A study on fine detection of moisture content in stone cultura relics by high-sensitivity wireless sensing

Abstract

As moisture is the main factor that causes weathering of stone cultural relics, probing their corresponding contents is the basis for all conservation work. In this work, the moisture content of stone cultural relics was examined using the non-Hermitian exceptional points in the second-order parity-time (PT) symmetric system. Tiny moisture changes inside the samples were determined through the resonant frequency difference. Using the difference in dielectric constants between moisture and sandstone, the database of dielectric constants of stone cultural relics with differing moisture contents can be established. Meanwhile, the fine detection of small changes in moisture contents of stone cultural relics can be realised. Compared with conventional passive wireless sensors, the second-order PT symmetric system has improved detection sensitivity and a smaller error, of less than 0.07% compared with the drying method. Furthermore, compared with other kinds of nondestructive testing technology, this system exhibits many advantages in detecting the moisture content of stone cultural relics, including compact size, high sensitivity, and low detection cost, and is thus of great significance for the protection and restoration of cultural relics.

Introduction

According to the porosity of sandstone, sandstone can be classified as dense sandstone, low porosity sandstone, medium porosity sandstone, high porosity sandstone and very high porosity sandstone, while the fresh rock sample from Yungang Grottoes has a porosity of 6.44%±0.2, which belongs to the low porosity rocks¹, while the salt exists in the pores. moisture acts as a medium in the whole weathering process². As humidity increases, salt dissolves in moisture and moves with it through the rock. As the moisture evaporates, the soluble salt crystallises and remains in place. Such a salt goes through a continuous process of dissolution, crystallisation, re-dissolution and re-crystallisation. As each crystallisation takes place in a different place, the rock can become loose and break up over time. Some of the moisture also reacts with the minerals in the rock to form new minerals. Typically, the newly formed minerals are less hard than the original minerals and will eventually become loose and fall off³. Therefore, the effect of moisture cannot be ignored throughout the weathering process.

Since cultural relics are not renewable, non-destructive testing methods are needed. At present, the non-destructive testing technology is relatively mature, mainly resistance method, capacitance method, infrared method, X-ray method and microwave method, etc., They can quickly, non-destructively and accurately measure the moisture content of the rock, but have their own shortcomings, the resistance method needs to destroy the structure of the body to be measured, is not suitable for detecting a small number of valuable materials to be tested for moisture content, and at the same time the measurement range is limited, is not suitable for detecting the moisture content range of a wide range of materials to be tested for moisture content⁴. The capacitance method is suitable for a wide range of rocks, but is sensitive to the external environment and must take factors such as temperature into account⁵. The infrared method can only measure moisture on the surface of the sample and the instrument is expensive⁶. Radiographic methods have the advantages of fast detection, high accuracy and the ability to detect moisture content inside the material, but the technology is ionising radiation, dangerous and expensive equipment⁷.

Microwave technology is the only method that can safely and accurately measure the moisture content of rocks.The microwave method can be used to measure the moisture content of materials by transmission method, reflection method, resonant cavity method, etc. The transmission method and the resonant cavity method are commonly used to measure the moisture content of rocks. At present, most of the commercial moisture analysers based on microwave technology generally adopt the transmission method as the measurement principle, and the microwave probe adopts the invasive structure, which can achieve the online high-precision measurement, but it cannot avoid the problem of probe cleaning and destruction. As a non-invasive structure, resonant cavity can effectively avoid the above problems in measurement, which has potential advantages and broad application prospects. At present, resonant cavities are mainly divided into two categories, one is rectangular resonant cavity and the other is cylindrical resonant cavity. The theoretical basis of rectangular resonant cavities is relatively mature, and many tests and researches on rectangular resonant cavities have shown that they have the characteristics of high quality factor and small transmission loss, so the selection of rectangular resonant cavities can better reduce the experimental error^{8, 9–10}.

However, how to improve its high resolution has become a problem to be solved.

