Comparison of Arrhenius model and artificial neuronal network for the

LWT - Food Science and Technology 60 (2015) 142e147

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Comparison of Arrhenius model and artificial neuronal network for the quality prediction of rainbow trout (Oncorhynchus mykiss) fillets during storage at different temperatures Xiaochang Liu a, Yan Jiang a, Song Shen a, Yongkang Luo a, *, Liang Gao b a

College of Food Science and Nutritional Engineering, China Agricultural University, Beijing Higher Institution Engineering Research Center of Animal Product, Beijing 100083, China Beijing Fisheries Research Institute, Beijing 100068, China

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 April 2014 Received in revised form 5 September 2014 Accepted 6 September 2014 Available online 16 September 2014

Quality changes in total aerobic counts (TAC), electrical conductivity (EC), K-value and sensory assessment (SA) of rainbow trout (Oncorhynchus mykiss) fillets during storage at 282, 279, 276, 273 and 270 K were determined. Simultaneously, Arrhenius model and feed-forward artificial neuronal network (ANN) were established to predict changes of rainbow trout fillets during storage, and a comparative study between these two models was also performed. The relative error between predicted and experimental value was used as the comparative parameter. The results showed that TAC, EC and K-value increased with storage time, while SA decreased with time. The change rate of all indicators increased as a function of temperature. Arrhenius models based on EC and TAC were acceptable, while those based on SA and Kvalue showed poor performances in some days. By contrast, ANN was more effective to predict changes in TAC, EC, K-value and SA throughout the storage, with relative errors all below 10%. Therefore, ANN could be a potential tool in modeling quality changes of rainbow trout fillets within 270e282 K.

Keywords: Rainbow trout fillets Quality changes Arrhenius model Artificial neuronal network

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction Rainbow trout (Oncorhynchus mykiss, family Salmonidae) is a cold-water fish species with high commercial value and much appreciated by European consumers (Cakli, Kilinc, Dincer, & Tolasa, 2006). The quality of rainbow trout has long been a major concern to processors and consumers. Like other freshwater fish, rainbow trout is an extremely perishable commodity, mainly owing to the high moisture level, rich nutrition content, microbial growth and enzymatic activity (Chytiri, Chouliara, Savvaidis, & Kontominas, 2004; Zhu, Luo, Hong, Feng, & Shen, 2013). Hitherto, numerous studies have been undertaken to extend the shelf life of rainbow trout, including sugar-salting (Lyhs et al., 2001), vacuum and modified atmosphere packaging (Arashisar, Hisar, Kaya, & Yanik, 2004), edible coating (Ojagh, Rezaei, Razavi, & Hosseini, 2010), among others. However, it is noteworthy that all the abovementioned methods were based on low temperature condition, under which microbial growth and enzymatic activity can be

* Corresponding author. Tel./fax: þ86 10 62737385. E-mail addresses: [email protected], [email protected] (Y. Luo). http://dx.doi.org/10.1016/j.lwt.2014.09.030 0023-6438/© 2014 Elsevier Ltd. All rights reserved.

minimized. Thus, it is of great importance to determine and predict changes of rainbow trout during low temperature storage. Kinetic model is widely applied nowadays to predict quality changes in food. Several kinetic models, which were based on Arrhenius equation, have been developed to model quality changes in aquatic products, such as sardine sheets (Corzo, Bracho, & Marjal, 2006), frozen shrimp (Tsironi, Dermesonlouoglou, Giannakourou, & Taoukis, 2009), gilthead seabream (Tsironi, Salapa, & Taoukis, 2009), grass carp (Zhang, Li, Lu, Shen, & Luo, 2011). The establishment of Arrhenius models does offer a good way to predict and optimize the quality of aquatic products during storage. However, several studies have proved that Arrhenius model was unsuitable to predict changes at later stages of spoilage during low temperature storage, in terms of such fish species as crucian carp (Yao, Luo, Sun, & Shen, 2011) and Songpu mirror carp (Bao, Zhou, Lu, Luo, & Shen, 2013). For this reason, a new model with better performance and generalization is urgently needed. ANN are a set of non-linear mathematical models which allow modeling by mimicking the real neural activity in human brain; they can develop meaningful relationships between input and output variables through a learning process, without requiring a prior rigid model structure, compared to other mathematical

