Safety Status Prediction Model of Transmission Tower Based on Improved Coati Optimization-Based Support Vector Machine

Abstract

Natural calamities have historically impacted operational mountainous power transmission towers, including high winds and ice accumulation, which can result in pole damage or diminished load-bearing capability, compromising their structural integrity. Consequently, developing a safety state prediction model for transmission towers may efficiently monitor and evaluate potential risks, providing early warnings of structural dangers and diminishing the likelihood of bending or collapse incidents. This paper presents a safety state prediction model for transmission towers utilizing improved coati optimization-based SVM (ICOA-SVM). Initially, we optimize the coati optimization algorithm (COA) through inverse refraction learning and Levy flight strategy. Subsequently, we employ the improved coati optimization algorithm (ICOA) to refine the penalty parameters and kernel function of the support vector machine (SVM), thereby developing the safety state prediction model for the transmission tower. A finite element model is created to simulate the dynamic reaction of the transmission tower under varying wind angles and loads; ultimately, wind speed, wind angle, and ice cover thickness are utilized as inputs to the model, with the safe condition of the transmission tower being the output. The predictive outcomes indicate that the proposed ICOA-SVM model exhibits rapid convergence and high prediction accuracy, with a 62.5% reduction in root mean square error, a 59.6% decrease in average relative error, and a 75.0% decline in average absolute error compared to the conventional support vector machine. This work establishes a scientific foundation for the safety monitoring and maintenance of transmission towers, effectively identifying possible dangers and substantially decreasing the likelihood of accidents.

1. Introduction

The rising demand for electricity in society makes transmission towers crucial for electric energy transmission, which is directly linked to the safe operational capacity essential for societal development and stability [1]. Due to their operational characteristics and geographical placement, transmission towers, particularly in mountainous regions, endure diverse static and dynamic loads over extended durations, including strong winds, heavy rainfall, and other intricate environmental conditions. This exposure renders them susceptible to the loosening of bolted connections, corrosion of joints, and deformation of structural components [2,3]. These variables will result in a deterioration of the load-bearing capacity of transmission towers, potentially leading to severe power incidents such as tower deformation or collapse [4]. Consequently, evaluating safety conditions for transmission towers in dynamic mountainous regions is essential.

Regarding the safety assessment of transmission towers, Chen et al. proposed a framework utilizing 3D point clouds and risk indices to accurately identify damage risks in flooding conditions and assist in grid maintenance [5]; Fu et al. examined the gust response coefficients of transmission towers during typhoons, discovering that these coefficients surpassed current standards, and recommended enhancing the gust response coefficient to ensure transmission tower safety [6]; Li et al. assessed the impact of wind fatigue on the brittleness of transmission towers subjected to multiple catastrophes using a probabilistic analytical framework. The findings indicated a significant reduction in structural capacity over time, offering guidance for the design and maintenance of transmission towers [7]; Zhu et al. proposed a method to evaluate the vulnerability of transmission towers in a downburst wind, and through the simulated wind field and parameterized analysis, they obtained the limit carrying capacity and the most unfavorable location, and showed that the lower storm winds are more destructive than the atmospheric boundary layer winds [8]; Zhu et al. proposed a wind vulnerability analysis method for transmission towers based on the wind direction, and determined the optimal layout and probability of failure, which provided a basis for the design and risk assessment of the transmission towers [9]; Kwon et al. analyzed the degradation of structural performance caused by corrosion of the 765 kV transmission towers in coastal areas, and a vulnerability assessment method was proposed and an ultimate collapse surface was created to assess its structural safety under different wind speeds and wind angles of attack [10]; Meng et al. analyzed the response of microtopography to transmission towers under the influence of typhoons through virtual wind tunnel simulation, and found that the microtopography significantly increased the local wind speed and the risk of collapse, which provided an essential reference for the assessment of the wind resistance of transmission lines under complex terrain [11]; Gao et al. examined the dynamic reaction of ice removal on wineglass-shaped transmission towers and determined that the central V-shaped section is more susceptible to collapse. They recommend reinforcing the critical linking component to enhance overall stability [12]; Mukherjee et al. examined the reliability of anchor foundations for transmission towers subjected to fluctuating wind loads and determined that soil cohesion significantly influences the resistance to uprooting capacity through a multivariate adaptive regression spline model. They underscored the necessity of accounting for variability to enhance structural stability and safety [13].

In terms of monitoring and warning of transmission towers, Shen et al. proposed a technique using clustered dynamic mode decomposition and adaptive block compression sensing to accurately monitor the looseness of transmission towers and safeguard their structural safety through MIMU signal analysis [14]; Min et al. designed a high-sensitivity fiber Bragg grating smart rod to achieve high-precision strain monitoring and temperature compensation for large-span transmission towers, which provides a reliable solution for transmission tower safety monitoring [15]; Huang et al. explored the effect of trains passing on the vibration response of transmission towers, and found that it reduces the specific modal frequency, which may lead to misjudgment of health monitoring, and thus optimized the vibration monitoring device to improve the safety [16]; Jin et al. predicted the foundation settlement displacement of transmission towers in the Salt Lake area by using the multi-temporal phase interferometric synthetic aperture radar, which provides a good solution for the transmission network’s ground settlement disaster monitoring [17]; Tian et al. developed a fiber Bragg grating flexible sensor with temperature self-compensation to realize automatic early warning of uneven settlement and horizontal sliding of tower base by real-time monitoring of three-dimensional deformation field of the tower base of transmission towers [18]; Lu et al. researched the factors related to the deformation of the ground surface of the transmission line in the mining area, and constructed a risk assessment and early warning system to effectively predict hidden dangers and improve transmission line safety [19]; Yao et al. proposed a multi-parameter localization method based on a hybrid distributed fiber optic sensing system, which significantly improves the localization accuracy and efficiency of transmission towers, and provides reliable support for online monitoring and early warning of high-voltage transmission lines [20]; He et al. conducted millimeter surface displacement of transmission lines with synthetic aperture radar (SAR) interferometry millimeter-level monitoring of surface displacements along transmission lines in the Loess Plateau by synthetic aperture radar interferometry, which provides critical data support for the early warning of geologic hazards in intelligent grids [21]; Zhang et al. designed a fiber Bragg grating-based on-line monitoring system for the transmission of tower strain, which achieves accurate early warning of transmission tower failures and provides effective support for condition maintenance and disaster prevention [22].

