Introduction

Ancient ceramics are essential pieces of cultural heritage and scientific research that shed light on the evolution of human civilization [1,2,3]. It is imperative to thoroughly examine, meticulously identify, and systematically classify the vast majority of ancient ceramics. For instance, within the esteemed Palace Museum in China, an extensive collection exceeding 100,000 kilns worth of ancient ceramic fragments weighing several tons is housed. Furthermore, during the archaeological excavation of the renowned Yaozhou kiln site, a staggering number of over 1.1 million pieces of fragmented Yaozhou porcelain were unearthed [4]. The identification and classification of a vast number of ancient ceramic fragments pose significant challenges due to their frequent intermingling within kiln fragments, hindering the determination of their porcelain origins. This issue presents obstacles in terms of safeguarding and restoring historical ceramics. In recent years, cutting-edge testing equipment has been extensively employed by scholars to conduct comprehensive studies on the form, color, ornamental design, microstructure, and composition analysis of ancient ceramics [5,6,7]. The identification and preliminary categorization of ancient ceramic fragments can be achieved based on their color, ornamentation, and shape [8,9,10]. The investigation is commonly extended through the utilization of X-ray fluorescence (XRF), X-ray diffraction (XRD), scanning electron microscopy (SEM), optical microscopy (OM), thermoluminescence dating, and other analytical techniques [11,12,13].

The glazing technique of Chinese porcelain originated from the utilization of monochromatic glazes, which consist of distinct chemical components that yield a diverse range of singular colors upon firing. Characterizing fragments from the same kiln with similar appearance, composition, and microstructure using these techniques and tools poses a significant challenge in terms of reliability. In order to address the identification problem of monochrome glazed ceramics in this case, numerous scholars employ time-consuming chemical composition analysis, which exhibits a slow detection speed. Moreover, the composition of ancient ceramics is highly intricate, even for identical pieces of porcelain, different measurement points yield considerable variations [14]. Moreover, machine vision struggles with accurately classifying and distinguishing these monochromatic ceramics due to their strikingly similar appearance.

When sound waves propagate in solids, adjacent particles periodically disturb the particles of the medium, resulting in wave propagation within the solid [15, 16]. The acoustic signal contains abundant data and offers distinct advantages for non-destructive testing. However, the characteristics of sound wave propagation in solids are influenced by physical properties, temperature, pressure, and other factors. Sound waves exhibit higher propagation speeds in rigid solids compared to softer ones [17]. Factors such as internal defects and interfaces significantly influence the propagation of sound waves in solids, giving rise to phenomena like reflection, refraction, scattering, and diffraction. Non-destructive identification of material properties and flaws based on acoustic characteristics is feasible [18]. Scholars have developed various theoretical models to investigate the propagation characteristics of sound waves in solids. These include the widely employed elastic wave propagation model derived from principles of elastic mechanics [19, 20], as well as other models such as the wave equation and transfer matrix that can be utilized for describing sound wave propagation in solids [21, 22]. Acoustic non-destructive testing technology is employed to assess the structural and textural alterations of an object based on the sound spectrum or vibration spectrum emitted by the measured entity under excitation conditions. In our previous investigations, we demonstrated the application of auditory sounds for non-destructive detection and identification of ancient metal coins and ceramics [23, 24].

The present study proposes a non-destructive testing technique for ancient porcelain fragments by utilizing audible frequencies ranging from 20 Hz to 20 kHz. Extensive examination of the acoustic characteristics influenced by the action of acoustic waves on monochrome porcelain fragments reveals that acoustic information can effectively reflect their structural and mechanical properties. The sample is subjected to specific acoustic excitation, and the overall mechanical properties of the sample are measured using a He–Ne laser beam (approximately 2 mm in diameter) from the laser Doppler vibrometer sensor system, instead of local parameters at the measurement point. These acoustic parameters possess characteristics such as high directivity (determinism and uniqueness), high resolution (high precision and sensitivity), and high stability (measurement consistency and non-interference). They reflect the overall health condition of the sample, which cannot be adequately represented by planar or three-dimensional scanning images. This non-contact collection method ensures maximum preservation of the original appearance of cultural relics, making it particularly suitable for capturing comprehensive state parameters of inorganic cultural relics. This finding clarifies the fundamental principles governing the interaction between sound waves and ancient ceramic fragments, providing a completely non-destructive and highly efficient method for classifying and restoring valuable solid cultural heritages like stone, jade, bronze, etc.

