In this study, we propose nondestructive testing methods and combined forecasting models-based stress wave and impedance measurements to obtain accurate internal defects information for wooden building components. Internal defects data for major wooden components of an ancient building in China and reverse laboratory test data on matching tree species indicated various degrees of damage on the pavilion wood structure surface and internal defects in certain pillars. The stress wave method enabled rapid acquisition of two-dimensional plots of test sections; however, the results revealed that the area of stress wave detection was greater than the actual defect area. Moreover, the impedance meter was able to determine the defect position and type in a single path, and the actual defect area was proportional to the absolute error of the drilling resistance. By distributing the errors from the two nondestructive testing methods on the basis of a Shapley value algorithm, we determined the weights of stress wave and impedance meter data in the forecasting models and established combined forecasting models that showed greater accuracy with a mean relative error of less than 6%. This method can improve the prediction accuracy of internal defects in ancient buildings and provide effective data support for practical engineering repair and reinforcement schemes.
Due to thousands of years of history, many ancient buildings in China have been registered on the World Cultural Heritage list for their unique structures and cultural, historic, and artistic value. Most principal load-bearing components of these ancient buildings are made of wood, which, in combination with tenon and mortise connectors and bracket systems, has the advantage of long service periods, earthquake resistance, and hazard mitigation. However, as a biological material, wood is anisotropic [
In contrast, nondestructive testing technology aims to have no effect on the appearance, internal structure, or usability of ancient wooden components; thus, it represents a significant improvement from conventional timber and wooden material testing methods [
In this study, we employ stress wave and drilling resistance tests to conduct nondestructive detection testing on the wooden components of an ancient building. We then match equivalent tree species to perform reverse laboratory tests, where we simulate common internal cavity defects in ancient architecture and then establish a nondestructive combined forecasting model to improve testing accuracy. By quantifying the internal defects, we develop a novel and practical combined prediction method for the nondestructive testing of internal defects in wooden components. Therefore, this research provides strong data support for future renovation and reinforcement of wooden components, thereby promoting the conservation and effective utilization of architectural heritage.
Located in the southern part of Beijing, China, the pavilion building analyzed in this study was built during the Ming Dynasty and is known as the altar. There are not many records regarding the renovation of this ancient building, and it was not renovated in recent years. In order to combat aging and damage at various levels, this building requires testing that does not damage its authenticity and involves minimal intervention.
According to the “
Currently, aging and damage exists in the wooden components of the pavilion at various levels, the most prominent of which are surface damage and pollution and damage to the building materials.
At the joints of the upper eaves and around the domes, the paint decorations on the rafters and sheathings have fallen off and the sheathings have rotten due to rain erosion (Figures
Surface damages of the pavilion: (a, b) eaves; (c) a pillar; (d) a fence; (e) the Ang.
The color of the sharp wooden components at the wooden member top has changed due to mold from microorganisms in the airless atmosphere (Figure
Wooden component damage at the top of the pavilion due to (a, c) mold and (b) bird excrement.
Nondestructive testing was conducted on the main wooden components of beams and pillars, and internal defect data were collected. Some of the beams and pillars were then chosen as samples for detecting the tree species of the components. We then matched equivalent tree species for an internal defect reverse laboratory test and analyzed the error values of each nondestructive method as well as their combined predicted values using the Shapley value algorithm. Thus, both nondestructive methods and prediction models were used to evaluate internal defect prediction of the wooden components.
Before that approximately ancient wooden buildings in the south and north of China were investigated (for example Shanxi Guanyin hall, Anhui Diao Xue Tang), revealing that the beam and pillar components are often damaged at both ends. Wooden pillars are eroded by rain and snow all year round, and the accumulated humidity at the bottom of the pillar, together with the normal load, encourages internal defects. The beams subject to the load of the upper wooden components all year round are easy to bend, and the overlap between beams is complex. Therefore, we focused on the internal defects of these two major wooden components. On the premise of “minimum intervention,” nondestructive testing was conducted on the load-bearing beams and pillars.
Internal nondestructive testing of the main load-bearing pillars and beams was conducted using the FAKOPP ten-probe stress wave measuring instrument. Stress wave sensors were installed in the top part (Section A), middle part (Section B), bottom part (Section C), beam end, and midspan (Figure
Stress wave sensor locations in (a) pillars and (b) beams.
The German-made IML-500 drill was used to conduct nondestructive drilling resistance testing on the wooden components. A microprobe with a length of 1.5 mm was driven into the interior of the components. The probe encounters different resistances as it moves forward, producing a relative resistance value of the path. This was plotted in two-dimensional plots of the internal defects where the
Figure
Analysis of wooden component samples for tree species analysis: (a) pillar B2, (b) beam between B3 and B4, (c) and (d) microscopic images of three types of section of the
Our analysis of the internal defects of the major wooden beam and pillar components shows no defects in the interior of beam components but serious defects in the interior of pillars B2 and D4. For example, Figure
Stress wave analysis of pillar B2 showing (a) different sections of the pillar and (b) a longitudinal sectional of the internal defects.
