Predicting Glossiness of Heat-Treated Wood Using the Back Propagation Neural Network Optimized by the Improved Whale Optimization Algorithm

Abstract

The properties of wood change after heat treatment, affecting its applications. Glossiness, a key aesthetic property, is of great significance in fields like furniture. Precise prediction can optimize the process and improve product quality. Although the traditional back propagation neural network (BPNN) has been applied in the field of wood properties, it still has issues such as poor prediction accuracy. This study proposes an improved whale optimization algorithm (IWOA) to optimize BPNN, constructing an IWOA-BPNN model for predicting the glossiness of heat-treated wood. IWOA uses chaos theory and tent chaos mapping to accelerate convergence, combines with the sine cosine algorithm to enhance optimization, and adopts an adaptive inertia weight to balance search and exploitation. A dataset containing 216 data entries from four different wood species was collected. Through model comparison, the IWOA-BPNN model showed significant advantages. Compared with the traditional BPNN model, the mean absolute error (MAE) value decreased by 66.02%, the mean absolute percentage error (MAPE) value decreased by 64.21%, the root mean square error (RMSE) value decreased by 69.60%, and the R² value increased by 12.87%. This model provides an efficient method for optimizing wood heat treatment processes and promotes the development of the wood industry.

1. Introduction

Many wood species are often used as decorative materials because of their appealing appearance and unique mechanical properties [1]. However, quite a few wood species have drawbacks such as weak biological durability and poor dimensional stability, restricting their application ranges. To address these issues, wood heat treatment, an eco-friendly approach, has gained popularity. It enhances wood’s durability and dimensional stability through short-term pyrolysis at 160–250 °C in a protective gas [2]. This treatment is especially useful in applications where long-term performance is crucial, such as outdoor structures [3]. It reduces maintenance and replacement costs by better resisting environmental factors [4]. Heat treatment also affects wood’s aesthetic properties, including glossiness. Glossiness is important not only for aesthetics but also for inferring wood strength and quality. In the furniture industry, high-gloss surfaces are highly sought-after. Variations in gloss can indicate internal wood structure differences, which may impact strength.

Numerous studies have been conducted on this topic. Zhou et al. [5] investigated the effect of density on color and gloss changes in heat-treated wood. Their results indicated that low-density samples exhibited greater total color and gloss changes than high-density samples following high-temperature heat treatment. Heat treatment reduced color and gloss variation due to density variation in untreated wood, with this effect being further enhanced at high temperatures. Lu et al. [6] examined the effect of measurement angle on gloss at different heat treatment temperatures and times, finding that gloss decreased in both vertical and parallel directions following heat treatment. This finding was corroborated by Gurleyen et al. [7]. Esteves et al. [8] reported changes in surface properties of untreated and heat-treated wood from 75 to 750 h after artificial weathering, observing a decrease in gloss for untreated wood but no significant change for heat-treated wood. Ayata et al. [9] demonstrated that gloss measured both parallel and perpendicular to the grain decreased with heat treatment, with longer treatment times resulting in greater decreases. These results were also obtained by Gurleyen et al. [10]. Bekhta et al. [11] studied the effect of short-term thermomechanical densification on gloss changes for different tree species, finding that densification temperature and pressure had a significant impact on wood gloss. For all species studied, densified wood exhibited increased gloss values with increasing densification temperature and pressure. Salca et al. [12] evaluated the gloss of black alder samples coated with two varnishes and found that samples coated with UV varnish exhibited higher gloss values than those coated with aqueous products in both measured gloss directions. Gloss plays a crucial role in the appearance of various materials and is an important consumer characteristic. High-gloss surfaces are becoming increasingly popular within the furniture industry. As the demand for high-gloss wood finishes grows, predicting the glossiness of heat-treated wood is vital. Since factors like temperature, grain size, pressure, and varnish type influence gloss, a reliable prediction method can optimize heat treatment and ensure product quality.

From the aforementioned studies, it is evident that the relevance between glossiness and heat treatment conditions is nonlinear and complex rather than simply linear, making it challenging to construct an ideal prediction model. Artificial neural network methods can be employed to predict wood gloss without significant time, cost, or effort. These methods possess self-learning capabilities and can rapidly identify optimal solutions. Artificial neural networks have been widely applied within wood science for predicting moisture content in wood, fracture toughness, and mechanical properties such as surface roughness and bond strength [13]. Due to their outstanding nonlinear mapping capability and adaptable network structure, the BPNN has been utilized especially extensively in heat-treated wood [14]. Chen et al. [15] used BPNN model to predict changes in equilibrium water content of wood due to heat treatment, while Yang et al. [16] employed BPNN to forecast the mechanical characteristics of timber that had been heat-treated. Chai et al. [17] utilized BPNN to predict variations in moisture level as wood was dried using a high-frequency vacuum. However, the BPNN is not without its limitations. It exhibits slow learning speed, is prone to becoming trapped in local minima, and possesses limited network generalization ability which restricts its practical engineering applications.

Meta-heuristic algorithms, as a class of optimization techniques that mimic natural phenomena or biological behaviors, are often used to optimize neural network parameters. Examples include the genetic algorithm (GA) [18,19,20], beluga whale optimization algorithm (BWA) [21], and the whale optimization algorithm (WOA) [22]. Among them, the WOA has gained widespread application due to its relatively simple structure and strong global search ability [23]. Inspired by the hunting behavior of humpback whales, the WOA can effectively explore the solution space in the early stage of optimization, allowing it to quickly approach the optimal solution region [24]. However, the WOA also exhibits several limitations. It has a slow convergence speed in some complex optimization problems, shows relatively low accuracy in certain scenarios, and has a tendency to get trapped in local optima. For practical engineering problems with high optimization accuracy requirements, further improvements to the WOA are necessary [25].

In summary, this paper proposes an improved whale optimization algorithm to optimize BPNN for wood glossiness prediction and enhance the WOA’s optimality-seeking performance. The IWOA addresses the WOA’s tendency to converge to local optima. The parameters and decision boundaries of the BPNN are optimized using the IWOA to solve issues of slow convergence and imprecise prediction. The model’s performance is evaluated using glossiness measurements from four types of wood. The results demonstrate that the proposed IWOA-BPNN model exhibits significantly higher prediction accuracy than conventional models and can effectively model the relationship between wood thermal modification process parameters and glossiness.

2. Materials and Methods

2.1. The Back Propagation Neural Network

The back propagation neural network’s computational process comprises two stages: forward propagation and backward propagation. During forward propagation, input information is processed sequentially from the input layer through the hidden unit layer to the output layer. The state of neurons in each layer influences only the state of neurons in the subsequent layer. If the desired output is not achieved at the output layer, back propagation commences. In this stage, an error signal is transmitted along the original connection path and minimized by adjusting each neuron’s weights [26]. Figure 1 illustrates this process in detail.

According to Figure 1, the initial parameters of the BPNN are generated randomly. Typically, these parameters are updated using the gradient descent method. Due to this mechanism, the BPNN is greatly affected by its initial weight values, which can make the algorithm more challenging to solve and increase convergence time. However, employing the IWOA to optimize the initial weights and thresholds of the BPNN can enhance its stability and accuracy [27].

2.2. The Whale Optimization Algorithm

The Whale Optimization Algorithm is a population intelligence optimization algorithm introduced by Mirjalili et al. in 2016 [28]. This novel algorithm emulates the feeding behavior of humpback whales [29]. Unlike other whales, humpback whales lack teeth and cannot hunt large prey. Consequently, long-term evolution has resulted in their unique bubble net feeding style. In the WOA, this iconic hunting style is modeled as three processes: encircling prey, spiral bubble-net feeding maneuver, and search for prey.