Material and methods

Acoustic non-destructive measurement devices

The acoustic non-destructive measuring equipment comprises a computer, laser Doppler vibrometer sensor system (LV-S01, China), and a vibration generator (AV-699BT, China) (Fig. 1a). In this experiment, the audio frequency was directly introduced into the fragments by placing them on the vibration player. The laser vibrometer sensor detected the structural sound transmitted by the ancient ceramic fragments from the opposite side of each fragment. It is important to note that the laser vibrometer sensor exclusively captures vibrations originating from within the ancient ceramic fragments rather than airborne sounds. The acoustic data was analyzed using a computer after being converted into a digital signal by the laser vibrometer sensor system. Subsequently, the recorded audio files are uploaded to the AFMG software for visual comparison of the audio curve in both time and frequency domains, as well as group delay analysis. The detailed parameters of the curve can be downloaded from this software. Additionally, Adobe Audition procedures can be utilized for frequency statistics and music analysis, offering powerful functionality (for more information, please refer to their official website: https://creativecloud.adobe.com/learn/app/audition). Furthermore, MATLAB software is employed for fine feature extraction and audio Fourier transform analysis. Lastly, Origin 2018 was used for data collation and mapping.

Fig. 1
figure 1

Measuring devices and monochrome porcelain samples. a Schematic diagram of device for non-destructive measuring acoustic parameters of ancient ceramics; b Time–frequency waveform diagram of sound source; c Schematic diagram of sound transmission of monochrome porcelain fragments; d SEM image of the fracture of monochrome porcelain fragments; e SEM picture of the middle layer of monochrome porcelain fragments; f The kiln site distribution of monochrome porcelain fragment samples, Y1–Y4 from Yaozhou kiln, H1–H4 from Hutian kiln, L1–L3 from Yue kiln and J1–J4 from Jian kiln. Scale bars, 500 μm (d), 20 μm (e) and 2 cm (f)

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The time domain waveform of the vibration frequency generator is illustrated in Fig. 1b. The vibration frequency generator consists of a sine wave with a logarithmic frequency range from 20 to 20 kHz, comprising approximately 1.6 million audio data points. This sinusoidal excitation signal rapidly sweeps from low to high frequencies over a sample period [25]. The sound absorption coefficient, commonly known as the ability of a substance to absorb sound [26, 27], is depicted in Fig. 1c for ancient ceramics' sound energy situation. Formulas (1) and (2) present the equations for calculating the acoustic loss coefficient (α) and total sound energy (E0) [28].

$$\upalpha = ({\text{E}}_{{\upalpha{1}}} + {\text{E}}_{{\upalpha{2}}} + {\text{E}}_{{\upalpha}3} )/{\text{E}}_{0}$$
(1)
$${\text{E}}_{0} = {\text{E}}_{{\text{r}}} + {\text{E}}_{\upalpha{1}} + {\text{E}}_{\upalpha{2}} + {\text{E}}_{\upalpha{3}} + {\text{E}}_{{\text{t}}}$$
(2)

where, E0 is the total sound energy attached to the material in unit time; Er is the sound energy lost by propagation; Eα1 is the sound energy absorbed by the ancient ceramic glaze layer; Eα2 is the sound energy absorbed by the body of ancient ceramic fragments; Et is the sound energy transmitted through the fragments. The transmission medium for acoustic waves consists of two glazing layers, two bonding layers, and one body layer (Fig. 1d, e). The bonding layer not only binds the body and glaze together but also maintains a balanced composition between them.