Nondestructive testing data of pillar B2.
Section names | Height (cm) | Moisture content (%) | Section area (cm2) | Stress wave testing defect area (cm2) | Impedance meter testing defect area (cm2) |
---|---|---|---|---|---|
Section A | 433.00 | 10 | 946.30 | 0 | 0 |
Section B | 216.50 | 10 | 963.82 | 0 | 0 |
Section C | 10.00 | 10 | 981.51 | 294.45 | 213.47 |
Section D | 60.00 | 10 | 981.51 | 333.71 | 246.85 |
As well as using the stress wave chart to determine internal defects in Section C, targeted drilling resistance test results also reveal the locations and sizes of internal defects along a single path (Figure
Two-dimensional plot of the drilling resistance results of Section C. (a) Path one. (b) Path two. (c) Path three. Note: horizontal coordinates indicate the depth of the probe path and vertical coordinates show that the density distribution and the early and late wood performance of the probe differ as the probe advances inside the pillar. Location of damaged section in red box.
Based on the internal defect results of the wood components in the ancient buildings, we matched equivalent tree species and then processed samples by manual digging and cutting them to size. To reduce the error value between the experimental results and the data collected from the ancient buildings, we simulated all defect types of the samples as internal holes. According to the defect locations in the wood components, the defect distribution in the specimen was simulated in the core materials and in the sapwood. The specific design parameters of specimens are shown in Table
Wooden component sample descriptions used for the reverse tests.
Specimen numbers | Tree species | Perimeter (mm) | Height (mm) | Moisture content (%) | Simulation type | Testing height (mm) |
---|---|---|---|---|---|---|
D-1 |
|
850 | 100 | 9.4 | Core material cavity | 50 |
D-2 |
|
850 | 100 | 8.7 | Sapwood cavity | 50 |
After production, the specimens were kept in the laboratory at a temperature of 20° and relative air humidity of 65% for 3 months. Tests were conducted when the air-dried moisture content was below 12%. Defect expansion over six different stages (when the defect area occupies 0, 1/9, 1/7, 1/5, 1/3, and 1/2 of the section area) demonstrates the initial, intermediate, and terminal stages of the defects. The average value of three hits on each sensor was taken as the propagation velocity. In order to avoid the discreteness of testing data due to specimens displaying diverse defect areas, stress wave data were collected three times. We analyzed 36 groups of nondestructive testing data and the average values of sections with the same defect areas.
Internal cavity simulation experiments of specimens D-1 and D-2 by the FAKOPP stress wave timer and IML impedance meter indicate that the larger the internal defect area, the more accurate the size and location of internal defect detection by the stress waves (Table
Comparison of nondestructive testing methods.
Number | Type | Proportion | Actual defect |
Stress wave |
Drilling resistance |
Combined prediction |
Absolute error value | Relative error value | |||
---|---|---|---|---|---|---|---|---|---|---|---|
Stress wave |
Drilling resistance |
Stress wave |
Impedance meter |
Combined prediction | |||||||
D-1 | Core material cavity | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1/9 | 63.96 | 86.35 | 52.85 | 65.92 | 22.39 | 11.11 | 35.01 | 17.37 | 3.06 | ||
1/7 | 82.24 | 138.16 | 68.11 | 95.43 | 55.92 | 14.13 | 68.00 | 17.18 | 16.04 | ||
1/5 | 115.13 | 149.67 | 95.41 | 116.57 | 34.54 | 19.72 | 30.00 | 17.13 | 1.25 | ||
1/3 | 191.89 | 178.45 | 158.88 | 178.21 | 16.56 | 33.01 | 8.63 | 17.20 | 7.13 | ||
1/2 | 287.83 | 316.61 | 237.94 | 268.62 | 28.78 | 49.89 | 10.00 | 17.33 | 6.67 | ||
|
|||||||||||
Average | 123.51 | 144.87 | 102.20 | 120.79 | 26.37 | 21.31 | 25.27 | 14.37 | 5.69 | ||
|
|||||||||||
D-2 | Sapwood cavity | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1/9 | 63.96 | 72.08 | 50.73 | 60.34 | 8.12 | 13.23 | 12.70 | 20.69 | 5.66 | ||
1/7 | 82.24 | 104.35 | 71.42 | 86.24 | 22.11 | 10.82 | 26.89 | 13.16 | 4.86 | ||
1/5 | 115.13 | 155.43 | 92.26 | 120.69 | 40.30 | 22.87 | 35.00 | 19.87 | 4.83 | ||
1/3 | 191.89 | 236.02 | 163.39 | 196.07 | 44.13 | 28.50 | 23.00 | 14.85 | 2.18 | ||
1/2 | 287.83 | 324.29 | 226.54 | 270.53 | 36.46 | 61.29 | 12.67 | 21.29 | 6.01 | ||
|
|||||||||||
Average | 123.51 | 148.70 | 100.72 | 122.31 | 30.22 | 27.34 | 18.38 | 14.98 | 3.92 |
Image of specimens and stress wave diagrams for different stages of defect expansion for (a) the core material cavity experiment and (b) the sapwood cavity experiment.
