# A Fusion Parameter Method for Classifying Freshness of Fish Based on Electrochemical Impedance Spectroscopy

Authors: Jian Sun; Yuhao Liu; Gangshan Wu; Yecheng Zhang; Rongbiao Zhang; X. J. Li
Journal: Journal of Food Quality
 (2021)

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## Abstract

Compared with using a single characteristic parameter of electrochemical impedance spectroscopy (EIS) to classify the freshness of fish samples from different origins, more characteristic parameters could bring higher accuracy as well as complexity, subjectivity, and uncertainty. In order to eliminate the disadvantages of the multiparameter model, a data fusion method based on model similarity (DFMS) was proposed in this study. The similarity relation between the freshness models based on EIS characteristic parameters and physicochemical indicator was analyzed and quantified accordingly, and then, the weighting factors of the fusion model were determined. The classification accuracy rate of fish freshness based on DFMS was 9.2∼15% greater than that of a single EIS characteristic parameter. The novel dimensionless fusion parameter method proposed in this article might provide a simple yet effective indicator for EIS-based food quality evaluation.


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## Body

## 1. Introduction

Freshness is an important quality attribute in the shelf life of freshwater fish, and the edible value reduces rapidly due to endogenous autolytic enzymes and microorganism after slaughter. The pathogenic microorganisms and microbial toxins produced in the process of spoilage pose a serious threat to the health of consumers [1]. Efficient, convenient, and real-time detection method of freshness plays an important role in the fields of food safety, quarantine of meat products, and agricultural products processing. Traditional freshness evaluation methods mainly include sensory assessment, physicochemical analysis, and microbiological experiment. As a rapid, nondestructive, and low-cost detection method, sensory assessment is widely used in daily life; however, the influence of personal subjective cannot be eliminated completely by this assessment, even for well-trained inspectors. Although physicochemical and microbiological methods can reach high detection accuracy, they require high professional skills of laboratory personnel, and the detection is destructive and time-consuming [2]. In the last two decades, different types of instrument detection technics, like electronic nose [3, 4], electronic tongue [5], near-infrared spectroscopy [6], dielectric spectra [7], hyperspectral imaging [8], and EIS [9–13], were developed to meet the demand of real-time detection in consumer market and online quality monitor in food processing factory [14].Compared with the other instrument detection methods, EIS not only has advantages in low cost, rapid detection, simple pretreatment, and portable carrying, but also can provide information of internal organization of biological tissue [15] or somewhere difficult to reach by conventional means [16]. Thus, it is widely used in the field of agricultural engineering [17], food science [18], medical diagnosis [19], and battery technology [20, 21]. For meat detection, EIS was applied to evaluate the taste and tenderness of beef [22], assess freshness of fish [23, 24], detect salt content of smoked products on production line [25–27], and real-time monitor the fat and moisture content during meat processing [28, 29]. However, the body composition of fish varies with the feeding environment, fishing season, genetic genes, and so on. Grigorakis [30] reported that there was a 13-fold difference in body fat percentage between wild and cultured sea bream. The basic electric property would inevitably vary widely depending on the individual due to good insulation property of the body fat. The influence of individual differences on EIS detection results is one of the most important bottlenecks restricting the commercialization and the further development of bioimpedance technology. In the former research work, Kramers–Kronig’s approach [11, 31–36] and Distribution of Relaxation Times (DRT) method [37–41] are effective tools to evaluate and process the mass electrochemical impedance data in certain fields.The characteristic parameters of the impedance spectrum can be divided into two main categories, i.e., absolute coordinate parameter and morphological characteristic parameter. The former is closely related to the coordinates of the Bode diagram, such as modulus and phase angle; the latter is independent of the coordinate value but related to the morphology of the curve of impedance spectrum. In our previous study [42, 43], the morphological characteristic was chosen to detect the samples from different origins. The results show remarkable effect on improving the accuracy of detection and classification, because the morphological parameter was less affected by the difference of basic electrical properties of samples. With further analysis, we found that each characteristic parameter had its advantages, insufficiencies, and best application scope. Specifically, morphological characteristic parameter changed significantly near the critical point of spoilage, no matter the samples are from the same origin or different ones. However, the correlation between morphological characteristic parameter and physicochemical indicator in autolytic stage of spoilage was poor. The measuring points during this period constituted the main body of misjudgment set of morphological characteristic parameter. In contrast, the changing trend of absolute coordinate parameter was a high coincidence with that of physicochemical indicator during the whole storage period under laboratory conditions when samples come from the same origin, but it was very sensitive to individual differences in practical applications. Due to potential complementarities between the two characteristic parameters, parameter fusion technique may be an effective approach to improve the classification accuracy in practical application environment.Parameter fusion technique has been employed in predicting capacities of lithium-ion battery [44, 45], estimating the freshness of food and other fields; however, the existing parameter fusion methods applicable to the field of food quality assessment have not yet proposed a standardized solution to the determination of weighting factors. This key point of parameter fusion method, such as global stability index (GSI) [46], was often implemented based on experience or semiexperience [47–49], which may lead to subjectivity and uncertainty.To improve the classification accuracy of fish freshness in practical applications, a data fusion method based on model similarity (DFMS) was proposed to integrate the advantages of morphological characteristic parameter and absolute coordinate parameter from EIS experiment. The classification accuracy rate based on DFMS and single characteristic parameter were compared to verify the effect of fusion model. The innovative method proposed in this article not only improved the classification quality of EIS, but also provided a new solution to the quality evaluation of food.


