Application of Artificial Neural Network to Predict K-Value, Inosine Mono-Phosphate, and Hypoxanthine Concentrations of Grass Carp (Ctenopharyngodon idellus) Fillets During Storage

Figures & data

FIGURE 1 ANN structure for predicting K-value and IMP, Hx concentrations of grass carp fillets during storage.

TABLE 1 Changes in the AMP-deaminase activity (U/mL) of grass carp fillets stored at 273, 277, 281, 288, and 293 K

Storage time (hours)	Temperature (Kelvin)
	273	277	281	288	293
0	107.56±11.93^Abcd	107.56±11.93^Abc	107.56±11.93^Ab	107.56±11.93^Abc	107.56±11.93^Ab
2	—	—	—	100.89±5.18^Ac	106.67±12.35^Ab
4	—	—	—	152.00±13.13^Aa	159.78±11.16^Aa
8	93.33±2.31^Be	107.78±8.60A^Bbc	96.89±8.34^Bbc	117.56±10.84^Ab	107.11±13.70^ABb
12	173.56±10.69^Ba	189.56±11.74^Aa	154.67±5.77^Ca	102.44±4.44^Dbc	103.78±8.28^Db
24	99.78±7.95^Bcde	114.89±2.78^Ab	96.00±1.15^Bbc	114.22±7.73^Abc	94.89±9.62^Bb
36	112.44±7.34^Abc	105.78±7.73^Abc	97.33±12.70^Abc	105.11±8.85^Abc	104.44±9.71^Ab
48	92.89±12.37^Be	104.00±7.69^ABbc	90.44±11.48^Bc	102.00±14.71^ABbc	113.11±7.07^Ab
72	99.11±0.77^Ade	108.89±17.71^Abc	96.44±7.19^Abc	114.22±0.38^Abc	—
96	113.33±9.17^Ab	106.22±11.93^ABbc	90.89±11.34^Bc	—	—
144	106.89±7.31^Abcd	106.67±10.73^Abc	94.44±8.88^Abc	—	—
192	112.22±0.38^Abc	92.00±8.08^Bc	—	—	—
240	97.56±2.04^Ade	99.33±3.33^Abc	—	—	—
288	103.56±3.01^Abcde	—	—	—	—

A–D: values with same superscript letters in the same row have no significant difference (p > 0.05).

a–e: values with same superscript letters in the same column have no significant difference (p > 0.05).

—: no detecting.

FIGURE 2 Changes in IMP, Hx concentrations, and K-value of grass carp fillets stored at 273, 277, 281, 288, and 293 K.

TABLE 2 Mean squared error (MSE) in the prediction of K-value, IMP, and Hx concentrations of grass carp with different numbers of neurons in the hidden layer

MSE × 100	Number of hidden neurons
	1	2	3	4	5	6	7	8	9	10
K-value	11.45 ± 0.23	8.77 ± 0.41	4.62 ± 0.14	1.43 ± 0.33	0.52 ± 0.06	0.33 ± 0.06	0.11 ± 0.01	0.23 ± 0.02	0.43 ± 0.07	0.96 ± 0.03
IMP	7.43 ± 0.09	5.71 ± 0.99	3.47 ± 0.11	3.01 ± 0.27	2.21 ± 0.31	0.63 ± 0.09	1.49 ± 0.18	2.07 ± 0.14	2.14 ± 0.03	2.66 ± 0.14
Hx	12.83 ± 1.55	7.67 ± 0.80	2.44 ± 0.19	1.64 ± 0.20	0.05 ± 0.01	0.53 ± 0.09	0.65 ± 0.07	0.89 ± 0.11	0.99 ± 0.30	1.14 ± 0.28

