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Modeling Quality Changes in Brined Bream (Megalobrama amblycephala) Fillets During Storage: Comparison of the Arrhenius Model, BP, and RBF Neural Network

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Abstract

To evaluate and predict the freshness of brined bream (Megalobrama amblycephala) fillets stored at different temperatures, changes in quality [nucleotide degradation products (IMP, HxR, Hx), K value, sensory assessment (SA), total aerobic counts (TAC), thiobarbituric acid reactive substances (TBARS), and total volatile base nitrogen (TVB-N)] were investigated. The Arrhenius model, back-propagation neural network (BP-NN), and radial basis function neural network (RBF-NN) were established and compared. The RBF-NN predicted changes of SA, TAC, K value, TVB-N, TBARS, and HxR of brined fillets during storage with relative errors all within ±5 %, while the BP-NN values were all within ±10 % (except for the values at day 2 for K value, day 2 and day 4 for HxR). For the Arrhenius model, the relative errors of TVB-N were all within ±10 %, and those of SA, TAC, K value, TBARS, and HxR ranged from 0.58 to 44.37 %. Thus, RBF-NN is a promising method for predicting the changes in the quality of bream during storage at 270–282 K.

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Acknowledgments

This study was supported by the National Natural Science Foundation of China (award nr 31471683) and the earmarked fund for China Agriculture Research System (CARS-46). I would like to thank Thomas A. Gavin, Professor Emeritus, Cornell University, for the help with editing the English in this paper.

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Authors and Affiliations

  1. College of Food Science and Nutritional Engineering, China Agricultural University, Beijing, 100083, People’s Republic of China

    Huiyi Wang, Chunli Kong, Dapeng Li, Na Qin, Hongbing Fan, Hui Hong & Yongkang Luo

  2. Beijing Higher Institution Engineering Research Center of Animal Product, Beijing, 100083, People’s Republic of China

    Yongkang Luo

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  1. Huiyi Wang
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  3. Dapeng Li
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Appendices

Appendix A

BP-NN: one hidden layer, 11 hidden neurons.

Input layer:

\( {X}_1=\frac{\mathrm{Temperature}-276}{6} \) (270 K < Temperature < 282 K)

\( {X}_2=\frac{\mathrm{Time}-11.75}{11.25} \) (Time >0 day)

Hidden layer:

$$ {X}_{p\left(p=3,4\dots 13\right)}=\frac{1}{\left[1+ \exp \left[-\sum {w}_{kj}{X}_j+{w}_{j0}\right]\right]} $$
$$ {W}_{ji}=\left[\begin{array}{c}-3.31\\ {}9.92\end{array}\right.\ \begin{array}{c}3.78\\ {}9.40\end{array}\ \begin{array}{c}-6.58\\ {}8.01\end{array}\begin{array}{c}0.79\\ {}-6.52\end{array}\begin{array}{c}-2.40\\ {}-21.19\end{array}\ \begin{array}{c}9.75\\ {}-8.14\end{array}\begin{array}{c}-3.71\\ {}-4.86\end{array}\begin{array}{c}-9.34\\ {}\ 1.73\end{array}\begin{array}{c}-4.58\\ {}-7.61\end{array}\begin{array}{c}-2.24\\ {}-7.12\end{array}{\left.\begin{array}{c}-9.53\\ {}-5.37\end{array}\right]}^T $$
$$ {w}_{j0}={\left[\ 11.59-7.00\ 11.82-0.86-13.49\ 6.43-0.66-0.03\ 2.99-5.95-7.04\right]}^T $$

Output layer:

