A novel rapid non-contact detection method for frozen and thawed foods : Based on bio-impedance spectroscopy analysis and neural network (FCNN) recognition model

Abstract

This paper proposed a novel rapid non-contact detection method for measuring frozen and thawed foods based on an innovative ”data + neural network model” strategy. The purpose of the study is to develop a fast and effective detection method for frozen–thawed food, thereby overcoming critical industrial limitations such as slow sweeping speed and wide frequency range. The proposed model replaces the conventional full-spectroscopy scanning approach by requiring only the measurement signal ratio ($Im(\nabla V/V)$) at three fixed frequency points: 100 kHz, 500 kHz, and 1 MHz. A dataset comprising 4000 samples (labeled as ”fresh” or ”frozen–thawed”) was constructed using finite element modeling and real measurement data. A fully connected neural network (FCNN) was employed as a binary classification model and trained on this dataset. The outcome of the study demonstrates that the proposed model achieves high classification accuracy on both the test set and physical validation samples. Compared to the conventional full-spectrum scanning method (7–8 min/sample), the new approach completes a single measurement in only 1–1.5 s. While some spectral information is sacrificed by not performing a full frequency sweep, the method significantly improves detection efficiency in the specific application scenario of frozen–thawed food identification, while substantially reducing instrument complexity and cost. These results provide both a theoretical foundation and a practical solution for implementing rapid, non-destructive, and non-contact identification of the frozen–thawed state of fresh ingredients in automated production lines, demonstrating considerable potential for industrial applications in the food sector.

Graphical abstract

Highlights

• •We introduced a non-contact measurement method of bio-impedance spectroscopy to distinguish fresh food from frozen–thawed samples. The accuracy of the measurement system is 0.01 S/m.
• •We built a finite element model for fresh and frozen–thawed food samples and validated with experimental measurement results. The finite element model exhibits a beta-dispersion spectrum over the frequency domain which strongly agree with the measurement result. However, it takes too long to obtain the whole bio-impedance spectroscopy of a single sample (about 7 mins), which makes it hard to apply on real food inspection industry.
• •Given above, we built up a database containing the data from measurement and FEM simulation results. We have trained and test the data by FCNN model to recognize fresh food and frozen–thawed food in real-time. We believe this improvement will contribute to the food inspection industry.

1. Introduction

In the food production and manufacturing industries, the freezing–thawing process is a common step in food processing and storage. However, it may lead to cell membrane rupturing, nutrient loss, and texture degradation. It is worth noting that some businesses label frozen–thawed food as “fresh” to gain illegal profits, a problem which is particularly prominent in meat and fresh agricultural products. Therefore, developing rapid, non-destructive detection technologies to distinguish between frozen–thawed and fresh food has significant practical significance. Existing methods primarily rely on contact-based electrode plates to measure impedance changes (Abasi et al., 2022), which, although responsive, has significant limitations. For instance, direct contact between electrodes and samples may trigger chemical reactions, low-frequency polarization effects, and tissue damage. Additionally, during fresh meat testing, the non-homogeneous nature of the samples can cause deformation, which can significantly affect the measurement results. Barai et al. (2012) proposed using an electromagnetic induction measurement system to measure the impedance spectrum of biological tissues. In magnetic induction spectroscopy (MIS), the defects of contact-type detection using electrode plates are eliminated by using completely non-contact inductive coupling between the sensor and the sample. Based on the MIS measurement principle, Tang et al. (2020) measured the bioimpedance spectra of pork loin and potatoes and constructed a novel finite element (FE) based cell model that can more realistically simulate the non-contact measurement process, providing a new perspective for understanding the effects of the freezing–thawing process on biological samples.

