^{1}

^{*}

^{2}

^{*}

^{3}

^{*}

^{4}

^{*}

An electronic method to estimate the moisture content (MC) of dry fruits by measuring the impedance (Z) and phase angle (θ) of a cylindrical parallel-plate capacitor with dry fruit sample between the plates, using a CI meter (Chari’s Impedance meter) at 1 and 9 MHz is described. Capacitance C was derived from Z and θ, and using the C, θ, and Z values of a set of dried cherries, whose MC values were later determined by the vacuum hot air-oven method, a calibration equation was developed. Using this equation, and their measured C, θ, and Z values, the MC of a group of cherries, not used in the calibration, was predicted. The predicted values were compared with their air-oven values. Similar predictions were done using the same method on dried blueberries. The method worked well with a good R
^{2} value, and showed a low standard error of prediction (SEP) in the measured MC range between 5% and 30% for cherries, and 9% and 22% for blueberries.

Dry fruit is fruit from which the majority of the original moisture content (MC) has been removed either naturally, or through the use of hot air dryers or dehydrators. Dried fruit has a long tradition of use dating back to the fourth millennium BC [

The capacitance of a parallel-plate capacitor with plate area A and plate separation d, filled with a dielectric material, at a frequency f_{1} is given by:

and at a frequency f_{2} is given by:

ε_{r1} and ε_{r2} are the dielectric constants of the dielectric material at the two frequencies and ε_{0} is the permittivity of free space (8.854 × 10^{−12} farad/m). Using these two equations we can write the difference in the dielectric constants as:

It was earlier found that (C_{1} − C_{2}) was a good estimate of the moisture content, but it was highly influenced by the size and shape of the peanut kernels [_{1} − D_{2}) and (θ_{1} − θ_{2}) were incorporated into an empirical equation, along with (C_{1} − C_{2}), from which the moisture content of single peanut kernels were calculated. Capacitance, phase angle and dissipation factor were measured on single kernels with each kernel between, and in contact with the two parallel plates at the two frequencies, 1 and 4.5 MHz, and the differences in the values of C, θ, and D were used in an empirical equation, to calculate the MC of the peanut sample placed between the plates. This method was extended to dry fruits and tested on dry fruits with an instrument called the CI meter (Chari’s Impedance meter) designed at the USDA laboratories [_{1} − Z_{2}) and phase angle (θ_{1} − θ_{2}) at 1 MHz and 5 MHz were measured. The capacitance value at each frequency was calculated from the equation:

where _{1} − C_{2}) was computed and used along with (Z_{1} − Z_{2}), and (θ_{1} − θ_{2}) in an empirical equation to determine the MC of a single or a small quantity (five to seven) of cherry samples placed between the plates. The method worked satisfactorily. However, for the dry fruit industry it would be more useful to rapidly and nondestructively determine the MC of larger samples of dry fruits, say about 100 to 150 g. The sample holder was modified for this purpose and the signals were suitably enhanced to traverse the longer distance between the two parallel-plate electrodes that were embedded in a non-conducting cylinder holding the fruit samples. Using the CI meter, the values of impedance Z, and phase angle θ were measured at 1 and 9 MHz, and the corresponding capacitance values were computed from Equation (4) for each sample. The variation in capacitance, impedance and phase angle with moisture content for dry fruits was substantial at 1MHz and 9MHz, and thus measurements were made at these two frequencies. An empirical equation was developed that has terms (C_{1} − C_{2}), (Z_{1} − Z_{2}), and (θ_{1} − θ_{2}) where, C_{1}, Z_{1}, θ_{1} and C_{2}, Z_{2}, θ_{2} are the measured values of capacitance, impedance and phase angle at 1 and 9 MHz. From the empirical equation, the MC of the dry fruit sample was obtained. The phase angle change, (θ_{1} − θ_{2}) accounts for the loss factor. Dissipation factor is a measure of energy loss that results from subjecting a dielectric to an alternating current electric field. It is related to the Q factor of the material under test and is a measure of the energy stored in the electric field relative to energy dissipated in any one period. The power dissipated depends on the equivalent resistance of the complex circuit, and thus the variation in the impedance values, (Z_{1} − Z_{2}) of the system at the two frequencies adequately represents the term (D_{1} − D_{2}), and was used to replace (D_{1} − D_{2}). Thus, from the values of (C_{1} − C_{2}), (θ_{1} − θ_{2}) and (Z_{1} − Z_{2}), measured with a two parallel-plate system fitted inside a cylinder, the MC of the grain, nuts or any other aqueous sample could be estimated to an acceptable accuracy [