The crest (maximum drilling resistance) and trough (lowest rate drilling resistance) of the relative resistance values are revealed by inserting needles during impedance meter testing; therefore, the internal defects can be defined as cavities. These cavities can be used to determine the internal defect boundary and length; however, an impedance meter only reflects the internal defects in single path, so entire section defects cannot be detected. The impedance meter testing values,
The data in Table
As shown in Table
Stress wave and impedance meter methods have both advantages and disadvantages for testing internal defect locations and areas, so their results are evaluated comprehensively in order to construct a combined prediction model. On the assumption that the same wooden component internal defects are predicted by
The combined predicted overall values of the two nondestructive testing methods are distributed by a weighting method based on the Shapley value algorithm to determine the weight of each testing value [ For any subset The overall value
On the assumption that the average method is
The weight allocation formula based on the Shapley value algorithm is
According to equations (
According to the results of stress wave and impedance meter tests on different defect locations and areas in Table
In accordance with the concept of the Shapley value algorithm, the member of shared overall values in the combined forecasting model is
According to equations (
Similarly, the error shared by specimen D-1 impedance meter nondestructive testing is
Similarly, the allocated weights of the nondestructive testing combined model for specimen D-2 are
All combined forecasting models are recombined based on their corresponding stress wave and impedance meter testing results to predict internal defect areas. Wooden component internal defect area
According to Table
Using Section C and Section D of pillar B2 as examples, we locate internal defects in the sapwood using stress wave two-dimensional plots, which are further confirmed by IML impedance meter tests, indicating that the internal defects are cavities. Internal defects of Section C and Section D are then predicted by hardwood pine and sapwood combined models on the basis of the Shapley value algorithm obtained from reverse laboratory tests. The results indicate that the internal cavity area of Section C is 285.94 cm2, accounting for 1/3 of Section C, and that of Section D is 249.91 cm2, accounting for 1/4 of Section D. According to the
Internal defects within wooden components tend to reduce the compressive area per unit area. Individual nodes or component parts cannot be subjected to normal forces, and then the components of the skew flash or displacement, thereby eventually leading to deformation of ancient building-wood components. In this study, reverse laboratory tests were conducted on major wooden components belonging to the same tree species through nondestructive testing methods. According to defect detection data and experimental results, the following conclusions are drawn: Internal defects mainly occur in key joints such as pillar bases and girders according to detection tests on wooden components of ancient buildings. Knowledge and analysis of wooden component internal defect characteristics can be used to determine preventive conservation and improve defect detection in ancient architecture. The sizes and locations of wooden component cavities can be quickly obtained through stress wave tests and effectively visualized using two-dimensional plane detection diagrams. However, stress wave testing area is greater than the actual testing area, errors exist, and internal defect boundaries are blurred. Using the stress wave results of internal defects in the wood, drilling resistance was used to detect the presence, type, and location of internal defects, which can be accurately confirmed by the corresponding two-dimensional plane detection diagrams. However, the results represent a single path of the testing section and weaker direct detection of internal defects in the entire section. The smaller the internal defects, the more accurate the drilling resistance testing result. The relative error values are directly related to expansion of the defect area. Moreover, more drilling resistance paths may provide more precise information. The stress wave test chart can determine the approximate position of the internal damage in a wooden component, and the drilling resistance test can determine the shape of the internal damage. The drill resistance test depends on the stress wave test chart, and the drill resistance test results are based on the stress wave test. Therefore, we determined the weight of each prediction method (stress wave and drill resistance tests) using the Shapley value algorithm weight allocation method. This exploits the advantages of both types of nondestructive testing, and using this model, we build an internal defect area prediction model. The predicted result of the combined model based on the Shapley value algorithm is more accurate than that of the single testing method; the internal defect area only exhibits a small prediction error. Through experimental analysis, we determine that the mean relative error of the defect area of the combined prediction model is less than 6%. However, the Shapley value algorithm separately provides weights to each parameter; thus, if one parameter depends on another, different conclusions could be drawn. Therefore, this study presents a new practical method for the quantitative evaluation of internal defects in wooden components, which will be beneficial for architectural heritage conservation as well as provide room for further research.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the Research Fund for Young Scientists of Da Bei Nong Group (17SK002), the Research Fund for Young Scientists of BUA (SXQN201809), and the National Natural Science Foundation of China (51808038).