1. Introduction
Wood density is the mass of wood per unit volume at a specific moisture content. This parameter is considered the most reliable predictor of wood quality [
1]. Wood density exhibits a strong correlation with other wood qualities, such as strength and stiffness, and plays a significant role in determining wood suitability for different end uses [
2]. Wood density is influenced by both genetic factors [
3,
4,
5] and the growth environment of trees [
6,
7,
8,
9]. Therefore, wood density serves as a vital evaluation parameter in studies related to tree genetic breeding and forest management methods. With the development of human society, the demand for wood products has gradually increased [
10,
11,
12,
13], while the availability of wood resources has significantly decreased. Improving the efficiency of timber use emerges as an effective measure to address the imbalance between wood supply and demand. Accurate measurement of wood density forms the basis for enhancing the efficiency of timber use. Forest managers and wood processors use wood density to effectively match raw materials with final products [
14]. Additionally, wood density is a vital important factor in forest carbon measurement [
15,
16,
17,
18]. Improving the accuracy of measuring wood density can contribute to enhanced precision in estimating forest carbon. Wood density exhibits significant variability among individual trees in forests [
19,
20,
21]. Therefore, promoting sustainable human development requires the advancement of rapid, accurate, and non-destructive methods for assessing wood density in standing trees.
The traditional approach for measuring wood density of standing trees is the volume method [
22]. This method first requires sampling wood samples from standing trees, then measuring the volume of fresh wood in the laboratory, and finally drying the samples to measure their absolute dry density. Although the volume method can accurately measure wood density, its dependence on sampling from the tested object leads to significant specimen damage. Moreover, the sampling and measurement processes are time-consuming and labor-intensive. The X-ray method indirectly measures wood density based on the intensity of X-rays absorbed by substances with different densities [
23,
24]. Moreover, this method accurately measures the density of wood in small areas and enables the assessment of average density in tree rings, early wood density, and late-wood density. However, X-ray instruments for measuring density are expensive, and the method also requires sampling from the tested object. Therefore, the X-ray method is costly, time-consuming, and labor-intensive. In contrast, the Pilodyn method indirectly measures wood density by inserting a fine needle with a fixed specification into the wood using a preloaded spring and then gauging the depth of the needle’s penetration into the wood [
25,
26]. Despite the convenience of this instrument, it only measures the average density of the outer wood surface. The micro drill resistance instrument uses a motor to control the constant-speed penetration of the drill needle into wood. The drill resistance is positively correlated with wood density and the instruments can measure wood density indirectly [
27,
28,
29,
30,
31,
32,
33]. The resistance drilling method has considerable advantages over other methods, including minimal tree damage, faster operation, and higher measurement sensitivity, making it a highly promising method for measuring wood density [
22].
Currently, scholars have mainly used linear models to investigate the relationship between drill resistance and wood density. For example, Rinn established a linear model with a correlation of r
2 = 0.943 between drill resistance and wood density [
27]. Isik et al. revealed strong correlations between average drilling resistance values and wood density, indicating strong genetic control at the family level. However, individual phenotypic correlations were observed to be relatively weak [
34]. Downes et al. found determination coefficients of the linear models between the average drill resistance and wood density of each tree in various plots ranging from 0.662 to 0.868 [
35]. Due to the significant differences in the parameters and determination coefficients among various linear models, the universality of these models was poor. Therefore, researchers needed to establish a mathematical model for every tree species, and the modeling workload was enormous. In addition, the scatter plots of drill needle resistance and wood density were relatively scattered, and some data points had a large distance from the fitting curve. Therefore, the reliability of this method needs further verification.
Owing to significant differences in the parameters and determination coefficients across various linear models, the universal applicability of linear models is limited. Presently, researchers typically need to establish specific linear models for different tree species when using micro drill resistance instruments to measure wood density. Establishing a unified mathematical model for multiple tree species poses a challenge. Additionally, the relationship between drill resistance and wood density does not follow a linear pattern. Numerous scholars have shown that the relationship between various wood mechanical properties and wood density can be expressed by a
k-th parabolic equation:
where
s represents a wood strength value;
α denotes the proportional constant; and
k is the density index, shaping the relationship curve between wood strength and wood density. Certain wood strength properties exhibit exponential variations with changes in wood density. For example, the density index of flexural strength is 1.25, while the density index of transverse compressive strength and hardness is 2.25 [
36]. Therefore, an exponential variation may occur between drill resistance and wood density.
