Citation: Yuncheng He, Zhen Liu, Zhi Li, Jiurong Wu, Jiyang Fu. Modal identification of a high-rise building subjected to a landfall typhoon via both deterministic and Bayesian methods[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7155-7176. doi: 10.3934/mbe.2019359
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There is increasing interest in algae as one of the alternative renewable sources of biomass for production of bioethanol, which is considered as third-generation biofuel [1,2]. Unlike terrestrial crops cultivated for biofuel production, algae do not require agricultural land for cultivation and various species are able to grow in brackish or salt water avoiding competition for land and fresh water required for food production [2]. Furthermore, bioethanol from marine-based biomass holds significant potential because of their low percentage of lignin and hemicellulose in comparison with other lignocellulosic biomasses [3].
Recently, marine macroalgae, an abundant and carbon-neutral renewable resource, have gained considerable global attention as a third-generation biomass that can be used in bioenergy production [4,5]. Different macroalgae groups belonging to brown seaweed such as Laminaria japonica, Undaria pinnatifida, and Sargassum horneri, and red algal species such as Gelidium amansii, Kappaphycus alvarezii, and Gracilaria salicornia have been considered as potential sources for bioconversion to ethanol [5,6,7,8,9,10]. Trivedi et al. [11] used the green macroalgae, Ulva fasciata Delile as a bioethanol feedstock. The feasibility of producing bioethanol from the green macroalgae Chaetomorpha linum was also investigated by Schultz-Jensen et al. [12]. C. linum was chosen as target, since it contains more cellulose (35-40 g/100g dry matter, DM) than other algae. Furthermore, the cellulose content of C. linum is similar to that of land-based biomass. However, any future successes of macroalgal-derived biofuel will be dependent on achieving optimised, energy efficient processes in cultivation, harvesting, post-harvest treatments and fuel production [13,14].
Similar to other cellulosic biomasses, glucan from seaweed can be converted by enzymes into sugars suitable for ethanol fermentation. To convert glucan into the fermentable sugars, either acid hydrolysis or enzymatic hydrolysis needs to be performed. The limitations of acid hydrolysis can be by-products inhibition on yeast growth, neutralization before fermentation and expensive constructional material due to corrosion risks. Furthermore, high enzymes prices play a crucial role when feasibility is of concern. Enzyme saccharification is chosen even though high cost of biocatalysts because of high conversion yield of glucose [11,15].
Optimization of enzymatic hydrolysis process is one of the most important stages in the development of an efficient and cost effective saccharification strategy. The process efficiency depends on several parameters such as enzyme, substrate loading, pH, temperature and incubation time [11,15]. The optimal enzymatic process conditions vary also depending on the composition of carbohydrates between the green, brown and red algae [15]. Optimization of multifactorial system by conventional techniques is generally done with one-factor at a time. However, this type of methodology is time consuming and does not reveal the interactive effects between the factors [16]. Response Surface Methodology (RSM) is mainly used for statistical model building and location of maxima [17,18,19,20]. Statistical designs such as RSM have proved efficient for optimization of enzymatic hydrolysis and fermentation of macroalgae feedstocks [5,15,21].
The objectives of this research are performed according to Box-Behnken experimental design and response surface methodology (RSM) to understand the relationship between the critical factor involved in enzymatic degradation of C. linum biomass and to optimize the condition for saccharification prior to ethanol fermentation. All the results obtained in this work would provide a sound basis for assessing the valorization of C. linum biomass into third-generation biofuel.
The green seaweed C. linum was harvested in February 2014 from the coastal region of Monastir, Tunisia. The Seaweed samples were washed thoroughly with tap water to remove salts, epiphytes and debris and dried to a constant weight at temperature of 50°C for 48 h. After drying, the seaweed samples were powdered using grinder for chemical characterization and enzymatic cellulose hydrolysis.
