Cinética de secagem de polpa de jabuticaba por modelos de regressão

A jabuticabeira é nativa da Mata Atlântica no Sul do Brasil, e seu fruto é muito consumido in natura, no entanto é altamente perecível, necessitando de técnicas de conservação. Objetivou-se descrever a cinética de secagem de polpa de jabuticaba nas temperaturas de 50 e 60°C, comparando os modelos de regressão Henderson, Exponencial Simples com Três Parâmetros, Lewis, Thompson, Fick e Wang e Sing e, obtendo a Taxa de Secagem Absoluta (TSA) para o melhor modelo. A estimação dos parâmetros foi realizada com o software SAS. A avaliação da qualidade no ajuste e na seleção dos modelos foi feita com base no coeficiente de determinação ajustado, Desvio Padrão Residual e Critério de Informação de Akaike. Os modelos apresentaram bom ajuste aos dados, sendo que o modelo de Lewis foi o mais indicado para descrever a secagem da polpa de jabuticaba nas temperaturas de 50 e 60°C, com taxa de secagem de 0,000063 e 0,000082 g de água/s, respectivamente. A TSA indicou que, em um terço do tempo de secagem, ocorreram de 70% da perda de umidade nas duas temperaturas e, após este período, houve desaceleração da perda de umidade até que se estabilizou ao alcançar o teor de umidade de equilíbrio.

Termos para indexação
conservação de alimentos; razão de umidade; regressão não linear; modelos estatísticos

Autoria

Thais Destefani Ribeiro Furtado

PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/ Lavras-MG, Brazil. E-mail: t.destefani.ribeiro@gmail.com Federal University of LavrasBrasilLavras, MG, Brasil PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/ Lavras-MG, Brazil. E-mail: t.destefani.ribeiro@gmail.com

Joel Augusto Muniz

PhD in Agricultural Statistics and Experimentation, Full Professor in Federal University of Lavras/Lavras-MG, Brazil. E-mail: joamuniz@des.ufla.br Federal University of LavrasBrasilLavras, MG, Brasil PhD in Agricultural Statistics and Experimentation, Full Professor in Federal University of Lavras/Lavras-MG, Brazil. E-mail: joamuniz@des.ufla.br

https://orcid.org/0000-0002-1069-4136

Edilson Marcelino Silva

PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/ Lavras-MG, Brazil .E-mail: edilsonmg3@hotmail.com Federal University of LavrasBrasilLavras, MG, Brasil PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/ Lavras-MG, Brazil .E-mail: edilsonmg3@hotmail.com

https://orcid.org/0000-0002-2800-3495

Jaqueline Gonçalves Fernandes

PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/Lavras-MG, Brazil. E-mail: jaqgonfer@gmail.com Federal University of LavrasBrasilLavras, MG, Brasil PhD student in Agricultural Statistics and Experimentation, Federal University of Lavras/Lavras-MG, Brazil. E-mail: jaqgonfer@gmail.com

https://orcid.org/0000-0002-7236-9718

SCIMAGO INSTITUTIONS RANKINGS

Figuras | Tabelas | Fórmulas

Figuras (4)
Tabelas (3)
Fórmulas (6)

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Figure 1
Analysis of residuals for the drying kinetics of jabuticaba pulp at 50 ° C, where (a), (b), (c), (d) and (e) represent the values adjusted for residuals, and in (f), (g), (h), (i) and (j), the residual values in relation to theoretical quantis for the Henderson, Lewis, Simple Three-Parameter Exponential (ESTP), Thompson and Wang and Sing models, respectively.

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Figure 2
Analysis of residuals for the drying kinetics of jabuticaba pulp at 60 ° C, where (a), (b), (c), (d) and (e) represent the values adjusted for residuals, and in (f), (g), (h), (i) and (j), the residual values in relation to theoretical quantis for the Henderson, Lewis, Simple Three-Parameter Exponential (ESTP), Thompson and Wang and Sing models, respectively.

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Figure 3
Curves of Lewis model adjustments for the Moisture Ratio (MR) as a function of Time (s), the drying kinetic data of jabuticaba pulp at temperatures of 50°C and 60°C in (a) and (b) respectively.

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Figure 4
Absolute drying rate relative to the Lewis model for the Moisture Ratio (MR) as a function of Time (s), for the drying kinetics data of jabuticaba pulp at temperatures of 50°C (a) and 60°C (b).

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Table 1
P-values for the Shapiro-Wilk (SW), Breuch-Pagan (BP) and Durbin-Watson (DW) tests with their respective significance in the analysis of estimated residuals after adjustment of the Henderson (H) models, (ESTP), Lewis (L), Thompson (T) and Wang and Sing (WS) models to the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C.

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Table 2
Estimations of parameters, with their respective confidence intervals (UL and LL), for the Henderson (H), Simple Three-Parameter Exponential (ESTP), Lewis (L), Thompson and Wang and Sing models for the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C, considering first-order autoregressive errors.

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Table 3
Performance quality evaluators of the Henderson (H), Lewis (L), Thompson (T) and Wang and Sing (WS) models with Ø1 component, referring to the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C.

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Figure 1 Analysis of residuals for the drying kinetics of jabuticaba pulp at 50 ° C, where (a), (b), (c), (d) and (e) represent the values adjusted for residuals, and in (f), (g), (h), (i) and (j), the residual values in relation to theoretical quantis for the Henderson, Lewis, Simple Three-Parameter Exponential (ESTP), Thompson and Wang and Sing models, respectively.

