A Quantitative Monitoring Study of Environmental Factors Activating Caihua and Wooden Heritage Cracks in the Palace Museum, Beijing, China

Abstract

Cultural heritage objects, including traditional Chinese polychrome paintings on architectures (Caihua) and wooden architectural components, frequently exhibit surface defects that are highly sensitive to environmental factors, resulting in progressive deterioration. However, due to limited data acquisition methods and quantitative analysis models, the stability and risks of defects such as cracks during environmental changes remain unclear. This study integrates photogrammetry and digital image processing to investigate through-cracks and craquelures on the surface of a well pavilion within the Palace Museum, Beijing. We confirmed the activity of these cracks, quantified crack widths, and studied the environmental influences on their development. Over a monitoring period of more than 15 months, the widths of seven cracks on four beams were measured alongside various environmental factors. Correlation analyses identified air humidity as the most significant factor influencing crack width fluctuations (p < 0.01). Numerical simulations revealed that short-term humidity exposure induces surface swelling and crack closure, whereas prolonged humidity leads to internal moisture transport and crack reopening. Furthermore, fitting parameters indicating the severity of crack variation correlated well with the degradation levels of the wooden components. In summary, this study establishes a monitoring and quantification procedure for assessing crack activity, explores the influence of humidity through numerical simulations, and identifies a potential indicator for the non-destructive assessment of timber component stability. The proposed framework offers an exploratory approach to addressing critical challenges in the health monitoring of wooden architectural components.

1. Introduction

The Palace Museum (also known as the Forbidden City), a UNESCO World Heritage Site, is the world’s largest and most intact ensemble of ancient imperial palace architecture, with a history spanning over five centuries. Its wooden structural components are adorned with traditional Chinese polychrome paintings known as “Caihua” [1,2], which hold not only artistic but also profound cultural and social value. These paintings delineate social hierarchies, underscore ethical values, and contribute to the study of ancient craftsmanship techniques.

Over time, the Caihua and the wooden substrates have experienced deterioration, manifesting as wood cracks and paint craquelure. While some cracks remain stable [3] and do not require immediate intervention, others deteriorate further under fluctuating environmental conditions, compromising both aesthetic and structural integrity.

Defects in historical buildings should be closely monitored as they often signify stress concentration or water intrusion, potentially leading to further damage. Monitoring these defects is crucial for ensuring component safety and structural health, as well as for determining the optimal timing for repairs and maintenance. Premature interventions risk excessive human interference, which may damage historical information [4], while delayed restoration increases costs and introduces uncertainty in outcomes [5]. Consequently, conservators require robust health monitoring frameworks to track defect evolution and predict structural responses to environmental stimuli [6].

Current methodologies for heritage monitoring prioritize non-destructive, in situ techniques to minimize physical interference. Techniques such as close-range photogrammetry [7], digital total stations [8,9], fiber optic sensing [10], acoustic emission [11], remote sensing, infrared thermography [12], crowdsourced imagery [13], and machine vision have been applied to the health monitoring of heritage structures. Machine vision, in particular, excels in swiftly locating [14] or segmenting [15] damaged areas on heritage structures, making it highly suitable for such scenarios.

Despite advancements, critical gaps persist, particularly in data acquisition and the identification of sensitive damage indicators. Many studies have focused on recognizing cracks in heritage structures [16], while few have quantitatively analyzed cracks or developed corresponding models. Existing studies assessing wood crack severity using machine vision rely on simplistic classifications [17] which are insufficient for studying crack mechanisms and predicting failure risks.

This study aims to quantify and monitor surface cracks on wooden components and Caihua, investigate the responses of heritage structural components to environmental factors, and explore the underlying mechanisms. To achieve these objectives, we developed and applied a method combining photogrammetry, digital image processing, and crack quantification at the Palace Museum. Correlation analyses between crack width and environmental factors were conducted, and numerical simulations were employed to study crack mechanisms. The results contribute to a deeper understanding of relic degradation mechanisms, while the methodologies provide valuable insights for future studies on structural health monitoring in cultural heritage.

2. Materials and Methods

2.1. Monitoring Target

The study focused on painted wooden components within the Dapaojing Well Pavilion, located in the Chuan Xin Dian area of the Palace Museum’s southeastern sector (Figure 1). The Dapaojing Well Pavilion is the largest of its kind in the Palace Museum and serves as the site for the annual worship of the God of the Wells in the lunar month of October [18,19]. According to the records in the Palace Museum archives and on-site observations, the building was constructed using pine wood.