## 2. Materials and Methods

### 2.1. Samples Preparation

To simulate the actual application scenario, 30 silver carp were purchased from 5 different retailers, 15 of which were used to determine the model parameters (group M), and the other 15 samples were used for model test (group T). Samples were delivered to the laboratory with oxygen supplement and killed by a thump on the head after filtrating anesthesia with ice water. Then scales and guts were removed. After cleaning, belly flesh was cut into 60 × 30 mm pieces by a clean stainless-steel knife. The fillets were sealed with sterile polyethylene bag and placed in a 4°C refrigerator.


### 2.2. Physicochemical Analysis

The total volatile base nitrogen (TVB-N) is the protein decomposition product in the fish spoilage process. Semimicro fixation of nitrogen method was used to measure TVB-N value. After elimination of fishbone and sinew, 10 g of fish flesh was weighed and grinded into fish mud. Distilled water was added to 100 mL, followed by stirring, soaking, and filtrating after 30 min. 5 mL of filtrate drop was taken into a Kjeldahl apparatus (Huanya Experimental Instrument Co., Ltd., Shanghai, China); 5 ml of MgO solution (10 g/L) subsequently was added quickly. TVB-N in the filtrate was distilled off with water vapor and collected by absorbent composed of boric acid solution (20 g/L) and a mixed indicator prepared by adding 0.1 g of methyl red and 0.1 g of methylene blue into 100 mL of ethanol. Immediately after distillation, absorbent was titrated with a dilute hydrochloric acid solution (0.01 mol/L). Subsequently, 5 mL of distilled water was used instead of the filtrate for the blank test. TVB-N was calculated as follows:(1)X=V1−V2×c×14m×V/V0×100,where X is the TVB-N value in terms of mg/100 g; V1 is the consumption of hydrochloric acid solution in the experiment (mL); V2 is the consumption of hydrochloric acid solution in blank test (mL); c is the molar concentration of the hydrochloric acid solution in terms of mol/L; m is the measured mass of the flesh (g); V is the filtrate volume added into apparatus (5 mL); and V0 is the total volume of the filtrate (100 mL).TVB-N was measured every day within 8 days after slaughter. The final result was the average of two repeated measurements.


### 2.3. EIS Measurement

CHI660E electrochemical workstation (CH Instruments, Inc., Texas, USA) was used to measure EIS of fillets. The excitation voltage amplitude was set as 30 mV. 60 points with equal intervals were chosen on logarithmic coordinate axis between 10 Hz and 1 M Hz as the measurement frequency.Two-electrode mode was used in measurement system. Two platinum (Pt) wire electrodes with diameter of 0.5 mm were vertically inserted into the flesh. The depth and spacing between the two electrodes were both 10 mm.The frequency of EIS detection was the same as that of TVB-N measurement.


### 2.4. Data Analysis

DFMS was calculated by MATLAB software (version 7.10). Correlation analysis was used to extract characteristic parameters from absolute coordinate parameters. The accuracy rate of freshness classification was used to evaluate model effects based on parameter fusion and single parameter.


## 2.1. Samples Preparation

To simulate the actual application scenario, 30 silver carp were purchased from 5 different retailers, 15 of which were used to determine the model parameters (group M), and the other 15 samples were used for model test (group T). Samples were delivered to the laboratory with oxygen supplement and killed by a thump on the head after filtrating anesthesia with ice water. Then scales and guts were removed. After cleaning, belly flesh was cut into 60 × 30 mm pieces by a clean stainless-steel knife. The fillets were sealed with sterile polyethylene bag and placed in a 4°C refrigerator.