The seaweedsamples were analysed for the total protein, carbohydrates, lipid, ash and crude fibre (dietary fibre) contents. Moisture and ash contents were determined according to the A.O.A.C. method [22] by drying the macroalgae at 105°C for 24 h followed by incineration at 550°C for 12 h. Total carbohydrates content was measured using the phenol-sulfuric acid method of Dubois et al. [23]. Crude protein determination involved the use of routine Kjeldhal nitrogen assay (N×5) [24]. Total fiber content was analyzed according to the AOAC enzymatic-gravimetric method of Prosky et al. [25]. Lipid content was determined by exhaustively extracting samples in a Soxhlet apparatus as described by Chirapart et al. [26]. All the analyses were done in triplicates with results expressed with standard deviations (n=3) against dry weight.
Commercial Aspergillus niger cellulase (0.8 enzyme Units/mg solid, Sigma C1184-25KU, Sigma-Aldrich, USA; 1 U corresponds to the amount of enzymes which liberates 1 μmol glucose from carboxymethylcellulose per minute at pH 5.0 and 37°C) was employed for C. linum cellulose hydrolysis. Dried algal powder (1 g) moistened with different volume of sodium acetate buffer (pH 5.0) was pretreated by autoclaving at 121°C and 1.5 bars for 20 min, cooled and then hydrolyzed with different concentration of cellulase and incubated for different time intervals on an orbital shaker with a speed of 100 rpm at 37°C. Each reaction system was fortified with 1% sodium azide to prevent contamination. Control of each reaction mixture was performed by replacing the active crude enzymes with heat inactivated (100°C, 10 min) enzymes. Samples were taken out periodically and centrifuged. The reducing sugar of each reaction mixture was measured spectrophotometrically using 3, 5-dinitrosalisylic acid (DNS) method [27]. Sugar yield was calculated on C. linum biomass, using the following equation [28]: Sugar Yield (%)=100 (sugar produced during hydrolysis/gram of C. linum biomass).
The optimization of enzymatic hydrolysis of biomass was carried out for enzyme concentration, incubation period and liquid to solid ratio following the Box-Behnken experimental design given by tables 1 and 2. The Box-Behnken experimental design was set up to look for the best experimental conditions of three independent factors affecting the efficiency of the saccharification.
Variable | Factor | Unit | Low level | High level |
X1 | L/S ratio | mL/g | 50.0 | 100.0 |
X2 | Enzyme conc. | U/g | 10.0 | 60.0 |
X3 | Time | h | 4.0 | 44.0 |
N°Exp | X1 | X2 | X3 | L/S (ml/g) | Enzyme (U/g) | Time (h) | Measured sugar yiel (%) | Estimated sugar yield (%) |
1 | –1.0 | –1.0 | 0.0 | 50.0 | 10.0 | 24.0 | 6.91 | 5.63 |
2 | 1.0 | –1.0 | 0.0 | 100.0 | 10.0 | 24.0 | 6.07 | 4.47 |
3 | –1.0 | 1.0 | 0.0 | 50.0 | 60.0 | 24.0 | 8.53 | 10.13 |
4 | 1.0 | 1.0 | 0.0 | 100.0 | 60.0 | 24.0 | 11.65 | 12.93 |
5 | –1.0 | 0.0 | –1.0 | 50.0 | 35.0 | 4.0 | 9.51 | 8.74 |
6 | 1.0 | 0.0 | –1.0 | 100.0 | 35.0 | 4.0 | 4.51 | 4.06 |
7 | –1.0 | 0.0 | 1.0 | 50.0 | 35.0 | 44.0 | 20.01 | 20.46 |
8 | 1.0 | 0.0 | 1.0 | 100.0 | 35.0 | 44.0 | 26.00 | 26.77 |
9 | 0.0 | –1.0 | –1.0 | 75.0 | 10.0 | 4.0 | 2.25 | 4.30 |
10 | 0.0 | 1.0 | –1.0 | 75.0 | 60.0 | 4.0 | 8.85 | 8.02 |
11 | 0.0 | –1.0 | 1.0 | 75.0 | 10.0 | 44.0 | 17.92 | 18.75 |
12 | 0.0 | 1.0 | 1.0 | 75.0 | 60.0 | 44.0 | 30.04 | 27.99 |
13 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 11.26 | 10.21 |
14 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.83 | 10.21 |
15 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 9.61 | 10.21 |
16 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 13.06 | 10.21 |
17 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.27 | 10.21 |
The sugar yield response can be described by the following second-order model adequate for predicting the responses in the experimental region:
η=β0+β1X1+β2X2+β3X3+β11X12+β22X22+β33X32+β12X1X2+β13X1X3+β23X2X3 | (1) |
where, η: the theoretical response function, Xj: coded variables of the system, β0, βj, βjk, and βjj: true model coefficients.