Despite the advancements in the security evaluation of transmission towers presented in the studies above, significant deficiencies still need to be addressed. These investigations predominantly depend on several data sources, including meteorological, geographic, and grid information, and exhibit a relative need for more intelligent algorithms. Although offering essential context for the evaluation, this dependence leads to inadequate model precision to accurately represent the actual risk in extreme weather scenarios or intricate geographic settings. Furthermore, the velocity and precision of forecasts are constrained, hindering the capacity for real-time monitoring and swift response. To enhance the efficacy of assessment models, it is imperative to implement sophisticated, intelligent algorithms, such as machine learning and deep learning, which can manage extensive, multi-dimensional data, discern potential nonlinear relationships, and consequently augment models’ predictive capacity and adaptability. Future studies should concentrate on incorporating intelligent technologies to enhance the invention and optimization of assessment models, thereby attaining a superior level of safety management.

The support vector machine (SVM) is a prevalent supervised learning method mainly employed for multi-class classification tasks [23,24]. It efficiently streamlines the computational procedure by selecting suitable hyperplanes and employing the concept of high and low-dimensional transformations, showcasing considerable benefits in examining nonlinear, high-dimensional, and small-sample issues [25,26]. Nonetheless, the conventional SVM exhibits prolonged training durations and elevated computational complexity when confronted with extensive datasets, and there exists variability in the values of the penalty parameter c and the kernel function parameter g [27]. This paper proposes an improved coati optimization algorithm (ICOA) to optimize the SVM’s penalty and kernel function parameters, effectively mitigating overfitting and underfitting, addressing slow computation speed, and improving the accuracy of the model’s classification results.

Currently, limited research has employed intelligent algorithms to assess the safety of transmission towers, and the prevailing evaluation methods for these towers exhibit significant subjectivity, as well as low accuracy and efficiency in their assessments. This research offers a transmission tower safety status model utilizing the improved coati optimization algorithm (ICOA) to enhance the SVM. The coati optimization algorithm (COA) is initially enhanced using back-refraction learning and the Levy flight strategy. The SVM’s penalty parameters and kernel functions are optimized utilizing the improved coati optimization algorithm (ICOA) to develop the transmission tower safety condition prediction model. Secondly, a finite element model of the transmission tower is constructed using ABAQUS 2020 software, and the dynamic response of the tower is simulated under various wind angles and loads. The simulated dataset and the ICOA-SVM method are employed to develop a predictive model for the safety condition of transmission towers, utilizing wind angle, wind speed, and ice thickness as inputs and the safety status of the transmission tower as the output. This not only enhances the maintenance and management of the transmission network but also mitigates potential safety risks and bolsters the reliability of the overall power supply, which holds significant practical significance for ensuring the safety of societal electricity use.

2. Coati Optimization Algorithm and Improvements

2.1. Coati Optimization Algorithm

The coati optimization algorithm is a novel meta-heuristic intelligent optimization technique introduced by Mohammad et al. in 2023. It is inspired by coati behaviors, specifically their methods of attacking and hunting iguanas while evading predators, to address optimization problems [28].

2.1.1. Population Initialization

The following equation can represent the original members of the coati population:

$$x_{i,j}=l{b}_j+r\cdot \left(u{b}_j-l{b}_j\right),i=1,2,\dots ,N,j=1,2,\dots ,m$$

(1)

where $x_{i,j}$ represents the jth dimensional position of the ith coati within the search space, r is a random actual number in the interval [0, 1], $u{b}_j$ and $l{b}_j$ signify the upper and lower bounds of the search for the optimal solution in the jth dimension, N indicates the number of coati populations, and m denotes the number of dimensions.

2.1.2. Hunting and Attack Strategies for Iguanas

Coatis will hunt iguanas by ascending trees, and the following equation can represent the coati’s position in the tree:

$$\begin{array}{l}{x}_{i,j}^{P1}=x_{i,j}+r\cdot (Iguan{a}_j-I\cdot x_{i,j}), \\ \mathrm{for} i=1,2,\dots ,⌊{\displaystyle \frac{N}{2}}⌋ \mathrm{and} j=1,2,\dots ,m\end{array}$$

(2)

The following equation can articulate the coati’s position on the ground after the iguana’s landing:

$$\begin{array}{l}Iguan{a}_j^G=l{b}_j+r\cdot (u{b}_j-l{b}_j),j=1,2,\dots ,m,\\ x_{i,j}^{P1}=\left\{\begin{array}{l}{x}_{i,j}+r\cdot (Iguan{a}_j^G-I\cdot x_{i.j}),F_{Iguan{a}^G}<F_i,\\ x_{i,j}+r\cdot (x_{i,j}-Iguan{a}_j^G),else,\end{array}\right.\\ \mathrm{for} i=⌊{\displaystyle \frac{N}{2}}⌋+1,⌊{\displaystyle \frac{N}{2}}⌋+2,\dots ,N \mathrm{and} j=1,2,\dots ,m\end{array}$$

(3)

If the coati’s new position enhances the goal function’s value, it is adopted; otherwise, it remains unchanged. This procedure is referred to as the greedy law and is articulated as follows:

$$x_{i,j}^{P1}=\left\{\begin{array}{l}{x}_{i,j}^{P1},F_i^{P1}<F_i,\\ x_{i,j},else.\end{array}\right.$$

(4)

where $x_{i,j}^{P1}$ signifies the new position of the ith coati in the jth dimension during the initial stage, r is a stochastic actual number within the interval [0, 1], $Iguan{a}_j$ denotes the jth dimensional position of the iguana within the search space, representing the position of the optimal member of the population, and I is an integer randomly chosen from the set {1, 2}. $Iguan{a}_j^G$ represents the jth dimensional position of the randomly produced iguana on the ground, $F_i$ signifies the objective function of the ith coati value, and $F_{Iguan{a}^G}$ indicates the objective function value of the iguana on the ground.