TABLE 3 Training, validation, and test data used in the development of ANN

Temperature (K)	Time(h)	ΔK (%)	Temperature (K)	Time (h)	ΔIMP (μmol/g)	Temperature (K)	Time (h)	ΔHx (μmol/g)
273 ^a	8	2.37	273	8	2.18	273	8	0.054
273 ^a	12	2.48	273	12	2.59	273	12	0.075
273 ^a	48	6.41	273	24	2.48	273	24	0.078
273 ^a	72	12.95	273	96	-0.38	273	36	0.106
273 ^a	144	30.14	273	144	-2.35	273	48	0.127
273 ^a	192	40.20	273	288	-4.29	273	72	0.195
273 ^a	240	55.86	277	8	1.65	273	144	0.322
273 ^a	288	75.87	277	36	1.63	273	240	0.790
277 ^a	24	5.54	277	72	2.44	273	288	2.731
277 ^a	72	18.55	277	96	-1.50	277	8	0.115
277 ^a	96	28.85	277	144	-1.39	277	12	0.107
277 ^a	144	28.56	277	192	-2.99	277	36	0.162
277 ^a	192	41.74	277	240	-3.44	277	48	0.139
277 ^a	240	67.21	281	8	1.84	277	72	0.163
281 ^a	12	5.58	281	12	1.14	277	144	0.233
281 ^a	24	12.37	281	24	1.22	277	192	0.213
281 ^a	36	18.29	281	36	1.57	277	240	2.311
281 ^a	48	40.02	281	48	-0.10	281	8	0.067
281 ^a	96	59.42	281	96	-3.16	281	12	0.122
288 ^a	2	0.47	281	144	-4.50	281	24	0.197
288 ^a	4	0.20	288	4	1.01	281	72	1.102
288 ^a	8	11.04	288	8	0.67	281	96	1.637
288 ^a	12	13.38	288	12	2.02	281	144	3.039
288 ^a	24	43.49	288	24	-1.51	288	2	0.042
288 ^a	48	74.95	288	48	-4.13	288	4	0.082
288 ^a	72	79.21	288	72	-4.59	288	36	1.156
293 ^a	2	3.40	293	4	1.14	288	48	4.085
293 ^a	8	22.68	293	12	-2.95	293	2	0.095
293 ^a	24	64.45	293	24	-3.52	293	8	0.145
293 ^a	48	82.65	293	36	-4.63	293	48	5.53
273 ^b	96	24.02	273	48	2.42	281	36	0.224
277 ^b	8	0.55	273	72	2.70	281	48	0.486
277 ^b	36	5.21	273	192	-2.37	288	8	0.132
281 ^b	8	3.12	288	2	0.63	288	12	0.308
281 ^b	48	26.49	288	26	-3.15	288	72	6.447
281 ^b	144	79.72	293	8	0.21	293	12	0.384
288 ^b	36	54.74	293	48	-4.65	293	24	2.050
273 ^c	24	2.77	273	36	2.07	273	96	0.263
273 ^c	36	3.09	273	240	-3.02	273	192	0.390
277 ^c	12	0.95	277	12	2.8	277	24	0.096
277 ^c	48	10.32	277	24	1.53	277	96	0.179
293 ^c	4	7.82	277	48	2.04	288	24	0.384
293 ^c	12	46.53	281	72	-0.78	293	4	0.132
293 ^c	36	81.00	293	2	1.89	293	36	4.822

^aTraining data used in the development of ANN.

^bValidation data used in the development of ANN.

^cTest data used in the development of ANN.

FIGURE 3 Correlation of predicted and experimental (a) K-value, (b) IMP, and (c) Hx concentrations with training and validation data, as well as the test data for grass carp fillets during storage using the optimal ANN.

TABLE 4 Relative errors (%) between predicted and experimental values of K-value of grass carp fillets stored at 281 K

K-value (%)	Storage time (hours)
	8	12	24	36	48	72	96	144
Arrhenius model	9.40	5.22	1.28	2.51	–3.48	–4.33	–13.04	4.38
ANN	–3.21	–3.98	–0.44	–1.30	–4.18	6.32	–3.38	–2.35