## 2.2. Physicochemical Analysis

The total volatile base nitrogen (TVB-N) is the protein decomposition product in the fish spoilage process. Semimicro fixation of nitrogen method was used to measure TVB-N value. After elimination of fishbone and sinew, 10 g of fish flesh was weighed and grinded into fish mud. Distilled water was added to 100 mL, followed by stirring, soaking, and filtrating after 30 min. 5 mL of filtrate drop was taken into a Kjeldahl apparatus (Huanya Experimental Instrument Co., Ltd., Shanghai, China); 5 ml of MgO solution (10 g/L) subsequently was added quickly. TVB-N in the filtrate was distilled off with water vapor and collected by absorbent composed of boric acid solution (20 g/L) and a mixed indicator prepared by adding 0.1 g of methyl red and 0.1 g of methylene blue into 100 mL of ethanol. Immediately after distillation, absorbent was titrated with a dilute hydrochloric acid solution (0.01 mol/L). Subsequently, 5 mL of distilled water was used instead of the filtrate for the blank test. TVB-N was calculated as follows:(1)X=V1−V2×c×14m×V/V0×100,where X is the TVB-N value in terms of mg/100 g; V1 is the consumption of hydrochloric acid solution in the experiment (mL); V2 is the consumption of hydrochloric acid solution in blank test (mL); c is the molar concentration of the hydrochloric acid solution in terms of mol/L; m is the measured mass of the flesh (g); V is the filtrate volume added into apparatus (5 mL); and V0 is the total volume of the filtrate (100 mL).TVB-N was measured every day within 8 days after slaughter. The final result was the average of two repeated measurements.


## 2.3. EIS Measurement

CHI660E electrochemical workstation (CH Instruments, Inc., Texas, USA) was used to measure EIS of fillets. The excitation voltage amplitude was set as 30 mV. 60 points with equal intervals were chosen on logarithmic coordinate axis between 10 Hz and 1 M Hz as the measurement frequency.Two-electrode mode was used in measurement system. Two platinum (Pt) wire electrodes with diameter of 0.5 mm were vertically inserted into the flesh. The depth and spacing between the two electrodes were both 10 mm.The frequency of EIS detection was the same as that of TVB-N measurement.


## 2.4. Data Analysis

DFMS was calculated by MATLAB software (version 7.10). Correlation analysis was used to extract characteristic parameters from absolute coordinate parameters. The accuracy rate of freshness classification was used to evaluate model effects based on parameter fusion and single parameter.


## 3. Results and Discussion

### 3.1. Change of TVB-N during Storage

The average TVB-N values of groupM during storage are shown in Figure 1. TVB-N increased monotonously as storage time increased. In the first 3 days, the change of TVB-N was gentle. The rate of increase began to speed up on the 4th day. According to the Chinese National Standard GB/T 2009.45-2003, the rejection limit for TVB-N in freshwater fish (20 mg/100 g) was reached on the 6th day.Figure 1
TVB-N values during the storage time.Autolytic enzymes and microorganisms were two main factors responsible for protein decomposition in spoilage process [50]. At the early stage of storage, microorganisms needed time to adapt to the new environment, autolytic enzymes played a leading role in TVB-N production, and the corresponding change of TVB-N was moderate. During the middle and late stages of storage, microorganisms gradually took the place of autolytic enzymes and became the main cause of protein decomposition due to the reproduction of dominant spoilage bacteria. The corresponding trend of change was rapid rise of TVB-N with the storage time.