2.1.3. Escape from Predators

When a coati confronts a predator and must evade, the following equation can represent the unpredictable destination of the coati’s escape:

$$\begin{array}{l}l{b}_j^{local}={\displaystyle \frac{l{b}_j}{t}},u{b}_j^{local}={\displaystyle \frac{u{b}_j}{t}},\mathrm{where} t=1,2,\dots ,T.\\ x_{i,j}^{P2}=x_{i,j}+(1-2r)\cdot (l{b}_j^{local}+r\cdot (u{b}_j^{local}-l{b}_j^{local})),\\ i=1,2,\dots ,N,j=1,2,\dots ,m,\end{array}$$

(5)

where $l{b}_j^{local}$ and $u{b}_j^{local}$ represent the local lower and upper bounds of the jth dimension, respectively; t signifies the current iteration count, while T indicates the maximum iteration limit. $x_{i,j}^{P2}$ denotes the new position of the ith coati in the jth dimension during the second stage, with all other parameters defined as previously stated.

2.2. Improvement Strategies

2.2.1. Refractive Reverse Learning Initialization Population

The quality of the initialized population is pivotal in the metaheuristic algorithm, significantly influencing both the convergence speed and the correctness of the final solution. The conventional COA employs a random method for population initialization, leading to a non-uniform distribution of solution individuals within the search space, thereby impairing its global search capability and optimization efficiency. In this paper, we enhance the population initialization process by employing the refractive inverse learning strategy to augment the algorithm’s performance by expanding its search range, as illustrated in Figure 1 below.

In Figure 1, [lb, ub] on the X-axis signifies the search interval, the Y-axis represents the standard line, O denotes the midpoint of the search interval, α and β indicate the angles of incidence and refraction. d and d* correspond to the lengths of the incident and refracted rays, while x and x* represent the current and optimal solutions after refractive inversion learning, respectively. The refractive index n is ascertained from the geometric relationship illustrated in the picture.

$$n={\displaystyle \frac{\sin \alpha }{\cos \beta }}={\displaystyle \frac{d^{*}((lb+ub)/2-x)}{d(x^{*}-(lb+ub)/2)}}$$

(6)

Let k = l/l*, included in the equation above and extended to the multidimensional space of the algorithm, produce the refractive inverse solution $x_{i,j}^{*}$:

$$x_{i,j}^{*}={\displaystyle \frac{l{b}_j+u{b}_j}{2}}+{\displaystyle \frac{l{b}_j+u{b}_j}{2k}}-{\displaystyle \frac{x_{i,j}}{k}}$$

(7)

2.2.2. Introduction of Levy Flight Strategy

In the development phase of COA, the coati modifies its location during the search process according to the current individual optimum, resulting in the algorithm prematurely converging to a local optimum solution, hence constraining its efficacy in global search. This research introduces a Levy flight technique to enhance the position update process and address this constraint.

The Levy flight approach produces randomized step lengths and broadens the search region, potentially enhancing the diversity of coati populations. The enhanced method for updating coati locations is as follows:

$$\sigma =\left({\displaystyle \frac{\mathrm{\Gamma }(1+\beta )\sin \left(\frac{\pi \beta }{2}\right)}{\mathrm{\Gamma }(\frac{1+\beta }{2})\beta \cdot 2^{\frac{\beta -1}{2}}}}\right)$$

(8)

$$Levy(\beta )=0.01\cdot u\cdot {\displaystyle \frac{r_5}{{\left|v\right|}^{\frac{1}{\beta }}}}$$

(9)

$\mathrm{\Gamma }$ is the usual Gamma function, β is a random variable in the interval [0, 2], r₅ is a random variable in the interval [0, 1], and u and v follow the normal distributions $u~N(0,{\sigma }_2)$ and $v~N(0,1)$, respectively.

The revised account of the coati’s location after the application of the Levy flying technique is as follows:

$$\begin{array}{l}{x}_{i,j}^{P2}=Levy(\beta )\cdot x_{i,j}+(1-2r)\cdot \\ (l{b}_j^{local}+r\cdot (u{b}_j^{local}-l{b}_j^{local}))\end{array}$$

(10)

The Levy flight strategy was introduced to the development phase of COA to enhance its global search ability and mitigate premature convergence. By generating long-distance jumps in the solution space, Levy flight enables a more diverse population distribution, improving the algorithm’s capacity to escape local optima and explore the global optimum effectively.

3. Benchmark Function Testing

3.1. Baseline Function and Parameterization

Six benchmark test functions are employed for performance evaluation to assess the optimization search capability of the improved coati optimization algorithm (ICOA), with the fundamental characteristics of these functions presented in

Table 1. Benchmark function.

Function	Dimension	Search Domain	Optimum
$f_1={\displaystyle \sum _{i=1}^n}{x}_i^2$	30	[−100, 100]	0
$f_2={\sum }_{i=1}^{n-1} \left[100{\left(x_{i+1}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]$	30	[−10, 10]	0
$f_3={\sum }_{i=1}^n x_i^2+{\left({\sum }_{i=1}^n {\displaystyle \frac{1}{2}}i{x}_i\right)}^2+{\left({\sum }_{i=1}^n {\displaystyle \frac{1}{2}}i{x}_i\right)}^4$	30	[−5, 10]	0
$f_4=-20\exp \left(-0.2\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n x_i^2}\right)-\exp \left({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n \cos \left(2\pi x_i\right)\right)+20+e$	30	[−32.768, 32.768]	0
$f_5={\displaystyle \frac{1}{4000}}{\sum }_{i=1}^n x_i^2-{\prod }_{i=1}^n \cos \left({\displaystyle \frac{x_i}{\sqrt{i}}}\right)+1$	30	[−600, 600]	0
$f_6=10n+{\sum }_{i=1}^n \left[x_i^2-10\cos \left(2\pi x_i\right)\right]$	30	[−5.12, 5.12]	0

. To enhance the reliability of the test results, f₁~f₃ are selected as high-dimensional single-peak test functions, typically possessing a singular global optimal solution aimed at evaluating the algorithm’s global search capability; f₄~f₆ are designated as high-dimensional multiple-peak test functions, necessitating superior local search proficiency from the algorithm, as these functions contain numerous local optimal solutions. Furthermore, six swarm optimization algorithms were selected: Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Northern Goshawk Optimization (NGO), Dung Beetle Optimizer (DBO), COA, and ICOA. The results of benchmark function tests for these algorithms were compared.

