Prediction Model of Farmland Water Conservancy Project Cost Index Based on PCA–DBO–SVR

Abstract

With the gradual cessation of budget quota standards and the emphasis on market-based pricing, accurately predicting project investments has become a critical issue in construction management. This study focuses on cost indicator prediction for irrigation and drainage projects to address the absence of cost standards for farmland water conservancy projects and achieve accurate and efficient investment prediction. Engineering characteristics affecting cost indicators were comprehensively analyzed, and principal component analysis (PCA) was employed to identify key influencing factors. A prediction model was proposed based on support vector regression (SVR) optimized using the dung beetle optimizer (DBO) algorithm. The DBO algorithm optimized SVR hyperparameters, resolving issues of poor generalization and long prediction times. Validation using 2024 farmland water conservancy project data from Liaoning Province showed that the PCA–DBO–SVR model achieved superior performance. For electromechanical well projects, the root mean square error (RMSE) was 1.116 million CNY, mean absolute error (MAE) was 0.910 million CNY, mean absolute percentage error (MAPE) was 3.261%, and R² reached 0.962. For drainage ditch projects, RMSE was 0.500 million CNY, MAE was 0.281 million CNY, MAPE was 3.732%, and R² reached 0.923. The PCA–DBO–SVR model outperformed BP, SVR, and PCA–SVR models in all evaluations, demonstrating higher prediction accuracy and better generalization capability. This study provides theoretical support for developing cost indicators for farmland water conservancy projects and offers valuable insights for dynamically adjusting national investment standards and improving construction fund management.

1. Introduction

Grain security is a critical element of national strategy. To implement the “storing grain in land and technology” policy effectively, alleviate water scarcity, and promote sustainable development [1,2], farmland development has become a priority for national investment. In this context, the significance and role of farmland water conservancy projects have grown increasingly prominent. However, the absence of a systematic standard for investment in such projects remains an issue. Cost indicators are vital in investment estimation during the decision-making phase and are integral to cost management throughout the project lifecycle. Accurately and efficiently predicting cost indicators is essential for scientifically controlling project investment. By forecasting these indicators, project costs and their trends can be identified, enabling the formulation of cost policies and controlling expenditures at various project stages.

Current research on cost indicator prediction methods primarily includes traditional and machine learning techniques. Traditional methods predominantly rely on mathematical statistics, such as linear regression analysis [3] and grey system prediction [4]. Linear regression analysis is limited to fitting linear relationships in original data, while grey system prediction exhibits low fault tolerance and requires large sample sizes. These methods are insufficient for nonlinear data fitting and are unsuitable for predicting farmland water conservancy project cost indicators. With advancements in artificial intelligence, researchers and experts have explored various cost prediction simulation models in the engineering field. Models such as BP neural networks, support vector machine (SVM) [5], and convolutional neural networks [6,7] are increasingly applied to construction cost forecasting. For example, Wahyu Hayati et al. [8] and Feng et al. [9] developed cost prediction models based on SVM and neural networks tailored to the characteristics of transmission and wind power projects, demonstrating high practical value in determining cost rationality for transmission projects. Wu et al. [10] proposed a two-stage integrated model combining SVM and least-squares support vector machines (LS-SVM) to predict the costs of green building projects, achieving high prediction accuracy and strong generalization capabilities. Compared to traditional neural networks and other learning methods, SVM effectively addresses challenges such as overfitting, local minima, and the curse of dimensionality [11], offering distinct advantages for predicting cost indicators of farmland water conservancy projects. The quality of input data significantly impacts the accuracy of prediction models, necessitating feature selection methods to reduce the dimensionality of raw data. Wyke et al. [12] utilized principal component analysis (PCA) to reduce dimensionality on high-dimensional data, minimizing redundancy and ensuring data independence. PCA is particularly suitable for integrating with other algorithms as an unsupervised learning method [13]. Studies have shown that parameter selection plays a critical role in determining the accuracy and generalization capability of models. In recent years, experts and researchers in cost prediction have frequently introduced optimization algorithms to improve prediction accuracy by optimizing model parameters [14]. At the same time, optimization algorithms can also optimize the design of engineering structural parameters to achieve the advantages of cost reduction, performance enhancement, cycle time reduction, etc. [15,16]. Lin et al. [17] identified key factors influencing substation project costs during the decision-making phase and applied particle swarm optimization (PSO) to determine optimal parameters for support vector machines, ultimately developing a PSO–SVM-based cost prediction model for substations. Cheng et al. [18] highlighted the challenge of predicting construction costs due to price fluctuations and proposed a hybrid model combining LS-SVM with differential evolution (DE) to forecast construction cost indices. The model achieved a prediction error of less than 10%, demonstrating its feasibility. Ai et al. [19] constructed a PSO–SVM-based model to predict environmental management costs, achieving higher prediction accuracy than other methods. Among these optimization algorithms, the dung beetle optimizer (DBO) stands out for its ability to rapidly approach optimal solutions and effectively optimize model parameters [20,21]. Its robust exploration capability has made it a valuable tool for optimizing hyperparameters in support vector machines and neural network models.

