- 6}}$ (ppm, parts per million), the unit of mean square error E is ${{10}^{- 12}}$ (As indicated in Table 1). Errors have been found in Fig. 7 and two sentences of our paper [1]. We omitted the units of E. The places where units need to be added are as follows:

  • 1. In Abstract, “The sample mean square error decreased from 248.6917 to 63.0359” should be corrected as: “The sample mean square error decreased from ${248.6917} \times {{10}^{- 12}}$ to ${63.0359} \times {{10}^{- 12}}$”.
  • 2. In Section 4, “E of the GA-ELM algorithm was 63.0359” should be corrected as: “E of the GA-ELM algorithm was ${63.0359} \times {{10}^{- 12}}$”.
  • 3. In Fig. 7, The E in the label is corrected as shown here.

Two typographical errors have been found in Eq. (4) and a sentence of our paper [1]. In Section 4, “is the background spectrum ${\bar I _0}$ envelope” should be corrected as: “${\bar I _0}$ is the background spectrum envelope”. The correct equations read:

$$T = \frac{{(I/\bar I)}}{{({I_0}/{{\bar I}_0})}},$$

All the simulations and experiments in the original paper were performed using the correct equations, and therefore, the corrections do not affect the results and conclusions of the original paper. We regret our carelessness.

Funding

National Natural Science Foundation of China (11727806).

Acknowledgment

We sincerely thank the editors and anonymous reviewers for their constructive and helpful comments on this paper.

Disclosures

The authors declare no conflicts of interest.

Data availability

The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Reference

1. H. Liu, J. Zhu, H. Yin, Q. Yan, H. Liu, S. Guan, Q. Cai, J. Sun, S. Yao, and R. Wei, “Extreme learning machine and genetic algorithm in quantitative analysis of sulfur hexafluoride by infrared spectroscopy,” Appl. Opt. 61, 2834–2841 (2022). [CrossRef]  

Data availability

The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (1)

Fig. 7.
Fig. 7. Imitative effects of the prediction sets of the extreme learning machine (ELM), genetic algorithm joint extreme learning machine (GA-ELM), genetic algorithm joint backpropagation (GA-BP), and partial least squares (PLS) algorithm.

Equations (1)

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T = ( I / I ¯ ) ( I 0 / I ¯ 0 ) ,
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