$$ {X}_{q\left(q=14,15,\dots 19\right)}=\sum {w}_{kj}{X}_j+{\mathrm{w}}_{k0} $$
$$ {w}_{kj}=\left[\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.81\\ {}-1.84\end{array}\\ {}-1.85\\ {}-2.05\end{array}\\ {}0.10\end{array}\\ {}1.65\end{array}\right.\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.67\\ {}0.95\end{array}\\ {}-0.27\\ {}0.07\end{array}\\ {}1.65\end{array}\\ {}2.03\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.87\\ {}2.41\end{array}\\ {}2.92\\ {}2.86\end{array}\\ {}0.26\end{array}\\ {}-0.88\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.00\\ {}0.86\end{array}\\ {}3.10\\ {}1.29\end{array}\\ {}-0.41\end{array}\\ {}-1.41\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.05\\ {}-0.41\end{array}\\ {}0.31\\ {}0.22\end{array}\\ {}-0.11\end{array}\\ {}-1.20\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.03\\ {}-0.09\end{array}\\ {}-2.27\\ {}-1.94\end{array}\\ {}-0.40\end{array}\\ {}4.56\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}2.92\\ {}-3.01\end{array}\\ {}-3.85\\ {}-3.56\end{array}\\ {}-0.60\end{array}\\ {}-0.18\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.22\\ {}1.36\end{array}\\ {}2.93\\ {}2.12\end{array}\\ {}0.30\end{array}\\ {}-1.60\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}1.33\\ {}-0.98\end{array}\\ {}-0.94\\ {}0.18\end{array}\\ {}0.58\end{array}\\ {}-3.42\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}2.54\\ {}-2.66\end{array}\\ {}-3.62\\ {}-3.60\end{array}\\ {}0.35\end{array}\\ {}0.97\end{array}{\left.\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}1.08\\ {}-1.06\end{array}\\ {}-2.65\\ {}-1.83\end{array}\\ {}-0.35\end{array}\\ {}1.60\end{array}\right]}^T $$
$$ {w}_{k0}={\left[-1.39\ 1.75\ 1.23\ 1.86-0.23\ 0.28\right]}^T $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\triangle SA=13.50*\mathrm{X}14-14.50\ \\ {}\triangle TAC=2.35*\mathrm{X}15+2.52\ \end{array}\\ {}\triangle K\ value=36.61*\mathrm{X}16+38.98\\ {}\triangle TVB-\mathrm{N}=5.42*\mathrm{X}17+6.54\ \end{array}\\ {}\triangle \mathrm{TBARS}=1.36*\mathrm{X}18+1.55\ \end{array}\\ {}\triangle HxR=1.64*\mathrm{X}19+1.84\end{array} $$

Appendix B

RBF-NN: one hidden layer, 47 hidden neurons.

Input:

\( {X}_1=\frac{\mathrm{Temperature}-276}{6} \) (270 K < Temperature < 282 K)

\( {X}_2=\frac{\mathrm{Time}-11.75}{11.25} \) (Time >0 day)

Radial basis layer:

$$ {X}_{p\left(p=3,4\dots 49\right)}= \exp \left[-{\left[\sqrt{{\sum \left[{w}_{ji}-{x}_i\right]}^2}\times {w}_{j0}\right]}^2\right]= \exp \left[-{0.8326}^2\times {\left[\frac{\parallel {w}_{ji}-{x}_i\parallel }{1.67}\right]}^2\right] $$
$$ wji=\left[\ \begin{array}{c}-0.50\\ {}-0.91\end{array}\right.\ \begin{array}{c}1.00\\ {}-1.00\end{array}\ \begin{array}{c}1.00\\ {}-0.54\end{array}\ \begin{array}{c}0.00\\ {}-0.05\end{array}\ \begin{array}{c}0.50\\ {}-0.85\end{array}\ \begin{array}{c}-1.00\\ {}-0.48\end{array}\ \begin{array}{c}-1.00\\ {}1.00\end{array}\begin{array}{c}-0.50\\ {}-0.05\end{array}\ \begin{array}{c}-1.00\ \\ {}0.45\end{array}\ \begin{array}{c}0.00\\ {}-0.78\end{array}\ \begin{array}{c}1.00\\ {}-0.60\end{array} $$
$$ \begin{array}{c}-0.50\ \\ {}0.08\end{array}\ \begin{array}{c}-0.50\\ {}-0.66\end{array}\ \begin{array}{c}-1.00\\ {}-0.66\end{array}\begin{array}{c}\ 1.00\\ {}-0.97\end{array}\ \begin{array}{c}\ 0.50\\ {}-0.42\end{array}\ \begin{array}{c}\ 0.50\\ {}-0.97\end{array}\ \begin{array}{c}-1.00\\ {}\ 0.82\end{array}\ \begin{array}{c}-0.50\\ {}-0.17\end{array}\ \begin{array}{c}\ 0.00\\ {}-0.17\end{array}\ \begin{array}{c}\ 1.00\\ {}-0.66\end{array}\ \begin{array}{c}-0.50\\ {}-0.29\end{array}\ \begin{array}{c}\ 0.50\\ {}-0.48\end{array} $$
$$ \begin{array}{c}-1.00\\ {}\ 0.63\end{array}\ \begin{array}{c}1.00\\ {}-0.94\end{array}\ \begin{array}{c}0.50\\ {}-0.54\end{array}\ \begin{array}{c}1.00\\ {}-0.72\end{array}\ \begin{array}{c}0.00\\ {}-0.91\end{array}\begin{array}{c}\ 1.00\\ {}-0.78\end{array}\ \begin{array}{c}0.50\\ {}-0.60\end{array}\ \begin{array}{c}0.50\\ {}-0.91\end{array}\ \begin{array}{c}0.00\\ {}-0.66\end{array}\ \begin{array}{c}-0.50\\ {}-0.78\end{array}\ \begin{array}{c}-0.50\\ {}-0.54\end{array}\ \begin{array}{c}-1.00\\ {}-0.85\end{array} $$
$$ \begin{array}{c}\ 1.00\ \\ {}-0.91\end{array}\ \begin{array}{c}\ 1.00\\ {}-0.88\end{array}\ \begin{array}{c}\ 1.00\\ {}-0.85\end{array}\ \begin{array}{c}\ 0.50\\ {}-0.78\end{array}\ \begin{array}{c}-1.00\\ {}\ 0.26\end{array}\ \begin{array}{c}-1.00\\ {}-0.29\end{array}\ \begin{array}{c}\ 0.50\\ {}-0.66\end{array}\ \begin{array}{c}\ 0.00\\ {}-0.42\end{array}\ \begin{array}{c}-0.50\\ {}-0.42\end{array}\ \begin{array}{c}\ 0.00\\ {}-0.29\end{array}\ {\left.\begin{array}{c}-1.00\\ {}\ 0.08\end{array}\ \begin{array}{c}-1.00\\ {}-0.11\end{array}\right]}^T $$