A review of research literature on the development and prediction of cost indicators shows that existing prediction models are primarily applied to building construction, highway engineering, and power transmission projects [22,23,24], with limited studies focusing on farmland water conservancy project cost indicators. Consequently, systematic and in-depth research in this area is necessary. This study applies PCA to preprocess model data, identifying key factors influencing the cost indicators of farmland water conservancy projects. Qualitative factors are further analyzed to construct a support vector regression (SVR) model optimized with the DBO. The proposed PCA–DBO–SVR model predicts cost indicators under varying regional, project-type, and environmental conditions. This approach aims to provide methodological and theoretical support for cost indicator prediction in farmland water conservancy projects, improving cost management throughout the project lifecycle in China.

2. Materials and Methods

2.1. Overview of the Study Area

Liaoning Province is located in the southern part of northeast China, with geographic coordinates ranging from 118°53′ E to 125°46′ E and 38°43′ N to 43°26′ N. The province covers a land area of 148,700 km² and a sea area of 150,000 km², with a total coastline length of 2290 km. Liaoning comprises 14 cities (including the sub-provincial cities of Shenyang and Dalian) and the Shenyang–Fushun Demonstration Zone. There are 100 counties (cities and districts), including 16 county-level cities, 25 counties, and 59 municipal districts. The administrative divisions include 513 subdistricts, 640 towns, 201 townships, 4617 communities, and 11,561 administrative villages, with a total permanent population of 41.97 million. In 2024, Liaoning added 22,670 hectares of newly constructed farmland. The main construction activities in this region involve canal lining and dredging, irrigation and drainage works, the construction of new bridges and culverts, rural road development, land leveling and soil improvement, and farmland protection projects. These initiatives aim to enhance the overall ecological environment of farmland, mitigate the impact of floods on crops, and improve agricultural productivity in the region. A geographic map of Liaoning Province is shown in Figure 1.

2.2. Data Sources and Processing

This study collected cost indicator data for farmland water conservancy projects across cities in Liaoning Province in 2024. The sample data were obtained through a combination of field surveys and engineering acceptance reports. The surveyed areas included Wanghua District in Fushun, Hunnan District in Shenyang, Fuxin County in Fuxin, Gongchangling District in Liaoyang, Shuangta District in Chaoyang, and Linghai City in Jinzhou. Data preprocessing includes missing value processing, outlier removal and data normalization. Missing value processing is conducted in accordance with the mean value of the same type of project and the proportion of the method of interpolation, according to the constraints on the composition of the cost and the reasonableness of the amount of work to eliminate outliers, and with the use of normalization methods to eliminate the impact of the data outline and scaling the data to the [0, 1] range. The normalization formula is shown in Equation (1). The dataset consisted of 40 electromechanical well projects and 100 drainage ditch projects, split into training and testing sets at a 7:3 ratio.

$$x_i^{*}={\displaystyle \frac{x_i-x_{min}}{x_{max}-x_{min}}}$$

(1)

where $x_{max}$ and $x_{min}$ represent the maximum and minimum values in the sample data, respectively; $x_i$ and $x_i^{*}$ represent the original and normalized data, respectively.

2.3. Analysis of Factors Influencing Cost Indicators in Farmland Water Conservancy Projects

The cost indicators of farmland water conservancy projects are influenced by numerous factors with complex interrelationships [25,26]. Selecting comprehensive and reasonable influencing factors is foundational in predicting these indicators. In this study, the investment characteristics of farmland water conservancy projects were analyzed to identify key factors affecting cost indicators. Relevant literature was consulted to ensure a robust selection of influencing factors, while practical considerations specific to the projects were also incorporated. To ensure the feasibility of the selected factors for model construction, PCA was employed to conduct an in-depth analysis of the identified influencing factors.

2.3.1. Preliminary Selection of Influencing Factors

To ensure the accuracy of the prediction model, the preliminary selection process involved gathering a comprehensive range of factors influencing the cost indicators of farmland water conservancy projects. Given the limited literature on the topic, efforts were made to ensure thoroughness and scientific rigor in factor selection. Relevant materials were collected and analyzed for comparison, including preliminary design documents, feasibility study reports [27,28], and data from actual engineering projects. The influencing factors were organized and summarized accordingly. This study focused on electromechanical well and drainage ditch projects within farmland water conservancy projects. The influencing factors considered included geographical environment, engineering, consumption, price, and management factors. The statistical results of the selected factors are presented in

Table 1. Summary of influencing factors for farmland water conservancy project cost indicators.