The electronic circuit of the CI meter developed by the first author was well described earlier [_{r} and e_{m} at each frequency, and the impedance Z, proportional to the ratio of these two values, was calculated at each frequency. Feeding these two signals into a phase detector, the phase angle θ between them was determined at the three frequencies.

The capacitance of the system at each frequency was computed as:

Two rectangular aluminum plates 40 mm wide and 60 mm long constitute the electrode system. The electrodes were embedded in the walls of a cylinder with an outer diameter of 60 mm and a length of 80 mm, made of an acrylic material. Thus, the electrodes cover the entire length of the cylinder except for 10 mm at the top and the bottom. The sample when placed in the cylinder occupies the space between the two electrodes. The parallel-plate system is connected to the CI meter as shown in

Cherries dried to seven moisture levels, ranging between 8% and 30% were obtained from Oceana Foods^{1}, Shelby, Michigan. They were put in seven air-tight containers and allowed to equilibrate in a cold storage at 4˚C for several days, rotating the samples periodically. The MC value^{2} the cherries in each container was determined by the vacuum-oven method. Three replicates were used for each MC level. The samples from each level were divided into two groups, and measurements were made on seven calibration and seven validation sets. The validation set have the same MC values of 8.23%, 10.12%, 14.22%, 18.32%, 22.23%, 26.33% and 30% as the calibration set but were not the same that were used in the calibration.

Blueberries dried to four different moisture levels were also obtained from Oceana Foods, and were placed in four air-tight containers and allowed to equilibrate in a cold storage at 4˚C for several days, rotating the samples periodically, as done for the cherries. Three replicate samples from each bottle were then used to determine their MC by the standard vacuum-oven method for dry fruits [

Measurements were first made on the cherry samples. All cherry samples were brought to room temperature before the CI meter measurements were made on them. With the drawer of the sample collection box pushed inside, cherries from the 8.23% calibration group were dropped into the cylindrical electrode system filling it up to the top. The cylinder accommodates about 100 g of cherries. Three measurements of impedance Z, and phase angle θ were made on this sample using the CI meter, and the values were recorded on the lap-top. The drawer is pulled out and the samples were removed from the cylinder. Measurements were repeated on another nine samples from the 8.23% moisture group. Similar measurements were done on 10 samples from the six other moisture levels in the calibration group, and 10 samples each from the seven moisture levels from the validation group. Similarly, measurements were repeated on 10 samples each from the four moisture levels of the calibration, and four moisture levels of the validation groups of blueberries.

The measured values of Z and θ and the derived values of C, at 1 and 9 MHz only, were used for calibration and prediction of MC of both cherries and blueberries. For cherries, the data on the seven calibration lots along with their vacuum-oven MC values was analyzed using multi linear regression analysis software package, Unscrambler [_{1} − C_{2}), (θ_{1} − θ_{2}), and (Z_{1} − Z_{2}) and their square terms. Using this equation the MC values of the validation group were predicted, and compared with their vacuum-oven values. The fitness of the calibration equation was assessed from the associated statistical parameters.

In the case of blueberries as the data available was limited to four moisture levels each for calibration and prediction, the statistical package SAS [

^{3}SEC = _{i} is the difference between the observed and reference value for the i^{th} observation.

^{4}SEP = _{i} is the difference in the moisture content predicted and that determined by the reference method for the i^{th} sample, and _{i} for all of the samples.