Bio-impedance spectroscopy(BIS) is a detection technique that characterizes the physiological state of biological samples by measuring their complex impedance response at different frequencies (Bera et al., 2016). Schwan, 1957, Schwan, 2007 first introduced the phenomenon that the relative permittivity and conductivity of most biological tissues exhibit frequency-dependent relaxations, as shown in Fig. 1. The relaxations are classified into three groups, respectively associated with cell membranes, intracellular organelles, double-layer counterion relaxation, and electromotive effects. These relaxations refer to the frequency responses of biological systems from the low-frequency to high-frequency ranges, which are named $\alpha$, $\beta$, and $\gamma$ dispersion, respectively. $\beta$-dispersion occurs in the frequency range of approximately 10 kHz to 100 MHz and is associated with the characteristics of cell membranes and their interactions with intracellular and extracellular electrolytes (Gabriel et al., 1996). In this specific radio frequency range, the cell membrane exhibits a dielectric relaxation effect that reflects the geometrical and physical characteristics of the cell membrane. The Cole equivalent circuit model (Kasiviswanathan et al., 2020), as shown in Fig. 2, is widely used to simulate these electrical behaviors, providing a foundation for non-destructive food quality assessment. Notably, the principles of BIS align with thermodynamic analyses in food processing, such as vacuum freeze-drying (VFD), where structural integrity is characterized through energy efficiency metrics (Oztuna Taner, 2024b, Oztuna Taner, 2025). However, BIS focuses on electrical characteristics, whereas VFD emphasizes thermal processes, highlighting the interdisciplinary potential for food quality optimization. When subjected to an external alternating electromagnetic field, the cell membrane behaves as a capacitor. Due to this specific electrical property, $\beta$-dispersion can be explained by the Maxwell–Wagner interface polarization effect, which is caused by the cell membrane’s obstruction of ion flow between the intracellular and extracellular spaces. This characteristic effectively reflects the integrity of the cell membrane.

Fig. 1.

Dispersive spectroscopy of biological samples.

Fig. 2.

Cole equivalent circuit model.

In recent years, the BIS method has gained widespread attention in the fields of industrial and food quality testing due to its non-invasive, label-free, and quantitative analysis advantages (Cheng et al., 2022, Grossi and Riccò, 2017, Zhang et al., 2025a). Studies have shown that impedance measurements can reflect the geometrical and physical properties of food, such as cellular structure, moisture content, and microbial activity, providing innovative solutions for freshness assessment (Banti, 2020, Grossi and Riccò, 2017, Kluza et al., 2025a), quality classification (Tara et al., 2025) and spoilage detection (Watanabe et al., 2023) in meat, fruits and vegetables. In the field of meat quality detection, BIS technology has been successfully applied to the quality assessment of various meats, including lamb (Huang et al., 2023, He et al., 2025, Wang et al., 2024), pork (Leng et al., 2024, Osen et al., 2022, Leng et al., 2019), beef (X. Li et al., 2025, Afonso et al., 2020), and salmon (Sun et al., 2020). In the field of fruit and vegetable quality detection, BIS technology achieves precise assessment of characteristics such as fruit ripeness (Kluza et al., 2025b, Nayak et al., 2025, Freitas et al., Roy et al.), potato frost damage (Feng et al., 2021), and tomato local damage (Zhang et al., 2024) by monitoring the correlation between impedance parameters and equivalent circuit models (ECM). For example, the fractional capacitance model can quantify banana ripeness and chemical composition (Nayak et al., 2025), while the characteristic frequency method combined with support vector machines (SVM) can effectively reduce the impact of individual differences on apple detection (Feng et al., 2024). For determining citrus storage temperature, Son et al. (2025) integrated impedance change data with diameter data to validate the effectiveness of multi-parameter joint analysis. In the application of BIS methods, technological innovation and model optimization are key to improving detection performance. Technological innovations, such as low-cost portable systems (Ibba et al., Masot et al., 2010, Simic et al., 2024), flexible sensors (Huang et al., 2023, Wang et al., 2024) and machine learning algorithms (He et al., 2025, Liang et al., 2023, Lu et al., 2024, Freitas et al., Roy et al., Allara et al., 2025, Deshpande et al.), have enhanced BIS performance through feature optimization and temperature compensation (Dipa et al., 2024). These advancements mirror energy efficiency strategies in food production, such as exergy analysis in yogurt processing, which achieved over 60% efficiency through thermodynamic optimization (Oztuna Taner, 2024a) . This synergy underscores the value of integrating electrical and thermal perspectives for comprehensive quality control. The introduction of temperature compensation strategies (Dipa et al., 2024), multi-scale detection frameworks (Y. Li et al., 2025) and Cole model parameter analysis (Simic et al., 2024) has further enhanced the technology’s applicability across various scenarios.