Samples

In this study, we selected four kinds of monochrome porcelain fragments as the research subjects (Fig. 1f). Samples L1–L3 represent fragments from Yue kiln in Zhejiang, China. Samples Y1–Y4 consist of fragments from Yaozhou kiln in Shaanxi, China. Samples H1–H4 comprise fragments from Hutian kiln in Jiangxi, China. Lastly, samples J1–J4 encompass fragments from Jian kiln in Fujian, China. All of the monochrome porcelain fragment samples were obtained from historical kilns and underwent thorough cleaning and gentle drying processes. The four kinds of monochrome porcelain samples exhibit variations in terms of their raw material composition and firing conditions due to their origins from geographically distant kilns.

Experimental

The microstructure of monochrome porcelain samples was observed by SEM (S-4800, Japan) and OM (CMM-55 E, China). The ceramic fragments in this experiment were not subjected to any damaging pretreatment. Instead, the surface of the samples was solely cleaned using water and a non-woven cloth, followed by drying and subsequent observation. The utilization of these two testing methods allows for non-destructive observation and evaluation of the microstructures of ceramic samples, making them suitable for analysis in this study.

The following describes how the absorption of sample water is measured. The samples are heated to a temperature between 105 and 110 degrees Celsius for two hours to dry them, after which they are placed in a dryer to cool down to room temperature. The unit exhibits an accuracy of 0.0001 g. Therefore, measure the mass of the samples after they have undergone a one-hour drying process. If the weight difference exceeds 0.0200 g, it is necessary to repeat the drying procedure before conducting measurements. Place the samples in a container separated by a wire frame and immerse them completely in distilled water, subsequently boiling them for three hours. Throughout this boiling process, maintain a liquid level (20 ± 5) mm above the sample surface. Once cooled to room temperature, delicately remove any remaining water from the samples using a cotton cloth soaked in distilled water. Immediately weigh the samples with an accuracy of 0.0001 g.

Results and discussion

Acoustic signal analysis

The frequency domain signals of the vibration frequency generator and the vibration frequency passing through 15 samples are depicted in Fig. 2a, respectively. It is evident that the laser vibrometer sensor captures a potent acoustic wave ranging from 20 Hz to 1.5 kHz. Notably, when the measured sound wave amplitude exceeds 55 dB, it was observed that the samples undergo shaking during experimentation. Substantial vibrations are exhibited by the samples when the measured sound amplitude surpasses 45 dB. In accordance with vibration theory, resonance frequency characterizes how a sample responds to environmental stimulation and manifests large-scale vibrations [29]. In order to mitigate the influence of sample curvature and shape variations on measurement stability, we employed couplings to immobilize the sample and achieve consistent acoustic parameter measurements for the fragments. The efficacy of this approach was previously validated in our study [23]. Under minimal damping conditions, resonance frequency approximates the sample's natural frequency. The sound signals detected by the laser vibrometer sensor exhibit lower power compared to those emitted by the sound source, indicating system losses (Fig. 2b). A pronounced amplitude in time-domain waveform of samples at 2 to 6 s signifies resonance.

Fig. 2
figure 2

Solid sound transmission analysis of audio source, laser pickup points of generator and samples. a Frequency and amplitude characteristics and resonance peak distribution; b Time domain diagram; c Group delay characteristic diagram; d Frequency domain diagram after FFT

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The delay characteristics of this measurement system were analyzed (Fig. 2c). Phase delay measures the time delay of harmonic components, while group delay measures the time delay of an amplitude wave packet [30]. The wave packet signal consists of narrow-band frequency components in the frequency domain and represents the amplitude modulation of an oscillation signal at a specific frequency in the time domain, reflecting the system response. Group delay is defined as the negative derivative of phase with respect to frequency [31]. Essentially, group delay corresponds to the signal obtained from the frequency generator without significant fluctuations (Fig. 2c). When the same signal passes through the samples, they exhibit fluctuations ranging from 20 Hz to 5 kHz. In this case, all samples undergo measurement using the same system, implying that variations in delay amplitude are caused by inherent differences among the samples themselves. This observation suggests that when different samples are measured within a frequency range of 20 Hz to 5 kHz using identical sound sources and measurement systems, distinct group delays will be observed in their acoustic signals.