In classical quantum mechanics, Hermitian Hamiltonians are usually required to ensure experimentally observable real energy spectra and probability conservation¹¹. Prior studies have found that non-Hermitian quantum mechanics systems with equilibrium loss/gain can also have pure real eigenvalues. Moreover, such systems can exhibit properties and functions that cannot be found in Hermitian systems, such as high sensitivity and robust mode conversion¹². As early as 1998, Bender et al.first proposed the parity-time PT symmetry theory, which is regarded as a milestone in the development of non-Hermitian systems^13,14. The essential difference between non-Hermitian systems and Hermitian systems is the existence of an exceptional point (EP), which is a unique degenerate state in the non-Hermitian system that satisfies the PT symmetry. Anomalies such as level repulsion, crossing, and phase jump, among others, tend to occur in the vicinity of this point5^15,16. At this point, the system exhibits ultra-high sensitivity, which can be utilised for high-precision detection in many fields^{17, 18, 19–20}. In particular, the eigenvalue of the non-Hermitian system has a 1/N power dependence on perturbation near an EP, which can greatly improve the sensing sensitivity compared to the conventional linear dependence^{21, 22–23}. In 2018, Chen et al. designed a new RF.

wireless microsensor system, which has an ultra-sensitive response and an ultra-high resolution. Their system exceeds the limitations of conventional passive sensors²⁴. In 2019, Mehdi Hajizadegan et al. experimentally demonstrated an ultra-sensitive wireless displacement sensing technique based on the concept of PT symmetry or spatiotemporal inversion symmetry. This PT symmetric telemetry system achieves wireless connection through inductive coupling, which enables strong frequency response and high sensitivity that surpasses the limitations of conventional passive wireless displacement sensors²⁵. At present, the research on PT symmetric non-Hermitian systems and their relative effects has gradually progressed and a wide range of corresponding application prospects have been achieved in the fields of laser technology, optical sensing, and materials engineering, among others^11,12.

Taking the stone artefacts in the Yungang Grottoes as the research object, this study developed a second-order PT wireless sensor system and applied it to the detection of moisture content in stone artefacts for the first time. Using the high sensitivity characteristics of EP points, this system is able to achieve real-time on-line fine detection of minute moisture content changes before the weathering of cultural relics. Meanwhile, the experimental results show that when the moisture content in the rock is less than or equal 0.3%, the sensitivity is high and the absolute error is less than 0. 07% compared with that of the drying method, Solve the current problem of moisture content measurement accuracy of stone cultural relics, the measurement accuracy is improved to two decimal places which is able to achieve fine detection of minute moisture content changes in the cultural relics before weathering, and through the analysis of the results, we get the grotto sandstone’s Through the analysis of the results obtained the moisture content of the grotto sandstone and the resonance frequency of the fitting relationship, the use of the fitting curve can be successfully predicted in the stone cultural relics of the moisture content. Thus, preventive protection of stone artefacts can be carried out.

Preparation of yungang grottoes samples

In the process of sample preparation, our samples were taken from the eastern rock face of the same mountain as the Yungang Grottoes, as shown in Fig. 1. At the same time, the rocks on the east side of the cliff wall were also at the same rock level as the statues in the Yungang Grottoes, and had been excavated by hand deep into the inner layers of the rocks, so we approximated that they had the same characteristics as fresh rock samples from the inner layers of the grottoes.

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Fig. 1

Eastern rock wall of Yungang Grottoes and the collected grotto samples.

Rock samples were collected from the grottoes in block form, and were further cut and processed. The length, width, and height of the cut rock samples were 4, 4, and 3 cm (total of 5 samples). Additionally, five thin slices with the length, width, and height of 4 cm, 4 cm, and 2 mm were cut and used for the experimental data measurements, as can be seen in Fig. 2.As different porosities can affect the dielectric constant of the rock, five thin sections of the rock were taken at different locations in the rock and then averaged.