2.2.1. Encircling Prey

During the optimization process of the algorithm, each individual’s position represents a solution searched by the algorithm in space. To accurately locate the optimal solution while performing the optimization task, each individual generated by the algorithm begins exploring near its initial position. The individual with the best fitness value in the current population is assumed to be the target prey, and other whales update their positions accordingly. The mathematical model for this stage is shown in Equations (1) and (2).

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X^{*}}\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D}$$

(1)

$$\overrightarrow{D}=\left|\overrightarrow{C}\cdot \overrightarrow{X^{*}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(2)

where t indicates the current iteration; $\overrightarrow{X}$ indicates the position of the individual whale; $\overrightarrow{X^{*}}$ indicates the position vector of the best solution obtained so far; and $\overrightarrow{A}$ and $\overrightarrow{C}$ are coefficient vectors, and they are calculated as Equations (3)–(5).

$$\overrightarrow{A}=2\overrightarrow{a}\cdot \overrightarrow{r_1}-\overrightarrow{a}$$

(3)

$$\overrightarrow{C}=2\overrightarrow{r_2}$$

(4)

$$\overrightarrow{a}=2-{\displaystyle \frac{2t}{T_{max}}}$$

(5)

where $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ are random numbers that obey a uniform distribution between [0, 1]; $\overrightarrow{a}$ is a linearly decreasing vector, being the regulation parameter that decreases from 2 to 0 with increasing number of iterations; and $T_{max}$ represents the maximum number of iterations set in the algorithm.

2.2.2. Bubble-Net Attacking Method

In mathematical modeling of humpback whale foaming net feeding behavior, both the contracting envelope mechanism and spiral update position are simultaneously employed. The contracting envelope mechanism of the whale group is simulated by altering parameter $\overrightarrow{a}$. Given that the value range of $\overrightarrow{A}$ in the algorithm is [−a, a], when $\overrightarrow{A}$ falls between [−1, 1], each individual’s position at generation $t+1\cdot \left(\overrightarrow{X}\cdot \left(t+1\right)\right)$ lies between its position at generation $t\left(\overrightarrow{X}\cdot \left(t\right)\right)$ and the global optimal position at generation t (X×(t)). This approach effectively encircles prey, as demonstrated in the following mathematical model.

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{D^{\prime }}\cdot e^{bl}\cdot cos(2\pi l)+\overrightarrow{X^{*}}\left(t\right)$$

(6)

where $\overrightarrow{D^{\prime }}=|\overrightarrow{X^{*}}(t)-\overrightarrow{X}(t)|$ denotes the distance between each individual and the individual at the optimal position at generation t; b represents a constant in the spiral progression equation of the whale group and its value is 1; and l is a random number that takes values in the range [−1, 1].

In pursuit of a target, individual whales employ two strategies: narrowing the envelope and spiraling forward. To facilitate simultaneous use of these approaches during optimization tasks, the probability of selecting either strategy is set to 50% in our model. This is mathematically represented in Equation (7).

$$\overrightarrow{X}\left(t+1\right)=\left\{\begin{array}{c}\overrightarrow{X^{*}}\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D} p<0.5\\ \overrightarrow{D^{\prime }}\cdot e^{bl}\cdot \mathit{cos}\left(2\pi l\right)+\overrightarrow{X^{*}}\left(t\right) p\ge 0.5\end{array}\right.$$

(7)

where p is a random number and follows the [0, 1] distribution.

2.2.3. Search for Prey

During the search for an optimal solution, when the value of parameter in the algorithm satisfies $\left|\overrightarrow{A}\right|$ ≥ 1, each individual’s position update depends on others’ positions. This update strategy enables individuals to move away from the current optimal solution location. If the algorithm becomes trapped in a local optimum, this approach may increase the likelihood of escaping that region. This is mathematically represented in Equations (8) and (9).

$$\overrightarrow{D_{rand}}=\left|\overrightarrow{C}\cdot \overrightarrow{X_{rand}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(8)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X_{rand}}\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D_{rand}}$$

(9)

where $\overrightarrow{X_{rand}}$ is the location of the randomly selected individual whale at generation t.

2.3. The Improved Whale Optimization Algorithm

2.3.1. Tent Chaotic Mapping

Chaos refers to complex dynamic behavior exhibited by nonlinear systems that appear irregular and random-like. Characteristics such as randomness and ergodicity can be leveraged to enhance algorithm performance. However, the WOA algorithm’s use of randomly generated data as an initial population can result in uneven distribution, adversely affecting convergence speed and reducing algorithm diversity [30]. To address this issue, we employed Tent chaos mapping to initialize the population. This approach yields a more uniform initial population, expands the search range, and accelerates convergence. The tent chaos mapping function generates chaotic sequences uniformly within the interval [0, 1]. In this model, parameters $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ are randomly generated using this method. This is mathematically represented in Equation (10).

$$X_{n+1}=\left\{\begin{array}{c}2X_n 0<X_n<0.5\\ 2\left(1-X_n\right) 0.5\le X_n<1\end{array}\right.$$

(10)

Tent chaos mapping yields a more uniform population initialization compared to randomly generated initial populations. The experimental results demonstrate that Tent chaos mapping produces relatively uniform system distribution and can be employed to generate an algorithm’s initial solution and enhance population diversity. The distribution of the initialized population is illustrated in Figure 2.

2.3.2. The Sine Cosine Algorithm

The sine cosine algorithm (SCA) is a recently proposed global optimization algorithm that differs from other population-based intelligence optimization algorithms reliant on bio-inspired mechanisms. The SCA features simple knots, robustness, and ease of implementation. It primarily employs the mathematical properties of sine and cosine functions to iteratively find optimal solutions [30]. In the SCA, $N$ represents population size and $D$ denotes individual dimension. The algorithm randomly generates $N$ population positions in space and calculates each individual’s fitness value. The optimal position and corresponding fitness value are determined by sorting fitness values. Individuals update their positions according to Equation (11).

$$\begin{array}{c}\overrightarrow{X_d^i}\left(t+1\right)=\left\{\begin{array}{c}\overrightarrow{X_d^i}\left(t\right)+\overrightarrow{a}\cdot \mathit{sin}\left(r_3\right)\cdot \left|r_4\cdot \overrightarrow{X^{*}}\left(t\right)-\overrightarrow{X_d^i}\left(t\right)\right| r_5<0.5\\ \overrightarrow{X_d^i}\left(t\right)+\overrightarrow{a}\cdot \mathit{cos}\left(r_3\right)\cdot \left|r_4\cdot \overrightarrow{X^{*}}\left(t\right)-\overrightarrow{X_d^i}\left(t\right)\right| r_5\ge 0.5\end{array}\right.\end{array}$$

(11)

where $\overrightarrow{X_d^i}$ is the position component of the d-th dimension of the i-th individual in the t-th generation, and $\overrightarrow{X^{*}}(t)$ is the current optimal position. The parameter $\overrightarrow{a}$ governs search direction and changes according to Equation (5). The random number $r_3$ drawn from the interval $[0, 2\pi ]$ controls the algorithm’s search distance. The random number $r_4$ drawn from the interval $[0, 2]$ and $r_5$ drawn from the interval [0, 1] determine whether position updates in generation $t+1$ occur via sine or cosine functions.