To ensure the optimal performance of the coati optimization algorithm (COA), a systematic approach was adopted for parameter selection, combining initial parameter settings, sensitivity analysis, and empirical testing. The population size and maximum iterations were initially set to 30 and 500, respectively, based on values commonly used in the optimization literature. A sensitivity analysis was then conducted to evaluate the impact of these parameters on convergence speed and solution accuracy. For instance, population size was varied from 10 to 100 in increments of 10, and the results indicate that a population size of 30 provided a balance between computational efficiency and optimization quality. Additionally, parameters related to the exploration–exploitation trade-off and the Levy flight scaling factor were fine-tuned using benchmark functions f₁ to f₆. Through multiple experimental runs, these parameters were adjusted to enhance the algorithm’s global search capabilities while maintaining robust performance in local search. The finalized parameters not only ensured the effectiveness of COA but also established a fair baseline for comparing its enhanced version, ICOA, with other algorithms.

3.2. Analysis of Optimization Results

The ICOA was employed to address six test functions and compared with five other algorithms. The optimal solution, mean, and standard deviation were calculated, and the statistical results are presented in

Table 2. Validation in the effectiveness of the ICOA.

Function	Category	GWO	WOA	NGO	DBO	COA	ICOA
$f_1(x)$	Optimum	7.71 × 10−29	8.01 × 10−89	1.39 × 10−91	1.55 × 10−165	0	0
	Mean	1.37 × 10−27	1.62 × 10−77	1.07 × 10−87	6.47 × 10−115	0	0
	Standard Deviation	1.54 × 10−27	3.90 × 10−77	1.44 × 10−87	2.05 × 10−114	0	0
$f_2(x)$	Optimum	2.61 × 101	2.69 × 101	2.55 × 101	2.55 × 101	0	0
	Mean	2.69 × 101	2.78 × 101	2.59 × 101	2.58 × 101	2.36 × 10−4	0
	Standard Deviation	8.26 × 10−1	5.28 × 10−1	2.58 × 10−1	3.63 × 10−1	7.44 × 10−4	0
$f_3(x)$	Optimum	1.20 × 10−9	3.88 × 102	5.38 × 10−10	1.03 × 10−76	0	0
	Mean	4.16 × 10−8	5.32 × 102	2.80 × 10−8	1.07 × 10−29	0	0
	Standard Deviation	8.61 × 10−8	1.10 × 102	8.08 × 10−8	3.34 × 10−29	0	0
$f_4(x)$	Optimum	8.57 × 10−14	4.44 × 10−16	4.00 × 10−15	4.44 × 10−16	4.41 × 10−16	0
	Mean	9.92 × 10−14	4.71 × 10−15	6.13 × 10−15	4.44 × 10−16	4.41 × 10−16	0
	Standard Deviation	1.28 × 10−14	2.80 × 10−15	1.83 × 10−15	0	0	0
$f_5(x)$	Optimum	0	0	0	0	0	0
	Mean	3.83 × 10−3	1.06 × 10−2	0	0	0	0
	Standard Deviation	6.27 × 10−3	3.36 × 10−2	0	0	0	0
$f_6(x)$	Optimum	5.68 × 10−14	0	0	0	0	0
	Mean	1.28	5.68 × 10−15	0	2.99 × 10−1	0	0
	Standard Deviation	2.37	1.80 × 10−14	0	9.46 × 10−1	0	0

.

The data analysis in Table 2 reveals that the ICOA method exhibits superior optimization search performance relative to other algorithms. In evaluating single-peak functions, the ICOA has superior accuracy in obtaining the optimal solution compared to other population optimization algorithms, indicating its exceptional global search capability. In the case of the multi-peak test functions f₅ and f₆, the performance disparity between ICOA and COA, both prior to and following the enhancement, is not pronounced; nonetheless, when juxtaposed with the other four algorithms that exhibit a more rapid convergence rate, ICOA retains a competitive edge. Regarding the multi-peak function f₄, only ICOA can achieve the theoretical optimal solution, indicating its robust local search capability.

Figure 2 depicts the convergence curves of each algorithm on six benchmark test functions to intuitively illustrate the superiority of ICOA over alternative algorithms regarding optimization accuracy and convergence speed. The curves indicate that, with the same test function, the convergence speed and accuracy of ICOA are significantly superior to those of other algorithms. Furthermore, ICOA demonstrates a more rapid iteration speed under identical convergence accuracy conditions. Whether applied to single-peak or multi-peak benchmark test functions, ICOA exhibits clear advantages in the optimization process.

4. ICOA Optimized SVM Model

SVM is a supervised learning model extensively used in classification and regression analysis. Its fundamental strength is its capacity to address both linear and nonlinear data classification challenges and to identify an ideal hyperplane during the training phase, which proficiently segregates distinct data classes.

This study employs the improved ICOA to optimize the two critical parameters of SVM: the penalty factor c and the kernel function parameter g, hence enhancing SVM performance. The ICOA-SVM predicts the safety condition of transmission towers utilizing ICOA-SVM. A transmission tower safety status prediction model utilizing ICOA-SVM is built, and the samples are trained to obtain optimal classification performance. The precise sequence of the ICOA-SVM method for forecasting the safety condition of transmission towers is illustrated in Figure 3:

(1)

Acquire sample data and preprocess them into two segments: training and test sets.