The observed response yi for the ith experiment is
yi=ηi+ei(ei: error) | (2) |
The model coefficients β0, βj, ..., and βjj are estimated by a least squares fitting of the model to the experimental results obtained in the 12 design points of the three-variable Box-Behnken design (Table 2). For the estimated values of these coefficients, the symbols b0, bj, ..., and bjj will be used. The computed values of the responses are designated by ˆyi
ˆy=b0+b1X1+b2X2+b3X3+b11X12+b22X22+b33X32+b12X1X2+b13X1X3+b23X2X3 | (3) |
The four replicates at the center point (runs n 13 to 17) are carried out in order to estimate the pure error variance. The fitted polynomial model was then expressed as two and three dimensional surface plots to illustrate the relationship between the responses and interaction effects of the variables and to look for the optimal experimental conditions [29,30]. Statistical analysis of the data and surface plots were performed using the experimental design software NemrodW [31].
To prepare a starter, the baker's yeast Saccharomyces cerevisiae was cultured in 250 mL cap flasks containing 100 mL Yeast extract Peptone (YP) medium and incubated in an orbital shaker at 150 rpm for 24 h at 30°C. Ethanol production was studied in triplicates using optimized enzymatic hydrolysate of C. linum. The saccharification broth was sterilized by filtration (0.2 µm filter membrane) and added to YP medium with the proportion (9/1). The prepared medium was inoculated with 10% v/v of starter culture of S. cerevisiae and incubated at 30°C with a shaking speed of 150 rpm [32]. After 48 h of incubation, the fermentation broth was centrifuged at 10, 000 rpm for 10 min at 4°C, and the supernatant was then analyzed for ethanol content using ethanol FS kit marketed by Diagnostic System International [33]. Ethanol yield was calculated as total amount of g ethanol obtained per 100 g DM of C. linum before pretreatment.
The chemical composition of C. linum was summarized in Table 3. It has a similar trend to that reported by Ben Yahmed et al. [32]. Generally, C. linum biomass is characterized by relatively high content of carbohydrates and fibers compared to other macroalgae such as G. salicornia [34] and S. japonica [35], which made it a good source for bioenergy production. Previous investigations of the detailed chemical composition of C. linum also showed high content in polysaccharides (20-40 g cellulose/100g DM) [12,32]. Schultz-Jensen et al. [12] reported that C. linum consisted of 34-38 g glucan, 9-10 g arabinan, 6 g xylan, 14 g pectin, 7 g non hydrolysable organic components, 21-23 g ash, and 6 g wax per 100 g DM. Other seaweeds used for biofuel production e.g. Ulva lactuca and Gracilaria longissima contained less glucan (6 g and 20 g/100g DM, respectively) [12,36].
In this study, an attempt was made to optimize enzymatic hydrolysis conditions of hydrothermally pretreated C. linum biomass using a three levels three factors Box-Behnken design. This experimental design reduced the number of experiments in comparison to others, so it is more efficient and easier to arrange and to interpret [37]. Furthermore, it has the advantage that it does not contain combinations for which all process variabes are simultaneously at their highest or lowest levels, thereby, it is useful in avoiding experiments performed under extreme experimental conditions, for which unsatisfactory results might occur [38].
The experimental saccharification conditions of pretreated C. linum biomass were shown in Table 2. The observed values of sugar yields were used to compute the model coefficients using the least square method [16]. The final empirical model describing the relationship between the variables and the sugar yield from enzymatic hydrolysis of pretreated C. linum biomass in terms of coded values can be written as follows:
ˆy=10.21+0.41 X1+3.24 X2+8.61 X3−0.84 X12−1.08 X22+5.64 X32+0.99 X1X2+2.75 X1X3+1.38 X2X3 | (4) |
Where ˆy: the sugar yield (%); X1, X2 and X3: the coded values of test variables L/S ratio, enzyme concentration and hydrolysis time, respectively. X1X2, X1X3 and X2X3: the interaction effects of L/S ratio and enzyme concentration, L/S ratio and hydrolysis time, enzyme concentration and hydrolysis time, respectively.