In the whale optimization algorithm, assigning the position with the best fitness value to the whale swarm leader at each iteration can cause the algorithm to become trapped in local optima, reducing optimization search accuracy. In contrast, the SCA can randomly select sine cosine cross-seeking optimization, allowing position updating methods to complement one another and better balance global exploration and local exploitation. This enables SCA to gradually converge and hover near target solutions. In this paper’s proposed sine cosine whale optimization algorithm, instead of proceeding directly to subsequent iterations, the current leader position is recorded after sorting to preserve superiority. Each individual’s position is updated according to Equation (11) using sine or cosine functions. The fitness value of each individual is then calculated, and a new leader position determined by comparing fitness values. A greedy mechanism is introduced by comparing fitness values between leaders before and after sine cosine operations and updating global optimal positions before proceeding to subsequent iterations. Notably, random parameters $r_3$, $r_4$, and $r_5$ in the SCA are generated via tent chaos mapping in this paper to accelerate algorithm convergence.

2.3.3. Chaos-Based Adaptive Inertia Weight

In most current swarm intelligence optimization algorithms, weights play a crucial role in balancing global exploration and local exploitation capabilities. Weights reflect the ability of followers to escape previous positions. Larger inertia weights typically enhance global exploration abilities while smaller weights improve local exploitation abilities [31]. Accordingly, this paper proposes using larger weights during early iterations of the whale algorithm to enable whales to quickly approach target values. Smaller weights should be used during later iterations to facilitate precise local search near target solutions. The standard WOA employs fixed weight values for search envelopes and position updates. This paper proposes a chaos-based adaptive inertia weight, as shown in Equation (12).

$$\begin{array}{c}\omega ={\omega }_s+\left({\omega }_e-{\omega }_s\right)\cdot {\mathit{log}}_{10}\left(1+{\displaystyle \frac{10t}{T_{max}}}\right)\end{array}$$

(12)

where $T_{max}$ denotes the maximum number of iterations set in the algorithm; ${\omega }_s$ denotes the initial value of inertia weights at the beginning of the iteration, and its value is 0.4; and ${\omega }_e$ represents the value of the inertia weight when the maximum number of iterations is reached, and its value is 0.9. The experimental results demonstrate that the algorithm exhibits superior search capabilities when $\omega$ varies between $[0.4, 0.9]$. As iterations progress, inertia weight decreases nonlinearly from 0.9 to 0.4, enabling dynamic weight changes and better balancing global search and local exploitation capabilities. This also increases the likelihood of escaping local optima to some extent. Considering random whale position vectors selected during prey search phases, this paper presents an IWOA position update formula in Equation (13).

$$\begin{array}{c}\overrightarrow{X}\left(t+1\right)=\left\{\begin{array}{c}\omega \cdot \overrightarrow{X^{*}}\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D} \left|\overrightarrow{A}\right|<1 , p^{Tent}<0.5 \\ \omega \cdot \overrightarrow{X_{rand}}\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D_{rand}} \left|\overrightarrow{A}\right|\ge 1 , p^{Tent}<0.5\\ \overrightarrow{D^{\prime }}\cdot e^{bl}\cdot \mathit{cos}\left(2\pi l\right)+\omega \cdot \overrightarrow{X^{*}}\left(t\right) p^{Tent}\ge 0.5\end{array}\right.\end{array}$$

(13)

2.4. The IWOA-BPNN Model

In this study, we employed the IWOA to optimize the weights and thresholds of the BP neural network model. This approach improved the model’s prediction accuracy [32]. The core concept of the IWOA optimization involves using the weights and thresholds in the BP neural network as whale location information. Updating the whale’s location is equivalent to updating the BP neural network’s weights and thresholds until a global optimal solution is achieved [33]. This enhances the BP neural network’s prediction capability and efficiency. By incorporating the IWOA, we were able to dynamically optimize the weights and thresholds of the BP neural network to obtain more stable prediction results. Figure 3 illustrates the flowchart of our proposed IWOA-BP model.

Firstly, we normalized the data using Equation (14). Secondly, we employed tent chaotic mapping to initialize the location of the whale population according to Equation (10). We generated random parameters such as uniformly distributed parameters $p^{Tent}$, $\overrightarrow{r_1}$, and $\overrightarrow{r_2}$ according to Equation (10) and used them to update the values of parameters $\overrightarrow{a}$, $\overrightarrow{A}$, $\overrightarrow{C}$, and l. The value of ω was calculated using Equation (12). By evaluating the values of $p^{Tent}$ and $\left|\overrightarrow{A}\right|$ and in accordance with Equation (13), we updated individual positions of the whale population using an adaptive weighting strategy to obtain the optimal position $\overrightarrow{X^{*}}(t)$. Finally, we updated the global optimal position by performing sine cosine operations on the position through Equation (11), comparing fitness values and filtering for a new leader position. When iteration reached its maximum value, we outputted an optimal solution and obtained optimal weights and thresholds for the BP neural network.

3. Results and Discussion

3.1. Data Preprocessing

The experimental data were obtained from the literature [12]. The material was obtained from alder (Alnus glutinosa Goertn.), beech (Fagus sylvatica L.), birch (Betula verrucosa Ehrh.), and pine (Pinus sylvestris L.) logs at the Sklejka-Multi S.A. plywood company in Bydgoszcz, Poland. Defect-free veneer sheets of 3,003,001.5 mm³ with 5% moisture were then transported to the laboratory. Tangential sheets of veneer were cut into 140,100 mm² rectangular pieces for the thermo-mechanical densification process and subsequent measurements. Prior to thermo-mechanical densification, all test samples were equilibrated at a temperature of 20 °C and relative humidity of 65%. Three different densification temperatures (100, 150, and 200 °C) and three densification pressures (4, 8, and 12 MPa) were applied to wood samples [34]. Each wood sample was thermo-mechanically densified for 4 min between smooth and thoroughly cleaned heated plates of the press at applied temperatures and pressures. In order to enhance the comparability of the research results and highlight the advantages of the proposed model, this study adopted the same data segmentation method as in the literature [12] and retained the same experimental parameters, including sample size, thermomechanical densification treatment temperature, time and pressure, and the choice of incident light angle when evaluating gloss.

Through these experiments, we obtained 216 sets of surface gloss data for heat-treated wood under varying conditions. To ensure data accuracy, we randomly selected 70% of these datasets as our training set and used the remaining 30% as our prediction set. Due to variations in dimensional sizes among the five input parameters, we normalized input data using Equation (14) to mitigate any impact on training speed and prediction accuracy of the model [35].

$$y=\left(y_{max}-y_{min}\right)\times {\displaystyle \frac{\left(x-x_{min}\right)}{\left(x_{max}-x_{min}\right)}}+y_{min}$$

(14)

where y is the normalized value of x; $y_{min}$ and $y_{max}$ are the normalized intervals set to −1, 1; and $x_{min}$ and $x_{max}$ are the minimum and maximum values of x, respectively.

3.2. Model Parameter Setting

The BP neural network in the IWOA-BP model employs a three-layer structure. Its input layer consists of five nodes corresponding to species, temperature, pressure, grain direction, and angle of incidence of input data. The output layer has one node representing wood surface gloss. The number of nodes in the hidden layer is typically determined using empirical Equation (15), where $\mathrm{w}$ is any number between 1 and 10. This yields a range of [4, 12] for hidden layer nodes, as shown in Equation (15).

$$\sqrt{\left(u+v\right)}+w,w\in \left[\mathrm{1,10}\right]$$

(15)

where h, u, and v represent the number of nodes in the hidden layer, input layer, and output layer, respectively.

After several calculations, we obtained the RMSE values for the training set corresponding to different hidden layer nodes, as shown in

Table 1. Implicit layer nodes and their corresponding model errors.