X. Liu et al. / LWT - Food Science and Technology 60 (2015) 142e147

models (Marini, 2009; Sofu & Ekinci, 2007). Previous studies have shown the benefits of using ANN in prediction. For instance, Erenturk and Erenturk (2007) used neural network to predict the moisture content of carrot during drying processing; Lu et al. (2010) developed an ANN model based on blanching time and temperature to estimate nutrient loss of asparagus during thermal treatments; Llave, Hagiwara, and Sakiyama (2012) applied ANN to predict cold spot temperature in retort sterilization of starch-based foods. Till now, no attempt has been made to use ANN for the quality prediction of aquatic products during storage. The aim of this work was to determine quality changes in sensory assessment (SA), electrical conductivity (EC), total aerobic counts (TAC), and K-value of rainbow trout fillets at different temperatures, and to develop prediction model for freshness indicators of rainbow trout fillets during low temperature storage using Arrhenius model and ANN. 2. Materials and methods 2.1. Materials Farmed rainbow trout (weight of 1097 ± 47 g, length of 40.0 ± 1.0 cm) were provided by Yanqing YuDuShan Coldwater Fishery Base (Beijing, China) in August 2013, and transported to the laboratory alive. The fish was killed by a blow to the head, followed by decapitated, eviscerated, filleted, and then washed in running water within 2 h. Fish fillets were individually packed in polyvinyl chloride bags, and thereafter stored at 282, 279, 276, 273 and 270 K, respectively. Three randomly chosen samples were taken for analysis at specified intervals for each storage temperature. 2.2. Total aerobic counts Twenty-five grams of sample were removed aseptically from the anterior-dorsal region of each fillet, homogenized with 225 mL sterile NaCl solution (0.9%) for 1 min, and followed by further tenfold serial dilutions. 1 mL of three appropriate dilutions was inoculated into nutrient agar, and then incubated for 72 ± 2 h at 30 C. All counts were expressed as log10 cfu g1. 2.3. Electrical conductivity Ten grams of sample were stirred in 100 mL deionized water for 30 min. Then, the mixture was filtered. The EC of the filtrate was measured by a digital-EC-meter (Mettler Toledo FE20/EL20, Shanghai, China). 2.4. K-value The determination of K-value was carried out by a high performance liquid chromatography (HPLC) method described by Song, Liu, Shen, You, and Luo (2011) with some modifications. One gram of sample was ground with 2 mL of cold perchloric acid (10%, v/v) before centrifugation (4000 g, 5 min). The sediment was washed with 2 mL of cold perchloric acid (5%, v/v) twice. All the collected supernatants were then neutralized (pH 6.35e6.45), centrifuged (3000 g, 3 min), diluted with perchloric acid (pH 6.40) to 10 mL, and finally stored at 18 C for further analysis. The prepared solution was filtered through a 0.22 mm filter prior to injection into the column. The instrumentation details were: COSMOSIL 5C18-PAQ column (4.6ID 250 mm) as stationary phase; phosphate buffer (pH 6.8) as mobile phase; SPD-10A (V) detector (254 nm); 1 mL min1 of flow rate; 50 mL of injection volume. ATP and its related compounds were identified and

143

quantified using Sigma external standards. The K-value was calculated as follows (Saito, Arai, & Matsuyoshi, 1959):

K value ð%Þ ¼ ½ðHxR þ HxÞ=ðATP þ ADP þ AMP þ IMP þ HxR þ HxÞ 100 in which ATP, ADP, AMP, IMP, HxR and Hx represented adenosine50 -triphosphate, adenosine-50 -diphosphate, adenosine-50 -monophosphate, inosine-50 -monophosphate, inosine and hypoxanthine, respectively. 2.5. Sensory assessment The sensory assessment was conducted by a panel of nine trained judges (six females and three males between 22 and 36 years old) from the laboratory staffs. The raw fish fillets were evaluated for color, odor, morphology and elasticity according to Ojagh et al. (2010) with some modifications. A rating scale of 5point was used, wherein five represented the best quality and one represented the worst. Scores of the four attributes were summed to give an overall sensory score. 2.6. Arrhenius model 2.6.1. Kinetic analysis The rate of change in fish freshness during storage can be characterized by the general rate law (Boekel, 1996; Zhang et al., 2011):

dC=dt ¼ kCn

(1)

where C is the freshness indicator (SA, EC, K-value or TAC) at time t (days), k is the rate constant, and n is the order of the reaction. The zero-, first- and second-order kinetic equation can be obtained by the integration of Eq. (1) as follows:

for a zero order reaction : C C0 ¼ kt

(2)

for a first order reaction : lnCelnC0 ¼ kt

(3)

for a second order reaction : 1=Ce1=C0 ¼ kt

(4)

where C0 is the initial value. A linear regression analysis was performed on the plot of freshness indicator (C, ln C, or 1/C) vs. time for the zero-, first- and second-order reaction, respectively. The fit of the line was evaluated by the coefficient of determination (r2). 2.6.2. Arrhenius equation The temperature dependence of the rate constant, k, follows the Arrhenius equation (Ratkowsky, Olley, McMeekin, & Ball, 1982):

k ¼ k0 expðEa =RTÞ

(5)

where k0 is the pre-exponential constant, Ea is the activation energy, R is the gas constant (8.314 J mol1 K1), and T is the absolute temperature. 2.6.3. Parameter estimation Once the reaction order is determined, a global equation incorporating Eq. (2), Eq. (3) or Eq. (4) with Eq. (5) can be formulated. For instance, for a zero-order reaction this would be:

C ¼ C0 þ k0 $t$expðEa =RTÞ

(6)

Ea and k0 were estimated by non-linear regression with a confidence level of 95%.

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2.7. Artificial neural network (ANN) ANN is comprised by a number of parallel artificial neurons and these neurons are connected with each other for data exchange. Generally, a neural network can be trained to perform a particular function by adjusting the connection parameters (weights and bias) between neurons, such that a particular input leads to a specific target output (Sofu & Ekinci, 2007). In this study, a one-hidden-layer network was used as presented in Fig. 1. The input layer had two neurons which represented temperature (K) and storage time (day). The output layer consisted of four neurons representing DTAC, DEC, DK-value and DSA, respectively. DC was calculated by:

DC ¼ C C0

(7)

where C is the freshness indicator (TAC, EC, K-value or SA) at time t, C0 is the initial value. In order to determine the optimal number of neurons in the hidden layer, the networks with 1, 2, 3, 4, 5, 6, 7 or 8 hidden neurons were compared. The performance of a trained network was measured by the mean square error (MSE) and coefficients of determination (r2) between the predicted and actual values. The best network corresponded to the lowest MSE and the highest r2. A log-sigmoidal activation function and a linear activation function was used in the hidden layer and output layer, respectively. The numerical values of input and output variables were automatically normalized into the range of 1 to 1 by the network. A supervised method of learning with back-propagation strategy and LevenbergeMarquardt algorithm was used for training. The train would continue till MSE became 0, or 10,000 iterations, or the performance on the validation sets failed to improve for 6 epochs. 2.8. Establishment and evaluation of Arrhenius model and ANN Data of 282, 279, 276 and 270 K were adopted to establish the Arrhenius model and ANN, while data of 273 K were to evaluate the prediction performance of both two models. To assess the accuracy of these two models in prediction, the relative error between predicted (Cpre) and experimental (Cexp) value was proposed:

relative error ¼ Cpre eCexp

Cexp 100%

According to Kaymak-Ertekin and Gedik (2005), a model with relative error below 10% is considered acceptable. 2.9. Statistical analysis The least significant difference (LSD) procedure was used to test for difference between means (significance level was set at 5%)