The time domain information of the samples is subjected to Fourier transform, and the resulting frequency domain representation is presented (Fig. 2b). It can be observed that each sample exhibits distinct peaks in its frequency response curve, with three prominent peaks being identified. Among these highest peaks, the first one corresponds to the fundamental frequency while the peak with maximum amplitude represents the dominant frequency. When a sample undergoes vibration, it typically resonates at multiple frequencies rather than just one specific frequency. The dominant frequency may correspond to either the natural or forced response frequency [32]. Notably, resonance does not occur solely at a single frequency (i.e., natural frequency), but within a certain bandwidth known as the resonant band. Within this range of resonance, ancient ceramic fragments exhibit varying degrees of resonance. Subsequently, a tuning fork with a natural frequency range of 512 Hz is employed for measurement purposes. The resonance frequencies of this tuning fork are measured ten times and an average value of 511.2 Hz is obtained. Consequently, the average precision of this testing system is calculated as: η = 511.2/ 512 = 99.84%.

Resonance frequency and displacement

The time–frequency diagram of a sound source illustrates the frequency values corresponding to different time points (Fig. 3a). To investigate the underlying cause of sample resonance, we conducted an analysis on the displacement acceleration in the x, y, and z directions during testing (Fig. 3b). It is evident that the sample exhibits significant displacement acceleration along the z-axis, while across all three axes (x, y, and z), the duration for generating such acceleration ranges from approximately 2 to 6 s.

Fig. 3
figure 3

Acceleration, displacement and resonance characteristics of monochrome porcelain fragment samples during measurement. a Time–frequency variation curve of sound source; b The displacement acceleration of samples in X, Y and Z directions during the measurement period; c The frequency spectrum diagram of sound source and samples

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The frequency spectrum of the sound source and 15 samples (Fig. 3c) reveal a prominent dominant frequency represented by a bright line, accompanied by multiple brighter lines above it. These lines correspond to pure tones with frequencies that are either integral multiples or non-integral multiples greater than one of the fundamental frequencies, known as "overtones". Additionally, harmonics refer to those frequencies that are integer multiples of the fundamental frequency. However, most of these fundamental tones and overtones appear to be attenuated in the spectral frequencies observed in the 15 samples, which aligns with the patterns depicted in Fig. 1a–c. Notably, between 2 and 6 s, there is a significant increase in sound wave transmission through the sample concentrated within the range of 20 Hz–1.5 kHz. This resonance region exhibits maximum sound wave penetration and displays numerous resonance frequency lines distributed above the dominant frequency. When exciting the sample at frequencies close to its natural resonant frequencies, there is a noticeable amplification in amplitude. At the same time, when the frequency of the incident sound wave equals the natural vibration frequency of the sample, sound energy is more easily transmitted through it. This results in a significant reduction in sound insulation. This also explains Fig. 2a, b where laser vibrometer sensor collected stronger sound waves at frequencies between 20 Hz–1.5 kHz due to resonance caused by some frequencies of the sound source being identical to that of sample's vibration frequency [33].

Acoustic loss and characteristic parameters

The appearance and microstructure of ancient ceramics were examined to analyze the influencing factors on the elastic modulus index and sound insulation index in different kiln sites. The matrix of ancient ceramics consists of crystal, gas, and glass phases, with a glaze layer attached to the body surface to eliminate any surface defects (Fig. 4a). The glaze in ceramic fragments is predominantly composed of numerous glass phases, forming a glass layer that serves multiple functions such as interfacial bonding, pore filling, reduction in firing temperature, and densification of the body.