For the experiments, the free soaking method was adopted in the natural state^{26, 27, 28–29}. Five samples into the moisture container at the same time, moisture injection to the rock sample 1/4 (at this time the depth of moisture is 1 cm), soaking for two hours after the removal of rock samples 1, into a sealed bag standby (each rock sample in the sealed bag should be weighed before processing), and then injected into Rock Sample 1/2 (at this time the depth of moisture is 2 cm), soak for two hours after removing Rock Sample 2, put into a sealed bag standby and then injected into Rock Sample 3/4 (at this time the depth of moisture is 3 cm), Soak for two hours after removing the rock sample 3, into a sealed bag standby, again injected moisture to the entire rock sample is completely submerged, soak for two hours after removing the 4th rock sample, weighing and put into a sealed bag standby, after an interval of two hours after removing the 5th rock sample, the weight of rock samples and the 4th no significant difference, then soak for another 2 h, the rock sample quality is almost unchanged, then depending on the soaking At this point, the sample is considered to be saturated after 10 h of soaking.

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Fig. 2

Experimental samples.

The samples were weighed and processed every two hours after the samples had cooled to room temperature and the weighing results are shown in Table 1. From the table it can be seen that the mass of the rock samples increased as the soaking time increased.

To investigate the electromagnetic properties of the samples, the corresponding di-electric constants were determined using a high- and low-frequency dielectric constant tester. A database for the dielectric constant of the samples was thus obtained, as shown in Table 2.(Shanghai Aiyi Electronic Equipment Co, Ltd AS2853A full digital display high frequency Q meter, the principle of operation is the resonance method, the working frequency range of 10 kHz to 260 MHz, the thickness of the sample can be between 1–5 mm ).The dielectric constant of the samples increases with increasing moisture content. The dielectric constant of moisture is around 80 while the dielectric constant of the samples is around 3. This indicates that moisture has a greater effect on the dielectric constant of the samples. Therefore, the change in dielectric constant is mainly determined by the moisture content and can be used for moisture content measurement.

Table 1. Mass of samples with different moisture contents

Soaking time (h)	0	2	4	6	8	10
Mass (g)	148.77	150.53	151.27	151.73	151.79	151.91

Table 2. Test data of dielectric constant of samples with different moisture contents.

Soaking time (h)	0	2	4	6	8	10
Dielectric constant	5.85	5.913	6.151	6.236	6.314	6.335

Theoretical model of second-order PT symmetric system

The theoretical model of the second-order PT symmetric system is depicted in Fig. 3, comprising two identical resonant Coils (transmitter coil and receiver coil) and two identical non-resonant coils (source coil and load coil). 1(2) denotes the coupling strength between the source (load) coil and the transmitter (receiver) coil. κ denotes the coupling strength between. the transmitter coil and the receiver coil. The motion equation of this model can be described using the coupled modular. Equations^30,31 as follows:

1

2

where ω0is the self-resonant frequency of the resonance coil and Γ is the intrinsic loss of the system. γ₁ and γ₂ satisfyγ₁ = γ₂.

=γ. A_1,2 e^− iωtdenotes the two resonance modes. The reflected wave is denoted as:

3

The motion equation at the perfect absorption state can be obtained by setting the zero reflection wave and substituting s1− = 0 into Eqs. (1) and (2)³²

4

where Therefore, the equivalent Hamiltonian of the system can be obtained as:

5

The ideal PT symmetric system is established in this open quantum system without considering the intrinsic loss Γ. Solving.

the secular equation of, the following can be obtained:

6

Where . When the critical condition of is satisfied, the Hamiltonians of the system converge at ω = ω0 and have real eigenvalues, i.e., the system reaches the second-order EP point. To understand how small resonance displacements in the resonator affect the detectable reflection spectrum, perturbation ε is placed on the transmitting resonator. The equivalent Hamiltonian of the system then becomes:

7

The normalization parameter of (Γ = 0, γ = κ = 1) is substituted into the secular equation of to obtain the following:

8

Figure 4 presents the variation curves for the real part (Re) and the imaginary part (Im) of the eigenfrequency ω of the system with respect to ε, which is obtained by solving Eq. (8). From the figure, the system has a real eigenvalue, i.e., the system reaches the second-order EP point. In addition, using the method in literature²¹, the approximate solution of Eq. (8) is derived as:

9

This equation demonstrates that the frequency shift of the second-order PT symmetric system near the EP has a 1/2 powerrelationship with the external perturbation.