using SPSS 17.0 (SPSS Inc., Chicago, IL). Linear regression, non-linear regression and ANN model were all performed using Matlab R2013b (Mathworks). 3. Results and discussion 3.1. Total aerobic counts Table 1 shows the effect of different temperatures on total aerobic counts (TAC) of rainbow trout fillets. The initial value of TAC (3.86 log10 cfu g1) indicated good quality of rainbow trout used in this study. Previous studies reported initial TAC of 2e6 log10 cfu g1 for freshwater fish species (Song et al., 2011). TAC of fillets stored at different temperatures increased at different rates, reaching 8e9 log10 cfu g1 at the end of the storage period. Bacteria grew most rapidly in samples stored at 282 K, and the TAC value exceeded 7 log10 cfu g1 on the 4th day. In addition, TAC showed a relatively slow growth during the later period. It is probably due to the decreasing availability of oxygen and energy substrate in the medium. 3.2. Electrical conductivity Table 1 presents changes in EC values of rainbow trout fillets stored at different temperatures. The initial EC value of rainbow trout fillet was 1325 ms cm1. EC values of all samples increased throughout the storage. Several researchers reported that the enhanced conductivity probably occurs as a result of increased membrane permeability and declined water-holding capacity of muscles fibers leading to an increase in extracellular volume (Byrne, Troy, & Buckley, 2000; Lepetit, Sale, Favier, & Dalle, 2002). Ionic substances, mainly produced during the growth of bacteria, also explained for the increased EC value in growth medium (Ekanem & Achinewhu, 2000). The increasing rate of EC decreased with storage temperature, which was due to the inhibitory effect of lower temperature on the decomposition of muscle tissues and bacterial growth. 3.3. K-value The initial K-value of rainbow trout fillets was 23.02%, similar to € the value of Atlantic herring (23%) (Ozogul, Taylor, Quantick, & € Ozogul, 2000), but higher than that of yellowfin tuna (17%) (Guizani, Al-Busaidy, Al-Belushi, Mothershaw, & Rahman, 2005). These variations were possibly owing to differences in species, handling conditions and killing methods (Olafsdottir et al., 1997). Table 1 shows continuous increase in K-values for all fillets. According to Saito et al. (1959), the upper acceptability limit of Kvalue for fresh fish was 70%. The K-value increased to 78.87%, 79.01%, 78.98%, 80.73% and 71.97% at 282, 279, 276, 273 and 270 K after 4, 6, 9, 12, and 15 days, respectively, exceeding the rejection level of 70%. The result showed that low temperature could inhibit the degradation of ATP. It could be explained by the effect of low temperature on minimizing the activity of 5-nucleotidase (Guizani et al., 2005). 3.4. Sensory assessment

Fig. 1. ANN structure for predicting quality indicators of rainbow trout fillets during storage.

As shown in Table 1, sensory scores of all samples decreased significantly (P < 0.05) with time. Fresh rainbow trout fillets had typical orange-pink color, tight morphology, elastic muscle and fresh odor; as time went on, the sensory quality degraded, reflected on discoloration, loose morphology, decreased elasticity and offodor. According to Christiansen, Struksnæs, Estermann, and Torrissen (1995) and Mørkøre et al. (2010), the discoloration was


145

Table 1 Experimental and ANN/Arrhenius model predicted values of TAC, EC, K-value and SA of rainbow trout fillets during storage at different temperatures. Temperature (K)

Storage time (d)

282

0 2 4 6 0 2 4 6 8 0 3 6 9 12 15 0 3 6 9 12 15 18 0 3 6 9 12 15 18 21 24

279

276

273

270

TAC (log10 cfu g1)

EC (ms cm1)

Experimental value

Experimental value

3.86 6.57 8.46 8.98 3.86 5.16 7.44 8.16 8.68 3.86 5.08 7.40 8.35 8.91 9.12 3.86 4.42 5.91 6.94 8.27 8.69 8.85 3.86 3.97 4.88 6.01 7.46 7.60 8.44 8.55 8.66

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.04 0.05 0.02 0.04 0.04 0.06 0.01 0.07 0.05 0.04 0.03 0.04 0.10 0.00 0.01 0.04 0.19 0.05 0.15 0.03 0.13 0.00 0.04 0.23 0.04 0.10 0.06 0.15 0.21 0.25 0.22

Predicted value Arrhenius

ANN

5.79 7.72 9.65

6.53 7.89 8.93

5.19 6.52 7.85 9.19

5.30 6.86 8.05 8.80

5.23 6.59 7.96 9.32 10.69

5.12 6.99 8.21 8.93 9.21

4.79 5.71 6.64 7.57 8.49 9.42

4.41 5.78 7.34 8.23 8.83 9.05

4.48 5.11 5.73 6.35 6.98 7.60 8.22 8.84

4.05 4.72 6.19 7.44 7.91 8.29 8.54 8.60

1325 1409 1441 1469 1325 1374 1395 1415 1509 1325 1381 1384 1446 1519 1536 1325 1370 1378 1412 1450 1483 1531 1325 1364 1377 1383 1433 1444 1495 1528 1543

