© R.J. Sánchez et al., Hosted by EDP Sciences, 2021

1 Introduction

Canola oil, widely consumed, has a high content of unsaturated fatty acids and vitamin E (780.2 ppm, Sánchez et al., 2018a). In recent years, emerging technologies for the extraction of this oil have been studied, such as the application of ultrasound, microwaves and the use of ethanol as a solvent, among others (Carré et al., 2018; Sánchez et al., 2019a, 2019b; Mohseni et al., 2020). The Taguchi method uses a special experimental design called orthogonal array to study the entire parameter space with a small number of experiments. This method has been widely used to improve the manufacturing processes of high-precision mechanical parts, and in recent years, it has been applied to study processes involving biological matrices, such as foods (Azin et al., 2007; Rao et al., 2008; Fernández et al., 2014). Traditionally the Taguchi method has been used for the optimization of a single performance characteristic, and in several works, it has applied to study oil extraction processes. Fernández et al. (2014) used the method to optimize the hydrothermal pretreatment of canola seeds, analyzing yield and quality responses individually, and selecting one of the responses for calculating the optimal parameters. Rombaut et al. (2015) studied the influence of different operating conditions on grape seed oil extraction by cold pressing using Taguchi methodology. Similarly to the case cited above, they optimized oil and polyphenol extraction yields as individual responses. Morakinyo and Bamgboye (2017) used Taguchi’s methodology to optimize the sterilization of palm oil from a novel vertical sterilizer on a pilot scale, and response surface methodology for the optimization of the experimental design. Artificial Intelligence were begun to study for the prediction and modeling of food processes. Sánchez et al. (2018b) applied an artificial neural network to model the yields of canola oil extraction with different pretreatments. In this context, fuzzy logic is a mathematical theory of inexact reasoning that allows modeling the human reasoning process in linguistic terms (Ross, 2016). It is a form of many-valued logic that deals with fluid or approximate reason rather than precise or exact statements. In contrast to “crisp logic”, where binary sets are “true or false”, the truth values of fuzzy logic variables range between 0 and 1. Fuzzy logic has also been used to handle the concept of partial truth by Kulekci et al. (2016), where the truth value may range between completely true and completely false.

The optimization of multiple performance characteristics of a process can be transformed into the optimization of a single performance index through fuzzy logic. Thus, the integration of fuzzy logic with the Taguchi method can be used to solve the optimization of multiple performance characteristics. This approach has been applied by several authors to improve the characteristics of welding processes and the milling of machine parts Tarng et al. (2000); Mahesh and Rajesh (2014); Kulekci et al. (2016). However, it has not yet been studied for technological processes that involve biological matrices such as oilseeds.

The purpose of this paper was to evaluate the use of fuzzy logic and the Taguchi method for the optimization of the hydrothermal pretreatment of canola seeds with multiple performance characteristics (oil extraction yield and quality indices). This work describes the application of the fuzzy logic analysis combined with the Taguchi method to optimize multiple performance characteristics that were previously subjected to a decision-making process. In this sense, the novel contribution of this work is the application of this technique to the hydrothermal pretreatment and extraction of canola oil, allowing to evaluate different and complex responses such as oil yield and quality index and facilitating its industrial application.

2 Materials and methods

Data reported by Fernández et al. (2014) who worked with the experimental design presented in Table 1 (L₉ orthogonal array), were used in the present study (Tab. 1).

Samples of canola seeds of the Barrel variety were subjected to hydrothermal pretreatments using steam in an autoclave whose base was perforated, under the conditions of temperature, time and granulometry presented in Table 2. The responses were measured as performance characteristics for oil yield ratio (ratio of the oil yield of pretreated samples to that of untreated samples), acidity value (AV) and peroxide index (PV). (Tab. 2).

2.1 Signal-to-noise ratio

The Taguchi method uses the signal-to-noise ratio (SN) to analyze the sources of variation, representing a relationship or comparison between the desirable value (mean) for the output characteristic and the “noise” or the undesirable value for the output characteristic. The SN ratio, often expressed in decibels, is a measure of the variation between experiments when noise factors are present (Zhou et al., 2010).

In order to maximize the oil yield ratio, the SN value was obtained by equation (1): (1)

In the case of the quality indices (AV and PV), where minimum values are desired, the SN ratio was calculated using equation (2): (2) where x_k is the response obtained experimentally, n is the number of experiments, and k is the number of repetitions. Figure 1 presents the SN values calculated by Fernández et al. (2014) for the studied responses (Fig. 1):

Fig. 1 Signal-to-noise ratios for the responses: (A) oil yield, (B) acidity, and (C) peroxide index.