Components | Contents (%) |
Moisture | 13.96 ± 1.32 |
Ash | 14.83 ± 0.36 |
Protein | 10.56 ± 0.22 |
Lipid | 1.89 ± 0.04 |
Carbohydrates | 42.45 ± 2.94 |
Crude fiber | 29.76 ± 1.54 |
The quality of the fitted model for enzyme hydrolysis of C. linum biomass was evaluated based on the correlation coefficient R2. The R2 for the obtained equation was found to be 0.961. This indicated that 96.1% of total variation in enzyme saccharification was attributed to the experimental factors studied. A regression model with R2 > 0.90 is considered to have a very high correlation [16] and then the R2 of 0.961 was considered as a good fit of the model. The value of the adjusted determination coefficient was also high (adjusted R2=0.910), supporting for high significance of this model.
The adequacy of the model was further justified through analysis of variance (ANOVA) of the quadratic model for the sugar yield reponse (Table 4). The Fisher’s test (F-test) carried out on experimental data make it possible to estimate the statistical significance of the proposed model [16]. The high F-test value of the model with p-value less than 0.01 and non-significant lack of fit suggested that the model was adequate to predict the percentage of sugar yield during enzyme hydrolysis within the range of the studied three factors.
Source of variation | Sum of squares | Degrees of freedom | Mean square | F-ratio | P-value (Significance) |
Regression | 857.4700 | 9 | 95.2744 | 19.0471 | < .0001(***) |
Residuals | 35.0143 | 7 | 5.0020 | ||
Lack of fit | 19.7614 | 3 | 6.5871 | 1.7274 | 29.9% (NS) |
Error | 15.2529 | 4 | 3.8132 | ||
Total | 892.4843 | 16 | |||
***Significant at the level 99.9%; N.S.: non significant. |
The parameter estimates and the corresponding P-values suggest that, among the independent variables, X2 (enzyme concentration) and X3 (hydrolysis time) have significant effects on sugar yield (%) and maximum effect was shown by hydrolysis time (p-value less than 0.001), followed by enzyme concentration (p-value less than0.01). The quadratic terms of X3 and interactions between X1 and X3 also have significant effects on the sugar yield (Table 5).
Source | Coefficient | Ecart-Type | t.exp. | Significance % |
b0 | 10.206 | 1.000 | 10.20 | * |
b1 | 0.409 | 0.791 | 0.52 | 62.5% (N.S.) |
b2 | 3.240 | 0.791 | 4.10 | * |
b3 | 8.606 | 0.791 | 10.88 | * |
b11 | –0.837 | 1.090 | –0.77 | 47.3% (N.S.) |
b22 | –1.079 | 1.090 | –0.99 | 35.7% (N.S.) |
b33 | 5.638 | 1.090 | 5.17 | * |
b12 | 0.990 | 1.118 | 0.89 | 40.9% (N.S.) |
b13 | 2.747 | 1.118 | 2.46 | * |
b23 | 1.380 | 1.118 | 1.23 | 25.7% (N.S.) |
*Significant at the confidence level 95.0%; NS not significant at the confidence level 95.0%. |
To examine the interaction of the variables and to determine the optimum level of each variable for maximum response, three-dimensional response surface plots and two dimensional isoresponse curves were plotted against two experimental factors while maintaining the other factor constant at itscentral value (Figure 1).
The effects of L/S ratio and enzyme concentration on the sugar yield (%), when the hydrolysis time was at its center point, are shown in Figure 1a. The reducing sugar yields were estimated to increase linearly with increase in enzyme concentration from 10 to 60 U/g and ranged between 5 and 12%. When enzyme concentration was at low levels, non significant improvement in the sugar yield was observed by increasing the L/S ratio. The reducing sugar yield was maximized at high levels of enzyme concentration and medium to high levels of L/S ratio.