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

8 2 7 12 8 3 5 1 11 8 8 4 5 1 45 8 4 13 7 8 12 10 8 14 12 12 11 6 11 8 15

K-value (%) Predicted value Arrhenius

ANN

1386 1447 1508

1406 1446 1466

1369 1412 1456 1499

1375 1410 1454 1495

1371 1418 1464 1511 1557

1376 1408 1454 1511 1533

1358 1390 1423 1456 1489 1521

1367 1385 1410 1445 1503 1534

1348 1371 1394 1417 1439 1462 1485 1508

1363 1371 1391 1412 1439 1493 1533 1542

generally associated with the changes in pigment concentration and muscle structure. Endogenous proteases were responsible to a large extent for the loss of textural quality during the early stage of deterioration, and off-odors were the result of microbial activity (Hansen, Gill, Røntved, & Huss, 1996; Hultmann & Rustad, 2004). The sensory shelf life, when the overall score became 10, was 4, 6, 9, 12, and 12 days for 282, 279, 276, 273, and 270 K, respectively. It suggested that low temperature could maintain good quality of fillets and prolong the shelf life of rainbow trout fillets.

Experimental value 23.02 49.70 78.87 96.50 23.02 38.58 57.71 79.01 88.01 23.02 48.70 67.23 78.98 92.27 96.30 23.02 41.30 58.63 68.75 80.73 88.43 94.19 23.02 40.60 44.61 56.60 60.24 71.97 84.07 92.57 94.41

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.14 7.26 7.46 0.29 0.14 9.08 9.60 6.51 5.51 0.14 0.80 3.61 3.24 1.37 0.75 0.14 0.37 5.06 2.99 2.11 1.64 1.54 0.14 0.22 3.07 7.24 4.80 0.92 2.33 0.75 1.34

SA Predicted value Arrhenius

ANN

47.70 72.38 97.05

51.24 73.91 94.22

40.49 57.96 75.43 92.90

38.37 57.11 74.84 89.00

41.43 59.85 78.26 96.67 115.09

45.88 62.20 76.82 91.39 98.00

35.86 48.70 61.53 74.37 87.21 100.05

43.40 53.41 64.76 75.16 88.75 95.67

31.90 40.78 49.66 58.54 67.42 76.30 85.18 94.06

41.80 46.45 56.25 65.19 71.86 83.63 92.04 94.12

Experimental value 20.00 12.89 10.89 5.00 20.00 15.67 11.11 9.78 4.22 20.00 18.22 11.67 9.89 4.78 4.00 20.00 18.78 15.11 11.67 7.89 5.56 4.00 20.00 19.00 17.00 13.67 9.00 7.44 6.44 4.67 4.00

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.00 0.78 1.05 1.00 0.00 0.50 1.17 1.20 0.44 0.00 0.44 0.71 0.60 0.67 0.00 0.00 0.83 0.93 1.22 1.05 0.73 0.00 0.00 0.71 1.00 1.00 0.71 0.53 1.74 0.50 0.00

Predicted value Arrhenius

ANN

14.53 9.07 3.60

13.16 8.57 4.97

16.19 12.38 8.56 4.75

15.89 10.66 6.78 4.66

16.04 12.09 8.13 4.18 0.22

17.17 11.67 7.95 5.31 4.44

17.29 14.57 11.86 9.14 6.43 3.71

18.58 14.83 10.75 8.07 5.58 4.36

18.15 16.30 14.46 12.61 10.76 8.91 7.07 5.22

19.22 17.43 13.61 10.14 8.16 5.90 4.41 4.04

3.5. Arrhenius kinetics The results of reaction order from graphical determination are presented in Table 2. TAC, EC, K-value and SA were found to be adequately described by zero-order kinetic equations with r2 values all above 0.90. Parameters of Arrhenius models for TAC, EC, K-value and SA are shown in Table 3. Quality predictive models of rainbow trout fillets based on TAC, EC, K-value and SA are as follows:

CTAC ¼ CTAC0 1:0 1015 t expð81060=RTÞ Table 2 Estimation of the reaction orders of quality indicators in rainbow trout fillets at different temperatures. Indicators

Temperature (K) Zero order First order

1

TAC (log10 cfu g

EC (ms cm1)

K-value (%)

Sensory score

) 282 279 276 270 282 279 276 270 282 279 276 270 282 279 276 270

Second order

C vs. time

lnC vs. time 1/C vs. time

r2

r2

r2

0.9246 0.9382 0.9091 0.9356 0.9229 0.9108 0.9585 0.9753 0.9904 0.9877 0.9469 0.9819 0.9615 0.9767 0.9619 0.9576

0.8737 0.9071 0.8670 0.9084 0.9153 0.9191 0.9602 0.9775 0.9335 0.9508 0.8364 0.9124 0.9327 0.9094 0.9531 0.9772

