Mass and volume modeling of lime and investigation of the correlation between different physical properties using principle component analysis (PCA)

Lime (Citrus aurantifolia L) is belonged to citrus family and has two varieties on the basis of sweet or sour taste; two well known varieties of sour lime are Persian and Key that are cultivated in the southern of Iran. Based on FAO statistics, Iran produced about 615,000 tons of lime in 2010, and is ranked among 10 lime producersinworld wide. Physical properties of fruits are essential information in designing equipments and processes being used in different manufacturing stages such as harvesting, cleaning, sorting and grading, transporting, packaging, as well as estimating of cooling and heating loads during heat transfer processes. Moreover, physical properties affect products acceptability since consumers usually prefer fruits and vegetables with brighter color, appropriate size and uniform shape. Among physical properties, weight, volume and projected area are important parameters for designing sorting equipment.

In this study, lime samples were selected from Key variety which is cultivated in southern of Iran. From the whole, physical properties of about 300 limes were investigated and regression model were developedto estimate weight and volume on the basis of length, width, thickness and projected area.In order to determine the initial moisture, tenlime samples were randomly selected and taken in to hot air oven at 80C for 24 h. The average values of three replicateswerereported.The major dimensions (Length (L), width (W), thickness (T)) were measured using a micrometer with an accuracy of 0.01 mm.Projected area of limes was calculated in three dimensions using image processing technique. Apparent color for the lime samples was also measured in terms of CIE ‘L*’ (lightness), “a*” (redness and greenness) and “b*” (yellowness and blueness), using image processing techniques. Step wise regression was used to develop multivariate models. In this method, the independent variables would enter the equation successively based upon their degree of dependency. In order to estimate weight and volume of lime samples,three category modelswere developed as follow. 1- Regression models based on length, width and thickness. 2-Regression models for predicting weight of lime based on calculated volume. 3- Regression models based on projected area. When there are a large number of variables in the database, it is very likely that subsets of variables are highly correlated with each other.In this study, principle component analysis (PCA)was applied in order to have an accurate and reliable evaluation from existed correlation between physical properties of lime.

The initialmoisture content of limeswas found to be 84.34%.The averaged values of length, width and thickness of limes were35.84, 32.92 and 32.56, respectively. The static coefficient of friction for limes was determined on fourdifferent surfaces namely plywood, galvanized iron sheet, rubber and glass. The glass and plywood showedmaximum and minimum static coefficient of friction respectively. In addition, the sphericity and aspect ratio of lime were found to be 94.32% and 92.18%, respectively. The obtained sphericityvalues were similar to values reported by Sharifi et al., (2007) for orange variety of Tamson and lower than orange varieties of Navel reported by Topuz et al., (2006). The obtained results showed high correlation between three major dimensions and lime’s weight. The predictive models for lime have lower coefficient in comparison with LorestaniandTabatabaeefar(2006) research report forheterogeneous shape of limes. Among regression models for weight prediction of limes, the best model was obtained on the basis of the third projected area with R2of 0.921. The regression models on the basis of calculated volume showed appropriate performance for prediction of lime’s weight. Among regression models on the basis of dimensions, the single parameter model based on lime’s width found to bethe highest coefficient for prediction of volume. Similar toweight prediction, single parameter model on the basis of the third projected area showed the best performance for volume prediction.

The results obtained from principle component analysis confirmed the regression models and showed high correlation between physical properties such as projected area, dimension, weight and volume with each other as well as positive correlation with coefficient of friction on the rubber surface and negative correlation on theglass surface.