Figure 2 Analysis of residuals for the drying kinetics of jabuticaba pulp at 60 ° C, where (a), (b), (c), (d) and (e) represent the values adjusted for residuals, and in (f), (g), (h), (i) and (j), the residual values in relation to theoretical quantis for the Henderson, Lewis, Simple Three-Parameter Exponential (ESTP), Thompson and Wang and Sing models, respectively.

Figure 3 Curves of Lewis model adjustments for the Moisture Ratio (MR) as a function of Time (s), the drying kinetic data of jabuticaba pulp at temperatures of 50°C and 60°C in (a) and (b) respectively.

Figure 4 Absolute drying rate relative to the Lewis model for the Moisture Ratio (MR) as a function of Time (s), for the drying kinetics data of jabuticaba pulp at temperatures of 50°C (a) and 60°C (b).

Table 1 P-values for the Shapiro-Wilk (SW), Breuch-Pagan (BP) and Durbin-Watson (DW) tests with their respective significance in the analysis of estimated residuals after adjustment of the Henderson (H) models, (ESTP), Lewis (L), Thompson (T) and Wang and Sing (WS) models to the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C.

Models	SW	BP	DW
Temperature of 50 °C
H	0.4639 ^ns	0.1374 ^ns	0.0010*
L	0.6054 ^ns	0.5101 ^ns	0.0010*
ESTP	0.3370 ^ns	0.3138 ^ns	0.0010*
T	0.4635 ^ns	0.1378 ^ns	0.0010*
WS	0.8187 ^ns	0.0012*	0.0010*
Temperature of 60 °C
H	0.1713 ^ns	0.0894 ^ns	0.0010*
L	0.1504 ^ns	0.8505 ^ns	0.0010*
ESTP	0.2816 ^ns	0.4299 ^ns	0.0010 ^ns
T	0.1717 ^ns	0.0104*	0.0010 ^ns
WS	0.3553 ^ns	0.9981 ^ns	0.0010 ^ns

^*
Significant at 5% probability level by respective SW, BP and DW tests.
^ns
Not significant in relation to respective SW, BP and DW tests.

Table 2 Estimations of parameters, with their respective confidence intervals (UL and LL), for the Henderson (H), Simple Three-Parameter Exponential (ESTP), Lewis (L), Thompson and Wang and Sing models for the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C, considering first-order autoregressive errors.

Temperature	Models	Parameters	Estimates	UL	LL
50°C	H	k₀	0.9995**	0.9500	1.0491
		k₁	0.000063**	0.000042	0.000085
		∅₁	0.9186**	0.7316	1.1057
	L	k₁	0.000063**	0.000043	0.000083
	L	∅₁	0.9182**	0.7351	1.1014
	ESTP	k₀	0.9807**	0.8068	1.1546
		k₁	0.000065**	0.000032	0.000097
		k₂	0.0189 ^ns	-0.1501	0.1879
		∅₁	0.9256**	0.7045	1.1467
	T	a	2.3242**	2.1291	2.5194
		b	0.000080**	0.000048	0.000117
		∅₁	0.9575**	0.8289	1.0861
60°C	H	k₀	1.0032**	0.9606	1.0458
		k₁	0.000082**	0.000052	0.000117
		∅₁	0.9315**	0.7097	1.1533
	L	k₁	0.000082**	0.000050	0.000113
	L	∅₁	0.9333**	0.7130	1.1536
	ESTP	k₀	1.0371**	0.8603	1.2139
		k₁	0.000078**	0.000037	0.000123
		k₂	-0.0341 ^ns	-0.2094	0.1412
		∅₁	0.9203**	0.6315	1.2092
	WS	a	-0.000064**	-0.000072	-0.000060
		b	1.04 x10^-9**	9.9 x10^-10	1.1x10^-9
		∅₁	0.8657**	0.6104	1.1210

^**
**Highly significant in relation to Student t-test (1% alpha); ns Not significant in relation to t-Studant test. UL-Upper Limit; LL-Lower Limit.

Table 3 Performance quality evaluators of the Henderson (H), Lewis (L), Thompson (T) and Wang and Sing (WS) models with Ø1 component, referring to the drying kinetics data of jabuticaba pulp at temperatures of 50 and 60°C.

Model	R²_aj		RSD			AIC
	50°C	60°C		50°C	60°C		50°C	60°C
H	0.9953	0.9964		0.0007	0.0005		-121.3	-105.7
L	0.9955	0.9966		0.0006	0.0004		-123.3	-107.7
T	0.9946	-		0.0007	-		-117.2	-
WS	-	0.9969		-	0.0044		-	-103.5

1

{M R}_{i} = k_{0} \exp (- k_{1} t_{i}) + u_{i}

2

{M R}_{i} = \exp (- k_{1} t_{i}) + u_{i}

3

{M R}_{i} = k_{0} \exp (- k_{1} t_{i}) + k_{2} + u_{i}

4

MR i = (\exp (- a - {(a^{2} + 4 b t_{i})}^{0.5}) / 2 b) + u_{i}

5

{M R}_{i} = \frac{6}{π^{2}} \sum_{n = 1}^{i} \frac{1}{n^{2}} \exp (- n^{2} π^{2} D_{e f} \frac{1}{t_{i}}) + u_{i}

6

{M R}_{i} = 1 + a t_{i} + {b t_{i}}^{2} + u_{i}

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Métricas

Cinética de secagem de polpa de jabuticaba por modelos de regressão

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Mensagem

[TFN0101] ^*
Significant at 5% probability level by respective SW, BP and DW tests.

[TFN0102] ^ns
Not significant in relation to respective SW, BP and DW tests.