0.8138 0.8651 0.8151 0.8704 0.9075 0.9265 0.9612 0.9789 0.8306 0.8596 0.6923 0.7551 0.8305 0.7624 0.8827 0.9257

CEC ¼ CEC0 þ 1:0 1015 t expð72970=RTÞ CKvalue ¼ CKvalue0 þ 1:1 1015 t expð75310=RTÞ CSA ¼ CSA0 1:0 1015 t expð78620=RTÞ

Table 3 Parameters of Arrhenius model for TAC, EC, K-value and SA of rainbow trout fillets at different temperatures. Indicators

r2

TAC (log10 cfu g1) EC (ms cm1) K-value (%) Sensory score

0.8066 81.06

±0.24

1.0 1015 ±5.8 1013

0.8426 72.97 0.8880 75.31 0.8411 78.62

±0.23 ±0.19 ±0.43

1.0 1015 ±1.3 1013 1.1 1015 ±4.9 1013 1.0 1015 ±8.9 1013

Ea k0 95% (kJ mol1) Confidence interval Ea

95% Confidence interval k0±

146


Table 4 MSE and r2 of ANN with different hidden neurons. No. of hidden neurons

MSE

r2

1 2 3 4 5 6 7 8

0.0453 0.0219 0.0160 0.0116 0.00824 0.00418 0.00772 0.00908

0.8716 0.9326 0.9556 0.9630 0.9630 0.9697 0.9053 0.9529

where CTAC, CEC, CK-value and CSA are predictive values in TAC, EC, Kvalue and SA of rainbow trout fillets after storage for time t (day); CTAC0, CEC0, CK-value0 and CSA0 are initial values in TAC, EC, K-value and SA of rainbow trout fillets; T is the storage temperature (K). 3.6. ANN In this work, experimental data of 282, 279, 276 and 270 K were used for training, of which 85% were randomly selected to generate the model, and 15% were used for validation to avoid overfitting. The optimal number of hidden neurons was determined using a trial and error method. Table 4 lists the changes of MSE and r2 in the prediction of relative values of TAC, EC, K-value and SA with different numbers of neurons (1, 2, 3, 4, 5, 6, 7 and 8) in the hidden layer. The network with six neurons in the hidden layer showed the lowest MSE (0.00418) and highest r2 (0.9697). Therefore, a three-layer network with six hidden neurons was developed on the training data. During the training process, the weights and bias between the neurons were optimized iteratively in a direction that minimized the MSE between the predicted and actual values. The simplified algorithms derived from the optimal network are presented in the Appendix, and they showed the activation functions, weights and bias. For the training set, r2 between actual values (TAC, EC, K-value and SA) and predicted values were 0.9788, 0.9535, 0.9850 and 0.9544, respectively. The high r2 values meant that the optimal ANN was reliable and fit well with the training data. The development of ANN can be time-consuming, however, once developed, its use is straight-forward and can be easily implemented in programs, spreadsheets, calculators, or hardware devices (Kerdpiboon, Kerr, & Devahastin, 2006). 3.7. Evaluation of Arrhenius model and ANN Arrhenius model and ANN predicted values of TAC, EC, K-value and SA of rainbow trout fillets at different temperatures and storage time are shown in Table 1. To quantify the overall fitting performance of Arrhenius and ANN model, the mean square error (MSE) and the determination coefficient (r2) between experimental and predicted values of each indicator (TAC, EC, K-value or SA) were calculated (Table 5). The Arrhenius model for predicting changes of

Table 5 MSE and r2 of Arrhenius and ANN model in the prediction of TAC, EC, K-value or SA of rainbow trout fillets during storage at different temperatures.

TAC EC K-value SA

Arrhenius model

ANN

r2

MSE

r2

MSE

0.8643 0.8718 0.9413 0.8780

0.3939 446.5173 42.3487 3.0185

0.9794 0.9587 0.9809 0.9645

0.0509 146.9020 7.8221 0.9143

Table 6 Relative errors (%) between predicted and experimental values of quality indicators of rainbow trout fillets stored at 273 K. Indicators

Storage time (day) 3

TAC

Arrhenius ANN EC Arrhenius ANN K-value (%) Arrhenius ANN Sensory score Arrhenius ANN