In current studies on food freshness assessment utilizing bioimpedance spectroscopy (BIS) principles, the most prevalent methodology employs electrode-based detection systems (He et al., 2025, X. Li et al., 2025, Mussnig et al., 2024). While this conventional approach demonstrates notable measurement precision and wide applicability, the inherent structural heterogeneity of biological tissues frequently induces sample deformation during measurement. Consequently, operator-induced factors substantially influence the detection outcomes, ultimately compromising measurement reliability. Furthermore, the requirement for adequate physical contact between electrodes and samples raises significant safety and hygiene concerns. In contrast, the non-contact detection method implemented in this study effectively circumvents these limitations while maintaining satisfactory measurement accuracy in practical applications.

Although significant progress has been made in using non-contact magnetic induction measurement base on BIS methods for food quality testing, a persistent fraud problem remains in the food industry: the misrepresentation of frozen–thawed food as fresh. Some merchants mislabel frozen–thawed foods as fresh, which is difficult to identify through conventional observation methods. Our previous study introduced a novel non-contact induction method based on bioimpedance spectroscopy (BIS) techniques, showing great potential for the nondestructive testing of food quality, especially for frozen–thawed food samples. However, challenges remain for industrial applications, such as slow sweeping speed (7–8 min/sample), a wide frequency range, and numerous sampling points, which collectively lead to low detection efficiency and high instrument costs. This sequential scanning detection method is unsuitable for real-time automated quality inspection in food industry production lines. Specifically, the method requires a wide detection frequency range and numerous sampling points, imposing high demands on the equipment and significantly increasing detection costs. This is incompatible with current industrial requirements for cost reduction and efficiency improvement.

This paper improves upon the existing shortcomings of the BIS method based on non-contact magnetic induction measurement systems (Tang et al., 2020). Specifically, leveraging the distinct $\beta$-dispersion characteristics, we propose a “Data + FCNN” detection method using eddy current detection signals to rapidly determine whether the sample has undergone a freezing–thawing process, thereby distinguishing between fresh and frozen–thawed food. The high consistency between the simulated cell model and the measured conductivity spectrum allows the use of simulation data to predict the performance on test samples. After training the model, the actual measurement data are fed into it for testing, which further verifies the method’s validity. This approach addresses the challenges posed by the wide sweeping frequency range and the large number of sampling points in instrument detection and reduces the cost of detection. It tackles quality testing issues at the data level, enabling dynamic real-time detection of frozen–thawed or fresh ingredients and significantly improving the testing efficiency. This approach holds both theoretical and practical significance for further applying the BIS method to automated food quality testing.

2. Measurement system and theory

2.1. Sample selection

Two 2 L containers were filled with physiological saline solution to a liquid level of 20 cm. The conductivity of the solutions was measured with a conductivity meter and adjusted to 3 S/m and 5 S/m, respectively. Fresh potatoes were selected as the biological tissue samples for measurement.

2.2. Measurement set up

The front-end measurement circuit, as shown inFig. 3, primarily consists of five components: a signal generator (with an embedded power amplifier), a transmitter, a receiver, and a real-time multi-channel digital EM device.

Fig. 3.

Schematic diagram of the bioimpedance spectroscopy measurement system.

When the measurement circuit system is in operation, the sine wave signal generated by the signal generator is amplified by the power amplifier and input into the transmit coil as a highly amplified current. This amplified current generates an electromagnetic field, known as the primary magnetic field. The primary magnetic field induces an electric field in the suspension sample of the measured cells, forming eddy currents. The eddy currents in the suspension sample generate a secondary magnetic field that can be detected externally. The composite signal resulting from the interaction between the primary and secondary magnetic fields is detected by the receiving coil (Barai et al., 2012, O’Toole et al., 2015) and transmitted to the real-time processor, ultimately stored in a PC. The magnitude of impedance in the suspension sample affects the phase and amplitude of the received signal. By comparing the signals detected by the receiving coil and the transmitting coil, the equivalent impedance of the calibrated sample can be calculated (Tang et al., 2020).