2.2 Fuzzy logic analysis

The multiple performance characteristics were obtained using the fuzzy logic analysis. A fuzzy logic unit consists of a fuzzifier, a fuzzy knowledge base, an inference engine and a defuzzifier. First, the fuzzifier converts the SN values into fuzzy inputs using membership functions. Then the inference engine applies compositional rules of inference using the implications of the knowledge base to generate fuzzy outputs. Finally, the defuzzifier converts the fuzzy values into a crisp output (Tzeng and Chen, 2007). The final structure of the fuzzy unit was the one presented in Figure 2.

In our case, the fuzzy logic unit took 3 inputs (x₁, x₂ and x₃) and produced 1 output (y₀). Each input refers to SN for oil yield ratio, acidity value and peroxide value, respectively. The output y is called multi-response performance index (MRPI) (Tarng et al., 2000; Tzeng and Chen, 2007; Mahesh and Rajesh, 2014).

The knowledge base consisted of 27 rules designed as “if-then” instructions. Such rules evaluate the values of the inputs over the fuzzy subsets to provide a suitable output. Each fuzzy subset was defined by the corresponding membership function (µ).

In this work, 3 fuzzy subsets Ei, Fi and Gi were assigned for each input i (Figs. 3–5). For example, in the case of x, the fuzzy subsets were defined as follows:

1. the fuzzy subset E1 defines the membership µ_E with a X function. Such a function is defined using the values 39.5 to 40.9 of SN ratio for yield as Low (L);

2. the fuzzy subset F1 defines the membership µ_E with a X function. Such a function is defined using the values 39.6 to 42.5 of SN ratio for yield as Medium (M);

3. the fuzzy subset G1 defines the membership µ_E with a X function. Such a function is defined using the values 41.1 to 42.6 of SN ratio for yield as High (H).

The fuzzy logic unit used 7 fuzzy subsets assigned to the output y (Fig. 6). In this case, each subset depicts the degrees of membership of the MRPI value to a subset H designed according the following categories: extremely low (EL), very low (VL), low (L), medium (M), high (H), very high (VH) and extremely high (EH).

Thus 27 fuzzy rules were designed considering that the performance characteristics increase with increasing SN ratios. The basic structure of these rules is an “if-then” definition that uses the 3 inputs and a single output as follows:

Rule #number: If x₁ is E1, x₂ is F2 and x₃ is G3 then y is H

where E, F, G and H are fuzzy subsets defined over each variable by the corresponding membership functions (e.g. µE1, µF2_, µG3 and µH).

Table 3 presents the full set of rules applied in the present work. For example, rule number 6 specifies that if Yield is Low (L), AV is Medium (M) and PV is High (H) then MRPI is Medium (M). It is important to point out that the set of fuzzy rules was applied following a switch composition (cascade operation). That is, if rule number N is not satisfiable, then rule number N+1 will be tested.

The fuzzy reasoning of the output obtained from these rules generates a fuzzy output. The membership function of the fuzzy output was designed adopting the “max-min” compositional operation over the membership functions detailed per each input. That is: (3) where ˄ is the “minimum” operation, and ˅ is the “maximum” operation (Tarng et al., 2000).

Finally, the center of gravity method was adopted as the defuzzification method to transform the fuzzy output into a crisp value y₀, given by equation (4): (4)

The software MATLAB was used for all the calculations.

Fig. 2 Structure of the fuzzy logic unit. X1: S/N ratio for the oil yield, x2: S/N ratio for the acidity value (AV), x3: S/N ratio for the peroxide index (PV), and y: multi-response performance index (MRPI).

Fig. 3 Membership functions for oil yield.

Fig. 4 Membership functions for acidity value (AV).

Fig. 5 Membership functions for peroxide index (PV).

Fig. 6 Membership functions for the multi-response performance index (MRPI).

3 Results and discussion

3.1 Multi-response performance index

Table 4 presents the experimental results for MRPI obtained using the experimental design described above.

Assuming the no interaction model proposed by Taguchi, the mean responses for each level were calculated (Fernández et al., 2014), in this case for the MRPI, which are presented in Table 5 and graphically in Figure 7.

The highest MRPI value corresponds to the lowest variance of the responses around the desired values. However, it is necessary to evaluate the relative effect of the analyzed parameters on the studied responses in order to determine the optimal conditions more accurately.

Fig. 7 Effect of the control factors on the multi-response performance index (MRPI).

3.2 Analysis of variance

ANOVA was used to study the significance of the experimental factors (Fernández et al., 2014). The ANOVA results are shown in Table 6.

The results of the analysis of variance showed a larger contribution of parameters B (temperature) and D (granulometry) on the process, with the latter being the most important, whereas the contribution of parameter C (time), due its low value, was treated as error using the pooling technique (Özdemir et al., 2004; Fernández et al., 2014) These results are in agreement with those obtained by analyzing the responses of yield, acidity and peroxide index individually (Fernández et al., 2014).