2.2. Camera Relocation

Images were obtained from the lower surfaces of the northern and southern beams (LS-N and LS-S) and the inward surfaces of the eastern and western beams (IS-E and IS-W), as shown in Figure 1. To minimize differences caused by camera relocation errors, a workflow for photo acquisition and processing was established, similar to Yue’s [20] camera relocation method.

First, the same instruments were used throughout the monitoring, including a camera (Canon EOS R5), lenses (RF24-105mm F4L IS USM), and supporting equipment such as tripods.

Second, the locations of the tripod feet and the plane position of the tripod head were recorded using retro-reflective targets on the ground, and the spatial position consistency of the camera was kept by ruler, plumb line, bubble level gauges, and records of tripod feet lengths.

Third, the camera’s gridline function was used during photography, aligning three or more gridline intersections with characteristic points of the paintings to maintain the camera’s angle.

2.3. Image Registration and Crack Quantification

Digital image processing methods were used to further reduce variances in image acquisition. Image registration was performed using the “Load the file onto the stack” function in Adobe Photoshop 2021 to align sequential images and compensate for minor camera positional variations during monitoring. Seven portions of crack images were extracted from the paintings, including five through-cracks and two craquelures located on the northern and southern beams, as shown in Figure 2. Histogram normalization was applied to minimize the influence of lighting conditions using the “imhistmatch” function on the MATLAB R2023a platform.

Crack identification and quantification were performed using the specialized software CIAS (Crack Image Analysis System) [21] on the MATLAB platform. Given the distinct contrast between cracks and surrounding areas, multiple methods—including the Otsu thresholding, edge detection operators, and neural networks—proved effective for crack identification. The advantage of CIAS is its ability to provide quantitative parameters such as width, length, area, fractal dimension, and intersection count of cracks after identification. Dark patches occasionally present in the photographs were manually removed prior to analysis.

To examine the influence of environmental factors on crack width, the average width of each crack (W_n) at each monitoring occasion (ordinal number n = 1, 2, …, 17) was divided by W_average, the overall average width for each crack (mean value of W_n):

$$R{W}_n={\displaystyle \frac{W_n}{W_{average}}}$$

(1)

Here, RW_n represents the relative average crack width at each monitoring occasion.

2.4. Environment Monitoring

Air temperature and humidity data were sourced from the Palace Museum’s micro-weather station located 4 m from the pavilion. Illuminance, surface temperature, and moisture content (MC) at the target area were measured simultaneously using a Testo 540 (Testo, Titisee-Neustadt, Germany), a Delixi infrared thermometer (Delixi, Yueqing, China), and a Testo 606-1 moisture meter (Testo, Titisee-Neustadt, Germany), respectively.

The monitoring spanned 15 months, with each monitoring point acquiring 15–17 data sets. Correlation analysis was performed using IBM SPSS Statistics 27, and curve fitting was conducted using Origin 2021.

2.5. Numerical Simulations

Numerical simulations were conducted to study the response of wooden cracks to environmental humidity fluctuations. The simulations were performed using COMSOL Multiphysics version 6.1 on a Windows platform with an Intel Core i7-12700KF (3.61 GHz).

To simplify the calculation, two study steps were used. The first step was a transient simulation. The “Transport of Diluted Species” interface in COMSOL modeled the time-dependent moisture transfer from the wood surface to its interior. The second step was a stationary simulation. The “Solid Mechanics” interface and the “Hygroscopic Swelling” multiphysics coupling node in COMSOL calculated material swelling at each time point.

Model geometry: A rectangular prism with dimensions of 1000 × 150 × 200 mm was modeled, with the top surface and both ends fixed. An ellipsoid with dimensions of 180 × 2 × 0.4 mm was simulated at the center of the front surface. Using the difference between the ellipsoid and the rectangular prism, a crack 0.4 mm wide on a beam was modeled. Given that the beam surface is covered with paintings hindering moisture absorption, the moisture absorption of wood was assumed to be restricted to the inner surface of the crack and the crack edge within 1.2 mm. Due to symmetry, only the right half of the model was calculated.

Humidity Rise Procedure: Environmental humidity was simulated to increase from 10% RH to 95% RH over a certain period, then maintained at 95% RH. The moisture content at the surface (C_surf) was assumed to equilibrate immediately with RH, eliminating the need to calculate moisture transfer from air to the wood surface. RH variation was simulated by assigning a specific C_surf variation, calculated using a literature-derived empirical relationship [22]:

$$RH=112.65+{\displaystyle \frac{1.4790-112.65}{1+{\left(\frac{C_{surf}}{2261.6}\right)}^{1.9406}}}$$

(2)

Here, RH is expressed as a percentage, and C_surf is in units of mol m⁻³. Based on local environmental humidity records, the moisture absorption rate was set to increase from 0.01 mol m³ s⁻¹ to 0.09 mol m³ s⁻¹, as detailed in Table S1 (Supplementary Material).