Fig. 4
figure 4

Microstructure of monochrome porcelain samples L1, J1, H1 and Y1. a Cross-sectional photos and structural diagrams of four samples; b–e Microscopic photos of the glaze of four samples; (f–i) SEM photos of four samples of green glaze. Scale bars, 4 mm (a), 500 μm (b–e), 100 μm (f), 200 μm (g-glaze), 20 μm (g-body), 5 μm (h-glaze), 50 μm (h-body) 4 μm (i-glaze) and 200 μm (i-body)

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The micrographs and SEM images of samples L1, J1, H1, and Y1 are shown in Fig. 5a–i. It can be observed that all samples have pores in their bodies, but the shape, distribution, quantity, and size of the pores vary. There are cracks, holes, and some unmelted mineral particles on the outer glaze of L1 (Fig. 4b). The glaze of sample L1 is too thin which leads to holes exposing a small amount of the green body. Oval bubbles can be seen in the body with sizes ranging from approximately 60 μm to 121 μm (Fig. 4f). A small amount of mullite crystals can be observed on the glaze surface of J1 which has a metallic luster (Fig. 4c). The pores in the body of J1 are irregular-shaped holes (Fig. 4g), possibly caused by calcination before glazing. The glaze surface of H1 is flat and uniform with some residual quartz particles visible on it (Fig. 4d). The bubbles in the body are round with sizes ranging from approximately 36 to 118 μm (Fig. 4h). The glaze surface of Y1 exhibits anorthite crystallization and residual quartz phenocrysts, as observed in Fig. 4e. Additionally, the bubbles present in the ceramic body are predominantly round in shape (Fig. 4i). Several factors contribute to the formation of round or oval bubbles within the sample, including excessively high firing temperatures, rapid temperature increases during firing, or unsuitable kiln atmospheres. At elevated temperatures, when a liquid phase is formed, it becomes challenging for gas to escape resulting in the development of closed pores with an oval morphology within the ceramic material. If these pores are caused by secondary crystallization processes, they tend to be primarily wrapped around phenocrysts. Based on our observations, it is evident that variations in composition and sintering temperatures among samples from different kiln sites lead to differences in bubble sizes and quantities. The order of open pore abundance across sample cross-sections follows H1 < Y1 < L1 < J1.

Fig. 5
figure 5

Sound transmission analysis of monochrome porcelain fragments. a Sound transmission and resonance. b Frequency amplitude attenuation curves of sound source and samples L1, Y1, H1 and J1. c The acoustic loss coefficient of sampls and vibration frequency generator. d The changing trend of elastic coefficient of samples. e The relationship between Eli (elastic modulus index) and Δαi (sound loss index) of samples at the three strongest resonance peak frequencies, and that of samples at 20 Hz–20 kHz. f Histograms of water absorption, porosity and bulk density of samples

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Figure 5a depicts a schematic diagram illustrating the simultaneous propagation and resonance of acoustic energy during the measurement process of ceramic fragments, and x, y, and z are the acoustic energy transmission parameters of the sample in the three directions of the polar axis, respectively. The velocity of sound energy passing through the sample at time t is \(\overrightarrow{U}(x, y,z,t)\), which can be written as \(\overrightarrow{U}(x, y,z,t)\)= \(\overrightarrow{U}\) x (x, y, z, t) \(\overrightarrow{i}\) +\(\overrightarrow{U}\) y (x, y, z, t) \(\overrightarrow{j}\)+\(\overrightarrow{U}\) z (x, y, z, t) \(\overrightarrow{k}\) in cartesian coordinate system. When the density of the sample is ρ(x, y, z, t), the mass flow density of the sample is: ρ \(\overrightarrow{U}\)= (ρ \(\overrightarrow{U}\) x \(\overrightarrow{i}\), ρ \(\overrightarrow{U}\) x \(\overrightarrow{j}\), ρ \(\overrightarrow{U}\) x \(\overrightarrow{k}\)), it can be seen that the mass of the medium per unit area passing through the samples in unit time and perpendicular to the flow rate \(\overrightarrow{U}\) is:

$$\Delta {\text{m}}= { }\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \bigcirc}\nolimits_{s} {\left( {\uprho \vec{U}x \vec{i},\uprho \vec{U}x \vec{j}, \uprho \vec{U}x \vec{k}} \right)} \cdot {\text{d}}\vec{s}$$
(3)