Category	Influencing Factors	Impact Factor Subcomponent
Geographic environmental factors	Geographic location	Differences in project locations lead to variations in economic development levels, address conditions, and design or construction complexity, all of which significantly impact project costs.
	Topography and geomorphology
	Geological structure
	Seismic intensity
	On-site and off-site temporary traffic
	On-site construction conditions
Consumption factors	Labor consumption	Differences in materials used and construction complexity influence project costs. Subcomponents of farmland water conservancy projects involve various quantity indicators, reflecting the scale of installation and construction, which subsequently affect cost indicators.
	Machinery consumption
	Key material consumption
Price factors	Labor costs	Price factors reflect the impact of market economic fluctuations on project costs. Changes in material and machinery prices and labor and other costs contribute to project cost variations.
	Material prices
	Machinery costs
	Other costs
Management factors	Contractor management level	Management factors and construction periods influence on-site construction, affecting project costs.
	Supervision management level
	Construction duration (days)
Electrical and mechanical well engineering	Borehole diameter (m)	Engineering factors related to structural design significantly affect resource estimation, playing a critical role in the overall construction process.
	Irrigation pipeline length (m)
	Designed flow rate/(m3·s−1)
	Well depth/m
	Pumping head/m
	Irrigation area/m2
Drainage ditch engineering	Drainage ditch length/m
	Drainage flow rate/(m3·s−1)
	Drainage ditch bottom width/m
	Gradient

.

Some of the qualitative factors need to be quantified. The quantification principle should be clearly defined. The quantification principles for geographic location are: 1 for the east, 2 for the south, 3 for the west, 4 for the north, and 5 for the central part; the quantification principles for topography and geomorphology are: 1 for the hills and 2 for the plains; the quantification principles for the geologic structure, the temporary traffic condition inside and outside the site, the management level of the contractors, the management level of the supervisory authority, and the construction conditions in the site are: 1 for the lack of influence on the construction, 2 for the general influence, and 3 for the significant influence; the quantification principles for the intensity of earthquake: for example, the intensity of 6 is quantified as 6.

2.3.2. Screening Key Influencing Factors Using Principal Component Analysis

Common dimensionality reduction methods include grey relational analysis (GRA) and PCA. Considering the non-temporal characteristics of the sample data and the importance of influencing factors as the foundation for constructing prediction models [29], PCA was employed in this study to identify key influencing factors. PCA is a statistical method that extracts and transforms multiple correlated variables into fewer independent composite variables through dimensionality reduction. This approach aims to maximize the information retained in the sample data with a reduced set of variables. The detailed method is as follows:

• Suppose the dataset consists of n samples, each containing m variables, forming an n × m sample matrix X, as shown in Equation (2):

  $$X_{n\times m}=\left[\begin{array}{ccc}{X}_{11}& \cdots & X_{1m}\\ ⋮& \ddots & ⋮\\ X_{n1}& \cdots & X_{nm}\end{array}\right],$$

  (2)
• Calculate the eigenvalues ${\lambda }_1$ ≥ ${\lambda }_2$ ≥ ⋯ ${\lambda }_m$ ≥ 0, and corresponding eigenvectors $u_1,u_2$, ⋯, $u_m$, of the correlation coefficient matrix R, where $u_j$ = ($u_{1j},u_{2j}$, ⋯, $u_{mj}$)^T. Find the composition of m new indicator variables from feature vectors.
• Determination of principal components: After standardizing the data, the variance contribution rate $b_j$ and cumulative contribution rate $a_j$ of each factor are calculated using Equations (3) and (4). Finally, only components with eigenvalue ≥ 1 and cumulative contribution greater than 80% are retained as principal components [30].

  $$b_j={\displaystyle \frac{{\lambda }_j}{\sum _{j=1}^m {\lambda }_j}},(j=\mathrm{1,2},\cdots ,m),$$

  (3)

  $$a_j={\sum }_{j=1}^m b_j,(j=\mathrm{1,2},\cdots ,m),$$

  (4)
• Calculation of comprehensive scores: The factor loading matrix is used to obtain the scoring coefficients of each influencing factor on the principal components. Comprehensive scores are calculated and ranked after normalization. This process ensures the identification of key influencing factors crucial for the prediction model.

2.4. DBO–SVR Prediction Model

2.4.1. Support Vector Regression (SVR)

Support vector machines (SVMs) are predictive methods based on structural risk minimization, offering significant advantages in handling high-dimensional, nonlinear, and small-sample problems. These methods demonstrate high predictive accuracy and robust nonlinear classification capabilities [31,32]. Support vector regression (SVR), an extension of SVM, addresses regression prediction problems by mapping data into a high-dimensional feature space through nonlinear transformations, thereby converting nonlinear regression problems into linear regression problems in higher dimensions. As this study involves regression prediction, the final decision function is:

$$f\left(x\right)=\left[w,\mathsf{\Phi }\left(x\right)\right]+b,$$

(5)

where $\mathsf{\Phi }\left(x\right)$ represents the mapping function, w is the weight coefficient, and b is the bias term.

The SVR problem can be described as:

$$\min {\displaystyle \frac{1}{2}}\parallel w{\parallel }^2+C{\sum }_{i=1}^n \left({\xi }_i+{\xi }_i^{*}\right),$$

(6)

where ${\xi }_i{, \xi }_i^{* }$ represent constants, and C is the penalty factor. C influences the stability of the SVR model; larger values of C result in higher model accuracy.