### 3.2. Characteristic Parameter Extraction

Absolute coordinate parameters, like impedance modulus, phase angle, real part, and imaginary part, are closely related to the coordinate value in plane of EIS curve. The measurement result of CHI660E is expressed in the form of complex number composed of a real part and an imaginary part. However, impedance modulus and phase angle, which represent the reduction and skewing effect on electric current, have clearer physical meanings. Impedance modulus and phase angle are calculated as follows:(2)Z=Zre2+Zim2,θ=−arctgZimZre×180π,where |Z| is impedance modulus in terms of Ω; θ is phase angle in terms of degree; and Zre and Zim are real and imaginary parts of impedance, respectively. In order to match the change trend of the impedance modulus and the PD, the phase angle was converted to positive number by the inverse operation.Figure2 is a Bode diagram showing the trends of the impedance modulus and phase angle in excitation frequency domain, where the abscissa is the measurement frequency, and the ordinates are the impedance modulus and phase angle, respectively.Figure 2
Bode diagram.The impedance modulus and phase angle varied with the frequency. Due to the capacitance caused by cell membrane and electric double layer on the electrode surface, the impedance modulus was more than 2000 Ω, and the phase angle was more than 40° in low-frequency region. With the increase of the excitation frequency, the value of capacitance mentioned above decreased. Meanwhile, the impedance modulus dropped below 1000 Ω, and the phase angle dropped to the interval between 10° and 30°.The trend of impedance modulus curve changed obviously at about 100 Hz. In the frequency range above 100 Hz, the impedance modulus decreased slowly with the increase of frequency. In the low-frequency interval between 10 and 100 Hz, the impedance modulus changed significantly. In this narrow frequency domain, the modulus value dropped rapidly from 7000 Ω to 2000 Ω. The rapidly changing trend in low-frequency range was coincident with the frequency response of the electric double layer capacitance which was connected in series in the measurement circuit. Thus, the electrical property of fish was obscured by the capacitance of electric double layer below 100 Hz. The effective frequency range reflecting the electrical property of fish was 100 to 1 M Hz. In this gradual interval, there was a certain linear correlation between the absolute coordinate parameter corresponding to different frequencies; therefore, only one value at a specific frequency was chosen as the fusion parameter for the impedance modulus and phase angle, respectively.As shown in Figure3, the coefficients of determination between absolute coordinate parameters and TVB-N were obtained by correlation analysis method, and the biggest coefficient of determination with TVB-N value was selected as fusion parameter.Figure 3
Determination coefficients between absolute coordinate parameters and TVB-N at different frequencies.The abscissa is the excitation frequency, while the ordinate is the determination coefficient (R2) between the absolute coordinate parameter and TVB-N; the red bar represents phase angle, and the blue bar is impedance modulus. To simulate the actual application environment, the samples were randomly purchased from multiple retailers. Due to the individual differences of samples from different origins, the results of correlation analysis were lower than those of similar studies with samples from the same origin and the same batch.The curve of determination coefficient between phase angle and TVB-N had two peaks in the frequency interval between 100 and 1 M Hz, where one located at about 300 Hz and the other was in the domain from 80 k to 400 k Hz. The maximumR2 was 0.60, and the corresponding frequency of that was 100 kHz. The maximum R2 of the impedance modulus appeared at 1 kHz which was in the valley region of the phase angle; the value was 0.56. Therefore, the phase angle at 100 kHz and the modulus at 1 k Hz were chosen as the absolute coordinate parameters for fusion modeling.Contrary to absolute coordinate parameter, morphological characteristic parameter is independent of the coordinate value in plane of EIS curve and only relates to the shape of the curve. Common morphological characteristic parameters include slope, radians, and pole difference. Pole difference (PD) was used in this study to participate in the modeling process. As shown in Figure4, PD was the y-axis projection distance between the highest point and the lowest point in phase angle curve.Figure 4
Extraction of the pole difference parameter.The change of PD during the storage time is shown in Figure5. There was a transient rise in PD during the period of pre- and post-rigor mortis stage shortly after slaughter (stage 1). In autolytic stage, PD decreased slowly with the prolongation of storage time (stage 2). After the 6th day when the critical point of spoilage was reached, the decline rate of PD accelerated significantly (stage 3).Figure 5
Pole difference values during storage time.PD is the projection distance on they-axis between the highest point and the lowest point of “S” shape part in the phase angle curve (Figure 1). According to the electrical principle, the phase angle curve of pure resistive element is a line segment on the x-axis and the PD value of that is 0; the PD values of the combined elements composed of resistances and capacitances are always greater than 0. In the middle and late stages of spoilage, the cell membrane ruptured. The electrolyte of intracellular fluid outflowed and then fused with the extracellular fluid. The macroscopic electrical property of fish changed from resistance-capacitance mixing to pure resistance, and the corresponding PD value also tended to 0.