Additionally, the moisture content of wood has a certain influence on its strength [
37,
38,
39]. Therefore, the moisture content also affects drill resistance. Lin et al. found that drill resistance values typically decreased with decreasing moisture content, transitioning from a water-saturated condition to air-dried status for
Taiwania cryptomerioides lumber [
37]. Sharapov et al. reported that the impact of moisture content on drill needle resistance and drill feeding force depended on the rotational speeds and rates of the drill [
38]. Ukrainetz et al. found that density prediction by drill resistance was influenced by tree moisture content [
39]. Owing to significant differences in moisture content among different tree species, locations, and times, further research is needed to investigate the impact of moisture content on measuring the basic density of standing trees.
In order to further investigate the possibility of the unified modeling of multiple tree species, the reliability of the micro drilling resistance method for measuring wood density, the relationship between drilling needle resistance and wood density, and whether moisture content has a significant impact on the model, this paper further studies the micro drilling resistance measurement method for wood density. The average drill resistance, the natural logarithm of average drill resistance, and absolute moisture content were used as independent variables, while the basic wood density served as the dependent variable. Total models for multiple tree species and sub models for each tree species were established with stepwise regression. The accuracy and standard deviation of the estimated results of the total model, sub models, and estimated results were compared with the average basic density of the building data.
4. Discussion
Higher wood density indicates stronger wood strength and an increased energy demand for drilling through the wood. Therefore, drill resistance serves as an estimate for wood density. Currently, researchers have mainly used linear models to estimate wood density based on drill resistance. Tomczak et al. measured the radial basic density of nine oak trees with an increment corer and IML (Instrumenta Mechanik Labor, Australia) power drill. The results indicated that the determination coefficient of the linear model between the average drill resistance and wood density was 0.396 [
40]. Close relationships existed in the regression model between the amplitude of the drilling resistance and wood density in previous research on trees in a breeding program (R
2 > 0.60) [
41], lumber and the linear regression model for agarwood (R
2 = 0.25) [
42]. However, owing to the exponential relationship between wood strength and wood density, the relationship between drill resistance and wood density does not follow a linear pattern. The results of this study revealed that except for
Cryptomeria fortunei, the natural logarithm of drill resistance significantly influenced the wood density model.
Figure 5 shows a comparison between the linear and logarithmic fitting curves of the average drill resistance and wood density on the modeling dataset.
Table 7 displays the linear and logarithmic fitting equations of the average drill resistance and wood density.
The logarithmic models exhibited higher fitting accuracy than linear models, except for
Cryptomeria fortunei (
Table 7).
Moisture content significantly influences the mechanical properties of wood, thereby affecting drill resistance. The results of this study revealed that moisture content significantly influenced the total model and sub-model of Pinus massoniana. Thus, measuring the moisture content of wood is challenging. Therefore, when using the micro drill resistance method for measuring wood density, most users do not measure the moisture content of wood. Therefore, to measure the wood density of standing trees, it is advisable to sample the drill resistance in a consistent environment to minimize the influence of moisture content on drill resistance.
From a macro perspective, higher wood density corresponded to greater drill resistance. However, the mathematical model established using data from multiple tree species featured lower test accuracy, even lower than predicting the density of each tree species based on the average basic density of each tree species. This difference may be attributed to the relationship between wood strength and density, which can be influenced by fiber length, cell wall thickness, resin content, and other factors. Thus, species with similar densities can still differ from each other in wood anatomical structure and resin content. Therefore, establishing a mathematical model for each tree species is vital.
The sub-model for each tree species a exhibited higher estimation accuracy than the average value of each tree species used as the density estimation value. This confirmed the feasibility of using the micro drilling resistance method to measure the wood density of standing trees. However, the estimated accuracy of the total test data for each sub-model was only 1.670 percentage points higher than the average of each tree species used as the density estimate. This difference may be attributed to the following reasons. First, the thin and long structure of the drill needle led to a significant vibration amplitude during high-speed rotation, resulting in the formation of noise signals in the resistance measurement. Second, the operator’s actions, such as breathing, trembling, and movement, can introduce vibrations in the micro drill resistance meter, thereby affecting the drill resistance measurements. Future research should focus on improving the mechanical strength of the drill needle to reduce vibrations and designing a bracket to stabilize the micro drill resistance instrument and mitigate the impact of the operator’s movements on the accuracy of drill resistance measurements.