Common kernel functions include linear, polynomial, and Gaussian kernels. This study adopts the Gaussian radial basis function (RBF) as the kernel function due to its superior noise resistance compared to other kernel functions. The formula for the RBF kernel is as follows:

$$k\left(x_i,x_j\right)=\exp \left[-g(x_i-x_j{)}^2\right]\left(g>0\right),$$

(7)

where $x_j$ represents the center of the Gaussian kernel function, and $g$ is the variance of the kernel function. The variance influences the complexity of sample distribution in the feature space; larger $g$ values lead to lower model precision.

In conclusion, the accuracy and stability of the SVR model are determined by the choice of kernel function type, the kernel parameter g, and the penalty factor C.

2.4.2. Dung Beetle Optimizer (DBO)

DBO is a novel population-based optimization algorithm introduced by Xue et al. in 2022 [33]. This algorithm simulates the social behaviors of dung beetles, such as rolling balls, dancing, reproducing, foraging, and stealing, to achieve optimization. DBO can efficiently identify optimal parameters, including the support vector weights and thresholds for the SVR model, within a short time frame [33]. Compared to traditional optimization algorithms like the genetic algorithm (GA), DBO offers advantages such as faster convergence and higher accuracy. It effectively addresses issues of insufficient prediction precision and weak generalization capability caused by the subjective selection of SVR hyperparameters [34]. Based on these advantages, a DBO–SVR model is constructed for predicting farmland water conservancy project cost indicators. The algorithm’s steps are detailed as follows:

When dung beetles roll balls forward, their positions are updated as shown in Equation (8). Upon encountering obstacles, the positions are re-updated using Equation (9):

$$x_i^{t+1}=x_i^t+ak{x}_i^{t-1}+b\left|x_i^t-x_{worst}^t\right|,$$

(8)

$$x_i^{t+1}=x_i^t+\tan \theta \left|x_i^t-x_i^{t-1}\right|,$$

(9)

where $a$ takes a value of 1 or −1; $k\in \left(\mathrm{0,0.2}\right]$; $b\in \left(\mathrm{0,1}\right)$; $x_i^t$ represents the position of the i-th dung beetle at the t-th iteration; and $x_{worst}^t$ indicates the worst position in the population.

The updated formula for simulating the selection of a safe area for reproduction by female dung beetles is given as follows:

$$x_i^{\prime +1}=x_{gbest}^{\prime }+b_1(x_i^{\prime }-L_{b^{\mathrm{*}}})+b_2|x_i^{\prime }-U_{b^{\mathrm{*}}}|,$$

(10)

where $L_{b^{\mathrm{*}}}$ and $U_{b^{\mathrm{*}}}$ denote the lower and upper boundaries of the breeding zone within the safe area, respectively, while $x_{gbest}^{\prime }$ represents the optimal position within the population.

When the small dung beetle forages in the optimal feeding area, the foraging position is calculated as follows:

$$x_i^{\prime +1}=x_i^{\prime }+C_1(x_i^{\prime }-L_{b^{\prime }})+C_2|x_i^{\prime }-U_{b^{\prime }}|,$$

(11)

where $C_1 \mathrm{and} C_2$ are random numbers within the range (0, 1), and $L_{b^{\prime }}$ and $U_{b^{\prime }}$ denote the lower and upper boundaries of the optimal feeding area for the small dung beetle, respectively.

When the dung beetle steals dung balls from others, the position update is calculated as follows:

$$x_i^{\prime +1}=x_{lbest}^{\prime }+Qg\left(\right|x_i^{\prime }-x_{gbest}^{\prime }|+|x_i^{\prime }-x_{lbest}^{\prime }\left|\right),$$

(12)

where $x_{lbest}^{\prime }$ represents the optimal position within the region, and $Q$ is a constant.

2.5. PCA–DBO–SVR Model Development Steps

The model is developed using the influencing factors obtained through PCA as input data and the unit cost of each sample project as output data. According to the sample data size of this study, in order to balance the model training adequacy and evaluation reliability, the sample data are split into training and testing sets at a ratio of 7:3, respectively, to train and validate input–output relationships. The DBO is used to optimize the hyperparameters C and g of the SVR model. These optimized parameters are then incorporated into the SVR model. Training continues using the same sample data until the training error approaches zero; at this point, the final SVR prediction model is established. The trained model is saved if the model demonstrates high accuracy and satisfactory performance. The input variables are standardized, and principal component scores are calculated and input into the trained SVR model to predict unit costs, representing the cost indicators obtained through the proposed method [35].

The detailed steps are as shown in Figure 2.

3. Results

3.1. Selection of Influencing Factors Using PCA

A total of 140 sample datasets from electromechanical well and drainage ditch projects were analyzed and processed. Correlation analysis was first applied to evaluate the relationship between influencing factors and cost indicators, and factors with a correlation coefficient of less than 0.5 were excluded.