6

9

12

15

18

8.29 3.33 4.33 8.51 2.27 6.44 0.27 2.14 5.83 0.52 1.59 2.22 model 0.90 0.90 0.79 0.41 0.38 0.63 0.25 0.52 0.15 0.34 1.36 0.20 model 13.18 16.94 10.50 7.87 1.38 6.22 5.07 8.90 5.81 6.89 0.37 1.57 model 7.96 3.57 1.59 15.84 15.56 7.25 1.09 1.87 7.88 2.22 0.31 8.95 model

TAC, EC, K-value and SA had MSE values of 0.3939, 446.5173, 42.3487 and 3.0185, and r2 values of 0.8643, 0.8718, 0.9413 and 0.8780, respectively. For ANN, MSE values for TAC, EC, K-value and SA were 0.0509, 146.9020, 7.8221 and 0.9143, and corresponding r2 values were 0.9794, 0.9587, 0.9809 and 0.9645, respectively. Thus, the overall fitting performance of ANN was superior to that of Arrhenius model, as evidenced by the lower MSE and higher r2 for each indicator. To evaluate the prediction performance of Arrhenius model and ANN, relative errors between predicted and experimental data of 273 K were calculated and presented in Table 6. The ANN model could predict changes of TAC, EC, K-value and SA during storage of rainbow trout fillets with relative errors all below 10%. For Arrhenius models based on TAC and EC, the relative errors between predicted and experimental values of TAC and EC were within 10%, while for those based on SA and K-value, the relative errors exceeded 10% for values at 3rd day, 6th day and 9th day of K-value, 12th day and 15th day of SA. Overall, the prediction ability of ANN was superior to that of Arrhenius model. 4. Conclusion In this work, a comparative study was performed between Arrhenius model and ANN to predict quality (TAC, EC, K-value and SA) of rainbow trout fillets as a function of storage temperature and time. Arrhenius models based on EC and TAC were acceptable, while those based on SA and K-value showed high deviation values in some days. ANN was successful in predicting quality changes during the whole period. It also demonstrated that the ANN offered several other advantages over Arrhenius model, such as selflearning (removing dependence on prior rigid models) and multioutput ability. In conclusion, the ANN, a convenient tool, is a promising method for modeling the quality changes of rainbow trout fillets during storage within 270e282 K. The success of this work will provide a new method for quality prediction of fish fillets during storage, distribution, and processing. Acknowledgment This study was supported by National Natural Science Foundation of China (award nr 31471683) and the earmarked fund for China Agriculture Research System (CARS-46). Appendix ANN: one hidden layer, six hidden neurons. logsig (x) ¼ 1/(1 þ exp (x)) purelin (x) ¼ x T1 ¼ temperature (270 K < T1 < 282 K) T2 ¼ time (T2 > 0 day)


Input layer: X1 ¼ (T1276)/6 X2 ¼ (T213)/11 Hidden layer: X3 X4 X5 X6 X7 X8

¼ logsig (2.5757*X1 þ (6.1918)*X2 þ (7.2044)) ¼ logsig ((6.4225)*X1 þ 2.6776*X2 þ 5.1262) ¼ logsig (6.002*X1 þ 3.8901*X2 þ (3.7014)) ¼ logsig ((4.5534)*X1 þ (6.8873)*X2 þ (1.8494)) ¼ logsig (2.2898*X1 þ 5.7202*X2 þ 4.563) ¼ logsig ((5.6589)*X1 þ 4.3959*X2 þ (6.3658))

Output layer: X9 ¼ purelin ((0.583)*X3 þ (0.0349)*X4 þ 0.3447*X5 þ (0.3989)*X6 þ 1.6844*X7 þ (0.2459)*X80.6078) X10 ¼ purelin ((0.2808)*X3 þ 0.0885*X4 þ (1.0672) *X5 þ (1.4244)*X6 þ 0.6155*X7 þ 0.0207*X8 þ 0.2929) X11 ¼ purelin ((0.9981)*X3 þ 0.1101*X4 þ 1.015*X5 þ (0.99) *X6 þ 0.9828*X7 þ (0.1236)*X8 þ (0.0424)) X12 ¼ purelin (1.3461*X3 þ 0.7448*X4 þ 0.5621*X5 þ 0.6242*X6 þ (1.4566)*X7 þ (0.0084)*X80.2857) DTAC ¼ 2.58*X9 þ 2.69 DEC ¼ 90*X10 þ 129 DK-value ¼ 28.96*X11 þ 44.52 DSA ¼ 7.5*X128.5

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