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Application of response surface methodology in scallop shelling

Shelling is a central and crucial step in the mechanized processing of scallops. However, current research on the peeling mechanism is insufficient, and a relatively complete theoretical system has not been established so far. This paper proposes an application of response surface methodology and the design of an experiment to provide and stimulate further research on the automation of scallop shucking. Effective factors on the binding force of scallops are evaluated and discussed in this paper. The relationship between responses with significant factors is established. By employing response surface methodology, mathematical regression model can be efficiently performed. This response model is applied to analyze the response surface contours and surface plots to estimate shelling performance by developing a better shucking process. At the same time, quadric model proposed is used not only for predicted optimal process parameters but also for process optimization, and enrich the theoretical system of shellfish shelling.


Introduction
Scallops, as one of the most essential economic shellfish, are widely distributed in coastal countries and regions [1][2][3]. Scallops are extremely popular among consumers because of fresh and tender meat, rich nutrients [4]. Besides, it also plays a crucially important role in improving blood lipids, fighting fatigue, and enhancing immunity. Adductor muscle, the main edible part of scallop, which could be made into massive delicious dishes after being dried, which is highly sought after by some food lovers [5][6][7][8]. The Scallop Skirt could be made into delicious seafood soy sauce, a good helper for stir-fry seasoning, and could also serve as processed into raw materials for bait. Using biochemical technology to prepare medicinal value of scallop extract from scallop viscera mass could be utilized to treat certain diseases. The variety of colors of the shells, which are crushed and ground to make powder, could be applied to decorate walls [9].
In short, no matter what products are processed, most of them need to be shelled first. In view of this, it is extremely important to deal with the problem for the separation of shellfish shell and meat. In the prior period, it has been one of the tough and challenging problems in this field. The traditional shucking way is by hand, with low efficiency and requires adequate physical strength [10]. Since the 19th century, shellfish shelling has applied mechanics, thermal, and pressure other technologies [11]. A steam shelling machine was proposed by Zhang et al. [12] to address scallop shelling. High pressure (HP) [13][14][15][16][17][18] technology is applied to scallops or oysters processing, after applying HP technology, scallops or oysters could be effectively detached from shells, peeled the scallops or oysters. High hydrostatic pressure (HHP) [19] also has potential in solving shelling problems. Yi et al. [20] proposed HHP is an alternative for shellfish detaching, experiment reveals that HHP peeling at 200MPa for 3 minutes can make the adductor muscle 100% shucked. Besides, Martin et al. [21,22] presented a heat-cool process to promote the separation of oysters, which could make the separation rate higher than 85%. Other classic methods are also applied to enrich this field. For example, Little et al. [23] presented laser added shellfish shelling. Due to the high energy of laser beam, it is irradiated on the adductor muscle, so that the adductor muscle falls off from the inner surface of shell. Because laser added shelling method is limited to the range of shellfish species, it has not been commonly used. So far, although there have been many methods to work around this issue. However, many studies only have focused on shellfish shelling methods. By contrast, less attention has been focused on the establishment and optimization of shellfish shelling model. The research of this paper describes areas where further research is required that will advance the technology of shellfish shucking. Water bath thermal shelling technology is adopted in order to study shellfish shucking. By researching under what conditions the binding force of scallop is the smallest and to improve the degree of scallop shelling. Under the design environment in Design-Expert 10.0, analysis of variance (ANOVA) is proposed for this paper to select the most significant factors level range and further analyze in a response surface model. Built on the experimental data and contour graphs, an approximate functional relationship was provided. According to the result of the smaller lack of fit of the model, it can be determined that the reliability of the model is high, which could be accepted to analyze and predict the binding force of scallops. This method enriches the theory for scallop shelling and builds a solid foundation in other shellfish shelling.

Measuring method of binding force
In the experiment, V-shaped probe of the digital force gauge was employed for measuring the binding force of scallop. The process was recorded when reaching the peak of the binding force, and the values were processed by Origin 2018 software so that the value on the digital force gauge could be read as shown in Figure 1.

The biological binding force of bay scallop
The biological binding force is a collective term for a series of intermolecular forces in organisms, including the ubiquitous van der Waals forces, hydrophobic bonds formed by the interaction of polar genes in molecules, and hydrogen bonds formed by the interaction of hydrogen atoms [24,25]. In the shucking process, the adductor muscles that are glued to the shell are cut off or released. In essence, the process of processing scallops is the process of overcoming these biological binding forces (hereinafter

Measurement of scallop dimensions
When measuring, clean and wipe the soil on the surface of the scallops. Next, using a vernier caliper (measurement accuracy: 0.02mm) to measure the dimensions of the selected scallops (see Figure 3), and the three morphological characteristics of the scallop shell length, shell width, and shell height were measured. Particularly to point out that the shell length refers to the maximum straight line distance between the left and right edges of the shell, the shell width refers to the maximum straight line distance between the two shells, and the shell height refers to the maximum straight line distance from the top of the shell to the ventral edge. Furthermore, the seawater on each surface absorbing dry with filter paper, and electronic balance (measurement accuracy: 0.01g) was employed to measure the quality of live scallops one by one, and the measurement data are presented in Table 1. Note: When the data is equal to the boundary value, it is divided into larger groups.