The influencing factors to obtain the cost index of electrical and mechanical well engineering are the diameter of the borehole (E₁), length of the irrigation pipeline (E₂), design flow rate (E₃), depth of the well (E₄), head (E₅), on-site construction conditions (E₆), consumption of main materials (E₇), consumption of machinery (E₈), consumption of labor (E₉), area of the irrigated area (E₁₀), seismic intensity (E₁₁), meteorological conditions (E₁₂), labor cost (E₁₃), machinery cost (E₁₄), material price (E₁₅), and duration (E₁₆).

Drainage ditch engineering cost indicators include the length of the drainage ditch (D₁), the flow of the drainage ditch (D₂), the bottom width of the drainage ditch (D₃), the height of the drainage ditch (D₄), the specific drop (D₅), machinery consumption (D₆), the consumption of major materials (D₇), the construction conditions on the site (D₈), seismic intensity (D₉), meteorological conditions (D₁₀), the site of the temporary traffic conditions on the site and off (D₁₁), labor cost (D₁₂), labor consumption (D₁₃), material price (D₁₄), machinery cost (D₁₅), and construction duration (D₁₆).

PCA was then used to identify the key influencing factors for cost indicators. Principal component eigenvalues, contribution rates, and eigenvectors were calculated based on Equations (3) and (4). The results are presented in

Table 2. Principal component eigenvalues, contribution rates, and eigenvectors.

Engineering Category	No.	Eigenvalue	Percentage/%	Cumulative Percentage/%	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5
Electrical and mechanical well engineering	1	6.313	39.458	39.458	−0.125	0.395	0.152	0.791	−0.134
	2	2.703	16.895	56.353	0.851	0.017	−0.235	0.110	−0.311
	3	1.758	10.987	67.340	0.714	0.010	−0.127	0.179	−0.247
	4	1.365	8.528	75.869	0.605	0.695	0.031	−0.014	−0.235
	5	1.212	7.574	83.442	0.570	0.631	−0.039	0.250	−0.143
	6	0.742	4.641	88.083	−0.103	−0.157	−0.629	−0.293	−0.127
	7	0.638	3.988	92.071	0.763	−0.087	0.346	−0.161	−0.266
	8	0.515	3.219	95.290	0.890	−0.264	0.219	−0.174	−0.052
	9	0.329	2.059	97.349	0.560	−0.196	0.580	−0.202	−0.141
	10	0.154	0.964	98.313	−0.165	0.692	0.289	−0.415	0.295
	11	0.096	0.600	98.913	0.042	−0.449	0.353	0.498	0.501
	12	0.090	0.564	99.477	0.117	0.825	0.206	−0.151	0.361
	13	0.051	0.320	99.796	0.870	−0.022	−0.321	0.041	0.336
	14	0.027	0.170	99.966	0.840	−0.011	−0.332	0.035	0.392
	15	0.005	0.029	99.995	0.881	−0.046	−0.292	0.011	0.337
	16	0.001	0.005	100.000	0.627	−0.401	0.461	−0.068	0.048
Drainage ditch engineering	1	7.688	48.052	48.052	−0.016	0.944	0.266	−0.051
	2	3.976	24.850	72.903	−0.167	0.507	0.579	−0.410
	3	2.527	15.795	88.698	0.489	0.250	0.809	−0.132
	4	1.076	6.726	95.424	−0.002	−0.126	0.931	−0.006
	5	0.433	2.703	98.127	−0.792	−0.065	−0.276	−0.277
	6	0.207	1.295	99.422	−0.024	0.898	−0.201	0.368
	7	0.064	0.402	99.824	−0.139	0.933	−0.272	0.119
	8	0.026	0.161	99.985	0.989	−0.042	0.017	0.129
	9	0.002	0.015	100.000	0.942	−0.124	0.072	−0.295
	10	0.000	0.000	100.000	−0.942	0.124	−0.072	0.295
	11	0.000	0.000	100.000	0.169	0.179	−0.122	0.949
	12	0.000	0.000	100.000	0.995	−0.072	0.037	−0.018
	13	0.000	0.000	100.000	0.989	−0.042	0.017	0.129
	14	0.000	0.000	100.000	0.971	−0.020	0.002	0.231
	15	0.000	0.000	100.000	0.951	−0.005	−0.008	0.300
	16	0.000	0.000	100.000	−0.016	0.944	0.265	−0.051

. The Kaiser–Meyer–Olkin (KMO) value was greater than 0.5, indicating that the data are suitable for PCA [36,37].

Principal components with a cumulative variance contribution rate exceeding 80% and an initial eigenvalue greater than 1 were selected for the next calculation step. As shown in Table 2, the first five components for electromechanical well projects achieved a cumulative contribution rate of 83.422%, with eigenvalues exceeding 1.212, indicating that these five components capture most of the information in the original data, making these five components sufficient to represent the data. The first four components reached a cumulative contribution rate of 95.424% for drainage ditch projects, with eigenvalues exceeding 1.076, which satisfied the principal component determination requirements and made these four components sufficiently representative of the data. Using the factor loadings and score coefficients of the principal components, the comprehensive scores for influencing factors in farmland water conservancy project cost indicators were calculated. As shown in

Table 3. Scores of each principal component and composite scores.