where d is the thickness of the samples, and \(\overrightarrow{s}\) is the closed area in the direction of the outer normal of the samples. It is worth noting that the sound loss index of a sample is calculated by dividing the amount of sound loss by its Δm and thickness. The formula can be expressed as follows:

$$\Delta \upalpha _{{\text{i}}} = \upalpha _{{\text{i}}} /{\text{d}}\cdot\Delta {\text{m}}\quad {\text{i}} = {1},{ 2},{ 3} \ldots$$
(4)

where Δαi is the sound loss index, αi is the amount of sound loss and Δm is the mass of medium per unit area passing through the sample per unit time and perpendicular to the flow rate \(\overrightarrow{U}\). Here, the structure factors influencing sound loss in ceramic samples are considered to be Δm and thickness. The sample's thickness refers to the distance between the vibration frequency generator and the laser point, wherein a greater distance leads to increased heat loss of sound within the solid material. By normalizing the amount of sound loss with respect to Δm and thickness, Δαi can be obtained as a more accurate reflection of the acoustic properties exhibited by ancient ceramics.

The attenuation of the sound source after passing through samples L1, Y1, H1, and J1 is shown (Fig. 5b). Among them, the amplitude of the sound source at the dominant frequency of 215 Hz is as follows: sound source > Y1 > L1 > J1 > H1. When a sound wave propagates in a solid, part of the mechanical energy will be converted into thermal energy, including thermoelastic loss, heat flow loss between grains, and grain scattering loss [34]. It can be observed that bubble size and sound transmission loss have little influence on ceramics (Figs. 4, 5b, c). However, the higher the opening rate is, the greater the sound transmission loss of the samples becomes; however, sample H1 does not conform to this law due to its first formant being at 400 Hz which is about twice that of other samples. When other samples resonate at 215 Hz, H1 has not yet reached resonance. The sound energy gradually decreases during the process of sound transmission, and the ratio of the sound loss during transmission to the original sound energy is called the sound loss coefficient (α). The curves of the sound loss coefficient for the vibration frequency generator and 15 samples are shown in Fig. 5c according to calculation results from formula (1). Then, the theoretical calculation formula for resonance frequency is as follows:

$${\text{ fi = 2}}\uppi \sqrt {\frac{{{\text{Ei}}}}{{\text{m}}}} {\text{ i = 1, 2, 3}} \ldots$$
(5)

where fi is the resonant frequency of the sample, m is the mass of the sample, and Ei is the elastic modulus of the sample. The resonance frequency of a material is influenced by two factors: mass and elastic modulus. The elastic modulus of ceramics is determined by inherent properties such as size and material composition. Furthermore, variations in the raw materials used in ancient ceramics lead to differences in their material properties, including density, elastic modulus, and quality [35]. The elastic modulus of ancient ceramics is dependent on the type, particle size distribution, proportion, and porosity of the constituent phases. Consequently, calculating the theoretical elastic modulus for these complex multiphase ceramic materials with significantly different moduli for each phase poses a challenge. Porosity plays a crucial role in ceramic formation and sintering processes while also affecting the decrease in elastic modulus of ancient ceramics according to formula (6).

$${\text{E = E}}_{{0}} \left( {{1}{-}{1}{\text{.9P + 0}}{\text{.9P}}^{{2}} } \right)$$
(6)

where E0 is the elastic modulus when the porosity is zero; the1.9 and 0.9 are constants determined by the shape of the pores, and the P is the porosity. The value of Ei in Eq. (5) is substituted with E0 and incorporated into Eq. (6), resulting in the derivation of Eq. (7) for closed pores within a continuous matrix.

$${\text{EI}}_{{\text{i}}} {\text{ = m (2}}\uppi {\text{f}}_{{\text{i}}} {)}^{{2}} \left( {{1}{-}{1}{\text{.9P + 0}}{\text{.9P}}^{{2}} } \right){\text{ i = 1, 2, 3}} \ldots$$
(7)

Where EIi is the elastic modulus index of samples, and is a characteristic parameter calculated according to resonance frequency. It is utilized for comparing the relative elastic modulus of ancient ceramics. The distribution of elastic modulus index corresponding to the three characteristic formants is illustrated (Fig. 5d). The water absorption rate, porosity, bulk density, mass, and thickness of the samples are presented (Fig. 5f). It can be observed that with an increase in the porosity of ancient ceramics, there is a decrease in both bulk density and elastic modulus.