2.3. Measurement data pre-processing

According to the Ref. Barai et al. (2012), the electromotive force $\nabla V$ measured by the receiving coil in the detection circuit is related to the excitation electromotive force $V$ of the transmitting coil as follows:

$$\frac{\Delta V}{v}=Pf{\mu }_0(2\pi f{\varepsilon }_0{\varepsilon }_r-j\sigma )+QX$$ (1)

Where $P$ and $Q$ are the geometric factor constants of the entire testing apparatus, whose values depend on the shape and size of the sample and its position relative to the two coils, calibrated using a saline solution with a certain conductivity. $f$ is the excitation frequency, ${\mu }_0$ and ${\varepsilon }_0$ are the magnetic permeability and dielectric constant in a vacuum respectively. And ${\varepsilon }_r$, $\sigma$, and $X$ are the relative dielectric constant, conductivity, and magnetic susceptibility of the sample being tested respectively. From Eq. (1), the relationship between conductivity and $Im(\nabla V/V)$ as a function of excitation frequency $f$ can be derived as shown in Eq. (2).

$$\sigma =-\frac{Im\left(\frac{\Delta V}{V}\right)}{Pf{\mu }_0}=K\frac{Im\left(\frac{\Delta V}{V}\right)}{f}$$ (2)

Where $K=-\frac{1}{P{\mu }_0}$ is a constant that can be calibrated by measuring a solution with a certain conductivity.

3. Equivalent model of cell suspension

3.1. Model establishment

Based on the FE simulation model of Tang et al. (2020), as shown in Fig. 4(b), and assuming that the displacement current can be neglected compared to the eddy current generated by the coil excitation, the system can be regarded as quasi-static, and the differential form of Maxwell’s equations for the time-varying magnetic field can be written as:

$$\left\{\begin{array}{c}div{B}_n=0\hfill \\ curl{E}_c=-\frac{\partial B_c}{\partial t}\hfill \\ curl{H}_n=J_n\hfill \\ curl{H}_c=J_c\hfill \\ div{J}_c=0\hfill \\ div{B}_c=0\hfill & \hfill \end{array}\right)$$ (3)

Fig. 4.

Measurement set up (a) and three-dimensional FE cell models (b)

In this context, $B_n$ and $B_c$ represent the magnetic flux density in the non-conductive region and conductive region, respectively; $H_n$ and $H_c$ represent the magnetic field strength in the non-conductive region and conductive region, respectively; $J_n$ and $J_c$ represent the current density in the non-conductive region and conductive region, respectively; and $E_c$ represents the electric field strength in the conductive region.

Solving this system of equations requires the assistance of Maxwell’s auxiliary equations as follows:

$$\left\{\begin{array}{c}\mathrm{B\; =\; \mu H}\hfill \\ H=\nu B\hfill \\ J_c=\sigma E_c\hfill \\ E_c=\rho J_c\hfill & \hfill \end{array}\right)$$ (4)

In the equation, $B$ and $H$ represent the magnetic flux density and magnetic field strength in the corresponding region, $\mu$ is the magnetic permeability, $\nu$ is the magnetic resistance, $\sigma$ is the electrical conductivity, and $\rho$ is the resistivity.

The three-dimensional eddy current simulation is based on Galerkin’s formulation of the edge-based finite element method, as given in Eqs. (5), (6). The model utilizes accelerated linear solvers (Georgii and Westermann, 2010, Fritschy et al., 2005) and incorporates acceleration techniques for finite element processing (Lu et al., 2017).

$${\int }_{{\Omega }_c}\mathrm{curl}{N}_i\cdot {\nu }_0\cdot \mathrm{curl}{A}_{s}d\Omega ={\int }_{{\Omega }_c}\mathrm{curl}{N}_i\cdot \nu \cdot \mathrm{curl}{A}^{\left(n\right)}d\Omega +{\int }_{{\Omega }_c}j\omega \sigma N_i\cdot A^{\left(n\right)}d\Omega +{\int }_{{\Omega }_c}\sigma N_i\cdot \mathrm{grad}{V}^{\left(n\right)}d\Omega$$ (5)

$${\int }_{{\Omega }_c}j\omega \sigma \cdot \mathrm{grad}{L}_i\cdot A^{\left(n\right)}d\Omega +{\int }_{{\Omega }_c}\sigma \cdot \mathrm{grad}{L}_i\cdot$$$$\mathrm{grad}{V}^{\left(n\right)}d\Omega =0$$ (6)

Where, $i=1,2,3,4,{\omega }_c$ denotes the conductive region, $N_i$ denotes the vector interpolation of the $i$th edge relative to its $n$th edge element; $A_s$ denotes the initial edge vector potential of the $n$th element; $L_i$ is the element interpolation of the $i$th node relative to its $n$th element; $V^n$ denotes the potential of the receiving coil excited by the $n$th element; $A^n$ denotes the induced potential generated by the edge vector on the $n$th element; $\nu$ is the magnetic resistance of the model, ${\nu }_0$ is the magnetic resistance of air, and $\sigma$ is the electrical conductivity of the model.