### 3.3. Data Fusion Method Based on Model Similarity (DFMS)

The determination of weighting factor is one of the most important steps of fusion algorithm, but there is no specification method to obtain the optimal combination of weighting factors so far. Unlike extraction of absolute coordinate parameters, there is no direct linear relationship between the absolute coordinate parameter and morphological characteristic parameter in terms of mechanism. Thus, if correlation analysis is used to determine the weighting factor, a large sample size is required to ensure the validity of the results. In addition, the weighting factor can also be estimated through experience, but there is inevitably a certain degree of subjectivity and uncertainty.Aimed at this problem, a data fusion method based on model similarity (DFMS) was proposed in this study. The models describing fish freshness, whether based on TVB-N or EIS characteristic parameters, all present as the curves varying with storage time. The core idea of this method is to compare and quantify the morphological differences between the curves of fusion parameters and control parameters and set a larger weighting coefficient for the fusion parameter which has smaller morphological differences with the curve of control parameter. The detailed calculation steps are as follows:(1)
Curve SyntropyMost indicators related to food freshness have a general upward or downward trend with storage time. The impedance modulus, phase angle, and PD all monotonically decreased with time since the second day after slaughter. However, the TVB-N, as the control parameter, increased with time in all over the storage period. In order to ensure that the fusion parameters and control parameters had the same trend time, opposite numbers of impedance modulus, phase angle, and PD were calculated as fusion parameters. Thus, fusion parameters included impedance modulus (M = m2, m3, …, m8), phase angle (A = a2, a3,…, a8), and PD (P = p2, p3, …, p8), and the control parameter was TVB-N (T = t2, t3, …, t8). Where ti was the average values of phase angle and TVB-N in each measurement day for group M, and mi, ai, and pi were the opposite numbers of corresponding values for modulus, phase angle, and PD.(2)
NondimensionalizationDifferent parameters were not comparable due to different dimensions. Mean value method was used to nondimensionalize the data. The dimensionless impedance modulus (M∗) was calculated as follows. A∗, P∗, and T∗ were calculated accordingly.(3)mi′=mi∑i=abmi/b−a+1,wherea equals 2 and b equals 8 representing the storage day.(3)
Alignment of Initial PointsInitial points of the curves were aligned though subtracting respective initial values.(4)mi∗=mi′−ma′,wherema′ was the impedance modulus after nondimensionalization in the second day; the corresponding values of phase angle (ai∗) and PD (pi∗) were calculated accordingly. The initial points of all curves were moved to coordinate origin.(4)
Calculation of Average Root Mean Squared Distance (RMSD)(5)RMSD¯=∑i=abti∗−mj∗2+∑j=abtj∗−aj∗2+∑k=abtk∗−pk∗23b−a+1.Average RMSD quantified the average morphological difference between the curves of fusion parameters and control parameter.(5)
Calculation of Minimum RMSD(6)RMSDmin=minminiti∗−mi∗2,minjtj∗−aj∗2,minktk∗−pk∗2.Minimum RMSD represented the minimum morphological difference between the curves of fusion parameters and control parameter.(6)
Calculation of RMSD of Fusion Parameters(7)RMSDM=∑i=abti∗−mi∗2b−a+1.RMSDM was RMSD between curves of modulus and TVB-N; the corresponding values of phase angle (RMSDA) and PD (RMSDP) were calculated accordingly.(7)
Calculation of Morphological Similarity of Curve (MSC)(8)MSCM=RMSDmin+RMSD¯RMSDM+RMSD¯.MSCM represented the morphological similarity between curves of modulus and TVB-N. Compared with the curves of all fusion parameters, the corresponding values of phase angle (MSCA) and PD (MSCP) were calculated accordingly.(8)
Calculation of Weighting FactorsWeighting factors of impedance modulus in equation (3) were obtained as follows; the corresponding values of phase angle (αA) and PD (αP) were calculated accordingly.(9)αM=MSCMMSCM+MSCA+MSCP.(9)
Normalization of Fusion ParametersNormalization of fusion parameters was implemented according to the equation in GSI method [30]. The variation term Vij was calculated as follows:(10)Vij=Cij−Ci0Li−Ci0,whereCij is the measured value of indicator i at time j units; Ci0 is the initial value of indicator i; and Li is the threshold value of indicator i. Vij describes the measured variation as compared to the maximum tolerated variation of indicator i at time j units.(10)
Weighted FusionThe value of DFMS indicator atj time is calculated as follows:(11)DFMSj=∑1nαiVij.wheren is the number of indicators involved in the model; Vij is the variation terms; and αi is the weighting factor of the indicator i.


### 3.4. Freshness Classification and Prediction Based on DFMS

EIS measurement results of groupM were processed though DFMS. Calculation result of the weighting factors of fusion parameters are, respectively, as follows: modulus is 0.327, phase angle is 0.296, and PD is 0.377. And the freshness classification and prediction based on DFMS vs. storage time are, respectively, shown in Figures 6(a) and 6(b).Figure 6
DFMS indicator during storage time.Contrary to TVB-N, DFMS indicator presented a monotonous downward trend with storage time. Compared with Figure1, TVB-N reached the rejection limit on the 6th day; the corresponding DFMS indicator value was 0.47 in Figure 6(a). At the corresponding storage time, the values of modulus, phase angle, and PD were 1120, 14.8, and 6.4, respectively. Those values were considered as critical points of spoilage for each characteristic parameter. The modulus, phase angle, PD, and DFMS indicator all decreased with time. The freshness classification results of those were judged to be correct when the measurement values between 1st and 5th days were greater than critical points, or the measurement values between 6th and 8th days were less than critical points. Moreover, a prediction based on DFMS launched by another independent experiment is shown in Figure 6(b). The accuracy rates of freshness determination based on DFMS indicator and single indicators are shown in Table 1.Table 1
Accuracy rate of freshness determination of different quality indicators.
GroupModulus (%)Phase angle (%)PD (%)DFMS indicator (%)M82.585.886.795.0T79.283.385.094.2The calibration samples (groupM) were used to filter the characteristic parameters and calculate the weighting factors in fusion model, and the test samples (group T) did not participate in the modeling process. The latter could more effectively reflect the classification effect under the actual application scenario. For group T, the classification accuracy rate of DFMS indicator was 94.2%, significantly higher than that of modulus (79.2%), phase angle (83.3%), and PD (85.0%).