The factors influencing the sound attenuation of solid materials encompass the heat dissipation of sound waves within the solid, intergranular heat dissipation, and scattering loss among grains [36]. As depicted in Fig. 5e, the correlation between the sound attenuation index and elastic modulus index is examined at three resonance frequencies, along with the relationship between total sound attenuation index and elastic modulus index across a frequency range of 20 Hz to 20 kHz. The overall trend in variations observed for both elastic modulus index and sound attenuation index among samples from different kilns aligns consistently with that of the three resonance peaks. Furthermore, it is evident that the elastic modulus index of all samples decreases as the sound loss index increases. This observation suggests that ancient ceramic fragments with higher elastic modulus exhibit lower sound loss and superior sound transmission efficiency. Notably, the four types of ceramics display remarkable similarity in this regard. Although this measurement method may not be sufficient to differentiate between different types of ancient ceramics, it proves highly accurate in discerning subtle variations within the same type. For instance, it can be observed that samples L1-L3 belong to the ancient Yue kiln category; however, when compared to L3, both L1 and L2 demonstrate noticeably closer proximity in terms of elastic modulus and sound loss. Based on experimental results encompassing water absorption, bulk density, porosity, and resonance frequencies analysis; sample L1 and L2 exhibit significant similarities while sample L3 from Yue kiln exhibits distinct differences from both L1 and L2 counterparts. Detailed data for all samples are presented in Table 1.

Table 1 Basic physical properties of ancient ceramic samples
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Verification results of modern samples

In order to further analyze the aforementioned results, we conducted experiments using four Yaozhou porcelain samples (MY1–MY4) and four Jian porcelain samples (MJ1–MJ4), all of which had identical size and composition. The firing temperature for MY1, MY2, MJ1, and MJ2 was set at 1200 degrees Celsius, while the firing temperature for MY3, MY4, MJ3, and MJ4 was set at 1300 degrees Celsius (Fig. 6a). Variations in sintering temperatures result in different porosity levels in ancient ceramics. Higher firing temperatures lead to increased density without causing over-firing. Through testing and analysis, it was observed that samples fired at 1300 degrees Celsius exhibited higher density with fewer bubbles formed. Detailed information about the samples can be found in Table 2. Additionally, our test also included three glass samples (Glass1–Glass3) as well as three glass bowl samples (Bowl1–Bowl3) (Fig. 6b).

Fig. 6
figure 6

Acoustic analysis of modern ceramic and glass samples. a The firing system diagram and physical photos of samples MY1–4 and MJ1–4. b Physical photos of glass samples Glass 1–3 and Bowl 1–3. c Amplitude-frequency curve of samples. d The relationship between Eli (elastic modulus index) and Δαi (sound loss index) of samples at the three strongest resonance peak frequencies. e Acoustic classification model for ceramics. Scale bars, 2 cm (a), 2 cm (b) and 3 cm (e)

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Table 2 Basic physical properties of modern ceramic samples
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The frequency-amplitude curves of each sample were obtained, and the peaks of the three highest formants were identified (Fig. 6c). Subsequently, the acoustic loss index and elastic modulus index at these three formants were calculated for each sample using formula (5) and (6), respectively (Fig. 6d). The elastic modulus of Glass1-Glass3 was measured to be approximately 2.2 × 104 MPa. Notably, the elastic modulus index derived from the first formant closely approximates the actual value of glass elastic modulus, enabling more accurate classification of ancient ceramic fragments based on EI1 calculated from this particular formant. Furthermore, a clear relationship between EI1 and Δα1 can be observed in Fig. 6d, indicating that samples with identical shape and size made from similar raw materials exhibit comparable elastic moduli when fired at the same temperature. Specifically, samples MY demonstrate slightly lower elastic moduli compared to samples MJ at equivalent firing temperatures—a trend consistent with Yaozhou and Jian kiln fragments as shown in Fig. 4e, f respectively. The glass products represented by Glass1–Glass3 and Bowl1–Bowl3 exhibit similar elastic moduli; however, Bowl1–Bowl3 demonstrates higher sound loss due to its curved shape, which hinders complete fitting onto the vibrating surface of the player.