Number of Hidden Layer Nodes	MAE/MPa
4	0.0039501
5	0.0055646
6	0.0013694
7	0.0065983
8	0.0020393
9	0.0017918
10	0.0043294
11	0.0034053
12	0.0023211

The bold formatting here is used to indicate that when the Number of Hidden Layer Nodes is 6, the MAE/MPa value of 0.0013694 represents the minimum error (i.e., the optimal value), signifying the best model prediction performance at this setting.

. We selected the hidden layer node with the smallest RMSE value as the optimal node for the BP neural network. As indicated in Table 1, the optimal number of hidden layer nodes is 6 with a corresponding RMSE value of 0.0013694.

In this study, we employed a BP neural network model to predict glossiness for four different tree species. Our model used tree species, temperature, pressure, grain direction, and incidence angle as input nodes and glossiness as output nodes. The resulting prediction model is illustrated in Figure 4.

We optimized the weights and thresholds of the BP neural network model using the IWOA to enhance prediction accuracy for wood surface glossiness. The BP neural network had a maximum iteration of 1000, the target error was 0.0001, the learning rate was 0.01, while the IWOA-BP model had a maximum iteration of 20 and population size of 30.

3.3. Analysis of Simulation Rxesults of the WOA-BP Model

To evaluate the effectiveness of the IWOA-BP model, we compared mean absolute error (MAE), root mean square error (RMSE), and goodness of fit (R²) for different algorithms. Smaller values indicated better prediction performance, as expressed in the following equation:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|A_i-F_i\right|$$

(16)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{\sum _{i=1}^N{\left(A_i-F_i\right)}^2}{N}}}$$

(17)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{100}{N}}\sum _{i=1}^N\left|{\displaystyle \frac{A_i-F_i}{A_i}}\right|$$

(18)

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum _{i=1}^N{\left(A_i-F_i\right)}^2}{\sum _{i=1}^N{\left(\overline{A_i}-A_i\right)}^2}}$$

(19)

where N is the total number of samples, and $A_i$ and $F_i$ represent the actual value and the predicted value, respectively.

This paper used MATLAB 2022 to process the experimental data and employed the IWOA-BP model to predict glossiness of heat-treated wood. The results are presented in Appendix A of

Table A1. Measured and predicted values of glossiness.

Grain Orientation	Temperature	Pressure	Angle of Incidence	Measured	Predicted	Measured	Predicted	Measured	Predicted	Measured	Predicted
				Alder		Beech		Birch		Pine
Radial	100 °C	4 MPa	20°	1.10	1.21	0.90	0.53	1.40	1.08	1.60	1.75
			60°	3.90	3.28	2.80	3.56	4.30	3.84	6.70	6.39
			85°	5.20	4.11	3.30	3.14	4.20	4.92	9.00	10.42
		8 MPa	20°	1.20	0.62	1.00	1.18	1.50	2.66	1.70	1.28
			60°	4.50	3.73	3.50	3.22	5.50	5.63	7.40	6.64
			85°	5.70	5.11	5.40	5.55	5.80	6.17	7.60	8.56
		12 MPa	20°	1.20	0.66	1.10	0.97	1.50	2.76	1.80	1.06
			60°	5.10	3.98	4.00	3.17	5.80	5.00	7.80	6.97
			85°	5.70	6.40	5.50	4.43	6.70	7.57	9.60	10.01
	150 °C	4 MPa	20°	1.10	0.64	1.00	1.14	1.30	1.01	1.60	2.37
			60°	4.50	4.73	3.20	3.67	4.50	4.15	6.60	8.37
			85°	7.30	8.25	4.80	5.56	7.80	7.12	10.30	10.82
		8 MPa	20°	1.30	0.78	1.10	1.01	1.60	0.61	1.90	1.74
			60°	5.50	5.35	4.10	3.39	6.30	5.50	8.70	9.15
			85°	10.80	10.15	8.10	6.23	13.90	12.85	18.70	17.09
		12 MPa	20°	1.30	1.11	1.10	0.93	1.70	1.83	1.70	0.81
			60°	5.40	3.68	4.20	4.19	6.80	7.66	8.30	7.94
			85°	8.20	9.63	7.40	7.85	17.20	15.25	21.50	20.59
	200 °C	4 MPa	20°	1.10	1.56	0.70	1.23	1.20	1.32	1.60	1.53
			60°	4.90	5.25	3.30	3.33	5.10	4.16	7.90	8.43
			85°	12.00	11.86	7.90	8.64	12.10	11.43	21.40	19.65
		8 MPa	20°	1.20	1.18	0.90	0.81	1.20	1.43	1.60	1.32
			60°	7.00	6.59	4.40	3.38	6.50	6.67	8.90	7.45
			85°	23.80	22.98	8.80	9.00	15.80	17.65	29.40	29.49
		12 MPa	85°	1.50	1.72	1.00	0.82	1.70	1.02	2.20	1.82
			20°	8.30	8.25	5.30	4.20	8.50	9.77	11.50	13.29
			60°	24.30	23.26	12.80	13.74	23.10	24.62	32.30	31.12
Tangential	100 °C	4 MPa	20°	1.20	1.54	1.10	1.05	1.50	2.26	1.80	1.65
			60°	5.40	5.89	4.00	5.14	6.20	5.66	9.80	8.84
			85°	10.50	9.44	5.50	4.99	7.70	9.09	18.60	17.85
		8 MPa	20°	1.30	1.40	1.10	1.12	1.60	1.56	1.90	1.73
			60°	6.00	4.78	4.50	3.99	7.30	6.72	10.50	9.22
			85°	12.60	10.92	8.90	9.17	14.70	13.25	17.90	17.44
		12 MPa	85°	1.30	0.83	1.10	1.56	1.70	1.41	1.80	1.96
			20°	6.60	7.02	4.70	4.52	8.30	10.09	10.00	10.19
			60°	14.20	13.11	12.00	12.35	17.30	15.95	18.30	19.11
	150 °C	4 MPa	20°	1.20	0.94	1.00	1.17	1.50	1.79	1.80	1.06
			60°	6.40	7.02	4.20	3.29	7.00	6.19	9.90	10.02
			85°	16.90	15.02	7.30	8.07	12.70	12.28	19.30	20.07
		8 MPa	20°	1.40	1.69	1.10	1.63	1.70	2.13	2.10	1.81
			60°	7.90	9.20	5.50	6.97	9.10	8.13	13.00	11.45
			85°	18.10	18.33	12.70	13.12	20.40	18.71	27.50	26.28
		12 MPa	20°	1.40	1.45	1.10	1.16	1.90	1.99	1.90	2.05
			60°	7.50	8.00	5.50	4.73	10.20	11.68	11.90	12.22
			85°	16.40	18.30	14.10	15.95	25.70	24.98	29.80	29.29
	200 °C	4 MPa	20°	1.20	1.30	0.80	0.73	1.30	1.69	1.70	2.06
			60°	7.50	7.91	4.70	3.57	8.00	7.56	11.00	10.65
			85°	21.20	21.26	13.90	14.90	19.40	18.79	27.10	26.06
		8 MPa	20°	1.40	1.74	0.90	0.73	1.40	0.98	1.80	1.04
			60°	10.70	10.22	6.00	6.95	9.90	9.55	13.30	13.42
			85°	31.50	31.41	17.30	18.14	24.70	26.88	35.30	34.59
		12 MPa	20°	1.70	1.56	1.00	0.80	1.90	1.01	2.30	2.46
			60°	12.30	13.05	6.80	7.09	13.60	14.09	16.30	16.87
			85°	32.20	33.69	21.70	21.76	37.20	37.18	39.50	39.53

.