The analysis of Figure 7 and Table 6 shows that in the case of temperature (B), the levels 1 and 2 (100 and 120 °C, respectively) are the levels with the highest MRPI value. A large contribution of granulometry (D) can also be observed, with levels 2 and 3 (broken and entire seeds, respectively) having the highest MRPI. When these values are compared to the results obtained for each response individually, the influence of the 3 responses on the MRPI values can be observed. For example, in the case of factor D, the oil yield obtained at level 2 was significantly higher than that obtained at level 3, but the quality indices showed the opposite behaviour, whereas MRPI maintained a constant value for these levels, showing a compensation of the effect of the responses.

Taking the above into account, it was possible to determine the following optimum parameters: temperature 100 and 120 °C (levels 1 and 2 of factor B), 5 minute pretreatments, corresponding to the lowest level of factor C (since the contribution of this factor was attributed to error), and broken and entire seeds (levels 2 and 3 of factor D). In order to evaluate and compare the obtained results with the experimental values and the predicted values reported in the literature, a temperature of 120 °C, 5 minutes and broken seeds were selected, which are the same conditions selected by Fernández et al. (2014).

3.3 Confirmation test

The predicted response for the additional experiment proposed by Fernández et al. (2014) for the optimum factor levels is calculated by equation (5): (5) where is the mean response of all the proposed experiments for the experimental design, and MB2, MC1 and MD2 correspond to the selected levels of factor B, C and D, respectively. Since the contribution of factor C can be treated as error due to its low mean square value in ANOVA (calculated as the ratio of the sum of square value to the degrees of freedom, Table 6), the terms of this factor can be simplified. The predicted MRPI value calculated by equation (5), the MRPI corresponding to the values predicted by Fernández et al. (2014) and the experimental MRPI are presented in Table 7. Since no experimental PV value was detected for E10, the PV value predicted by the Fernández et al. (2014) model was adopted for the calculation of MRPI.

The predicted MRPI value obtained by applying fuzzy logic to the Taguchi method was similar to that obtained by Fernández et al. (2014), indicating the correlation of the proposed approach with the conventional Taguchi method. It is worth noting that using a multi-response index allows to explore all the studied responses (yield, acidity value and peroxide index) to obtain the optimum parameters, thus representing an improvement over the traditional method, by which the optimum parameters are obtained by considering a single response.

4 Conclusions

In this paper, the use of Taguchi-based fuzzy logic for the optimization of the hydrothermal pretreatment of canola seeds allowed to successfully analyze yield and quality responses simultaneously by means of a multi-response performance index (MRPI). The predicted MRPI values were compared to experimental MRPI values and to predicted values reported in the literature, observing an agreement between the results. However, the use of MRPI from the application of the fuzzy logic tool allowed to take into account all the studied responses to obtain the optimal conditions, in contrast to other works where from different responses it was necessary to select the main one for the decision making. The approach proposed in this work is an efficient method for the optimization of manufacturing systems by considering multiple performance characteristics of both process and product. Its application in industrial processes with multiple objectives is promising.

Nomenclature

E: Experiment

AV: Acidity value

PV: Peroxide index

SN: Signal-to-noise ratio

x_i: Input of fuzzy engine

y_i: Output of fuzzy engine

E_i, F_i, G_i , H_i: Fuzzy subsets

µ_ji: Membership function

˄: Minimum operation

V: Maximum operation

EL: Fuzzy rule. Extremely low

VL: Fuzzy rule. Very low

L: Fuzzy rule. Low

M: Fuzzy rule. Medium

H: Fuzzy rule. High

VH: Fuzzy rule. Very high

EH: Fuzzy rule. Extremely high

MRPI: Multi-response performance index

MB2, MC1, MD2: Selected levels of factor B, C and D, respectively

Subscripts

i: 0,1,2,....,n: series terms

j: E, F, G, H.

Conflict of interest

The authors declare no conflict of interests.

Acknowledgments

The authors acknowledge the financial support from ANPCyT (Agencia Nacional de Promoción Científica y Tecnologica) (Grant Number: PICT 2012-1442) and Facultad de Ingeniería, Universidad Nacional del Centro de la Provincia de Buenos Aires, Argentina (Grant Number: 03-E170).

References

All Tables

All Figures

	Fig. 1 Signal-to-noise ratios for the responses: (A) oil yield, (B) acidity, and (C) peroxide index.
In the text

	Fig. 2 Structure of the fuzzy logic unit. X1: S/N ratio for the oil yield, x2: S/N ratio for the acidity value (AV), x3: S/N ratio for the peroxide index (PV), and y: multi-response performance index (MRPI).
In the text

	Fig. 3 Membership functions for oil yield.
In the text

	Fig. 4 Membership functions for acidity value (AV).
In the text

	Fig. 5 Membership functions for peroxide index (PV).
In the text

	Fig. 6 Membership functions for the multi-response performance index (MRPI).
In the text

	Fig. 7 Effect of the control factors on the multi-response performance index (MRPI).
In the text