Figure 1b shows the effects of L/S ratio and hydrolysis time on sugar yield (%), when the enzyme concentration was at its center level. A positive interaction between L/S ratio and hydrolysis time was observed. Indeed, it was observed that at middle to high level of L/S ratio (80-100 mL/g) and high level of hydrolysis time (> 40 h) the reducing sugar yield was high (≈25%).
The effects of enzyme concentration and hydrolysis time on the sugar yield (%), when the time was at its center level, are shown in Figure 1c. This figure revealed the low yields of reducing sugar at low levels of enzyme concentration and low levels of incubation time. Reducing sugar yield was found to be consistently increased with raise in hydrolysis time and enzyme concentration. It was also found that the effect of reaction time was more significant than that of the enzyme concentration. High reducing sugar yield (25%) was observed with high levels of enzyme concentration (40-60 U/g) and high level of incubation time (44 h).
As the sugar yield can be maximized especially with a long treatment duration (Figures 1b and c), we fixed the incubation time at its high level (44.0 h), and we ploted enzyme concentration versus redox L/S ratio (Figure 2) to look for the highest sugar yield. Response analysis using NemrodW software predicted the maximum sugar yield of 30±3% during enzyme hydrolysis of C. linum biomass under the optimum process conditions i.e. when L/S ratio was 100 mL/g, hydrolysis time was 44 h and enzyme concentration was 52 U/g. To validate the predicted sugar yield, an experiment was conducted with the above mentioned optimum conditions of each variable as developed by the model. The optimal experimental sugar yield response for pretreated C. linum biomass was 29.6 g sugars/100g DM and it was in good agreement with predicated value.
The conversion efficiencyof polymeric carbohydrates from C. linum into simpler sugars by Aspergillus niger enzymes under optimal conditions was 71%. It was about 18-fold higher than the yield obtained before optimization (hydrothermally pretreated C. linum biomass). Our results revealed the superiority of C. linum biomass for achieving high sugar yield under enzymatic optimized conditions in comparison to other green seaweed biomasses. For examples, pre-heat treatment of biomass from the green seaweed Ulva fasciata Delile in aqueous medium at 120°C for 1 h followed by incubation in 2% (v/v) enzyme (cellulase 22119) for 36 h at 45°C gave a maximum yield of 20.6 g sugars/100g DM [11]. The green seaweed Monostroma nitidum, has also been used as the raw material for the production of reducing sugars [38]. Glucan in this seaweed was hydrolyzed using a commercial enzyme (Cellulosin T2) at 37°C for 48 h. Although the conversion rate of glucans reached 79.9%, as a result of applying hydrothermal pretreatment at 100°C for 30 min prior to enzymatic saccharification, the yield of glucose was still only 11 g glucose/100g biomass [39].
The ethanol yield after fermentation of optimized enzymatic hydrolysate from C. linum with S. cerevisiae reached an average of 8.6 g ethanol/100g DM. This yield was similar to those reported in other studies [12,32]. Indeed, the hydrolysis of C. linum feedstock with a crude enzyme preparation, produced from Aspergillus awamori, at 45°C, pH 5 for 30 h gave the maximum yield of fermentable sugar of 22 g/100g DM. An ethanol yield of about 9.3 g/100g pretreated algae was obtained after alcoholic fermentation by S. cerevisiae [32]. The ethanol yields produced from C. linum pretreated with hydrothermal treatment, wet oxidation, steam explosion, plasma assisted pretreatment and ball milling were varied between 11 to 18 g ethanol/100g DM [12]. The seasonal variability and environmental constraints which affect the chemical composition of C. linum as well as the type of saccharification treatments were the most significant factors affecting the ethanol yield from C. linum biomass [12,32].
In the present study, a three factors three levels Box-Behnken design and the response surface methodology provide the development of a polynomial model for optimization of enzymatic saccharification of Chaetomorpha linum biomass for the production of macroalgae-based third generation bioethanol. Response surface plot in three-dimension obtained from the empirical quadratic model can show the interaction effect of two variables on the studied response and the optimum values of the selected variables are obtained from response surface plot, too. Based on the statistical optimization, optimal sugar and ethanol yields were 30.2 g sugars/100g DM and 8.6 g ethanol/100g DM, respectively. These results will provide basic information applicable to further studies on the use of the green seaweed C. linum as a renewable feedstock for bioenergy production.