Table A1 presents a comparison between actual measured glossiness values for different tree species under varying conditions and predicted values from the IWOA-BP model. The predicted values closely matched the actual measured values. Appendix A of

Table A2. Comparison of prediction errors of three models: BP, WOA-BP, and IWOA-BP.

Grain Orientation	Temperature	Pressure	Angle of Incidence	Alder			Beech			Birch			Pine
				BP	WOA-BP	IWOA-BP	BP	WOA-BP	IWOA-BP	BP	WOA-BP	IWOA-BP	BP	WOA-BP	IWOA-BP
Radial	100 °C	4 MPa	20°	−2.07	0.78	0.11	−1.73	−0.47	−0.36	1.55	−1.50	−0.31	−0.32	−1.03	0.15
			60°	0.42	0.20	−0.61	1.48	−0.16	0.76	0.36	−0.44	−0.45	−0.17	1.48	−0.30
			85°	0.61	1.07	−1.08	2.80	0.28	−0.15	2.47	0.13	0.72	0.24	2.47	1.42
		8 MPa	20°	−0.56	1.33	−0.57	0.97	−1.11	0.18	−0.12	−0.31	1.16	0.11	0.55	−0.41
			60°	−0.14	−0.37	−0.76	−0.02	−0.50	−0.27	1.10	2.59	0.13	−0.13	4.80	−0.75
			85°	0.56	0.77	−0.58	1.42	−0.01	0.15	−0.33	−0.20	0.37	3.95	5.50	0.96
		12 MPa	20°	0.41	−0.92	−0.53	0.58	−0.09	−0.12	−0.70	−0.25	1.26	−1.39	2.47	−0.73
			60°	−0.21	−0.84	−1.11	−1.32	−0.31	−0.82	2.24	3.58	−0.79	−0.65	0.89	−0.82
			85°	0.59	2.32	0.70	−0.36	−0.35	−1.06	2.40	5.01	0.87	3.07	5.84	0.41
	150 °C	4 MPa	20°	1.57	0.16	−0.45	−1.56	−0.17	0.14	−1.16	−0.88	−0.28	1.49	−0.14	0.77
			60°	0.16	−0.01	0.23	1.01	−0.44	0.47	0.18	−0.62	−0.34	−1.68	1.79	1.77
			85°	0.11	−0.63	0.95	3.14	1.21	0.76	1.06	2.46	−0.67	1.51	2.65	0.52
		8 MPa	20°	1.54	1.78	−0.51	0.94	0.97	−0.08	1.13	0.39	−0.98	−0.28	−1.66	−0.15
			60°	2.53	−0.84	−0.14	0.49	−0.59	−0.70	0.23	−1.56	−0.79	−0.87	0.63	0.45
			85°	−1.59	−2.01	−0.64	2.05	0.30	−1.8	3.75	−2.46	−1.04	−2.59	−2.93	−1.60
		12 MPa	20°	−2.89	0.72	−0.18	−1.66	−0.14	−0.16	−0.75	−0.58	0.13	−0.09	−2.08	−0.88
			60°	−2.03	−0.56	−1.71	1.88	3.94	−0.01	6.50	−1.09	0.86	−2.62	−0.78	−0.35
			85°	2.49	4.19	1.43	4.71	1.87	0.45	−1.80	−1.69	−1.94	−2.10	−1.59	−0.90
	200 °C	4 MPa	20°	−1.82	0.56	0.46	−0.55	0.06	0.53	1.75	0.92	0.12	2.04	1.32	−0.06
			60°	−0.16	−0.04	0.35	0.58	2.21	0.03	−2.92	−0.44	−0.93	−1.85	0.63	0.53
			85°	0.38	0.69	−0.13	−0.45	1.47	0.74	0.61	−0.35	−0.66	−5.54	−4.95	−1.74
		8 MPa	20°	1.79	1.56	−0.01	1.61	−0.79	−0.08	1.01	0.63	0.23	1.01	1.35	−0.27
			60°	−1.00	−1.16	−0.40	1.87	0.13	−1.01	1.69	−1.06	0.17	0.80	1.09	−1.44
			85°	−9.52	−9.25	−0.81	7.12	5.22	0.20	3.09	0.95	1.85	−6.11	−7.74	0.09
		12 MPa	20°	1.67	−0.53	0.22	−0.10	0.37	−0.17	0.56	2.16	−0.67	−0.08	−0.14	−0.37
			60°	−2.46	−1.31	−0.04	2.06	1.22	−1.09	2.43	−0.63	1.27	0.56	1.30	1.79
			85°	−5.91	−3.29	−1.03	7.91	7.99	0.94	2.12	0.85	1.52	−2.73	−3.20	−1.17
Tangential	100 °C	4 MPa	20°	−1.39	1.42	0.34	1.67	−0.56	−0.04	0.42	−0.74	0.76	1.05	0.48	−0.14
			60°	−0.59	0.73	0.49	0.99	−0.23	1.14	−1.00	−0.86	−0.53	−4.36	0.04	−0.95
			85°	−3.22	0.19	−1.05	1.45	1.30	−0.50	0.73	2.57	1.39	−9.42	−4.64	−0.74
		8 MPa	20°	−0.81	−1.00	0.10	0.91	−0.69	0.02	0.33	0.57	−0.03	0.11	2.55	−0.16
			60°	−1.59	1.97	−1.21	−1.15	−0.55	−0.50	−2.31	−1.13	−0.57	−5.04	−3.00	−1.27
			85°	−3.82	−3.22	−1.67	0.25	0.39	0.27	−3.94	−1.98	−1.44	−5.93	−1.47	−0.45
		12 MPa	20°	0.54	1.50	−0.46	−2.17	0.56	0.46	1.01	−1.48	−0.28	−0.06	2.34	0.16
			60°	−0.29	−0.42	0.42	0.56	0.90	−0.17	0.59	2.17	1.79	−3.61	1.61	0.19
			85°	−3.15	−1.57	−1.08	−1.48	−1.94	0.35	7.01	6.28	−1.34	−2.59	1.73	0.81
	150 °C	4 MPa	20°	−3.45	−1.28	−0.25	1.60	−0.34	0.17	−2.36	−0.53	0.29	−0.85	1.56	−0.73
			60°	−0.60	−0.84	0.62	0.05	0.04	−0.90	−0.59	−1.57	−0.80	1.52	−0.02	0.12
			85°	−6.58	−6.53	−1.87	4.03	2.61	0.77	−0.19	0.06	−0.41	−5.44	−2.25	0.77
		8 MPa	20°	0.07	1.10	0.29	1.67	0.01	0.53	−0.05	1.27	0.43	−0.07	1.09	−0.28
			60°	3.53	−1.49	1.30	−1.18	1.66	1.47	−1.83	−2.66	−0.96	−4.85	−1.89	−1.54
			85°	−4.31	−3.64	0.23	2.65	1.43	0.42	−3.29	−3.12	−1.68	−8.41	−5.81	−1.21
		12 MPa	20°	1.68	0.28	0.05	0.23	0.23	0.06	1.55	1.32	0.09	0.62	1.15	0.15
			60°	−0.22	−0.55	0.50	2.30	−0.79	−0.76	−1.26	−1.68	1.48	−1.61	1.59	0.32
			85°	1.93	4.06	1.90	6.44	6.31	1.85	−2.74	−1.74	−0.71	−4.17	−1.24	−0.50
	200 °C	4 MPa	20°	1.58	1.01	0.10	0.28	0.02	−0.06	0.89	1.03	0.39	0.40	−0.39	0.36
			60°	0.01	0.28	0.41	3.35	0.40	−1.12	0.60	−1.63	−0.43	−1.94	−0.18	−0.34
			85°	−5.30	−4.23	0.06	−1.78	2.45	1.00	0.20	−0.46	−0.60	−5.34	−3.27	−1.03
		8 MPa	20°	0.74	0.39	0.34	−1.60	−0.54	−0.16	0.14	−1.40	−0.41	0.46	2.56	−0.75
			60°	−1.46	−1.66	−0.47	4.26	−0.44	0.95	−3.15	−0.68	−0.34	−0.41	0.80	0.12
			85°	−9.56	−7.61	−0.08	−3.38	−0.98	0.84	2.15	1.90	2.18	−5.70	−3.56	−0.70
		12 MPa	20°	0.29	−1.09	−0.13	−1.53	−0.75	−0.19	0.81	−1.62	−0.88	1.61	0.61	0.16
			60°	−0.44	0.95	0.75	0.67	5.89	0.29	1.35	0.87	0.49	0.97	3.49	0.57
			85°	−2.94	−0.42	1.49	10.42	10.04	0.06	−2.13	−2.11	−0.01	−1.34	0.81	0.03