(2)

Develop the SVM and set the appropriate parameters.

(3)

Initialization of COA parameters to enhance the stochastic initialization process of the coati population with a refractive reverse learning technique.

(4)

Upon concluding the cooperative phases of iguana predation and dispersal, the Levy flight strategy is implemented to revise the coati’s position, finalizing the COA optimization and achieving the ICOA model.

(5)

The ICOA model updates the coati’s optimal location, and the revised fitness value is compared to the established optimal fitness value. The global optimal solution is achieved upon reaching a predetermined convergence accuracy or a maximum iteration limit.

(6)

Utilize the optimal solution of ICOA acquired in the preceding step as the parameters of SVM (c, g), thereby constructing the ICOA-SVM classification model. Proceed to execute the model until it achieves the specified convergence accuracy or attains the maximum iteration limit, concluding the model training.

(7)

Execute the trained ICOA-SVM classification model to assess the safety status of transmission towers.

5. Example Analysis and Predicted Results

To assess the efficacy of the ICOA-SVM prediction model in optimizing practical problem solutions, a finite element model of transmission towers was developed in ABAQUS. The ICOA-SVM model was employed to classify and predict the safety status of the transmission towers by applying ice and wind loads while also varying the wind direction angle.

5.1. Modeling

This study examines a 500 kV transmission line utilizing a straight-line tower, namely the SG2-42 model. The tower’s height is 68.35 m, with a nominal height of 42 m, and the distances between the front and rear gears are 421 m and 368 m, respectively. The primary material of the transmission towers is Q420 and Q345 steel, while the auxiliary components consist of Q235 steel. Based on the features of its rod load-bearing capacity, a finite element model is established using the B31 beam unit. The material characteristics of angle steel are presented in

Table 3. Angle steel material parameters.

Model	Poisson’s Ratio	Density/(kg·m−3)	Young’s Modulus/N·mm−2	Yield Stress/MPa
Q420	0.3	7,850,000	206,000	420
Q345	0.3	7,850,000	206,000	345
Q235	0.3	7,850,000	206,000	235

.

Figure 4 illustrates the ABAQUS finite element model of the transmission tower.

5.2. Calculation and Application of Loads

Both tower–wire separation and coupling models require substantial modeling and computing effort, particularly when assessing wind speeds, wind angles, and other contributing factors. Similar static loading is employed for the finite element analysis of transmission towers to enhance efficiency and obtain a sufficiently big dataset.

Alongside the primary wind load, the transmission tower and the ground conductor must also account for their self-weight and the horizontal stress due to ice accumulation. The base of the transmission tower is established as a fixed constraint, disregarding the mutual vibrational effects between the tower and the conductor line. The horizontal wind load and the vertical load of the conductor are directly applied at the suspension point. At the same time, the tower structure is still subjected to wind load, followed by static analysis.

The self-weight load of the conductor–earth line is determined using the formula

$$G_1=n\cdot q\cdot g\cdot L_v$$

(11)

The weight load of the ice is computed as

$$G_2=27.728n\cdot b(d+b)\cdot L_v$$

(12)

The associated horizontal wind loads on the conductors and ground are computed as follows:

$$W_X=\alpha \cdot W_0\cdot {\mu }_z\cdot {\mu }_{sc}\cdot {\beta }_c\cdot (d+2b)\cdot L_p\cdot B\cdot {\sin }^2\theta$$

(13)

where n represents the number of sub conductors per phase; q denotes the unit mass per unit length of the overhead line; α signifies the unevenness coefficient of wind pressure; W₀ represents the standard value of the base wind pressure, while μ_z is the height-dependent coefficient of wind pressure. μ_sc represents the coefficient of the geometry of the conductive line. β_c is the correction coefficient for the wind load on the conductive line; d represents the outer diameter of the conductive line, whereas b denotes the thickness of the overlying ice. L_p denotes the horizontal gear distance of the tower; L_v signifies the vertical gear distance of the tower; B denotes the wind load amplification coefficient due to underlying ice; θ represents the angle between the wind direction and the ground wire direction.

5.3. Simulation Conditions and Results

The transmission tower is intended for a wind speed of 30 m/s and an ice thickness of 10 mm. A wind speed ranging from 0 to 30 m/s is applied to the transmission tower, with increments of 2 m/s. Concurrently, the ice thickness is increased by 2 mm. Wind angles of 30°, 45°, 60°, and 90° are utilized, resulting in a total of 384 distinct wind and ice load conditions for simulation calculations. To facilitate comparison and analysis, the following four representative conditions are shown as examples of finite element simulation stress and displacement clouds, as seen in Figure 5a–d.

Figure 5a,b illustrate that at a wind speed of 10 m/s, with no overlying ice, altering the wind angle does not significantly affect the maximum stress of the tower; however, the maximum displacement rises from 11.37 mm to 28.91 mm. Figure 5b,c indicate that, with a wind angle of 90 degrees, the maximum stress escalates from 49.68 MPa to 170 MPa, while the maximum displacement increases from 28.91 mm to 232.2 mm. Figure 5c,d demonstrate that the tower’s maximum stress and maximum displacement rise when only the ice thickness is modified. The alteration in wind angle primarily influences the stress distribution of the tower’s main material and the displacement magnitude of the tower head, whilst variations in wind speed and ice thickness impact the total stress magnitude and displacement size of the tower body.

5.4. Judging Criteria and Dataset Creation

To better illustrate the key factors influencing the safety status of transmission towers,

Table 4. Influencing parameters and their impact on transmission tower safety.