Shown in ^{2} (squared correlation coefficient) of 0.98, and a standard error of calibration (SEC)^{3} of 0.99, and a low RMSEC (root mean square error of calibration) show that the model is quite suitable for prediction of MC of cherries by this method. Shown in

Shown in ^{2}, RMSEP (root mean square error of prediction) and SEP^{4} (standard error of prediction). An R^{2} value of 0.97 and a SEP of 1.10 are quite compatible with the R^{2} and SEC values of the calibration group indicating the suitability of the model for the prediction of MC of dry cherries in the range of 8% to 30% by the CI meter. Shown in

Similarly for blueberries, from the measured values of Z and θ, the capacitance values C were computed using Equation (7), for the four moisture levels each in the calibration and validation groups. The Z, θ, C values of each sample (10 samples in each moisture level and a total of 40 samples) from the calibration group, along with the corresponding oven determined MC value, were subjected to SAS procedures for regression analysis to determine the constants A_{0} to A_{6} in Equation (5). Substituting the values of the constants in Equation (5) we get the prediction equation for blueberries as:

Substituting the measured values of C, θ and Z at the two frequencies in Equation (7) the calculated values of MC of the four moisture levels of the calibration group are shown in ^{2} value of 0.98 and an SEC of 0.63. These parameters indicate that Equation (7) is suitable for prediction of MC by the CI meter. To confirm this, from the measurements on the four validation sets, the MC of each sample was determined

S.NO | Oven % MC | CI meter %MC | Standard Deviation | Difference (Oven-CI) |
---|---|---|---|---|

1 | 8.23 | 8.73 | 0.61 | −0.50 |

2 | 10.12 | 9.77 | 0.49 | 0.35 |

3 | 14.22 | 15.16 | 0.60 | −0.95 |

4 | 18.32 | 17.96 | 0.35 | 0.36 |

5 | 22.23 | 22.30 | 1.30 | −0.07 |

6 | 26.33 | 26.58 | 1.98 | −0.25 |

7 | 30.00 | 30.19 | 0.94 | −0.19 |

R^{2 } | RMSEC | SEC | Bias (×10^{−6}) |
---|---|---|---|

0.98 | 0.98 | 0.99 | −2.59 |

S.NO | Oven % MC | CI meter % MC | Standard Deviation | Difference (Oven-CI) |
---|---|---|---|---|

1 | 8.23 | 8.72 | 0.51 | −0.49 |

2 | 10.12 | 9.75 | 0.51 | 0.37 |

3 | 14.22 | 15.34 | 0.64 | −1.12 |

4 | 18.32 | 17.96 | 0.38 | 0.36 |

5 | 22.23 | 22.33 | 1.34 | −0.10 |

6 | 26.33 | 26.73 | 2.57 | −0.40 |

7 | 30.00 | 29.88 | 1.47 | 0.12 |

R^{2 } | RMSEP | SEP | Bias |
---|---|---|---|

0.97 | 1.18 | 1.10 | −0.35 |

S.NO | Oven % MC | CI meter % MC | Standard Deviation | Difference (Oven-CI) |
---|---|---|---|---|

1 | 9.82 | 9.98 | 0.67 | −0.16 |

2 | 10.11 | 10.45 | 0.78 | −0.34 |

3 | 14.07 | 13.57 | 0.72 | 0.50 |

4 | 21.53 | 21.53 | 0.42 | 0.00 |

S.NO | Oven % MC | CI meter % MC | Standard Deviation | Difference (Oven-CI) |
---|---|---|---|---|

1 | 9.82 | 10.40 | 0.68 | −0.58 |

2 | 10.11 | 10.88 | 1.00 | −0.77 |

3 | 14.07 | 14.69 | 1.05 | −0.62 |

4 | 21.53 | 21.63 | 0.62 | −0.10 |

using Equation (7), averaged over the 10 samples in each moisture group, and compared with the corresponding vacuum-oven value. The results are shown in ^{2} value of 0.96 and an SEP of 0.76, indicating that the CI meter using Equation (7) can be used to predict the MC of blueberries with sufficient accuracies, useful for the industry. Either the Unscrambler or the SAS method of regression analysis could be used for developing the calibration model with similar performance. Shown in

The authors are grateful to the Oceana Foods, Shelby, MI for supplying the dried cherries and blueberries and their collaboration in this work.

Chari V.Kandala,RonHolser,JayaSundaram,NaveenPuppala, (2015) Nondestructive Determination of Moisture Content in Dry Fruits by Impedance and Phase Angle Measurements. Journal of Sensor Technology,05,73-80. doi: 10.4236/jst.2015.54008