compares error values for predicted glossiness from BP, WOA-BP, and IWOA-BP models. The IWOA-BP model had smaller prediction errors than BP and WOA-BP models, with most errors being less than 1. And the IWOA-BP model demonstrated high accuracy in predicting glossiness of heat-treated wood with minimal error between predicted and actual measured values.

Table 2. Comparison of the errors of the three models.

Model	Dataset	Performance Criteria
		MAE/MPa	RMSE/MPa	MAPE/%	R2
BP	Train	1.9142	0.4026	2.7318	0.8768
	Test	2.0683	0.4937	2.9391	0.8758
WOA-BP	Train	1.5444	0.3106	2.2625	0.9155
	Test	1.8179	0.4118	2.6275	0.9007
IWOA-BP	Train	0.6210	0.1287	0.7834	0.9898
	Test	0.7029	0.1767	0.8935	0.9885

presents performance evaluation results for BP, WOA-BP, and IWOA-BP models. For the training set, the MAE value of the BP prediction model was 1.9142, the MAPE value was 0.4026, the RMSE value was 2.7318, and the $R^2$ value was 0.8768, while the MAE value of the WOA-BP prediction model was 1.5444, the MAPE value was 0.3106, the RMSE value was 2.2625, and the $R^2$ value was 0.9155. In comparison, the MAE value of the IWOA-BP prediction model was 0.6210, the MAPE value was 0.1287, the RMSE value was 0.7834, and the $R^2$ value was 0.9898. Compared to the BP model, the IWOA-BP model reduced MAE by 67.56%, MAPE by 68.03%, and RMSE by 71.32%. For the test set, the MAE value of the BP prediction model was 2.0683, the MAPE value was 0.4937, the RMSE value was 2.9391, and the value was 0.8758, while the MAE value of the WOA-BP prediction model was 1.8179, the MAPE value was 0.4118, the RMSE value was 2.6275, and the $R^2$ value was 0.9007. In contrast, the MAE value of the IWOA-BP prediction model was 0.7029, the MAPE value was 0.1767, the RMSE value was 0.8935, and the $R^2$ value was 0.9885 for the test set. Compared to the BP model, the IWOA-BP model reduced MAE by 66.02%, MAPE by 64.21%, and RMSE by 69.60%. Our results demonstrate that incorporating IWOA significantly improved prediction accuracy for the BP model. We also optimized the BP model using the original WOA, but its performance was inferior to our proposed IWOA-BP model. Therefore, the IWOA-BP model outperformed traditional BP neural networks and WOA-BP models in predicting glossiness for different external environments, heat treatment conditions, and wood types with superior prediction capability.

Meanwhile, as can be seen from Table 2, although glossiness is a small-scale measurement, the MAPE values were low (such as less than 1% in the IWOA-BP model). This may have been due to the following reasons:

Firstly, the IWOA-BP model was designed with advanced optimization techniques. The improved whale optimization algorithm (IWOA) enhances the performance of the back propagation neural network (BPNN). It initializes the population using tent chaos mapping, which provides a more uniform distribution of initial solutions. This reduces the randomness and unevenness in the initial search space, allowing the model to converge more effectively towards the optimal solution. The combination of IWOA with the sine cosine algorithm further improves the model’s ability to explore and exploit the solution space. By leveraging the advantages of both algorithms, the IWOA-BP model can better capture the complex relationships between input variables (such as species, temperature, pressure, grain direction, and incidence angle) and glossiness.

Secondly, the data preprocessing steps also contribute to the low MAPE values. A consistent data segmentation method is adopted, and all data are uniformly normalized. All data are normalized using a specific equation, which mitigates the impact of different dimensional sizes among input parameters on the training speed and prediction accuracy of the model. This normalization ensures that each variable is on a comparable scale, enabling the model to learn from the data more efficiently.

Figure 5 depicts the prediction outcomes of BP, WOA-BP, and IWOA-BP models for the glossiness of heat-treated wood. The results demonstrate that the predicted values obtained from BP neural networks optimized with WOA and IWOA were in closer agreement with the actual values, suggesting that the application of WOA or IWOA significantly enhances the prediction accuracy of BP neural networks. Notably, the IWOA-BP model exhibited superior prediction accuracy compared to the WOA-BP model. The exceptional performance of the IWOA-BP model in predicting glossiness confirms its applicability and indicates its potential for predicting glossiness values across various tree species and processing conditions.

3.4. Performance Analysis in CEC Tests

CEC tests has achieved significant acclaim and is regarded as a gold standard for evaluating the effectiveness of optimization algorithms, offering a highly reliable and authoritative benchmark [36]. To conduct a fair and comprehensive assessment of the performance of the improved whale optimization algorithm (IWOA), four benchmark functions from the CEC2022 test set were carefully selected, as detailed in

Table 3. Specific information of the test functions.

Function	Formula	Dim	Search Range	Best Value
F1	$f(x)={\sum }_{i=1}^D{x}_i^2+{\left({\sum }_{i=1}^{D}0.5x_i\right)}^2+{\left({\sum }_{i=1}^{D}0.5x_i\right)}^4$	10/20	[−100, 100]	300
F2	$f(x)={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{D}-1}}\left[100{\left({\mathrm{x}}_{\mathrm{i}+1}-{\mathrm{x}}_{\mathrm{i}}^2\right)}^2+{\left({\mathrm{x}}_{\mathrm{i}}-1\right)}^2\right]$	10/20	[−100, 100]	600
F7	$f(x)={\left|{\left({\sum }_{i=1}^D{x}_i^2\right)}^2-{\left({\sum }_{i=1}^D{x}_i\right)}^2\right|}^{0.5}+(0.5{\sum }_{i=1}^D{x}_i^2+{\sum }_{i=1}^D{x}_i)/D+0.5$	10/20	[−100, 100]	2000
F9	$f(x)={\displaystyle \frac{10}{D^2}}{\prod }_{1=1}^D{(1+i{\sum }_{j=1}^{32}{\displaystyle \frac{\left|2^j{x}_i-round\left(2^j{x}_i\right)\right|}{2^j}})}^{{\displaystyle \frac{10}{D^{1.2}}}}-{\displaystyle \frac{10}{D^2}}$	10/20	[−100, 100]	2300

.

The unimodal function F1 was employed to evaluate convergence accuracy, as it features a single global optimum. This function effectively reflects an algorithm’s ability to locate the global optimum without being distracted by local optima. In the context of gloss prediction, accurate convergence toward the optimal weights and thresholds of the BPNN is critical. IWOA’s rapid convergence on F1 thus translates directly into improved training efficiency and predictive accuracy.