## 3.1. Change of TVB-N during Storage

The average TVB-N values of groupM during storage are shown in Figure 1. TVB-N increased monotonously as storage time increased. In the first 3 days, the change of TVB-N was gentle. The rate of increase began to speed up on the 4th day. According to the Chinese National Standard GB/T 2009.45-2003, the rejection limit for TVB-N in freshwater fish (20 mg/100 g) was reached on the 6th day.Figure 1
TVB-N values during the storage time.Autolytic enzymes and microorganisms were two main factors responsible for protein decomposition in spoilage process [50]. At the early stage of storage, microorganisms needed time to adapt to the new environment, autolytic enzymes played a leading role in TVB-N production, and the corresponding change of TVB-N was moderate. During the middle and late stages of storage, microorganisms gradually took the place of autolytic enzymes and became the main cause of protein decomposition due to the reproduction of dominant spoilage bacteria. The corresponding trend of change was rapid rise of TVB-N with the storage time.


## 3.2. Characteristic Parameter Extraction

Absolute coordinate parameters, like impedance modulus, phase angle, real part, and imaginary part, are closely related to the coordinate value in plane of EIS curve. The measurement result of CHI660E is expressed in the form of complex number composed of a real part and an imaginary part. However, impedance modulus and phase angle, which represent the reduction and skewing effect on electric current, have clearer physical meanings. Impedance modulus and phase angle are calculated as follows:(2)Z=Zre2+Zim2,θ=−arctgZimZre×180π,where |Z| is impedance modulus in terms of Ω; θ is phase angle in terms of degree; and Zre and Zim are real and imaginary parts of impedance, respectively. In order to match the change trend of the impedance modulus and the PD, the phase angle was converted to positive number by the inverse operation.Figure2 is a Bode diagram showing the trends of the impedance modulus and phase angle in excitation frequency domain, where the abscissa is the measurement frequency, and the ordinates are the impedance modulus and phase angle, respectively.Figure 2
Bode diagram.The impedance modulus and phase angle varied with the frequency. Due to the capacitance caused by cell membrane and electric double layer on the electrode surface, the impedance modulus was more than 2000 Ω, and the phase angle was more than 40° in low-frequency region. With the increase of the excitation frequency, the value of capacitance mentioned above decreased. Meanwhile, the impedance modulus dropped below 1000 Ω, and the phase angle dropped to the interval between 10° and 30°.The trend of impedance modulus curve changed obviously at about 100 Hz. In the frequency range above 100 Hz, the impedance modulus decreased slowly with the increase of frequency. In the low-frequency interval between 10 and 100 Hz, the impedance modulus changed significantly. In this narrow frequency domain, the modulus value dropped rapidly from 7000 Ω to 2000 Ω. The rapidly changing trend in low-frequency range was coincident with the frequency response of the electric double layer capacitance which was connected in series in the measurement circuit. Thus, the electrical property of fish was obscured by the capacitance of electric double layer below 100 Hz. The effective frequency range reflecting the electrical property of fish was 100 to 1 M Hz. In this gradual interval, there was a certain linear correlation between the absolute coordinate parameter corresponding to different frequencies; therefore, only one value at a specific frequency was chosen as the fusion parameter for the impedance modulus and phase angle, respectively.As shown in Figure3, the coefficients of determination between absolute coordinate parameters and TVB-N were obtained by correlation analysis method, and the biggest coefficient of determination with TVB-N value was selected as fusion parameter.Figure 3
Determination coefficients between absolute coordinate parameters and TVB-N at different frequencies.The abscissa is the excitation frequency, while the ordinate is the determination coefficient (R2) between the absolute coordinate parameter and TVB-N; the red bar represents phase angle, and the blue bar is impedance modulus. To simulate the actual application environment, the samples were randomly purchased from multiple retailers. Due to the individual differences of samples from different origins, the results of correlation analysis were lower than those of similar studies with samples from the same origin and the same batch.The curve of determination coefficient between phase angle and TVB-N had two peaks in the frequency interval between 100 and 1 M Hz, where one located at about 300 Hz and the other was in the domain from 80 k to 400 k Hz. The maximumR2 was 0.60, and the corresponding frequency of that was 100 kHz. The maximum R2 of the impedance modulus appeared at 1 kHz which was in the valley region of the phase angle; the value was 0.56. Therefore, the phase angle at 100 kHz and the modulus at 1 k Hz were chosen as the absolute coordinate parameters for fusion modeling.Contrary to absolute coordinate parameter, morphological characteristic parameter is independent of the coordinate value in plane of EIS curve and only relates to the shape of the curve. Common morphological characteristic parameters include slope, radians, and pole difference. Pole difference (PD) was used in this study to participate in the modeling process. As shown in Figure4, PD was the y-axis projection distance between the highest point and the lowest point in phase angle curve.Figure 4
Extraction of the pole difference parameter.The change of PD during the storage time is shown in Figure5. There was a transient rise in PD during the period of pre- and post-rigor mortis stage shortly after slaughter (stage 1). In autolytic stage, PD decreased slowly with the prolongation of storage time (stage 2). After the 6th day when the critical point of spoilage was reached, the decline rate of PD accelerated significantly (stage 3).Figure 5
Pole difference values during storage time.PD is the projection distance on they-axis between the highest point and the lowest point of “S” shape part in the phase angle curve (Figure 1). According to the electrical principle, the phase angle curve of pure resistive element is a line segment on the x-axis and the PD value of that is 0; the PD values of the combined elements composed of resistances and capacitances are always greater than 0. In the middle and late stages of spoilage, the cell membrane ruptured. The electrolyte of intracellular fluid outflowed and then fused with the extracellular fluid. The macroscopic electrical property of fish changed from resistance-capacitance mixing to pure resistance, and the corresponding PD value also tended to 0.