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Fig. 3

Theoretical model of the second-order PT symmetric wireless sensing system.

The transmitter and receiver coils are resonant coils, and the source and load coils are non-resonant coils. γ₁(γ₂) denotes the coupling strength between the source (load) and transmitter (receiver) coils. κdenotes the couplingstrength between the transmitter and receiver coils.

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Fig. 4

Variation curves for the real (Re) and imaginary (Im) parts of the eigenfrequency ωwith perturbation ε.

Structural design and experimental scheme

Figure 5 shows a structural diagram of the second-order PT symmetric wireless sensing system, including the source coil,

transmitter coil, receiver coil, and load coil from bottom to top. The transmitter and receiver coils were both spiral coils made of 1 mm copper wire wrapped in polyesterimide with the inner diameter of 40 mm and spacing of 20 mm. The source and load coils were both circular coils with the radius of 120 mm, which were made of 1 mm copper wire. They were connected with 50 Ω SMA connectors at the open ends of the coil, which were then connected to the two ports of the vector network analyser (VNA) to monitor the reflection spectrum S₁₁. To adjust the resonant frequency of the resonant coils, an adjustable capacitor of 510 pF and a fixed ceramic capacitor of 5 pF were loaded onto each resonant coil.

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Fig. 5

Schematic of structure of the wireless sensing system with second-order PT symmetry.

In addition, a parallel plate capacitor was connected in series with the transmitter coil to set up a container capable of holding the sample, forming an LC circuit with the transmitter coil. The parallel plate capacitor constituted two aluminium plates with the thickness of 1 mm, length of 40 mm, and width of 20 mm. The spacing between the two plates was 40 mm. Figure 6 shows the experimental setup of the second-order PT symmetric wireless sensing system. All four coils were fixed on transparent acrylic plates and remained on the same axis. Then, the second-order EP of the system was realised through adjustments to the distance between the coils. Finally, the experimental samples with different composition ratios were placed into the capacitor separately. The reflection spectra (S₁₁) corresponding to different samples were measured using the VNA.

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Fig. 6

Experimental setup of the second-order PT symmetric wireless sensing system.

To better demonstrate the sensitivity enhancement effect of the second-order PT symmetric wireless sensing system, a conventional passive wireless sensor based on a single LC cavity was adopted as a reference object. The structure of the conventional passive wireless sensor is shown in Fig. 7, and comprises only two coils: a single-turn excitation coil and a multi-turn spiral receiver coil. The receiver coil was loaded with an adjustable capacitor of 510 pF and a fixed ceramic capacitor of 10 pF, and was connected in series with a parallel plate capacitor to form an LC circuit. The resonant frequency of the sensor can be adjusted via the adjustable capacitor. The structural parameters of the excitation coil and the receiver coil specified in Fig. 7 were the same as those of the source coil and the transmitter coil detailed in Fig. 5. Similarly, a 50 Ω SMA connector was set at the coil opening of the excitation coil and connected to port 1 of the VNA to monitor the reflection spectrum of the sensor (S₁₁). According to the theory of the LC circuit, the resonant frequency (f_n) of the conventional passive wireless sensor satisfies the following equation:

10

where f_n is the resonant frequency of the sensor, L is the inductance of the coil, C₀ is the capacitance of the fixed capacitor loaded on the coil, and C_n is the capacitance of the parallel plate capacitor. In the experiment, a perturbation was applied to the sensor by changing the medium in the parallel plate capacitor. The calculation formula for the capacitance of the parallel plate capacitor is given by:

11

In the case of maintaining the same plate area A and plate spacing d, the larger the dielectric constant ε_r, the larger the capacitance of the capacitor. According to Eq. (10), the larger the capacitance, the smaller the resonant frequency of the sensor, i.e., the redshift phenomenon occurs. Conversely, the larger the capacitance, the larger the resonant frequency, i.e., the blueshift phenomenon occurs.