The multimodal function F2 is used to test global exploration capabilities and the ability to escape local optima. In gloss prediction, the relationship between input parameters (e.g., species, temperature, pressure, grain direction, and incident angle) and gloss is complex and nonlinear, with many potential suboptimal solutions. IWOA’s strong performance on F2 demonstrates its capacity to effectively explore diverse parameter spaces and avoid premature convergence.

Function F7, a hybrid function composed of several sub-functions with varying characteristics, simulates complex real-world scenarios with strong interdependencies among variables. IWOA’s adaptability on F7 underscores its robustness in modeling intricate variable relationships in gloss prediction tasks.

Function F9 is a composite function designed to mimic high-dimensional constrained problems. While gloss prediction is not strictly high-dimensional, it involves multiple interacting parameters, presenting similar challenges. IWOA’s competence on F9 indicates its ability to manage this complexity, enabling accurate and efficient modeling of gloss in thermally modified wood.

In summary, the four CEC2022 functions—F1, F2, F7, and F9—represent distinct aspects of optimization problems relevant to gloss prediction in thermally treated wood. They facilitate a thorough evaluation of IWOA’s performance in terms of convergence speed, global search capability, adaptability to complex interactions, and handling of intricate data structures.

For a more in-depth understanding of the algorithms’ performance across different levels of complexity, two different dimensionalities, 10 dimensional and 20 dimensional, were selected for each test function. This allowed us to evaluate how the algorithms perform in both low-dimensional and high-dimensional search spaces. The details of the selected test functions, including their formulas, dimensionalities, search ranges, and known best values, are presented comprehensively in Table 3.

In the experimental setup, the maximum number of iterations was set to 500, the number of independent runs for each method was 30, and the population size was 30. These parameters were carefully chosen to ensure a reliable and consistent evaluation. After running each algorithm 30 times independently, the optimal value, maximum value, mean value, and standard deviation were calculated. These statistical measures provide a quantitative assessment of the algorithms’ performance.

The convergence curves of the IWOA, whale optimization algorithm (WOA), particle swarm optimization (PSO), and genetic algorithm (GA) are presented in Figure 6.

Figure 6 vividly depicts the convergence behavior of the IWOA, WOA, PSO, and GA across different dimensions and test functions. A detailed analysis of these curves reveals significant differences in the performance of these algorithms. The IWOA demonstrated a remarkable convergence rate that outperformed the WOA, PSO, and GA. In most cases, the IWOA reached the optimal or near-optimal solution much faster than the other algorithms.

The convergence process of the IWOA was almost linear in many instances, which indicates its highly efficient search strategy. This linear-like convergence implies that the IWOA can effectively explore the search space and move towards the global optimum in a relatively straightforward manner. Additionally, by examining the curve fitting, it became evident that the IWOA had stronger local exploration capabilities compared to the other three algorithms. This advantage is particularly crucial when dealing with high-dimensional and complex problems, where a balance between global exploration and local exploitation is essential.

In high-dimensional problems, the search space becomes extremely large and complex, and algorithms often struggle to find the optimal solution. The IWOA’s ability to efficiently explore the local regions around potential solutions allows it to fine-tune its search and achieve higher precision. When considering the mean values and standard deviations calculated from the 30 independent runs, the IWOA also showed greater stability. The relatively small standard deviation indicates that the IWOA can consistently produce solutions that are close to the optimal value, while the other algorithms may have more variability in their results.

Overall, through comprehensive comparison and analysis, it is clear that the IWOA provides solutions with higher accuracy, greater stability, and faster convergence. These findings highlight the superiority of the IWOA over the WOA, PSO, and GA in solving optimization problems using the CEC2022 test functions. This research not only validates the effectiveness of the IWOA but also provides valuable insights for further improving optimization algorithms and solving complex real-world problems.

3.5. Analysis of Input Feature Importance

Feature importance analysis offers valuable perspectives on which features exert the most substantial influence on the prediction result. When it comes to predicting the glossiness of heat-treated wood, this analysis enables us to pinpoint the crucial elements that impact the glossiness. Additionally, it can assist us in comprehending how sensitive the prediction outcome is to alterations in the input features. Such an understanding can direct us in precisely adjusting the input parameters to attain the best possible prediction outcomes.

The XGBoost model is highly regarded for its excellent performance and efficiency in dealing with complex data patterns [37]. One of its notable strengths is its proficiency in conducting feature importance analysis. This feature allows us to delve into the contribution of each feature to the prediction outcome, deepening our comprehension of the prediction mechanism. In our research, we opted for the XGBoost model to assess the significance of various input factors in predicting the glossiness of heat-treated wood. These factors encompass grain direction, treatment temperature, treatment pressure, incidence angle, and tree species. To more accurately determine the contribution rate of each feature, we normalized the feature importance values to fall within the range of 0 to 1. The outcomes of the importance analysis for each input feature are vividly presented in the provided chart.

As shown in Figure 7, the importance of the five input features in predicting the glossiness of heat-treated wood varied.

Grain Direction: With an importance score of 36.64%, it emerged as the most influential factor affecting wood glossiness in this study. This significant weight suggests that the orientation of the wood fibers relative to the surface plane critically determines how light interacts with the material. The anisotropic nature of wood means that its surface properties, including roughness, reflectance, and microstructural arrangement, vary with grain orientation [38]. Specifically, when the grain runs parallel to the measurement or viewing direction, the surface may appear smoother and more uniform, enhancing specular reflection and perceived gloss [39]. In contrast, when the grain is oriented perpendicularly or at an angle, increased micro-roughness and diffuse reflection can lead to a reduction in glossiness. Furthermore, thermal treatment accentuates this effect by altering the cell wall structure and surface chemistry differently along and across the grain [40]. The differential thermal degradation of hemicellulose and lignin, as well as pressure-induced densification during processing, may lead to uneven surface topography depending on the grain orientation. These variations can further modify how incident light is scattered or absorbed, thereby amplifying the visual differences in glossiness between radial, tangential, and longitudinal surfaces [41]. Therefore, grain direction not only affects the intrinsic optical response of wood but also interacts with thermal and mechanical treatment parameters to shape the final surface appearance. This finding underscores the need to account for grain orientation when designing heat treatment protocols or surface finishing strategies aimed at achieving specific gloss characteristics.

Treatment Temperature: The second most important feature is the treatment temperature, with an importance score of 24.57%. Temperature and pressure are critical factors influencing wood gloss during thermal treatment, and their effects are driven by intricate physical and chemical mechanisms [42]. Previous studies have shown that different wood species respond distinctively to thermal treatment temperatures. For alder, beech, birch, and pine, the common treatment temperature range of 160–250 °C brings about significant changes. In our study, we specifically examined these four species at 100 °C, 150 °C, and 200 °C. Elevated temperatures in the 160–250 °C range cause hemicellulose thermal degradation. Glycosidic bond cleavage reduces its polymerization degree, loosening the wood surface microstructure, increasing roughness, enhancing light scattering, and reducing gloss [6]. For example, in alder wood, 100 °C causes mild hemicellulose degradation with less-obvious gloss and roughness changes, while 200 °C accelerates degradation, leading to more significant changes. Simultaneously, lignin undergoes pyrolysis and condensation. These reactions fragment molecules and may cause cross-linking, altering its distribution and optical behavior, and affecting light absorption and reflection [43]. Lignin in birch responds differently to temperature than in alder; at 150 °C, birch lignin may form more cross-links, uniquely impacting gloss. Previous studies support our findings. Bekhta and Niemz [35] found that higher treatment temperatures in spruce decreased hemicellulose and increased lignin-related changes, affecting surface properties. Esteves et al. [9] observed that treatment temperatures influenced heat-treated pine’s long-term surface properties due to hemicellulose degradation and lignin transformation. These are consistent with our observations in alder, beech, birch, and pine, validating the complex relationship between temperature, wood components, and gloss.