Engineering Category	Influencing Factors	Score Coefficients on Each Principal Component					Factor 4	Factor 5
		1	2	3	4	5
Electrical and mechanical well engineering	E1	−0.125	0.395	0.152	0.791	−0.134	0.098	0.717
	E2	0.851	0.017	−0.235	0.110	−0.311	0.123	0.792
	E3	0.714	0.010	−0.127	0.179	−0.247	0.118	0.778
	E4	0.605	0.695	0.031	−0.014	−0.235	0.182	0.972
	E5	0.570	0.631	−0.039	0.250	−0.143	0.191	1.000
	E6	−0.103	−0.157	−0.629	−0.293	−0.127	−0.137	0.000
	E7	0.763	−0.087	0.346	−0.161	−0.266	0.131	0.817
	E8	0.890	−0.264	0.219	−0.174	−0.052	0.137	0.836
	E9	0.560	−0.196	0.580	−0.202	−0.141	0.110	0.751
	E10	−0.165	0.692	0.289	−0.415	0.295	0.071	0.634
	E11	0.042	−0.449	0.353	0.498	0.501	0.073	0.639
	E12	0.117	0.825	0.206	−0.151	0.361	0.161	0.907
	E13	0.870	−0.022	−0.321	0.041	0.336	0.160	0.906
	E14	0.840	−0.011	−0.332	0.035	0.392	0.159	0.902
	E15	0.881	−0.046	−0.292	0.011	0.337	0.160	0.905
	E16	0.627	−0.401	0.461	−0.068	0.048	0.112	0.760
Drainage ditch engineering	D1	−0.086	0.966	0.136	−0.085		0.119	0.721
	D2	−0.179	0.565	0.656	−0.080		0.104	0.686
	D3	0.541	0.441	0.661	0.225		0.240	1.000
	D4	0.118	0.086	0.753	0.543		0.148	0.788
	D5	−0.825	−0.207	0.003	−0.244		−0.193	0.000
	D6	−0.112	0.861	−0.479	−0.005		0.042	0.543
	D7	−0.256	0.844	−0.382	−0.231		0.008	0.465
	D8	0.990	0.043	−0.119	−0.025		0.171	0.842
	D9	0.928	−0.073	0.192	−0.305		0.158	0.811
	D10	−0.928	0.073	−0.192	0.305		−0.158	0.080
	D11	0.204	0.259	−0.696	0.619		0.040	0.539
	D12	0.991	0.003	−0.012	−0.124		0.171	0.840
	D13	0.990	0.043	−0.119	−0.025		0.171	0.842
	D14	0.975	0.070	−0.193	0.046		0.169	0.837
	D15	0.959	0.089	−0.243	0.095		0.167	0.831
	D16	−0.086	0.966	0.135	−0.085		0.119	0.720

, the influencing factors with normalized comprehensive score results greater than 0.5 were identified as key factors. Accordingly, the key influencing factors for electromechanical well projects included 15 factors, such as borehole diameter and irrigation pipeline length, while drainage ditch projects identified 13 key factors, including length and flow rate.

Finally, the key influencing factors identified through PCA were used as input variables for the SVR model, with cost indicators as output variables, to predict the cost indicators of farmland water conservancy projects.

3.2. Comparison of Prediction Models

This study compared four models using the same sample database to validate the effectiveness of the PCA–DBO–SVR model in predicting cost indicators for farmland water conservancy projects. The BP neural network, SVR, PCA–SVR, and PCA–DBO–SVR were used.

The BP neural network was configured with 1000 training iterations, a learning rate of 1 × 10⁻², a minimum error target of 1 × 10⁻⁵, and five hidden layer neurons. The DBO optimization algorithm was applied to tune the hyperparameters of the SVR model. DBO settings included a population size of 10, a maximum of 100 iterations, and boundaries of [−8, 8]. The dataset was divided into 70% training and 30% testing samples.

Four metrics were used to evaluate the prediction accuracy of the models: root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination ($R^2$). Smaller RMSE, MAE, and MAPE values and $R^2$ values closer to 1 indicate better model performance, lower error, and more reliable predictions. The formulas for these evaluation metrics are as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2},$$

(13)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n \left|Y_i-\widehat{Y_i}\right|,$$

(14)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n \left|{\displaystyle \frac{Y_i-\widehat{Y_i}}{Y_i}}\right|\times 100\%,$$

(15)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n {\left(Y_i-\widehat{Y_i}\right)}^2}{{\sum }_{i=1}^n {\left(Y_i-\overline{Y_i}\right)}^2}},$$

(16)

where $Y$ is the actual value of the i-th sample, $\widehat{Y }$ represents the predicted value of the i-th sample, and $\overline{Y}$ is the mean of the actual values across n samples.