Parameter	Description	Impact on Safety
Wind Speed	Range: 0–30 m/s, with 2 m/s increments	Higher wind speeds significantly increase stress and displacement across the tower structure.
Wind Direction Angle	Angles of 30°, 45°, 60°, and 90°	Affects stress distribution and displacement magnitudes; maximum displacement observed at 90°.
Ice Thickness	Range: 0–10 mm, with 2 mm increments	Greater ice thickness adds weight and increases stress and displacement, particularly in vertical rods.
Operating Condition	Categories: Safe (1), Safer (2), Basic Safety (3), Unsafe (4)	The combination of wind speed, angle, and ice thickness determines the safety classification of the tower.
Tower Geometry	Tower height: 68.35 m; rod configuration	Structural dimensions influence the distribution of forces and the tower’s load-carrying capacity.
Material Properties	Steel grades (Q420, Q345, Q235) with specific yield stress limits	Variations in material strength affect the tower’s ability to withstand external loads.

summarizes the primary parameters considered in this study, along with their specific impacts on structural safety. These parameters were incorporated into the finite element modeling and dataset creation processes to ensure a comprehensive representation of real-world conditions. By systematically accounting for these influencing factors, this study aims to build a robust dataset that captures the variability and complexity of real-world scenarios.

Each parameter plays a critical role in determining the structural performance of transmission towers. For instance, wind speed significantly impacts the overall stress and displacement levels, with higher wind speeds leading to exponential increases in structural strain. Wind direction angles, such as 90°, cause asymmetrical stress distribution, often leading to maximum displacement at specific tower sections. Ice thickness, on the other hand, adds substantial weight to the structure, disproportionately affecting vertical rods and increasing both stress and displacement. These environmental factors interact with the tower’s material properties and geometry, determining its load-bearing capacity and overall safety classification under various conditions. The operating condition classification system, ranging from “Safe” to “Unsafe”, provides a standardized framework for quantifying safety risks. This classification is derived from a combination of key parameters, ensuring a holistic evaluation of structural stability. Additionally, the geometry and material properties of the tower define its resilience to these external forces. High-strength steel grades, such as Q420, enhance the tower’s ability to withstand severe conditions, while specific geometrical configurations help optimize force distribution and minimize structural deformations. The integration of these parameters into the finite element model ensures that the ICOA-SVM prediction framework is trained and evaluated on a dataset that accurately reflects real-world operational conditions. This comprehensive approach enhances the robustness of the proposed model and underscores its applicability to diverse environmental scenarios. Future work could further refine the parameter ranges and explore additional influencing factors, such as long-term material degradation and dynamic interactions between accessories and the tower structure, to improve the model’s accuracy and generalizability.

This study evaluates the safety state of transmission towers under various operational settings by analyzing their operational status and safety level through a risk assessment methodology. This risk evaluation graphically quantifies and delineates the safety level of transmission towers under various loading circumstances, offering a scientific foundation for routine operation and maintenance. Numerous experts and researchers, both domestically and internationally, have researched the assessment of transmission tower structural system failures [29,30]. The transmission tower construction is often deemed to have failed if it reaches one of the following three conditions:

(1)

The structure transforms into a mechanism: the criterion for judgement is that, when some members fail, the total stiffness matrix of the remaining members exhibits singularity, resulting in the non-convergence of the ABAQUS calculation program;

(2)

Structural deformation surpasses the allowable threshold: It is generally accepted that the maximum displacement response limit of the transmission tower is situated at its apex, and if the displacement at the top of the tower exceeds a specified value, it is deemed indicative of structural damage;

(3)

The structure cannot endure additional loads or the initial occurrence of bearing capacity decline, mostly evidenced by excessive stress ratios in the tower’s main components. This results in damage and is subsequently classified as structural failure.

Integrating the three points above and referencing the pertinent literature [31,32] and regulations [33,34], the criteria for assessing the safety state of transmission towers, as delineated in

Table 5. Criteria for judging the structural failure of transmission.

Category	Safe	Safer	Basic Safety	Unsafe
Component Stress Ratio	$\xi$ < 0.5	0.5 ≤ $\xi$ ≤ 0.75	0.75 ≤ $\xi$ ≤ 1.0	$\xi$ > 1.0
Top Tower Displacement	l < h/1000	h/1000 ≤ l ≤ 2 h/1000	2 h/1000 ≤ l ≤ 3 h/1000	l > 3 h/1000

, categorize the operational state into four classifications: safe, safer, basic safety, and unsafe. Here, $\xi$ represents the component stress ratio (the ratio of the maximum stress position to its yield stress), l denotes the tower top displacement, and h signifies the tower height.

According to the above transmission tower safety status assessment standard, the simulation data are classified. The tower status is divided into four categories: safe, relatively safe, basically safe, and unsafe, and the numbers 1, 2, 3, and 4 are used for abbreviation (the most unfavorable state is taken when the operating status categories are inconsistent). Then, 384 sets of data obtained by simulation are selected for experiments, and 75% of the sample data are randomly divided as the training set for the training of the transmission tower safety status prediction model. The remaining 25% of the sample data are used as the test set to test the accuracy of the model. The transmission tower safety status dataset is shown in

Table 6. Transmission tower safety status dataset.

Wind Direction Angle/(°)	Wind Speed/(m/s)	Ice Thickness/(mm)	Operating Condition
30	10	0	1
30	30	10	2
45	30	0	2
45	20	10	2
60	30	0	3
60	30	10	4
90	10	0	1
90	20	0	2
90	20	10	3
90	30	10	4
…	…	…	…

.

5.5. Forecast Results and Analysis

To ascertain that the SVM model enhanced by the improved coati optimization algorithm (ICOA-SVM) possesses superior efficacy in predicting the outcomes of the safety state classification of transmission towers, a comparative analysis is conducted against the conventional SVM model and the unimproved COA-SVM model. The findings of the comparison are presented in Figure 6, Figure 7 and Figure 8.

The ICOA-SVM model demonstrates superior predictive performance relative to the other two models when analyzing the same transmission tower safety state data, exhibiting minimal error with only five erroneous datasets and an accuracy of 94.7368%. In contrast, the COA-SVM model presents nine erroneous datasets and an accuracy of 90.5263%. The unoptimized SVM model shows 14 erroneous datasets and an accuracy of 85.4167%, indicating that the traditional SVM model is less effective in predicting the classification results when it is not optimized.