Classification model for ceramic fragments

To improve the accuracy of classifying the origin kiln of an unknown ceramic fragment, we have established a comprehensive voiceprint database specifically designed for ceramic fragments. The key discriminant parameters utilized in this study were the EIi (elastic modulus index) and Δαi (sound loss index). A total of 228 ancient samples from Jian kiln, Yaozhou kiln, Hutian kiln, and Yue kiln underwent acoustic data collection and feature data labeling. Based on EasyDL platform, we successfully developed a classification model and an extensive database dedicated to identifying the origin kilns of ceramics (Fig. 6e). The EasyDL sound classification model is a deep learning-based model that can recognize specific features of ceramic fragments during the vibration process and classify them [23, 24]. The EasyDL SDK (Software Development Kit) provides interfaces in multiple programming languages, including Python, enabling developers to seamlessly integrate their applications. Firstly, it is essential to preprocess and convert the dataset into a format compatible with EasyDL. Then, leverage the provided EasyDL API to establish a project, upload the dataset for model training, and subsequently deploy it.

When faced with ceramic fragments originating from an unidentified kiln, this model possesses the capability to determine the specific kiln to which the fragments belong and even compare unfamiliar samples against those present in the database. It utilizes key distinguishing parameters such as EIi and Δαi to preliminarily assess whether the composition and firing system of the unknown sample align with existing data within the database. Taking an unrecorded fragment as an example, discriminant analysis was employed to demonstrate that the system achieves a classification accuracy of no less than 95% for firing samples with identical components and firing temperature (Fig. 6e). This determination aligns with the actual kiln site from which this sample was excavated. Due to the limited sample size in the database of the ceramic kiln classification model, it is imperative to gradually adjust the discriminant parameters through deep learning on a larger dataset in order to enhance the accuracy of this discrimination method for recognizing and classifying a substantial number of samples.

Conclusions

This acoustic classification method enables a more precise assessment of the acoustic and mechanical characteristics of ancient ceramics, rendering it better suited for the comprehensive classification and detection of monochrome porcelain fragments, particularly those that pose challenges in discernment and categorization using human or machine vision. The acoustic properties determined through this method reveal the interplay between resonance frequency, elastic modulus, and acoustic loss in ancient ceramics. Furthermore, it aids in identifying similarities in material composition, components, and firing temperature among monochrome porcelain fragments. These mechanical and acoustic properties are closely linked to the composition, structure, and manufacturing processes of ancient ceramics. As a result, this method can help researcher to determine if these monochrome porcelain fragments came from the same kiln site or were fired using similar techniques within a shared furnace. The correlation between sound loss and elastic modulus was also investigated for performance analysis and categorization purposes. By extracting acoustic features from ceramic fragments, the establishment of a sound classification model for ceramic fragments can provide a fundamental assessment for unidentified ceramic fragments.

Simultaneously, this study proposes appropriate calculation techniques for the elastic modulus index and sound loss index of ancient ceramics. The non-destructive and efficient technology for detecting acoustic characteristics of monochrome porcelain fragments presented in this work clarifies the fundamental principles governing the interaction between sound waves and ancient ceramic fragments, providing a completely non-destructive and highly efficient method for classifying and restoring valuable solid cultural heritages like stone, jade, bronze, etc. Moreover, this technique can be applied to assess the elastic modulus of advanced ceramics without causing any damage, enabling identification of minor cracks, wear, aging, and other flaws in advanced ceramic devices.