According to the literature (Asami, 2006), the numerical method was validated using a single-shell model, where the resulting geometry is a sphere characterized by a complex relative permittivity, as illustrated in Fig. 5.

Fig. 5.

Schematic of the spherical cell model.

The relative permittivity of the spherical cell model has the following form:

$$\left\{\begin{array}{c}{\varepsilon }_m^{\prime }=\frac{{\sigma }_m^{\prime }}{j\omega {\varepsilon }_0}=\frac{k_m+j\omega {\varepsilon }_m{\varepsilon }_0}{j\omega {\varepsilon }_0}\hfill \\ {\varepsilon }_c^{\prime }=\frac{{\sigma }_c^{\prime }}{j\omega {\varepsilon }_0}=\frac{k_c+j\omega {\varepsilon }_c{\varepsilon }_0}{j\omega {\varepsilon }_0}\hfill \\ {\varepsilon }_a^{\prime }=\frac{{\sigma }_a^{\prime }}{j\omega {\varepsilon }_0}=\frac{k_a+j\omega {\varepsilon }_a{\varepsilon }_0}{j\omega {\varepsilon }_0}\hfill & \hfill \end{array}\right)$$ (7)

Among these, ${\varepsilon }_m^{\prime }$ is the complex relative permittivity of the membrane, ${\varepsilon }_c^{\prime }$ is the complex relative permittivity of the intracellular fluid, and ${\varepsilon }_a^{\prime }$ is the complex relative permittivity of the extracellular fluid. In the entire cell model, the definitions of these parameters (Asami, 2006) are shown in Table 1.

Asami, 2006, Stubbe and Gimsa, 2015 developed a theory using the single-shell cell model in Fig. 5 to represent the equivalent complex relative permittivity of cell suspensions. This theory is described in the following form:

$${\varepsilon }_p^{\prime }={\varepsilon }_m^{\prime }\frac{2(1-v){\varepsilon }_m^{\prime }+(1+2v){\varepsilon }_c^{\prime }}{(2+v){\varepsilon }_m^{\prime }+(1-v){\varepsilon }_c^{\prime }}$$ (8)

Among them, the volume factor $\nu ={(1-\frac{d_m}{R_m})}^3$, and ${\varepsilon }_p^{\prime }$ represents the complex relative permittivity of the cell model. The overall equivalent complex relative permittivity can be derived using the Wagner equation:

$${\varepsilon }^{\prime }={\varepsilon }_a^{\prime }\frac{2(1-P){\varepsilon }_a^{\prime }+(1+2P){\varepsilon }_p^{\prime }}{(2+P){\varepsilon }_a^{\prime }+(1-P){\varepsilon }_p^{\prime }}$$ (9)

In the equation, the value of cell volume fraction $P$ depends on the physiological characteristics of the sample being tested. In this simulation experiment, $P=0.45$ and ${\varepsilon }^{\prime }$ represents the complex relative permittivity of the entire suspension system.

Table 1.

Parameter designation and corresponding value.

Symbol	Value	Description
$k_m$	$10^{-7}$ (S/m)	Membrane conductivity of cells
$k_a$	$1$ (S/m)	Extracellular fluid conductivity
$k_c$	$1$ (S/m)	Intracellular fluid conductivity
${\varepsilon }_0$	$8.85\times 10^{-7}$ (F/m)	Vacuum permittivity
${\varepsilon }_a$	$80$ (F/m)	Extracellular fluid dielectric constant
${\varepsilon }_c$	$80$ (F/m)	Intracellular fluid dielectric constant
${\varepsilon }_m$	$5$ (F/m)	cell membrane dielectric constant
$d_m$	$5\times 10^{-9}$ (m)	Cell membrane thickness
$R_m$	$5\times 10^{-6}$ (m)	Cell diameter
$\omega$	$2\pi f$	Angular frequency

4. BIS measurement result and FEM validation

4.1. Sample BIS measurement

Following the method described by Tang et al. (2020), non-contact inductive measurement techniques were employed to first obtain data from fresh samples. These test samples were then frozen at 5 °C–6 °C for 24 h and subsequently thawed at room temperature (14 °C–15 °C) for 12 h before being re-tested. The bioimpedance spectra of the biological samples before and after freezing and thawing were obtained within the frequency range of 100 kHz to 10 MHz as shown in Fig. 6.