To effectively demonstrate that the ICOA-SVM model exhibits superior accuracy in forecasting the outcomes of safety state classification for transmission towers, we assess the predictive performance of the three models by computing the root mean square error (RMSE), the mean absolute percentage error (MAPE), and the mean absolute error (MAE). Utilize mean absolute error (MAE) to evaluate the predictive efficacy of the three models. The equations for the three error calculation formulas above are shown in Equations (14)–(16), and the computational results are displayed in

Table 7. Comparison results of the errors of the models.

	Error	RMSE	MAPE	MAE
Model
SVM		0.6124	0.0911	0.2083
COA-SVM		0.3078	0.0439	0.0947
ICOA-SVM		0.2294	0.0368	0.0521
RF		0.3415	0.0562	0.1017
COA-RF		0.3124	0.0497	0.0873
ICOA-RF		0.2953	0.0472	0.0828
NN		0.2843	0.0417	0.0895
COA-NN		0.2598	0.0389	0.0782
ICOA-NN		0.2476	0.0375	0.0729
GB		0.2567	0.0382	0.0728
COA-GB		0.2435	0.0361	0.0683
ICOA-GB		0.2347	0.0354	0.0651

.

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(y_i-{y^{\prime }}_i)}^2}}$$

(14)

$$MAPE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{{y^{\prime }}_i-y_i}{y_i}\right|}$$

(15)

$$MAE={\displaystyle \frac{1}{n}}({\displaystyle \sum _{i=1}^n\left|y_i-{y^{\prime }}_i\right|})$$

(16)

where n represents the quantity of predicted values, y_i signifies the true value, and y_i′ indicates the forecasted value.

To further ensure the robustness and generalizability of the ICOA-SVM model, a 5-fold cross-validation strategy was applied during the training phase. This approach divides the dataset into five equal parts, where four parts are used for training and the remaining part for validation in each iteration. The process is repeated five times, ensuring that each subset serves as a validation set exactly once. This strategy minimizes the risk of overfitting and provides a comprehensive evaluation of the model’s performance across varying data splits. The cross-validation results demonstrate consistent improvements across all metrics (RMSE, MAPE, MAE), further validating the reliability of the proposed framework.

Table 7 indicates that the SVM model exhibits the highest error values across all metrics, with an RMSE of 0.6124, a MAPE of 0.0911, and an MAE of 0.2083, highlighting its relatively poor predictive performance compared to other models. While random forests (RFs), neural networks (NNs), and gradient boosting (GB) show improved accuracy, their performance remains inferior to that of the ICOA-SVM model. The reduction in errors (RMSE, MAPE, MAE) in the ICOA-SVM model can be attributed to the efficient parameter optimization achieved by the improved coati optimization algorithm (ICOA). Specifically, the inverse refraction learning and Levy flight strategy in ICOA facilitate a more effective exploration of the solution space, preventing the algorithm from becoming trapped in local optima and ensuring optimal SVM parameters, such as the penalty parameter c and the kernel parameter g.

Notably, ICOA-SVM achieves the best results among all models, with an RMSE of 0.2294, a MAPE of 0.0368, and an MAE of 0.0521, demonstrating significant improvements of 62.5%, 59.6%, and 75.0%, respectively, over the baseline SVM model. This reduction stems from the precise tuning of SVM parameters, which allows the model to capture complex nonlinear relationships in the data more effectively than other models. Even when RFs, NNs, and GB are optimized using COA and ICOA, their errors remain slightly higher than those of ICOA-SVM, underscoring the superior suitability of SVM for this task when combined with ICOA. Additionally, the ICOA framework enhances predictive performance in RF, NN, and GB models by refining their parameter settings, yet the flexibility and structure of SVM seem to align better with the optimization capabilities of ICOA. These findings highlight the effectiveness of ICOA in enhancing predictive accuracy and the robustness of the ICOA-SVM framework for forecasting the safety status of transmission towers. Together, these results provide a reliable reference for the secure operation and proactive maintenance of critical infrastructure.

5.6. Discussion of Analytical Results

From the above results, several critical insights can be analyzed regarding the performance and applicability of the proposed ICOA-SVM model. First, the results indicate that the integration of the improved coati optimization algorithm (ICOA) with the support vector machine (SVM) significantly enhances prediction accuracy compared to the conventional SVM and COA-SVM models. As shown in Table 7, the ICOA-SVM model achieved the lowest RMSE (0.2294), MAPE (0.0368), and MAE (0.0521), representing reductions of 62.5%, 59.6%, and 75.0%, respectively, when compared to the traditional SVM. These substantial reductions in error metrics highlight the effectiveness of the ICOA in optimizing SVM parameters, specifically the penalty parameter c and kernel parameter g. The use of inverse refraction learning and the Levy flight strategy within the ICOA framework ensured better exploration of the solution space, thereby mitigating issues of local optima that often hinder conventional optimization methods.

Second, the finite element modeling (FEM) results provide valuable insights into the structural response of the transmission towers under different environmental conditions. For instance, the stress and displacement patterns in Figure 5a–d reveal that the wind angle significantly influences the stress distribution and displacement magnitude, while wind speed and ice thickness directly impact the overall stress and displacement levels. These observations validate the importance of incorporating diverse environmental factors, such as wind speed, wind angle, and ice thickness, into the training data for the predictive model. By simulating a comprehensive range of conditions (384 cases), the FEM results provided a robust dataset for training and evaluating the ICOA-SVM model, ensuring its applicability to real-world scenarios.

Third, the classification results from the ICOA-SVM model demonstrate its robustness and adaptability. As seen in the safety state predictions, the model accurately classified the transmission tower’s safety status across varying conditions with an accuracy of 94.74%, outperforming both COA-SVM (90.53%) and traditional SVM (85.42%). This consistency across different environmental scenarios underscores the model’s ability to generalize well, making it a reliable tool for structural risk assessment. The ability to handle diverse input conditions ensures that the ICOA-SVM model can provide early warnings for potentially unsafe states, supporting proactive maintenance and reducing the likelihood of structural failures.