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Fig. 7

Experimental setup of conventional passive wireless sensor based on LC cavity.

Experimental measurement process and data analysis

First, the two sets of experimental samples were tested using conventional passive wireless sensors. The results are shown in Fig. 8. With an increase in soaking time, the resonant frequency of the system shifts leftwards, but the change is small. Figure 9(a) presents the experimental results for the samples with different moisture contents. The resonant frequency of the conventional passive wireless sensor decreased with increasing moisture content. According to Table 2, the dielectric constant of the samples increased as the moisture content of the samples increased. Moreover, a theoretical analysis of conventional passive wireless sensors showed that the larger the dielectric constant, the smaller the resonant frequency, which is in good agreement with the experimental results.

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Fig. 8

Reflection spectrum of conventional passive wireless sensing at different interference intensities ε.

To further illustrate the relationship between the sample moisture content and the resonant frequency, perturbation ε was expressed as the frequency shift of the sample (|f_n − f₀|). From Eq. (10), ε has a first-order linear relationship with the sample moisture content. Figure 9(b) shows the variation curves for resonant frequency (f_n) versus resonance frequency shift |f_n − f₀| at different moisture contents. The red solid line represents the first-order linear fitting curve. The results show that the resonant frequency of the conventional passive wireless sensor and its displacement have a first-order linear relationship.

with the sample moisture content.

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Fig. 9

(a) Resonant frequencies and (b) resonant frequency shifts at different moisture contents.

The second-order PT symmetric wireless sensing system was then investigated referring to the research results of conventional passive wireless sensors. In the corresponding experiments, a completely dried initial sample was placed into the parallel plate capacitor, and the system was brought to the second-order EP via adjusting the distance between the coils. Then, the samples were placed into the capacitor according to different soaking times to obtain the reflection spectrum variation curves shown in Fig. 10. With the increase in perturbation ε, the resonant frequency corresponding to the reflection spectrum appears to be redshifted, i.e., the resonant frequency gradually decreased.

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Fig. 10

Reflection spectra of the second-order PT symmetric wireless sensing system with varying perturbationε.

Figure 11 quantitatively shows the effect of the perturbation on the resonant frequency shift of the system (|f_n − f₀|): (f_n) denotes the dip frequency of the reflection spectrum and (f₀) denotes the initial frequency of the sample. Figure 11(a) shows that as εincreased, the resonant frequency shift became consistent with the theoretical calculation (red curve), conforming to the ε^1/2 relationship. Meanwhile, the frequency shift is more apparent at the early stage of soaking, caused by the significant change in the moisture content inside the sample during this period. With the increase in soaking time, the moisture absorption of the sample decreased. Compared with Figs. 8 and 9, the frequency shift in Fig. 10 is clearer, further indicating that the second-order PT symmetric wireless sensing system is more sensitive than the conventional passive wireless sensing system. Figure 11(b) presents the logarithmic result of Fig. 11(a): Their linear relationship (red solid line) clearly shows a square-root relationship between them.

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Fig. 11

(a) Resonant frequency shifts |f_n − f₀| with varying perturbation ε: the red curve presents the theoretical calculation of ε^1/2; (b) Fig. 11(a) in logarithmic coordinates.

Figure 12 shows the relationship between the sensitivity enhancement factor of the system and the perturbation. From the figure, the sensitivity enhancement factor of the system decreased as perturbation ε increased. Therefore, the smaller the variation in the composition of the test sample in the system, i.e., the smaller the perturbation, the larger the sensitivity enhancement factor of the system and the easier it can be detected.In Yungang Grottoes, the average moisture content of the rock is 4.703% in the upper part of the rock wall, 3.088% in the lower part of the rock wall and 1.181% in the middle part of the rock wall. Therefore, this system can achieve the low moisture content measurement of the rock face³³. This is of great significance for the highly sensitive and fine detection of moisture content in grottoes.

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Fig. 12

Results of sensitivity enhancement factor for second-order PT symmetric wireless sensing system |f_n − f_o|/ε.