Output layer:

$$ {X}_{q\left(q=50,51\dots 55\right)}=\sum {w}_{kj}{X}_j+{w}_{k0} $$
$$ {w}_{kj}=\left[\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-5.03\mathrm{E}+06\\ {}\ 1.74\mathrm{E}+07\end{array}\\ {}\ 1.28\mathrm{E}+06\\ {}\ 3.90\mathrm{E}+06\end{array}\\ {}\ 2.05\mathrm{E}+06\end{array}\\ {}\ 6.04\mathrm{E}+06\end{array}\right.\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.58\mathrm{E}+10\\ {}\ 4.31\mathrm{E}+10\end{array}\\ {}-1.95\mathrm{E}+10\\ {}\ 1.17\mathrm{E}+10\end{array}\\ {}-2.40\mathrm{E}+09\end{array}\\ {}-1.24\mathrm{E}+11\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 5.59\mathrm{E}+09\\ {}\ 1.01\mathrm{E}+10\end{array}\\ {}-4.35\mathrm{E}+09\\ {}\ 3.16\mathrm{E}+09\end{array}\\ {}-5.15\mathrm{E}+08\end{array}\\ {}-2.76\mathrm{E}+10\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.29\mathrm{E}+06\\ {}\ 4.52\mathrm{E}+06\end{array}\\ {}-1.64\mathrm{E}+06\\ {}\ 2.31\mathrm{E}+06\end{array}\\ {}-9.06\mathrm{E}+04\end{array}\\ {}-1.12\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-2.35\mathrm{E}+10\\ {}\ 2.07\mathrm{E}+10\end{array}\\ {}\ 1.18\mathrm{E}+10\\ {}-1.10\mathrm{E}+09\end{array}\\ {}\ 5.58\mathrm{E}+09\end{array}\\ {}\ 7.47\mathrm{E}+10\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.59\mathrm{E}+06\\ {}\ 1.88\mathrm{E}+07\end{array}\\ {}\ 1.06\mathrm{E}+06\\ {}\ 4.59\mathrm{E}+06\end{array}\\ {}\ 2.14\mathrm{E}+06\end{array}\\ {}\ 4.09\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.95\mathrm{E}+05\\ {}\ 2.09\mathrm{E}+06\end{array}\\ {}\ 1.14\mathrm{E}+05\\ {}\ 5.16\mathrm{E}+05\end{array}\\ {}\ 2.33\mathrm{E}+05\end{array}\\ {}\ 4.38\mathrm{E}+05\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.73\mathrm{E}+07\\ {}-1.02\mathrm{E}+08\end{array}\\ {}-6.22\mathrm{E}+06\\ {}-2.36\mathrm{E}+07\end{array}\\ {}-1.18\mathrm{E}+07\end{array}\\ {}-2.67\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 7.34\mathrm{E}+06\\ {}-3.16\mathrm{E}+07\end{array}\\ {}-1.60\mathrm{E}+06\\ {}-7.87\mathrm{E}+06\end{array}\\ {}-3.53\mathrm{E}+06\end{array}\\ {}-5.71\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.76\mathrm{E}+06\\ {}-9.63\mathrm{E}+06\end{array}\\ {}\ 1.69\mathrm{E}+06\\ {}-3.78\mathrm{E}+06\end{array}\\ {}-4.13\mathrm{E}+05\end{array}\\ {}\ 1.25\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.21\mathrm{E}+10\\ {}-7.48\mathrm{E}+10\end{array}\\ {}\ 3.26\mathrm{E}+10\\ {}-2.31\mathrm{E}+10\end{array}\\ {}\ 3.91\mathrm{E}+09\end{array}\\ {}\ 2.07\mathrm{E}+11\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-8.03\mathrm{E}+07\\ {}\ 2.87\mathrm{E}+08\end{array}\\ {}\ 1.93\mathrm{E}+07\\ {}\ 6.55\mathrm{E}+07\end{array}\\ {}\ 3.35\mathrm{E}+07\end{array}\\ {}\ 8.78\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.98\mathrm{E}+06\\ {}-8.01\mathrm{E}+06\end{array}\\ {}-4.71\mathrm{E}+05\\ {}-1.94\mathrm{E}+06\end{array}\\ {}-9.14\mathrm{E}+05\end{array}\\ {}-1.87\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-7.83\mathrm{E}+10\\ {}-1.31\mathrm{E}+11\end{array}\\ {}\ 5.93\mathrm{E}+10\\ {}-3.60\mathrm{E}+10\end{array}\\ {}\ 7.33\mathrm{E}+09\end{array}\\ {}\ 3.78\mathrm{E}+11\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-2.32\mathrm{E}+09\\ {}\ 1.04\mathrm{E}+09\end{array}\\ {}\ 1.24\mathrm{E}+09\\ {}-4.24\mathrm{E}+08\end{array}\\ {}\ 4.88\mathrm{E}+08\end{array}\\ {}\ 7.89\mathrm{E}+09\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.44\mathrm{E}+09\\ {}\ 1.48\mathrm{E}+09\end{array}\\ {}\ 7.06\mathrm{E}+08\\ {}-1.21\mathrm{E}+06\end{array}\\ {}\ 3.55\mathrm{E}+08\end{array}\\ {}\ 4.46\mathrm{E}+09\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.91\mathrm{E}+06\\ {}-8.13\mathrm{E}+06\end{array}\\ {}-4.32\mathrm{E}+05\\ {}-2.01\mathrm{E}+06\end{array}\\ {}-9.07\mathrm{E}+05\end{array}\\ {}-1.62\mathrm{E}+06\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-7.52\mathrm{E}+07\\ {}\ 2.87\mathrm{E}+08\end{array}\\ {}\ 1.64\mathrm{E}+07\\ {}\ 6.73\mathrm{E}+07\end{array}\\ {}\ 3.28\mathrm{E}+07\end{array}\\ {}\ 6.81\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-8.22\mathrm{E}+06\\ {}-1.62\mathrm{E}+07\end{array}\\ {}\ 5.85\mathrm{E}+06\\ {}-8.24\mathrm{E}+06\end{array}\\ {}\ 2.98\mathrm{E}+05\end{array}\\ {}\ 4.00\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.42\mathrm{E}+11\\ {}\ 2.49\mathrm{E}+11\end{array}\\ {}-1.09\mathrm{E}+11\\ {}\ 7.54\mathrm{E}+10\end{array}\\ {}-1.33\mathrm{E}+10\end{array}\\ {}-6.96\mathrm{E}+11\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.32\mathrm{E}+08\\ {}-5.04\mathrm{E}+08\end{array}\\ {}-2.89\mathrm{E}+07\\ {}-1.18\mathrm{E}+08\end{array}\\ {}\ 5.77\mathrm{E}+07\end{array}\\ {}-1.20\mathrm{E}+08\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.49\mathrm{E}+10\\ {}-7.47\mathrm{E}+09\end{array}\\ {}-7.92\mathrm{E}+09\\ {}\ 2.47\mathrm{E}+09\end{array}\\ {}-3.18\mathrm{E}+09\end{array}\\ {}-5.03\mathrm{E}+10\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.38\mathrm{E}+06\\ {}\ 1.88\mathrm{E}+07\end{array}\\ {}\ 9.72\mathrm{E}+05\\ {}\ 4.66\mathrm{E}+06\end{array}\\ {}\ 2.10\mathrm{E}+06\end{array}\\ {}\ 3.57\mathrm{E}+06\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.00\mathrm{E}+00\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.07\mathrm{E}+10\\ {}\ 2.27\mathrm{E}+10\end{array}\\ {}\ 2.15\mathrm{E}+10\\ {}-6.02\mathrm{E}+09\end{array}\\ {}\ 8.83\mathrm{E}+09\end{array}\\ {}\ 1.36\mathrm{E}+11\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-2.81\mathrm{E}+11\\ {}-4.86\mathrm{E}+11\end{array}\\ {}\ 2.16\mathrm{E}+11\\ {}-1.45\mathrm{E}+11\end{array}\\ {}\ 2.64\mathrm{E}+10\end{array}\\ {}\ 1.37\mathrm{E}+12\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.65\mathrm{E}+05\\ {}\ 2.95\mathrm{E}+06\end{array}\\ {}-3.63\mathrm{E}+05\\ {}\ 1.06\mathrm{E}+06\end{array}\\ {}\ 1.73\mathrm{E}+05\end{array}\\ {}-2.84\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 3.58\mathrm{E}+11\\ {}\ 6.12\mathrm{E}+11\end{array}\\ {}-2.73\mathrm{E}+11\\ {}\ 1.79\mathrm{E}+11\end{array}\\ {}-3.36\mathrm{E}+10\end{array}\\ {}-1.74\mathrm{E}+12\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 5.90\mathrm{E}+10\\ {}-3.63\mathrm{E}+10\end{array}\\ {}-3.08\mathrm{E}+10\\ {}\ 7.61\mathrm{E}+09\end{array}\\ {}-1.30\mathrm{E}+10\end{array}\\ {}-1.95\mathrm{E}+11\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 9.15\mathrm{E}+09\\ {}-8.72\mathrm{E}+09\end{array}\\ {}-4.55\mathrm{E}+09\\ {}\ 2.22\mathrm{E}+08\end{array}\\ {}-2.21\mathrm{E}+09\end{array}\\ {}-2.87\mathrm{E}+10\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 3.14\mathrm{E}+06\\ {}\ 1.17\mathrm{E}+07\end{array}\\ {}-2.61\mathrm{E}+06\\ {}\ 4.94\mathrm{E}+06\end{array}\\ {}\ 3.26\mathrm{E}+05\end{array}\\ {}-1.88\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.91\mathrm{E}+07\\ {}-1.02\mathrm{E}+08\end{array}\\ {}-7.22\mathrm{E}+06\\ {}-2.31\mathrm{E}+07\end{array}\\ {}-1.20\mathrm{E}+07\end{array}\\ {}-3.36\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.38\mathrm{E}+08\\ {}-5.04\mathrm{E}+08\end{array}\\ {}-3.20\mathrm{E}+07\\ {}-1.16\mathrm{E}+08\end{array}\\ {}-5.84\mathrm{E}+07\end{array}\\ {}-1.41\mathrm{E}+08\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.96\mathrm{E}+05\\ {}\ 1.99\mathrm{E}+06\end{array}\\ {}\ 1.20\mathrm{E}+05\\ {}\ 4.82\mathrm{E}+05\end{array}\\ {}\ 