Lastly, the practical implications of this study are significant. The proposed methodology not only improves prediction accuracy but also offers a scalable approach for assessing the safety of transmission towers in mountainous or harsh environments. By combining advanced simulation techniques, such as FEM, with intelligent optimization algorithms, this study establishes a framework that can be extended to other structural systems requiring safety assessments. The results demonstrate that the ICOA-SVM model is a reliable and efficient tool for power transmission infrastructure management, enabling early detection of structural risks and reducing maintenance costs while ensuring operational reliability.

6. Research Implications

The findings of this study have both theoretical and practical implications. Theoretically, the proposed ICOA-SVM model extends the application of intelligent optimization algorithms to structural safety prediction. By integrating advanced techniques like inverse refraction learning and Levy flight strategies, this study improves the predictive capabilities of SVMs for nonlinear, high-dimensional, and small-sample problems. These advancements contribute to the broader field of machine learning and optimization, offering a novel approach for addressing safety-critical tasks in infrastructure management.

Practically, this study provides a reliable and efficient methodology for assessing the safety of transmission towers under complex environmental conditions. The ICOA-SVM model demonstrated superior performance in accurately predicting the safety states of transmission towers across a range of wind speeds, wind angles, and ice thicknesses. This predictive capability enables timely detection of unsafe conditions, supporting proactive maintenance strategies and reducing the risk of structural failures. Furthermore, the methodology is scalable and can be adapted to other types of infrastructure, making it valuable for improving the reliability and resilience of power transmission systems in diverse geographic and environmental contexts.

The findings also highlight the model’s adaptability to varying geographic conditions. While this study primarily focuses on transmission towers in mountainous regions, the ICOA-SVM framework is flexible and can be applied to non-mountainous areas by incorporating location-specific environmental factors such as wind speed, wind angles, and ice loads into the dataset. This adaptability ensures the model’s practical utility for diverse transmission tower types, supporting its scalability across a wide range of geographic and environmental contexts. Future studies can further validate its effectiveness by incorporating real-world data from non-mountainous terrains to ensure robust generalization.

These implications underscore the significance of combining finite element simulations with intelligent optimization techniques, paving the way for future studies to explore similar approaches in other fields, such as civil engineering, transportation, and renewable energy systems.

7. Conclusions

This paper addresses safety issues that may arise in mountain transmission towers due to complex natural conditions, including rod damage and reduced bearing capacity. We propose a prediction model for the safety status of transmission towers utilizing the ICOA-SVM, enabling the forecasting of their safety state. The following conclusions are drawn:

(1)

During the finite element simulation, the force condition of the tower structure was assessed by varying the wind angle, wind speed, and ice thickness. The alteration of wind angle primarily influences the stress distribution of the tower’s main material and the displacement of the tower head. However, variations in wind speed and ice thickness impact both the force and displacement of the entire tower structure.

(2)

This paper addresses the prolonged training time and computational complexity of traditional SVM methods by employing reverse refraction learning and incorporating the Levy flight strategy to enhance the COA. The resulting ICOA demonstrates superior convergence speed and optimization capability compared to alternative algorithms.

(3)

Propose an ICOA-SVM for predicting the safety state of transmission towers, demonstrating superior prediction accuracy compared to the SVM. The RMSE value of the ICOA-SVM model decreased by 62.5%, the MAPE value decreased by 59.6%, and the MAE value decreased by 75.0%. This advancement can provide a scientific foundation for the safe operation of the electric power system by enhancing the accuracy and efficiency of the assessment.

Although the proposed ICOA-SVM model demonstrates significant advancements in predicting the safety status of transmission towers, certain limitations need to be acknowledged. Firstly, the dataset used in this study is derived from finite element simulations under predefined conditions. While these simulations provide a controlled and comprehensive framework, they may not fully capture the complexity and variability in real-world scenarios, such as unexpected structural defects, extreme environmental conditions, dynamic interactions with hanging accessories like insulators and conductors, or long-term material degradation. Secondly, the computational complexity of the ICOA framework, although improved compared to traditional methods, remains a limitation, particularly for large-scale applications or real-time monitoring systems. This complexity may pose challenges when scaling the model to process large datasets or operate in environments requiring rapid decision-making. Thirdly, this study focuses specifically on transmission towers, which limits the model’s generalizability to other types of infrastructure. Similar predictive frameworks could potentially be adapted and validated for other structures, such as bridges, pipelines, or wind turbines. These limitations emphasize the need for further research to enhance the model’s computational efficiency, expand its applicability to diverse infrastructure systems, and validate its performance using real-world datasets to ensure its broader applicability and practical feasibility.

Future research should aim to address these limitations by expanding the dataset to include real-world measurements under more diverse environmental conditions, thereby improving the model’s robustness and enhancing its generalizability to complex, real-world scenarios. Efforts should also focus on improving the computational efficiency of the ICOA framework, potentially through further refinements in algorithmic design or the integration of hybrid approaches. Such advancements could enable the deployment of the ICOA-SVM model in real-time monitoring systems, providing timely and accurate safety assessments for critical infrastructure. Additionally, to better capture the nonlinear relationship between wind speed and direction, future studies will include finer granularity in wind direction data beyond the current discrete angles (30°, 45°, 60°, 90°). This refinement will ensure a more comprehensive understanding of how varying wind directions impact the safety and stability of transmission towers.

Additionally, the application of the ICOA-SVM model should also be extended to other structural systems, such as bridges, wind turbines, or pipelines, to demonstrate its adaptability and effectiveness across a broader range of contexts. Incorporating factors like material aging, long-term fatigue effects, and dynamic loading conditions into the model could further enhance its predictive accuracy and comprehensiveness. These improvements would not only refine the current methodology but also establish a more scalable, adaptive, and practical framework for managing infrastructure safety in diverse and challenging environments. By addressing these areas, the proposed approach has the potential to significantly contribute to the fields of structural engineering and intelligent infrastructure management.