Treatment Pressure: The treatment pressure has an importance score of 22.90%. When wood undergoes thermal compression, cell walls are compacted. This is not just simple mechanical squeezing, it is a complex process that impacts the wood’s internal microscopic structure [44]. The microfibrils in the cell walls, vital for the wood’s mechanical and surface properties, become realigned. This realignment increases the local density of the wood, directly affecting the refractive and scattering properties of the wood surface [45]. Physically, a higher density changes how light interacts with the wood. For example, it can cause more light absorption or different-pattern scattering, influencing the wood’s gloss [46]. During thermal treatment, pressure also helps extractives, especially chromophoric compounds (which absorb visible-spectrum light and determine wood color), migrate to the wood surface. This migration can significantly alter the wood’s color and gloss [47]. The reason is that pressure changes the solubility and mobility of these compounds. As pressure rises, the solubility of some extractives in the wood matrix may change, enabling freer movement, which is further enhanced by thermal energy [48]. Once at the surface, chromophoric compounds interact with light differently than when inside the wood, such as causing more absorption at certain wavelengths (changing color) and affecting the surface’s uniform light-reflection ability, thus influencing gloss [49]. Previous research has shed light on pressure’s effects on wood during thermal treatment. For instance, Bekhta et al. [12] studied the gloss of thermally densified alder, beech, birch, and pine wood veneers. They found that both densification temperature and pressure significantly impact wood gloss. Higher pressure can compact the surface, seemingly increasing gloss due to reduced roughness. But the migration of extractives, especially chromophoric compounds, can counteract this if it changes the surface’s optical properties. In some cases, these compounds on the surface can decrease gloss due to increased light absorption.

Incidence Angle: The incidence angle has an importance score of 12.32%. The importance of the incidence angle indicates that the angle at which light strikes the wood surface can affect the measured glossiness. Different angles of incidence can lead to variations in the amount and direction of light reflection, thereby influencing the perceived glossiness.

Tree Species: The tree species has the lowest importance score of 3.57%. While one might expect the type of tree to have a more significant impact on the properties of heat-treated wood, including glossiness, this result suggests that within the context of this study and the other factors considered, the tree species has a relatively minor influence on the glossiness. This could be due to the fact that the other factors, such as grain direction and treatment conditions, have more dominant effects on the surface characteristics that determine glossiness.

4. Conclusions

This study focused on predicting the glossiness of heat-treated wood. Four types of wood, namely, alder, beech, birch, and pine, were selected for research. We established an IWOA-BPNN model by using tree species, temperature, pressure, grain direction, and incidence angle as input variables. A total of 216 sets of experimental data on the surface gloss of heat-treated wood under different conditions were collected. Among them, 70% of the datasets were randomly selected as the training set, and the remaining 30% were used as the prediction set.

The research findings were of great significance. They could help the wood processing industry better understand the influencing factors of the glossiness of heat-treated wood, so as to optimize the heat treatment process, improve product quality, and reduce production costs. At the same time, the proposed IWOA-BPNN model provided a new method and idea for predicting the glossiness of heat-treated wood, which was conducive to promoting the development of related fields. Key conclusions were summarized as follows:

• In this study, the IWOA was introduced as an improvement to the traditional WOA, which was prone to converge to local optima. To address this issue, this paper proposed several enhancements to the WOA, which were detailed in this paper. Firstly, the proposed IWOA incorporated chaos theory to initialize the population position of the algorithm and employed tent chaos mapping to generate random parameters within the whale algorithm, thereby accelerating its convergence rate. Furthermore, the WOA was combined with the sine cosine algorithm and screen the leadership position of the whale group by leveraging the strengths of cosine algorithm. This approach enhanced the algorithm’s ability to escape local optima and increased its optimization accuracy. Additionally, an adaptive strategy with inertial weights was proposed to balance global search and local development within the algorithm.
• This study investigated the glossiness of four different wood species, namely, alder, beech, birch, and pine, after heat treatment. The IWOA-BP model was developed using tree species, temperature, pressure, grain direction, and incidence angle as input variables. The model was trained on 152 randomly selected datasets and tested on 64 datasets to predict gloss values and compare them with actual measurements. The results demonstrated that the IWOA-BP model effectively predicted the glossiness of heat-treated wood with an RMSE value of 0.7834 and an R2 value of 0.9898 for the training set and an RMSE value of 0.8935 and an R2 value of 0.9885 for the test set. These findings indicated that the IWOA-BP model could accurately predict the gloss values of heat-treated wood under various conditions.
• In addition, this study compared the performance of the IWOA-BP model with that of the WOA-BP model and the original BP neural network model. The results demonstrated that, compared to the BP neural network model, the IWOA-BP model exhibited a 66.02% reduction in MAE value, a 64.21% reduction in MAPE value, a 69.60% reduction in RMSE value, and a 12.87% increase in R2 value. Similarly, when compared to the WOA-BP model, the IWOA-BP model showed a 61.33% decrease in MAE value, a 57.09% decrease in MAPE value, a 65.99% decrease in RMSE value, and a 9.75% increase in R² value. These findings indicated that the IWOA-BP model had superior prediction accuracy and faster convergence rate. Notably, the most relevant characteristics of heat-treated wood were surface glossiness and color brightness, which our model accurately predicted with high performance. This would significantly enhance the utilization of wood processing industries and provide valuable insights for algorithm research in related fields.

While this study has achieved promising results in predicting the glossiness of heat-treated wood, several avenues remain open for deeper exploration to advance the field further.

• At the level of wood property correlation, future research will focus on establishing intrinsic links between glossiness and key properties such as mechanical strength, biological durability, and dimensional stability. By systematically measuring these properties under varying thermal treatment conditions and applying advanced data analytics, we aim to uncover underlying patterns and develop comprehensive correlation models. This approach will not only enhance the understanding of wood performance evolution during heat treatment but also provide a more scientific and holistic method for quality evaluation. In this context, glossiness may serve as a practical indicator of overall wood quality, increasing its value in both processing and application.
• From the perspective of input parameter optimization, this study was limited by the scope of available data, excluding potentially influential variables such as wood age, growth environment, and harvest season. These factors, though not considered in the current model, may have a significant impact on the glossiness of heat-treated wood. Due to data constraints, we were unable to assess their influence within the present research framework. Future studies should aim to collect expanded datasets either by scouring a broader range of existing literature or by conducting our own experimental operations to obtain and incorporate these variables, particularly wood age, and examine their interactions with existing inputs such as species, temperature, and pressure. This would allow for a more refined model structure that captures the complex, real-world relationships influencing glossiness. Enhancing the model in this way would improve its predictive accuracy and generalizability, offering more robust theoretical support and practical value for wood processing applications.
• Regarding model enhancement, factors such as wood density, moisture content, and treatment duration—known to significantly affect glossiness—were not included in this study. To address this, future research will adopt sensitivity analysis techniques, such as Sobol index analysis, to quantify the relative importance of these variables. This will help identify underrepresented factors in the current model and guide its optimization. By incorporating these critical variables, the model will better adapt to real-world complexities, offering a more robust and practical tool for the wood processing industry and contributing to technological innovation and product quality improvement.