Moreover, the experimental tests on the samples confirmed the improved detection sensitivity of the second-order PT symmetric wireless sensing system, which can provide an important technical support for moisture content detection in grottoes. For the second-order PT symmetric wireless sensing system, the dielectric constant is an important parameter: As the dielectric constant of moisture is larger than that of sandstone, moisture is easier to detect in the system.

Meanwhile, we fitted the experimental data of the second-order PT symmetric wireless sensing system for samples with different moisture contents and obtained the fitting curves of moisture content versus resonant frequency, represented by the solid red line in Fig. 13. The fitting function is expressed as:

12

The relationship between moisture content x and resonant frequency y can be obtained using:

13

From Eq. (13), moisture content x of a sample with unknown moisture content in the Yungang Grottoes can be predicted simply via measuring its resonant frequency y using the proposed system.

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Fig. 13

Plot of resonant frequency versus moisture content (the red solid line is the fitting curve).

Comparative analysis of experimental results with drying method

The drying method is widely used as a standard method for moisture content detection due to its relatively stable performance, high measurement accuracy, and easy availability of experimental methods and conditions. To further verify the reliability of this device, the results obtained from the new detection method proposed in this paper were compared with the drying method. For the drying method, the moisture content can be calculated using the following equation:

14

where M₁ is the mass after soaking and M₂ is the mass before soaking. The comparison results are provided in Table 3. It was found that the results of these two methods were basically in agreement with each other, and the absolute error is less than 0.07%, showing good consistency. Further, the second-order PT symmetric passive wireless sensing system can reveal small changes in the moisture content of the samples, thus realising the fine measurement of moisture content of the stone cultural relics. Overall, the second-order PT symmetric passive wireless sensing system can detect the moisture content of stone cultural relics accurately and reliably, and the results have analytical and reference value.

Table 3. Comparison table of second-order PT symmetric system with drying method.

Frequency(MHZ)	Methodology of this experiment	drying method	Absolute error
14.956	1.15%	1.18%	0.03%
14.663	1.68%	1.73%	0.05%
14.591	1.87%	1.89%	0.02%
14.531	2.1%	2.03%	0.07%
14.516	2.17%	2.11%	0.06%

Conclusion

A second-order PT-symmetric wireless sensor system is proposed for moisture content detection in Yungang Grottoes, based on the high sensitivity at the EP point in non-Hermitian systems. When the system is near the second-order EP point, the disturbance amount of different moisture content samples has a 1/2 power relationship with the frequency offset of the system, which improves the detection sensitivity compared with the traditional passive wireless sensors. In addition, after the experimental study of the grotto samples, the fitted relationship between the moisture content in the grotto rocks and the resonance frequency was obtained, and the moisture content of the grottoes can be predicted by using the fitted curves, which provides an important reference for the restoration of the Yungang Grottoes. However, the significance of this method is not limited to this field, but also has great potential applications in food storage, wood processing, environmental monitoring, etc. This study not only provides a new solution for detecting moisture content in the Yungang Grottoes, but also shows the great potential of this sensor in terms of application areas. In the future, the technology can be extended to more fields such as the cosmetics industry to detect the moisture content in products such as creams and lotions to ensure product quality, and research can also be conducted to develop the detection of other contents with moisture content monitoring as the core function.

Author contributions

Author Lina Chen(First Author): Conceptualization, Methodology, Software, Investigation, Formal Analysis, Writing - Original Draft; Author Yuanhong Meng: Data Curation, Writing - Original Draft; Author Yong Sun: Visualization, Investigation; Author Yanhong Liu: Resources, Supervision; Author Fusheng Deng: Software, Validation; Author Xiaoqiang Su: Visualization, Writing -Review& Editing; Author Caixia Feng: Formal analysis, Validation, Software; Author LIjuan Dong (Corresponding Author): Conceptualization, Funding Acquisition, Resources, Supervision, Writing - Review& Editing.All authors reviewed the manuscript.

Data availability

All data generated or analysed during this study are included in this published article .

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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