The authors thank the South African/Tunisia-research partnership programme bilateral agreement 2014 and the Tunisian Ministry of Higher Education and Scientific Research for financial support.
The authors declare that they have no conflict of interest.
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Variable | Factor | Unit | Low level | High level |
X1 | L/S ratio | mL/g | 50.0 | 100.0 |
X2 | Enzyme conc. | U/g | 10.0 | 60.0 |
X3 | Time | h | 4.0 | 44.0 |
N°Exp | X1 | X2 | X3 | L/S (ml/g) | Enzyme (U/g) | Time (h) | Measured sugar yiel (%) | Estimated sugar yield (%) |
1 | –1.0 | –1.0 | 0.0 | 50.0 | 10.0 | 24.0 | 6.91 | 5.63 |
2 | 1.0 | –1.0 | 0.0 | 100.0 | 10.0 | 24.0 | 6.07 | 4.47 |
3 | –1.0 | 1.0 | 0.0 | 50.0 | 60.0 | 24.0 | 8.53 | 10.13 |
4 | 1.0 | 1.0 | 0.0 | 100.0 | 60.0 | 24.0 | 11.65 | 12.93 |
5 | –1.0 | 0.0 | –1.0 | 50.0 | 35.0 | 4.0 | 9.51 | 8.74 |
6 | 1.0 | 0.0 | –1.0 | 100.0 | 35.0 | 4.0 | 4.51 | 4.06 |
7 | –1.0 | 0.0 | 1.0 | 50.0 | 35.0 | 44.0 | 20.01 | 20.46 |
8 | 1.0 | 0.0 | 1.0 | 100.0 | 35.0 | 44.0 | 26.00 | 26.77 |
9 | 0.0 | –1.0 | –1.0 | 75.0 | 10.0 | 4.0 | 2.25 | 4.30 |
10 | 0.0 | 1.0 | –1.0 | 75.0 | 60.0 | 4.0 | 8.85 | 8.02 |
11 | 0.0 | –1.0 | 1.0 | 75.0 | 10.0 | 44.0 | 17.92 | 18.75 |
12 | 0.0 | 1.0 | 1.0 | 75.0 | 60.0 | 44.0 | 30.04 | 27.99 |
13 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 11.26 | 10.21 |
14 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.83 | 10.21 |
15 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 9.61 | 10.21 |
16 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 13.06 | 10.21 |
17 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.27 | 10.21 |
Components | Contents (%) |
Moisture | 13.96 ± 1.32 |
Ash | 14.83 ± 0.36 |
Protein | 10.56 ± 0.22 |
Lipid | 1.89 ± 0.04 |
Carbohydrates | 42.45 ± 2.94 |
Crude fiber | 29.76 ± 1.54 |
Source of variation | Sum of squares | Degrees of freedom | Mean square | F-ratio | P-value (Significance) |
Regression | 857.4700 | 9 | 95.2744 | 19.0471 | < .0001(***) |
Residuals | 35.0143 | 7 | 5.0020 | ||
Lack of fit | 19.7614 | 3 | 6.5871 | 1.7274 | 29.9% (NS) |
Error | 15.2529 | 4 | 3.8132 | ||
Total | 892.4843 | 16 | |||
***Significant at the level 99.9%; N.S.: non significant. |
Source | Coefficient | Ecart-Type | t.exp. | Significance % |
b0 | 10.206 | 1.000 | 10.20 | * |
b1 | 0.409 | 0.791 | 0.52 | 62.5% (N.S.) |
b2 | 3.240 | 0.791 | 4.10 | * |
b3 | 8.606 | 0.791 | 10.88 | * |
b11 | –0.837 | 1.090 | –0.77 | 47.3% (N.S.) |
b22 | –1.079 | 1.090 | –0.99 | 35.7% (N.S.) |
b33 | 5.638 | 1.090 | 5.17 | * |
b12 | 0.990 | 1.118 | 0.89 | 40.9% (N.S.) |