The actual values in Figure 3 are the test set divided by the sample data collected in Section 2.2 according to the 7:3 ratio. A comparison between the BP neural network model and the SVR model highlights notable differences. The BP neural network forms a complex structure by simulating human brain neurons, allowing for enhanced learning and adaptability through adjustments to the number of neurons and layers. However, when comparing the prediction results for electromechanical well projects and drainage ditch projects, the BP model prediction lines show significantly greater deviation from the actual value lines than those of the SVR model. These results demonstrate that the SVR regression prediction model is well-suited to the sample data and engineering characteristics in this study, greatly improving the prediction accuracy of cost indicators for farmland water conservancy projects. To evaluate the effectiveness of PCA in dimensionality reduction, a PCA–SVR model was constructed for comparison. As shown in Figure 3, the prediction results indicate that the PCA-reduced SVR model achieves smaller distances between the prediction lines and the actual value lines across sample points compared to the SVR model without dimensionality reduction. To further examine the impact of the DBO on parameter optimization, a PCA–DBO–SVR model was developed. The results demonstrate that the PCA–DBO–SVR model achieves the closest alignment between the prediction and actual value lines, with the smallest distances between sample points. In addition, the scatter plot in Figure 4 and the residual plot in Figure 5 show that the PCA–DBO–SVR model is closest to the 1:1 fitting line in terms of scatter and closest to the zero level line in terms of residuals compared to the other models, with no obvious non-stochastic tendency, which suggests that the predicted values of the model are the closest to the actual values and have the highest prediction accuracy. Therefore, the PCA–DBO–SVR model significantly outperforms the standalone BP neural network, SVR, and PCA–SVR models in prediction accuracy and simulation performance.

The evaluation metrics for the BP, SVR, PCA–SVR, and PCA–DBO–SVR models are shown in

Table 4. Comparison of assessment metrics across models.

Engineering Category	Model	RMSE (10,000 CNY)	MAE (10,000 CNY)	MAPE (%)	R2
Electrical and mechanical well engineering	BP	4.439	3.631	12.526%	0.851
	SVR	2.291	2.256	8.283%	0.869
	PCA–SVR	2.021	1.853	6.408%	0.926
	PCA–DBO–SVR	1.116	0.910	3.261%	0.962
Drainage ditch engineering	BP	2.214	1.156	15.010%	0.793
	SVR	1.373	0.702	11.133%	0.812
	PCA–SVR	0.986	0.646	7.315%	0.874
	PCA–DBO–SVR	0.500	0.281	3.732%	0.923

. A comparison of the single models demonstrates that the standalone SVR model outperforms the BP neural network in both electromechanical well and drainage ditch projects. Specifically, the SVR model reduces RMSE by 48.39% and 37.99%, MAE by 37.87% and 39.27%, and MAPE by 33.87% and 25.83%, while improving R² by 2.07% and 2.34%, respectively. These improvements can be attributed to the BP neural network’s tendency to encounter issues such as local optima and longer training times, which the SVR model effectively avoids. Therefore, the SVR model provides superior prediction results to the BP neural network for cost indicator predictions.

To enhance model efficiency and prediction accuracy, PCA was incorporated to construct the PCA–SVR model. Compared to the standalone SVR model, the PCA–SVR model achieves significant improvements. For electromechanical well and drainage ditch projects, RMSE decreases by 11.79% and 28.19%, MAE decreases by 17.86% and 7.98%, MAPE decreases by 22.64% and 34.29%, and R² increases by 6.16% and 7.09%, respectively. These results indicate that applying PCA to analyze and reduce the dimensionality of SVR input variables eliminates redundancy in the input data, improving the validity of training samples and resulting in higher model accuracy.

With its excellent optimization capabilities, the DBO algorithm addresses the challenge of determining hyperparameters in the SVR model. Compared to the PCA–SVR model, the PCA–DBO–SVR model achieves significant improvements in predictive accuracy. For electromechanical well and drainage ditch projects, the PCA–DBO–SVR model reduces RMSE by 44.78% and 49.26%, MAE by 50.89% and 56.50%, and MAPE by 49.11% and 48.98%, and increases R² by 3.74% and 5.31%, respectively. These results indicate that the model without an optimization algorithm will have instability in prediction accuracy due to the stochastic nature of hyperparameters, while the DBO algorithm compares with traditional PSO, GA, and other algorithms, as the mechanism of simulating dung beetles’ social behavior of DBO improves the hyperparameter search space coverage and reduces the number of iteration convergences, which indicates that it has stronger robustness and optimality searching performance in high-dimensional parameter space, and can further improve the model’s prediction accuracy.

In summary, the PCA–DBO–SVR model outperforms standalone SVR and BP neural network models in all evaluation metrics, demonstrating enhanced efficiency and effectiveness by integrating PCA and DBO. The inclusion of DBO eliminates the subjectivity in parameter selection for SVR, resulting in significantly better predictive accuracy and generalization capability than single SVR or PCA–SVR models. Moreover, the R² values for the PCA–DBO–SVR model exceed 0.9 in all cases, further highlighting its stability and superior performance in predicting farmland water conservancy project cost indicators. Given the lack of comprehensive cost indicator data for such projects, the PCA–DBO–SVR model provides robust data support and a theoretical foundation for prediction tasks.