2.27\mathrm{E}+05\end{array}\\ {}\ 4.85\mathrm{E}+05\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.74\mathrm{E}+11\\ {}\ 2.93\mathrm{E}+11\end{array}\\ {}-1.32\mathrm{E}+11\\ {}\ 8.22\mathrm{E}+10\end{array}\\ {}-1.63\mathrm{E}+10\end{array}\\ {}-8.41\mathrm{E}+11\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}0.00\mathrm{E}+00\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\end{array}\\ {}0.00\mathrm{E}+00\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-3.04\mathrm{E}+11\\ {}-5.15\mathrm{E}+11\end{array}\\ {}\ 2.31\mathrm{E}+11\\ {}-1.48\mathrm{E}+11\end{array}\\ {}\ 2.86\mathrm{E}+10\end{array}\\ {}\ 1.47\mathrm{E}+12\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 2.71\mathrm{E}+10\\ {}-2.19\mathrm{E}+10\end{array}\\ {}-1.37\mathrm{E}+10\\ {}\ 1.85\mathrm{E}+09\end{array}\\ {}-6.29\mathrm{E}+09\end{array}\\ {}-8.69\mathrm{E}+10\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-9.79\mathrm{E}+06\\ {}\ 4.25\mathrm{E}+07\end{array}\\ {}\ 2.08\mathrm{E}+06\\ {}\ 1.06\mathrm{E}+07\end{array}\\ {}\ 4.74\mathrm{E}+06\end{array}\\ {}\ 7.25\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 7.59\mathrm{E}+06\\ {}-3.18\mathrm{E}+07\end{array}\\ {}-1.70\mathrm{E}+06\\ {}-7.82\mathrm{E}+06\end{array}\\ {}-3.59\mathrm{E}+06\end{array}\\ {}-6.29\mathrm{E}+06\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-4.21\mathrm{E}+10\\ {}\ 2.85\mathrm{E}+10\end{array}\\ {}\ 2.18\mathrm{E}+10\\ {}-4.61\mathrm{E}+09\end{array}\\ {}\ 9.43\mathrm{E}+09\end{array}\\ {}\ 1.38\mathrm{E}+11\end{array} $$
$$ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-7.65\mathrm{E}+06\\ {}-1.81\mathrm{E}+07\end{array}\\ {}\ 5.62\mathrm{E}+06\\ {}-8.65\mathrm{E}+06\end{array}\\ {}\ 3.24\mathrm{E}+03\end{array}\\ {}\ 3.91\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-1.61\mathrm{E}+08\\ {}\ 6.04\mathrm{E}+08\end{array}\\ {}\ 3.61\mathrm{E}+07\\ {}\ 1.40\mathrm{E}+08\end{array}\\ {}\ 6.94\mathrm{E}+07\end{array}\\ {}\ 1.54\mathrm{E}+08\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.19\mathrm{E}+07\\ {}\ 2.51\mathrm{E}+07\end{array}\\ {}-8.55\mathrm{E}+06\\ {}\ 1.25\mathrm{E}+07\end{array}\\ {}-2.72\mathrm{E}+05\end{array}\\ {}-5.89\mathrm{E}+07\end{array}\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 1.08\mathrm{E}+07\\ {}-4.67\mathrm{E}+07\end{array}\\ {}-2.28\mathrm{E}+06\\ {}-1.16\mathrm{E}+07\end{array}\\ {}-5.22\mathrm{E}+06\end{array}\\ {}-7.92\mathrm{E}+06\end{array}\ \left.\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-9.96\mathrm{E}+06\\ {}\ 4.26\mathrm{E}+07\end{array}\\ {}\ 2.15\mathrm{E}+06\\ {}\ 1.06\mathrm{E}+07\end{array}\\ {}\ 4.78\mathrm{E}+06\end{array}\\ {}\ 7.68\mathrm{E}+06\end{array}\right] $$
$$ {w}_{k0}=\left[\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\ 4.57\mathrm{E}+04\\ {}-1.89\mathrm{E}+05\end{array}\\ {}-1.10\mathrm{E}+04\\ {}-4.62\mathrm{E}+04\end{array}\\ {}-2.10\mathrm{E}+04\end{array}\\ {}-4.43\mathrm{E}+04\end{array}\right]\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\triangle SA=\mathrm{X}50\ \\ {}\triangle TAC=\mathrm{X}51\ \end{array}\\ {}\triangle K\ value=X52\ \\ {}\triangle TVB-\mathrm{N}=X53\ \end{array}\\ {}\triangle \mathrm{TBARS}=0.98*\mathrm{X}54+0.02\ \end{array}\\ {}\triangle HxR=1.01*\mathrm{X}55\end{array} $$

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Wang, H., Kong, C., Li, D. et al. Modeling Quality Changes in Brined Bream (Megalobrama amblycephala) Fillets During Storage: Comparison of the Arrhenius Model, BP, and RBF Neural Network. Food Bioprocess Technol 8, 2429–2443 (2015). https://doi.org/10.1007/s11947-015-1595-8

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