Moisture transportation: As RH and time changed, moisture diffused from the inner wall of the crack and hygroscopic areas on the wood surface towards the interior. The diffusion coefficient of water in peach wood was set to 2 × 10⁻¹⁰ m² s⁻¹ [23,24]. This coefficient was assumed to be isotropic.

Hygroscopic Swelling: The hygroscopic swelling coefficients were set to 1.230 × 10⁻³ m³/kg in the longitudinal direction (the longest edge of the beam) and 2.201 × 10⁻³ m³/kg in the tangential direction, derived from pine swelling curves reported by Nopens et al. [22].

Due to strict restrictions on sampling cultural heritage wood, this study relied on literature values and empirical estimates for material parameters. While the calculated results may deviate in specific values, they are expected to reflect the general trends of crack behavior in the wooden components of the Dapaojing Well Pavilion.

3. Results

3.1. Crack Activity

Enlarged photographs (Figure 3) revealed cyclic opening and closure of each through-crack, whereas variations in craquelures were not directly visible. During the monitoring period, the maximum crack widths (W_n) remained below 0.51 mm. The overall average crack widths (W_average) at each monitoring point ranged from 0.108 to 0.364 mm, with standard deviations ranging from 0.006 to 0.075 mm. These relatively small widths made crack activity difficult to detect, which likely explains why they had not been studied previously.

Notably, changes in crack width showed no significant correlation with time during the monitoring period, indicating that the wooden components and polychrome paintings in the Palace Museum remained relatively stable over the observation period.

3.2. Correlation Between Monitored Variables and Crack Width

Processed photographs of cracks and their masks are available on Mendeley Data (https://doi.org/10.17632/3x3hwrpd9f.1). Records of crack width and monitored variables are listed in the Supplementary Material (Table S2).

The relative average crack width (RW_n) was treated as the dependent variable, while monitored data—including air temperature, humidity, surface temperature, wood moisture content, date, and illuminance—were treated as independent variables. Correlation analysis (

Table 1. Results of correlation analysis using Kendall’s Tau-b. Various variables are listed as Parameter I and II. The significance of the correlation coefficient is calculated.

Parameter I		RH		RWn of Major Crack			RWn of Minor Crack/Craquelure
Parameter II		MC	Tair	Tair	RH	MC	Tair	RH	MC	RWn of Major Crack
IS-E	Correlation Coefficient	0.571 *	0.333	−0.317	−0.617 **	−0.429	\	\	\	\
	Significance	0.048	0.072	0.087	0.001	0.138	\	\	\	\
	N	8	16	16	16	8	\	\	\	\
IS-W	Correlation Coefficient	0.704 **	0.362 *	−0.324	−0.627 **	−0.611 *	−0.250	−0.613 **	−0.667 *	0.750 **
	Significance	0.009	0.043	0.070	<0.001	0.022	0.161	<0.001	0.012	<0.001
	N	9	17	17	17	9	17	17	9	17
LS-S	Correlation Coefficient	0.733 *	0.364	−0.402 *	−0.581 **	−0.733 **	−0.110	−0.543 **	−0.333	0.505 **
	Significance	0.039	0.060	0.037	0.003	0.039	0.584	0.005	0.348	0.009
	N	6	15	15	15	6	14	15	6	15
LS-N	Correlation Coefficient	0.689 **	0.295	−0.067	−0.657 **	−0.511 *	0.143	0.143	−0.222	−0.276
	Significance	0.006	0.125	0.729	<0.001	0.040	0.477	0.477	0.404	0.444
	N	10	15	15	15	10	14	14	9	6

* The correlation was significant at level 0.05 (two-tailed). ** The correlation was significant at level 0.01 (two-tailed).

) revealed significant negative correlations between relative humidity (RH) and crack width (p < 0.01) for nearly all observed cracks, underscoring the pivotal role of humidity in crack variation. An exception was LS-N-craquelure, which showed no significant correlation.

Notably, the correlation between wood moisture content and crack width was less pronounced, likely due to the limitations in the precision of the moisture meter used in this study.