Fig. 6.

Conductivity spectra of fresh and thawed potatoes.

Through the above methods, we can clearly see the trend of conductivity changes in fresh test samples and frozen–thawed test samples as the excitation frequency increases. The conductivity of the fresh potatoes measured showed $\beta$-dispersion between excitation frequencies of 100 kHz and 2 MHz. However, the conductivity curve of the thawed samples was basically flat, indicating that $\beta$-dispersion did not occur in the thawed samples.

4.2. Simulation verification

A three-dimensional FE model was developed to represent the cellular structure of fresh ingredients, modeling individual cells as structurally intact spheres, as shown in Fig. 4(b). Following freezing and thawing processes, the cell membranes of the fresh ingredients are typically ruptured. This damaged state is represented in the model as punctured spheres, as illustrated in Fig. 7.

Fig. 7.

Three-dimensional FE model of thawed sample.

The equivalent complex relative permittivity ${\varepsilon }^{\prime }$ of the suspension system is calculated using Eqs. (7)–(9) and the parameters in Table 1. The conductivity ${\sigma }^{\prime }$ of the system is contributed by the imaginary part of ${\varepsilon }^{\prime }$.

$${\sigma }^{\prime }=-Im\left({\varepsilon }^{\prime }\right)\cdot \omega {\varepsilon }_0$$ (10)

The conductivity changes of the simulation model at $10^5\mathrm{Hz}$ to $10^7\mathrm{Hz}$ are calculated using Eq. (10), as shown in Fig. 8.

Fig. 8.

Simulation verification results.

The simulation results in Fig. 8 show good agreement with the actual measurements in Fig. 6, confirming that fresh raw ingredients exhibit $\beta$-dispersion in the mid-frequency range. After freezing, the rupture of cell membranes results in the loss of the Maxwell interface polarization effect, so that $\beta$-dispersion does not occur in the mid-frequency range. The FEM results agree with the measurement results, with an error of less than 0.01 $S/m$.

5. Classifier implementation

5.1. Biological impedance data collection and description

In traditional bioimpedance-based detection of prolonged freezing in fresh food ingredients, it is often necessary to perform a full frequency sweep, measuring the conductivity at each frequency point to generate a complete bioimpedance spectrum. This spectrum can then be analyzed to determine the freshness of the ingredients. However, such procedures are time-consuming and impractical for high-throughput industrial applications.

As shown in Fig. 8, the simulated conductivity results of the established cell suspension model exhibit high consistency with the empirical measurements presented in Fig. 6. This strong agreement indicates that the simulation accurately captures the dielectric properties of the physical samples and can serve as a reliable virtual representation of the actual biological material. Furthermore, building upon the work of Sekine et al. (2015)—who employed the finite difference method to numerically investigate the frequency-dependent electrical conductivity and impedance of skeletal muscle using a three-dimensional cellular model—this study leverages the established correlation between simulated and measured conductivity profiles. To further enhance the realism of the simulation, Gaussian noise was introduced to emulate detection variability, as illustrated in Fig. 9.

Fig. 9.

Three-dimensional FE simulation for bioimpedance spectroscopy.

To address the inefficiencies associated with full-spectrum frequency sweeps, this study proposes a simplified yet effective approach that samples impedance-related features at only three fixed frequency points: 100 kHz, 500 kHz, and 1 MHz. For each frequency, the following parameters were recorded: the frequency $f$, the conductivity ${\sigma }^{\prime }$, and the ratio $Im(\nabla V/V)$, which represents the imaginary component of the normalized voltage difference. This strategy significantly reduces measurement time while preserving key discriminative features for classifying sample freshness.

To simulate the detection speed in an automated assembly line setting, simulation models of both “fresh” and “thawed” samples were executed 2000 times each, incorporating random Gaussian noise to reflect real-world variability. These simulations were performed across a frequency range from $10^5\mathrm{Hz}$ to $10^7\mathrm{Hz}$. The impedance data for “fresh” and “thawed” samples were recorded separately, yielding a total of 4000 data points. These data were then randomly shuffled to construct the final dataset. In this dataset, samples that were simulated as frozen were labeled “thawed”, while those simulated as unfrozen were labeled “fresh”. The complete data collection and preprocessing workflow is illustrated in Fig. 10.