Statistical analysis
After sorting out the quality and dimensions of the measure scallops, Excel 2016 and Origin 2018 software are employed to analyze and process, and distribution histograms were drawn. Figure 4 displays the distribution histograms of the quality, shell length, shell width, and shell height of 50 experimental scallops. The abscissa represents the experiment grouping situation and the ordinate represents the number of traits. From the distribution histograms, it can be noted that the quality and shape of scallops content the normal distribution. The measurement results provide data support for subsequent experiments and sample selection.

Binding force experiments design for scallop shelling process Experimental procedure and design
In this paper, fresh bay scallops are employed as the research object, and three factors of water temperature, heating time, and scallop quality are studied to analyze the law of influence on the binding force and provide positive guidance for subsequent automated shelling production. On this basis, first of all, based on the single factor tests, the optimal level range of the influence of parameters on the binding force was screened out, which reduced variance and established a good foundation for the later response surface methodology. On second thoughts, the Box-Behnken response surface methodology was utilized to optimize and test the selected optimal parameter range to obtain the response surface methodology model and optimal match of the working parameters of scallop shell meat separation.

The factors range of selection for tests
In this experiment, in terms of the size level, bay scallops with shell length of 66-72mm were selected as the experimental research object.
In the single factor test process, three parameters (water temperature, heating time, and scallop quality) were determined as the factors of tests, and the binding force is chosen as the test index. Under single factor test process, other factors are fixed, the influence of a certain factor on its binding force is analyzed. Under each test factor level, 20 bay scallops were selected for repeating tests. The test conditions are given in Table 2. Scallop quality (g) 31-36-、41-、46-、51-、

The influence of water temperature on binding force
As the water temperature increases, the temperature inside the scallop shell gradually increases, and the binding force between the shell and the adductor muscle gradually decreases. The effect of water temperature on the binding force is shown in Figure 5.

Fig. 5
The relationship between water temperature and binding force Because the scallop adductor muscle is fibrous tissue, rich in protein, has a certain toughness, and is exceedingly sensitive to temperature changes. When the water temperature gradually increases and arrives at a certain level, the actomyosin in the fibrous tissue will continuously shrink. When the maximum temperature exceeds its tolerance, actomyosin will experience relative dislocation, slip and rupture, and even lose its original biological activity [26]. At this time, the adductor muscle gradually loosens and falls off until it is separate. Therefore, within a certain water temperature range, the higher the water temperature, the more distinct the decrease in binding force, and the better the separation effect of scallop adductor muscle from the shell.

The influence of heating time on binding force
As the heating time increases, the heat absorbed in the scallop will increase, and the binding force between the shell and the adductor muscle gradually decreases. The effect of heating time on the binding force is shown in Figure 6. In the heating process, heat is transferred from the outside to the inside of shell, only when the junction between the adductor muscle and the shell reaches a certain temperature could be detached.
However, it takes a certain period of time to come to the temperature at which the shell flesh falls off and separates. If the heating time is too short, the temperature at the junction of the adductor muscle and the shell will not reach the shedding temperature, and the binding force between them will be too late to weaken or weaken very little. The degree of shedding of the adductor muscle and the shell is not distinct. As the heating time increases, the heat transferred to the shell increases, and the heat absorbed by the adductor muscle also increases, which enormously undermine the binding force between the adductor muscle and the shell, and enhanced the effect of scallops shucking. Therefore, within 5 minutes, the longer the heating time, the smaller the binding force, and the better the shelling effect.

The influence of scallop quality on binding force
As the quality of scallop increases, the quality of other scallop structures such as adductor muscle also gradually increases, and the binding force between the shell and the adductor muscle gradually increases. The effect of scallop quality on the binding force is shown in Figure 7.

Fig. 7 The relationship between scallop quality and binding force
It is particularly emphasized that compared with smaller scallops, the mass and diameter of the adductor muscle of larger scallops increase accordingly. When heated, larger scallops require higher temperature and longer time to make adductor muscle fall off and separate. Similarly, for larger scallops, the binding force is greater than smaller scallops, and the degree of shedding is not distinct or even more difficult to fall off. Thus, when scallop quality gradually increases, the binding force is large, the shelling effect of scallop is poor, and the shucking rate is low.

Response surface methodology
The response surface methodology (RSM) was first presented by Box and Wilson (1951) and has been a powerful technique in many different application areas [27][28][29][30]. The objective is to solve the relationship between the input (several experimental variables) and outputs (responses or test index) [31][32][33]. In addition, the RSM model is used to determine the levels of experimental parameters and to optimize the responses [34].
Characteristics and advantages of the RSM are to provide a mathematical model including the first-order term, the square term of each significant factor, and the first-order interaction term between any two factors through a reasonably designed limited number of an experiment, to fit these factors [35]. Thus, the RSM is useful for quickly modeling, shortening optimization time, and improving application credibility. Through the analysis of the function response surface and contour lines, the level of various factors affecting the response value and their interaction is optimized and evaluated, and the optimal conditions of the multi-factor system are quickly and effectively determined. The response surface function expression is generally shown in Equation (1).
, , , are the coefficient to be determined, and ε represents the error of y.
This is a second-order polynomial that can approximately replace the actual function within a certain range. After obtaining experimental data, least squares method was employed to gain the response surface function.