The relationship between through-crack width and air temperature (T_air) showed statistical significance only at the southern monitoring point (LS-S-Major), with a p-value of 0.05. In contrast, the significance levels for crack widths at the eastern, western, and northern monitoring points were 0.087, 0.070, and 0.72, respectively. Interestingly, the correlation coefficient between crack width and relative humidity was smallest at the southern monitoring point and largest at the northern point, indicating that the north beam exhibited greater variation in response to RH changes. This suggests that the influence of temperature on crack width may be overshadowed by the more substantial variations induced by humidity.

The behavior of craquelures and minor cracks varied inconsistently. On the western and southern beams, they showed a strong correlation with RH and nearby major cracks, following a pattern similar to that of through-cracks. However, the LS-N-craquelures displayed no significant association with any monitored variables. It is hypothesized that the southern craquelures’ variations are caused by internal wood cracks.

Additionally, correlations between other parameters, including surface temperature, illuminance, time, and average crack width, were found to be insignificant.

In summary, the swelling and shrinkage of wood primarily influenced crack width. Six out of the seven monitored cracks exhibited regular cyclic opening and closing patterns during the monitoring period, with the exception of LS-N-Minor. Relative humidity emerged as the most influential factor affecting crack variation, while temperature showed a limited impact.

3.3. Linear Fitting of Humidity and Relative Crack Width

The relationship between relative crack width and humidity at six monitoring points is illustrated in Figure 4. As humidity increased, crack widths generally decreased. Notably, two data points in June (highlighted by purple points in Figure 4) are often significant outliers and lie above the fitted curve. Excluding these anomalous points improved the R² values of the linear fit by approximately 0.1 for all beams except LS-N-Major. After excluding these points, the R² values ranged from 0.693 to 0.763, as shown in

Table 2. Influence of prolonged rain on data fitting quality.

		Linear Fit R2
Data in June		Included	Excluded
Crack	LS-S-Major	0.5797	0.6932
	IS-E	0.6344	0.7626
	IS-W-Major	0.6311	0.7574
	IS-W-Minor	0.6907	0.7322
	LS-N-Major	0.7730	0.7160
Craquelure	LS-S-Craquelure	0.5871	0.7071

and Figure 4.

Meteorological records revealed a key characteristic of these outlier points: they were recorded on a cloudy day, followed by more than four consecutive days of rainfall. While Beijing typically experiences dry weather throughout most of the year, summer rainfall can result in prolonged periods of high humidity. Under these conditions, the wood may experience full swelling due to extended exposure to moisture, leading to the anomalous measurements observed.

4. Discussion

4.1. Simulation of Crack Width Variation

It was observed that higher air humidity causes wood to swell due to moisture absorption, leading to a decrease in crack width. However, prolonged exposure to high humidity can result in a slight increase in crack width. This phenomenon is explained through numerical simulations of the moisture absorption process in the wood substrate.

As illustrated in Figure 5b,c, during the initial stages of moisture absorption, swelling occurs predominantly on the wood’s surface due to the limited rate of humidity diffusion into the interior. This surface swelling causes vertical deformation around the crack and closes it. When the humidity approaches saturation and stops increasing, surface swelling slows while moisture absorption within the wood becomes more prominent. The resulting horizontal swelling displaces the crack from its original position, causing bulging and an increase in the crack’s opening width, as depicted in Figure 5d. This dynamic process is shown in the Supplementary Material (Figure S1).

Consequently, in a high-humidity environment, cracks initially close and subsequently reopen after prolonged exposure (Figure 5a). This explains why crack widths increase following extended periods of rainfall. The calculated range of crack width variation is 0.3 ± 0.1 mm, which aligns well with the observations of the LS-N-Major crack.

4.2. Indicators for Timber Degradation

The natural aging of wood typically reduces its elastic modulus and increases its moisture absorption capacity [25]. To simulate aged wood, key parameters, including equilibrium moisture content, hygroscopic swelling coefficient, and diffusion coefficient, were proportionally increased, whereas the elastic modulus was reduced. Due to the absence of specific data, these parameters were uniformly adjusted by 10% and 20%, allowing the simulations to reflect general trends rather than precise values.

The results indicate that as the degree of wood aging increases, the range of crack width variation also expands (Figure 5a), suggesting that aged wood exhibits more dramatic crack width changes under identical relative humidity conditions.

Based on on-site surveys, the degradation degree of the four wooden beams was ranked as northern > western > eastern > southern. This ranking was deduced from moisture content and total crack length, as aged wood tends to exhibit more surface defects and greater moisture absorption. The ranking also corresponds to the preservation environment: southern components, exposed to sunlight, are best preserved; eastern components are shielded by trees and walls, reducing precipitation exposure compared to western components. This study proposes a quantitative indicator to reflect the aging degree of wooden components.