## 3.3. Data Fusion Method Based on Model Similarity (DFMS)

The determination of weighting factor is one of the most important steps of fusion algorithm, but there is no specification method to obtain the optimal combination of weighting factors so far. Unlike extraction of absolute coordinate parameters, there is no direct linear relationship between the absolute coordinate parameter and morphological characteristic parameter in terms of mechanism. Thus, if correlation analysis is used to determine the weighting factor, a large sample size is required to ensure the validity of the results. In addition, the weighting factor can also be estimated through experience, but there is inevitably a certain degree of subjectivity and uncertainty.Aimed at this problem, a data fusion method based on model similarity (DFMS) was proposed in this study. The models describing fish freshness, whether based on TVB-N or EIS characteristic parameters, all present as the curves varying with storage time. The core idea of this method is to compare and quantify the morphological differences between the curves of fusion parameters and control parameters and set a larger weighting coefficient for the fusion parameter which has smaller morphological differences with the curve of control parameter. The detailed calculation steps are as follows:(1)
Curve SyntropyMost indicators related to food freshness have a general upward or downward trend with storage time. The impedance modulus, phase angle, and PD all monotonically decreased with time since the second day after slaughter. However, the TVB-N, as the control parameter, increased with time in all over the storage period. In order to ensure that the fusion parameters and control parameters had the same trend time, opposite numbers of impedance modulus, phase angle, and PD were calculated as fusion parameters. Thus, fusion parameters included impedance modulus (M = m2, m3, …, m8), phase angle (A = a2, a3,…, a8), and PD (P = p2, p3, …, p8), and the control parameter was TVB-N (T = t2, t3, …, t8). Where ti was the average values of phase angle and TVB-N in each measurement day for group M, and mi, ai, and pi were the opposite numbers of corresponding values for modulus, phase angle, and PD.(2)
NondimensionalizationDifferent parameters were not comparable due to different dimensions. Mean value method was used to nondimensionalize the data. The dimensionless impedance modulus (M∗) was calculated as follows. A∗, P∗, and T∗ were calculated accordingly.(3)mi′=mi∑i=abmi/b−a+1,wherea equals 2 and b equals 8 representing the storage day.(3)
Alignment of Initial PointsInitial points of the curves were aligned though subtracting respective initial values.(4)mi∗=mi′−ma′,wherema′ was the impedance modulus after nondimensionalization in the second day; the corresponding values of phase angle (ai∗) and PD (pi∗) were calculated accordingly. The initial points of all curves were moved to coordinate origin.(4)
Calculation of Average Root Mean Squared Distance (RMSD)(5)RMSD¯=∑i=abti∗−mj∗2+∑j=abtj∗−aj∗2+∑k=abtk∗−pk∗23b−a+1.Average RMSD quantified the average morphological difference between the curves of fusion parameters and control parameter.(5)
Calculation of Minimum RMSD(6)RMSDmin=minminiti∗−mi∗2,minjtj∗−aj∗2,minktk∗−pk∗2.Minimum RMSD represented the minimum morphological difference between the curves of fusion parameters and control parameter.(6)
Calculation of RMSD of Fusion Parameters(7)RMSDM=∑i=abti∗−mi∗2b−a+1.RMSDM was RMSD between curves of modulus and TVB-N; the corresponding values of phase angle (RMSDA) and PD (RMSDP) were calculated accordingly.(7)
Calculation of Morphological Similarity of Curve (MSC)(8)MSCM=RMSDmin+RMSD¯RMSDM+RMSD¯.MSCM represented the morphological similarity between curves of modulus and TVB-N. Compared with the curves of all fusion parameters, the corresponding values of phase angle (MSCA) and PD (MSCP) were calculated accordingly.(8)
Calculation of Weighting FactorsWeighting factors of impedance modulus in equation (3) were obtained as follows; the corresponding values of phase angle (αA) and PD (αP) were calculated accordingly.(9)αM=MSCMMSCM+MSCA+MSCP.(9)
Normalization of Fusion ParametersNormalization of fusion parameters was implemented according to the equation in GSI method [30]. The variation term Vij was calculated as follows:(10)Vij=Cij−Ci0Li−Ci0,whereCij is the measured value of indicator i at time j units; Ci0 is the initial value of indicator i; and Li is the threshold value of indicator i. Vij describes the measured variation as compared to the maximum tolerated variation of indicator i at time j units.(10)
Weighted FusionThe value of DFMS indicator atj time is calculated as follows:(11)DFMSj=∑1nαiVij.wheren is the number of indicators involved in the model; Vij is the variation terms; and αi is the weighting factor of the indicator i.