b13 | 2.747 | 1.118 | 2.46 | * |
b23 | 1.380 | 1.118 | 1.23 | 25.7% (N.S.) |
*Significant at the confidence level 95.0%; NS not significant at the confidence level 95.0%. |
Variable | Factor | Unit | Low level | High level |
X1 | L/S ratio | mL/g | 50.0 | 100.0 |
X2 | Enzyme conc. | U/g | 10.0 | 60.0 |
X3 | Time | h | 4.0 | 44.0 |
N°Exp | X1 | X2 | X3 | L/S (ml/g) | Enzyme (U/g) | Time (h) | Measured sugar yiel (%) | Estimated sugar yield (%) |
1 | –1.0 | –1.0 | 0.0 | 50.0 | 10.0 | 24.0 | 6.91 | 5.63 |
2 | 1.0 | –1.0 | 0.0 | 100.0 | 10.0 | 24.0 | 6.07 | 4.47 |
3 | –1.0 | 1.0 | 0.0 | 50.0 | 60.0 | 24.0 | 8.53 | 10.13 |
4 | 1.0 | 1.0 | 0.0 | 100.0 | 60.0 | 24.0 | 11.65 | 12.93 |
5 | –1.0 | 0.0 | –1.0 | 50.0 | 35.0 | 4.0 | 9.51 | 8.74 |
6 | 1.0 | 0.0 | –1.0 | 100.0 | 35.0 | 4.0 | 4.51 | 4.06 |
7 | –1.0 | 0.0 | 1.0 | 50.0 | 35.0 | 44.0 | 20.01 | 20.46 |
8 | 1.0 | 0.0 | 1.0 | 100.0 | 35.0 | 44.0 | 26.00 | 26.77 |
9 | 0.0 | –1.0 | –1.0 | 75.0 | 10.0 | 4.0 | 2.25 | 4.30 |
10 | 0.0 | 1.0 | –1.0 | 75.0 | 60.0 | 4.0 | 8.85 | 8.02 |
11 | 0.0 | –1.0 | 1.0 | 75.0 | 10.0 | 44.0 | 17.92 | 18.75 |
12 | 0.0 | 1.0 | 1.0 | 75.0 | 60.0 | 44.0 | 30.04 | 27.99 |
13 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 11.26 | 10.21 |
14 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.83 | 10.21 |
15 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 9.61 | 10.21 |
16 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 13.06 | 10.21 |
17 | 0.0 | 0.0 | 0.0 | 75.0 | 35.0 | 24.0 | 8.27 | 10.21 |
Components | Contents (%) |
Moisture | 13.96 ± 1.32 |
Ash | 14.83 ± 0.36 |
Protein | 10.56 ± 0.22 |
Lipid | 1.89 ± 0.04 |
Carbohydrates | 42.45 ± 2.94 |
Crude fiber | 29.76 ± 1.54 |
Source of variation | Sum of squares | Degrees of freedom | Mean square | F-ratio | P-value (Significance) |
Regression | 857.4700 | 9 | 95.2744 | 19.0471 | < .0001(***) |
Residuals | 35.0143 | 7 | 5.0020 | ||
Lack of fit | 19.7614 | 3 | 6.5871 | 1.7274 | 29.9% (NS) |
Error | 15.2529 | 4 | 3.8132 | ||
Total | 892.4843 | 16 | |||
***Significant at the level 99.9%; N.S.: non significant. |
Source | Coefficient | Ecart-Type | t.exp. | Significance % |
b0 | 10.206 | 1.000 | 10.20 | * |
b1 | 0.409 | 0.791 | 0.52 | 62.5% (N.S.) |
b2 | 3.240 | 0.791 | 4.10 | * |
b3 | 8.606 | 0.791 | 10.88 | * |
b11 | –0.837 | 1.090 | –0.77 | 47.3% (N.S.) |
b22 | –1.079 | 1.090 | –0.99 | 35.7% (N.S.) |
b33 | 5.638 | 1.090 | 5.17 | * |
b12 | 0.990 | 1.118 | 0.89 | 40.9% (N.S.) |
b13 | 2.747 | 1.118 | 2.46 | * |
b23 | 1.380 | 1.118 | 1.23 | 25.7% (N.S.) |
*Significant at the confidence level 95.0%; NS not significant at the confidence level 95.0%. |