This study employs a combination of PCA, DBO, and SVR to predict cost indicators. The results demonstrate the high applicability and accuracy of this model, offering critical support for the dynamic adjustment of investment standards, enhanced planning of construction funding, and improved cost management in farmland water conservancy projects.

4. Discussion

Using prediction models as a novel approach for compiling cost indicators provides inspiration to explore predictive methods in other fields. Identifying methods aligned with the characteristics of farmland water conservancy project cost indicators can offer valuable insights for adaptation and application. Considering the numerous factors influencing project cost indicators, incorporating all variables into machine learning prediction models often leads to excessive computation time and reduced accuracy. Factor selection is essential. Zhang et al. [38] utilized LASSO regression to compile highway project cost indicators. Their method involved quantitatively identifying key cost drivers, selecting highly correlated indicators as input variables, and inputting these variables into the LASSO regression model to calculate comprehensive cost indicators. The quantification and selection of influencing factors significantly improved the model’s efficiency and accuracy. Similarly, Elmousalami et al. [27] analyzed the dynamics and patterns of cost information in engineering projects, identifying major qualitative factors influencing project costs. These factors included project characteristics, construction location, and project start/completion times. Drawing on these insights, the current study established a system of influencing factors for farmland water conservancy project cost indicators. The system encompasses engineering characteristics, geographic environment, and management factors. These factors were quantified, and PCA was used to identify key influencing factors with normalized comprehensive score results above 0.5. Experimental results demonstrate that prediction models processed using PCA achieve significantly higher accuracy.

In the selection of prediction models, Zhou et al. [39] constructed artificial neural network (ANN), K-nearest neighbor (KNN), random forest (RF), and SVR models to predict operating expenses for U.S. light rail transit (LRT) projects. Using data from 22 LRT systems in the United States from 2008 to 2018, the performance of these models was validated and analyzed. The results showed that the SVR model outperformed the other three models in prediction accuracy. Based on these findings, the SVR model was selected as the cost indicator prediction model for this study.

Mahmoodzadeh et al. [40] applied the grey wolf optimizer (GWO) algorithm to optimize the parameters of an SVR model for predicting tunnel construction costs. The optimized model significantly improved prediction accuracy, with a notable reduction in mean squared error compared to linear and standalone SVR models. These findings demonstrated the enhanced predictive performance and feasibility of combining optimization algorithms with SVR. However, the GWO algorithm and other traditional intelligent optimization algorithms often face issues such as susceptibility to local optima, low convergence accuracy, and weak theoretical foundations. Wu et al. [34] employed the DBO algorithm to optimize SVR parameters, resulting in a model with high prediction accuracy and strong fitting ability, with prediction errors consistently below 1%. Based on these findings, the present study adopts the DBO algorithm for hyperparameter optimization in the SVR model, achieving a precise and effective improvement in prediction accuracy.

The PCA–DBO–SVR model constructed in this study can predict the differentiated cost indices of farmland water conservancy projects by inputting factors such as different regions and different engineering characteristics, which provides basic data and theoretical support for the accurate prediction of project investment in the absence of budget quotas for farmland water conservancy projects at this stage. At the same time, in the feasibility study stage, the key influencing factors in the project can be input into the prediction model to output the predicted value of cost indices, which can assist in the optimization of the design scheme, and accordingly, project managers can reasonably formulate the capital investment and arrangement during the construction period. Currently, this study focuses on the cost prediction of farmland water conservancy projects in Liaoning Province and verifies the applicability to electromechanical wells and drainage ditches, but it lacks research on other provinces and does not yet cover water conservancy projects such as sluices, bridges, and culverts. In the future, we plan to expand the dataset to cover the sample range of different geographic regions and increase the diversity of project types to further improve the generalization and reasonableness of the model and provide theoretical support for the dynamic adjustment of the national investment standard.

5. Conclusions

To address the lack of unified standards and low prediction accuracy for farmland water conservancy project cost indicators, this study focused on these projects and proposed a prediction method based on the PCA–DBO–SVR model. PCA was used to identify key influencing factors, and the resulting model demonstrated high prediction accuracy and strong generalization capability. The main conclusions are as follows:

(1)

Based on the characteristics of farmland water conservancy projects, influencing factors were selected from engineering features, environmental conditions, and management aspects. Principal component analysis was used to identify key factors and establish an influencing factor system for cost indicators, providing important support for constructing prediction models.

(2)

The proposed PCA–DBO–SVR prediction model was compared with other models using case studies. Results showed that the maximum absolute relative error was only 3.732%, demonstrating the highest prediction accuracy and best-fitting performance. Compared to BP, SVR, and PCA–SVR models, the PCA–DBO–SVR model achieved the lowest error metrics. For electromechanical well and drainage ditch projects, RMSE values were 1.116 million CNY and 0.500 million CNY, MAE values were 0.910 million CNY and 0.281 million CNY, and R2 values were 0.962 and 0.923, respectively. The PCA–DBO–SVR model combines the advantage of factor selection from PCA with the high prediction accuracy of DBO–SVR, delivering optimal predictive performance. It provides a robust scientific foundation and theoretical support for cost indicator prediction in farmland water conservancy projects.