## 3.4. Freshness Classification and Prediction Based on DFMS

EIS measurement results of groupM were processed though DFMS. Calculation result of the weighting factors of fusion parameters are, respectively, as follows: modulus is 0.327, phase angle is 0.296, and PD is 0.377. And the freshness classification and prediction based on DFMS vs. storage time are, respectively, shown in Figures 6(a) and 6(b).Figure 6
DFMS indicator during storage time.Contrary to TVB-N, DFMS indicator presented a monotonous downward trend with storage time. Compared with Figure1, TVB-N reached the rejection limit on the 6th day; the corresponding DFMS indicator value was 0.47 in Figure 6(a). At the corresponding storage time, the values of modulus, phase angle, and PD were 1120, 14.8, and 6.4, respectively. Those values were considered as critical points of spoilage for each characteristic parameter. The modulus, phase angle, PD, and DFMS indicator all decreased with time. The freshness classification results of those were judged to be correct when the measurement values between 1st and 5th days were greater than critical points, or the measurement values between 6th and 8th days were less than critical points. Moreover, a prediction based on DFMS launched by another independent experiment is shown in Figure 6(b). The accuracy rates of freshness determination based on DFMS indicator and single indicators are shown in Table 1.Table 1
Accuracy rate of freshness determination of different quality indicators.
GroupModulus (%)Phase angle (%)PD (%)DFMS indicator (%)M82.585.886.795.0T79.283.385.094.2The calibration samples (groupM) were used to filter the characteristic parameters and calculate the weighting factors in fusion model, and the test samples (group T) did not participate in the modeling process. The latter could more effectively reflect the classification effect under the actual application scenario. For group T, the classification accuracy rate of DFMS indicator was 94.2%, significantly higher than that of modulus (79.2%), phase angle (83.3%), and PD (85.0%).


## 4. Conclusions

In order to improve the freshness classification accuracy of samples from multiple origins, impedance modulus, phase angle, and PD were fused by DFMS. Compared with the single characteristic parameter, the freshness classification accuracy rate based on fusion model increased from 79.2%–85.0% to 94.2%. The results indicated that DFMS can effectively distribute weighting coefficient in the key step of fusion model. The innovative method proposed in this article not only improved the classification quality of EIS in practical application environment, but also provided a new idea on the quality evaluation of food which could eradicate subjectivity and uncertainty from classification results. EIS freshness classification method based on parameter fusion could be a potential solution to the development of portable detection device in consumer market and online monitor system in food processing factory.



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*Source: 6664291-2021-03-11.xml*