The first indicator, derived from the linear fitting results of through-cracks, is the absolute value of the slope (│b│), as shown in

Table 3. Fitting parameters as indicators for timber degradation degree.

Fitting Parameter		Sigmoid p	Linear b (10−3)	Degradation Degree of the Beam
Crack	LS-S-Major	5.468	−1.39	Low
	IS-E	4.987	−4.89	Relatively low
	IS-W-Major	4.536	−10.11	Relatively high
	IS-W-Minor	1.973	−7.52
	LS-N-Major	0.895	−8.58	High
Craquelure	LS-S-Craquelure	2.308	−3.62	\

. However, this measure ranked the beams as west ≈ north > east > south, which was inconsistent with the degradation ranking.

To address this discrepancy, the data were refitted using a sigmoid model from the OriginLab software’s basic function library, represented by the following equation:

$$RW=A_2+{\displaystyle \frac{A_1-A_2}{1+{\left(RH/x_0\right)}^p}}$$

(3)

Here, RW represents the relative average width of cracks. Parameters A₁ and A₂ represent the fitted upper and lower limits of the dependent variable, and the exponent p represents the steepness of the curve, with smaller p-values indicating a steeper curve.

The results indicated that the sigmoid model provided a slightly better fit than linear fitting, with the ranking of the fitting exponent factor p for through-cracks being northern < western < eastern < southern (Table 3). This ranking aligns with the degradation degree of the wooden components, as a lower p-value corresponds to a steeper curve, which reflects a more pronounced response to humidity changes. Consequently, the fitting parameter p for through-cracks can be considered an indicator of the degradation degree of wooden components.

The superiority of p over │b│ may lie in its focus on the steepness of the curve’s middle section, where humidity changes exert the greatest influence. In contrast, the ends of the curve—representing extremely high or low humidity conditions—are heavily affected by absorption/desorption dynamics over time, which diminishes the accuracy of linear fitting.

For LS-N-Major, the data exhibited unique behavior. Linear fitting outperformed the sigmoid model, achieving the highest R² value of 0.773 among all linear fittings, even without excluding data points collected after prolonged rainfall. This anomaly can be attributed to the most severe degradation of the northern beam, where LS-N-Major is located. The high degree of aging enhances moisture transfer within the wood, minimizing the time-dependent effects typically observed during moisture absorption or desorption. This rapid moisture equilibrium reduces the distortion caused by prolonged exposure to high humidity, making linear fitting more effective in this specific case.

5. Conclusions

Wooden architectural structures are dynamic, “breathing” entities, with surface damages such as cracks and craquelures being actively influenced by environmental factors. However, quantifying this activity, uncovering its mechanisms, and exploring its applications have remained insufficiently addressed. This study establishes a cost-effective monitoring method to quantify crack dynamics, supplemented by numerical simulations and fitting models, providing a mechanistic understanding of humidity-driven crack behavior and advances non-destructive health monitoring strategies for heritage structural components.

The monitoring framework combines camera relocation, photogrammetry, and digital image processing techniques. Applied to the Dapaojing Well Pavilion in the Palace Museum over a 15-month period, this study examined through-cracks and Caihua craquelures on the inward and lower surfaces of wooden beams. Results revealed that surface cracks, with average widths ranging from 0.108 mm to 0.364 mm, exhibit dynamic activity. Relative humidity emerged as the most influential environmental factor, demonstrating statistically significant correlations (at the 0.01 level) with crack activity in six out of seven cases. Linear fitting explained 69% to 76% of the variation in relative crack width, highlighting the role of environmental humidity.

Numerical simulations further clarified the relationship between humidity duration and crack width. Under short-term high humidity, wood surface expansion narrowed the cracks. Prolonged exposure, however, allowed moisture to penetrate deeper into the wood, causing internal swelling that pushed surface cracks outward, slightly increasing their width again.

Moreover, the study demonstrated that as wood ages, the variability in crack width intensifies. Fitting using a sigmoid model showed that the exponent parameter p is inversely correlated with curve steepness, which aligned with the observed aging degrees of the wooden beams. This parameter outperformed the linear fitting slope (│b│) as an indicator for wood degradation, offering a practical tool for characterizing crack activity and assessing aging in wooden components.

In conclusion, the proposed methods and models provide a practical, in situ, and non-destructive approach for monitoring the health of timber components in architectural heritage. Considering the challenges posed by the height and inaccessibility of many ancient structures, integrating this methodology with advanced technologies such as machine vision and drones could enable large-scale automated monitoring of building cracks, further enhancing efforts in heritage conservation and structural health management.