Response surface methodology design
Single factor test results were carried out to pick out the independent variables levels which affect  Table 3. Experimental results and discussion Estimated binding force characteristics Table 4 shows the results of the response surface methodology experiment. Estimating the effects of each factor Table 5 shows the ANOVA for the experimental results. The ANOVA analysis was performed based on the RSM for various factors characteristics, and was employed to efficiently explore the important factors that affect scallop shelling process. From Table 5, it can be readily seen that the F value > > , in the ANOVA table indicates that the larger the F value, the more significant the influence of this factor on the test results. Therefore, it can be further concluded that factors A and B are the most important factor, whereas, C is less significant, that is, water temperature and heating time have the greatest influence on the binding force, which is the main factor, followed by scallop quality.

Response surface methodology analysis
The regression types of model for the RSM were selected according to the results of the ANOVA.
The ANOVA results present the fitting linear in the experiments. The ANOVA table reveals that the model P < 0.0001，indicating that the corresponding quadratic model obtained by fitting has a high degree of significance, which has an extremely significant impact on the response value Y. In order to evaluate each influential factors in the quadratic RSM, Design-Expert 10.0 software was used to perform multiple regression fitting on the experimental data of binding force obtained in the experiment in Table 5.
Furthermore, from the ANOVA Table 5  The relative importance of the parameters and their interaction between the parameters can be observed from the values of the above polynomial coefficients.

Response surface contour analysis
To further study the interaction between related factors and determine the best point, based on  temperature and scallop quality, respectively. It is obvious that the binding force tends to decrease with the increase of water temperature. Analysis of the reasons is primarily because the temperature is too high, which reduces the elasticity of the adductor muscle and even causes its maturation. Under the action of high temperature, the actomyosin (main functional protein in the adductor muscle) will unwind, and some tissues will be eroded and deform, which will cause the adductor muscle fall off. As can be seen in Figure 8(a) and (c) show the response surface contour between temperature and heating time and heating time and scallop quality of the interaction influence on the binding force. For the binding force tends to decrease with the increase of heating time. Analysis of the causes is chiefly because as the heating time increases, the heat absorbed in the scallop shell will increase. At the same time, the fibrous tissue structure of the adductor muscle shows a gradual breaking trend. Figure 8(b) and (c) present the response surface contour between temperature and scallop quality and heating time and scallop quality of the interactive influence on the binding force. As the increase of scallop quality, the binding force is increasing. The reason is that the larger the scallop, the quality of the scallop structure such as the adductor muscle also has increase accordingly. Therefore, the higher the quality of the scallop, the less likely it is to fall off the adductor muscle.

Optimization of shelling process conditions
To obtain the best solution, it is necessary to optimize the generated quadratic mode under constraints. It can be seen from the response surface graphs in Figures 8 that the response value Y has a minimum value and the shell and flesh are completely separated, that is, the smaller the binding force Y or zero, the more significant the separation effect of scallop shell flesh. In the optimization standard, target=0 can be selected for the Y term, and click on the optimization results (solutions). At the same time, generated optimization results are presented in Figure 9.
As shown in Figure 9, it is obvious that the optimization results of response surface methodology that the state parameters for realizing shell and meat separation are not unique, and the excellent state parameters can be freely selected according to economic benefits and actual conditions. At the same time, the optimization results provide a certain theoretical basis for a better selection of shells and meat separation parameters.

Conclusions
This paper puts forward a general method to obtain and optimize water bath thermal shelling solutions for scallops based on RSM. It is experimentally revealed that the RSM with designed experiments is a simple and intensely method for improving high efficiency shelling rate of scallops.
Higher shelling rate with lower binding force and optimal conditions on the scallop thermal shelling has been achieved. Based on the experimental results, the main contributions of this paper are described as follows.
(1) In order to design an experiment plan for measuring the binding force of scallops, the bay scallop was used as the experimental object. The most significant factors identified by ANOVA affecting the binding force process are the factors A (water temperature) and B (heating time) for scallop shelling, and the factor C (scallop quality) less important.
(2) In this paper, a quadratic model with interaction terms was fitted to the data, and the correlation coefficient 2 and correction coefficient for quadratic regression model was 0.9851 and 0.9659, respectively. This implies that 96% of the total variance of the binding force percentage could be explained through the regression model. It is clear that the quadratic response surface model provides a new direction for scallop shelling field, which established a good foundation for subsequent other shellfish shelling technology. This method enriches the field of shellfish shelling and suitable for the research of the shellfish shelling.
(3) In addition, the concept of optimization is introduced to further enrich the theory in the field of shellfish shelling. The RSM is extremely effective in determining the most influential parameters and the optimal conditions in scallop shelling process. The optimized results obtained provide a theoretical basis for better application to actual production in the future.