Fig. 10.

Data acquisition and processing flow.

5.2. Training and evaluation of neural network models

The first 80% of the dataset is used as the training set, and the remaining 20% as the test set. This paper employs a fully connected neural network (FCNN) architecture to construct a binary classification model based on a multilayer perceptron (MLP) for the task of identifying the frozen/fresh state of fresh food ingredients in industrial inspection scenarios. The model training structure is shown in Fig. 11.

Fig. 11.

Testing structure with FCNN model.

The proposed fully connected neural network (FCNN) for binary classification demonstrates strong generalization capabilities through the integration of multi-layer nonlinear transformations and regularization techniques, including Batch Normalization, Dropout, and label smoothing. By incorporating dynamic learning rate scheduling (OneCycleLR) and mixed-precision training, the model achieves efficient convergence while reducing computational overhead. Robust data preprocessing and a comprehensive evaluation framework further enhance its applicability to real-world engineering scenarios.

Despite its minimalist architecture, the FCNN achieves performance comparable to state-of-the-art (SOTA) models (Abd El-Wahab et al., 2023), significantly outperforming similar approaches in terms of computational efficiency, sparsity optimization, and adaptability to small datasets. These capabilities are enabled by the introduction of innovative path context structures and embedding strategies. A key strength of the model lies in its ability to balance architectural simplicity with generalization performance, effectively mitigating overfitting while maintaining high classification accuracy. These characteristics make the model particularly well-suited for medium- to small-scale structured data classification tasks.

5.3. Results and analysis

During the training and validation phases, the learning rate, training loss, and accuracy were recorded, as illustrated in Fig. 12 and Fig. 13, respectively. Additionally, the confusion matrices for both the training and test sets were generated, as shown in Fig. 14, to facilitate subsequent performance analysis.

Fig. 12.

Dynamic learning rate curve.

Fig. 13.

Training loss function curves(a) and Training accuracy curves(b).

Fig. 14.

Confusion matrix of training results. (a) Train set. (b) Test set.

The dynamic learning rate adjustment strategy shown in Fig. 12 effectively balances training efficiency and model performance by coordinating the learning rate and momentum within a single training cycle. This approach offers several advantages, including accelerated convergence, enhanced generalization, and reduced need for extensive hyperparameter tuning.

Fig. 13(a) shows the variation of the cross-entropy loss function over 100 training epochs for the proposed neural network model. Both the training and testing loss curves exhibit a consistent, monotonically decreasing trend, approximately following a typical exponential decay pattern. The loss value decreases from approximately 0.72 at the initial stage to around 0.38 by the end of training, eventually plateauing. This behavior indicates that the model effectively minimizes its objective function throughout the training process, demonstrating strong numerical stability and convergence properties.

As illustrated in Fig. 13(b), the accuracy on the training set exhibits a steady upward trend with increasing training iterations, eventually approaching saturation and reaching nearly 99%. This reflects the model’s strong fitting capacity and its ability to effectively capture underlying patterns within the training data. Similarly, the test set accuracy increases progressively throughout the training process, closely tracking the trend of the training accuracy. Notably, the rate of improvement in test accuracy is slightly higher, and it too displays a saturation effect in the later stages. By the end of training, the test accuracy stabilizes at an exceptionally high level of 100%, indicating the model’s outstanding generalization performance.

As shown in Fig. 14, among the 3200 training samples, 36 fresh samples were misclassified as “thawed”, representing approximately 1.13%. Additionally, 9 freeze–thawed samples were incorrectly classified as ”fresh”, accounting for about 0.28%. In contrast, the classification accuracy on the 800 test samples reached 100%, indicating excellent generalization and classification performance on unseen data.

The experimental results demonstrate that the proposed model achieves a classification accuracy exceeding 98% on the bioimpedance dataset. The incorporation of dynamic learning rate scheduling accelerates convergence by approximately 40%, while the application of label smoothing could reduce calibration error effectively . When evaluated on impedance data from physical samples, the trained model maintains a test accuracy of 100%, underscoring its robustness and practical applicability. These findings collectively suggest that the “Data + FCNN” framework offers a rapid and effective end-to-end solution for non-destructive quality assessment of fresh food products.

In contrast, prevailing methodologies in BIS-mediated food analysis predominantly employ conductive electrode plates (Leng et al., 2024, Zhang et al., 2025b) for signal acquisition. A significant drawback of this contact-based paradigm is its susceptibility to operator-dependent variability in compression force—an effect exacerbated by tissue heterogeneity—which compromises measurement reproducibility. Additionally, the requisite direct contact introduces risks of electrochemical reactions and cross-contamination, raising substantive safety and hygiene concerns. The non-contact electromagnetic induction strategy implemented in our work inherently precludes direct physical interaction, thereby neutralizing both sources of error. Furthermore, existing related studies typically rely on full-spectrum data (X. Li et al., 2025, Kluza et al., 2025a), which provides richer chemical and structural information suitable for broader and more complex quality assessment tasks. These methods aim to extract valid information from massive datasets, such as multi-level classification and regression prediction of TVB-N values. While their high accuracy rates of 94%–96% (He et al., 2025, Deshpande et al., Roy et al.) represent notable achievements, they are comparatively lower than the exceptional 100% accuracy demonstrated in this study.

Overall, the high-precision experimental results obtained in this work benefit from the tightly integrated closed-loop system formed by the “non-contact BIS + three fixed frequency points + FCNN” methodology. This approach adopts a targeted “surgical strike” strategy, successfully building upon a well-defined physical phenomenon ($\beta$-dispersion) and addressing a highly specific industrial challenge (freeze–thaw identification). Its advantage lies not in solving more complex problems, but in perfectly resolving a clearly defined and industrially significant issue through an exceptionally efficient and low-cost approach. This provides a novel and more feasible technical pathway for transitioning BIS technology from laboratory settings to industrial applications.

6. Conclusion and outlook

6.1. Conclusion

This study proposes a novel “BIS + FCNN” detection framework, built upon existing non-contact magnetic induction bioimpedance measurement systems, to address prevailing challenges such as high detection costs and low operational efficiency. Initially, bioimpedance spectroscopy (BIS) measurements were conducted on fresh food ingredients before and after undergoing freezing and thawing processes. Concurrently, a three-dimensional finite element (FE) cellular model was constructed to simulate and validate the measured bioimpedance spectra. The simulation results exhibited strong agreement with the experimental measurements, confirming that the model accurately captures changes in the electrical behavior of cell membrane structures resulting from freezing-induced damage. This mechanistic consistency provides a theoretical basis for understanding the dielectric property evolution of biological tissues under physical stress.

To emulate the detection conditions of an automated production line, and leveraging the consistency between empirical and simulated data, conductivity values at three fixed frequency points were repeatedly extracted from the simulation model to construct a training dataset. A fully connected neural network (FCNN) was then employed to classify the data into “fresh” and “freeze–thawed” categories, achieving a classification accuracy exceeding 98%. While generating a complete bioimpedance spectrum for a single sample through frequency scanning typically requires 7–8 min, acquiring data at fixed frequency points takes only 1–1.5 s. This approach significantly enhances detection efficiency.

By integrating neural network-based classification with targeted frequency sampling, the proposed method enables rapid and accurate identification of sample freshness based solely on bioimpedance data. The framework provides a robust theoretical and practical foundation for implementing automated, non-contact magnetic induction detection systems in the food industry.

6.2. Outlook

In the future, this method can be extended to the detection of various types of fresh food ingredients, with the potential to adapt to complex detection environments involving diverse sample geometries and varying detection distances, thereby enabling real-time assessment of food freshness. Furthermore, the proposed approach holds promise for broader applications beyond the food industry, including medical diagnostics and biological research, where non-invasive and efficient bioimpedance-based analysis is of growing interest.

CRediT authorship contribution statement

Degang Xu: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. Qixiong Wen: Methodology, Software, Validation, Investigation, Data curation, Writing – review & editing. Yuedong Xie: Resources, Methodology, Data curation, Writing – review & editing, Supervision. Wuliang Yin: Resources, Software, Validation, Writing – review & editing, Supervision, Project administration. Jiawei Tang: Conceptualization, Methodology, Software, Validation, Resources, Writing – review & editing, Supervision, Project administration.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Handling editor essor Georgios Leontidis