Model Optimization and Application of Straw Mulch Quantity Using Remote Sensing

Abstract

Straw mulch quantity is an important indicator in the detection of straw returned to the field in conservation tillage, but there is a lack of large-scale automated measurement methods. In this study, we estimated global straw mulch quantity and completed the detection of straw returned to the field. We used an unmanned aerial vehicle (UAV) carrying a multispectral camera to acquire remote sensing images of straw in the field. First, the spectral index was selected using the Elastic-net (ENET) algorithm. Then, we used the Genetic Algorithm Hybrid Particle Swarm Optimization (GA-HPSO) algorithm, which embeds crossover and mutation operators from the Genetic Algorithm (GA) into the improved Particle Swarm Optimization (PSO) algorithm to solve the problem of machine learning model prediction performance being greatly affected by parameters. Finally, we used the Monte Carlo method to achieve a global estimation of straw mulch quantity and complete the rapid detection of field plots. The results indicate that the inversion model optimized using the GA-HPSO algorithm performed the best, with the coefficient of determination (R²) reaching 0.75 and the root mean square error (RMSE) only being 0.044. At the same time, the Monte Carlo estimation method achieved an average accuracy of 88.69% for the estimation of global straw mulch quantity, which was effective and applicable in the detection of global mulch quantity. This study provides a scientific reference for the detection of straw mulch quantity in conservation tillage and also provides a reliable model inversion estimation method for the estimation of straw mulch quantity in other crops.

1. Introduction

Known for its high organic matter and fertility, black soil is a non-renewable resource that plays a very important role in agricultural development [1]. In order to curb the degradation of black soil and restore and enhance ground strength, conservation tillage has become a world-recognized sustainable production method in agriculture; it is an important part of modern eco-agriculture and plays an important role in environmental protection [2]. Conservation tillage techniques centered on no- and minimum-tillage plus crop straw mulching have become important measures to improve soil degradation on farmland and increase soil organic matter content and moisture retention capacity. Straw mulching has greatly improved the degree of protection of black soil, facilitated the function of carbon metabolism in no-till soil microbial communities, and increased crop yields. Conservation tillage requires that the straw mulch rate be not less than 0.3 [3]. Straw mulch quantity is also an important indicator for determining the level of straw mulching. Straw mulch rate refers to the ratio of the area covered by crop straw or stubble on the surface soil to the total surface area; straw mulch quantity refers to the quantity of crop straw or stubble covered per unit area of surface soil. Our team is committed to the study of straw mulch detection, and we have obtained good results in the detection of straw mulch [4,5,6]. However, it was found that the straw mulch rate can only accomplish the detection of “with” and “without” straw mulch and not the detection of “more” and “less” straw mulch. Liu et al. [7] suggested that different straw mulch quantities have different effects on soil improvement and that a straw return quantity of about 7500 kg/hm² had the best effect on soil improvement. Therefore, the accurate detection of straw mulch quantity in the field is an important judgment index to measure the level of straw mulching and also reflects the quality and effect of straw return to the field [8]. However, in the detection of straw mulch quantity, there are problems with cumbersome work tasks, diversified influencing factors, and huge measurement errors, and there is no automated measurement method of straw mulch quantity on a large scale yet.

In recent years, remote-sensing technology has been developed with the advantage of being available on temporal and spatial scales, allowing for rapid and accurate large-scale feature detection [9]. Aerial multispectral technology has potential in remote sensing research, which combines the integrated features of UAV monitoring and spectral remote sensing and describes external characterization information more accurately while acquiring rich information [10]. The input–output ratio of UAV multi-spectral cameras is higher, so they have a short data acquisition cycle and are more flexible in operation and suitable for multiple scenarios. Huang et al. [11], Daughtry et al. [12], Daughtry et al. [13], and Burud et al. [14] proposed detecting crops in farmland through remote sensing data and achieved good results. Kavoosi et al. [15] compared the feasibility of satellite and drone images in monitoring straw mulch, and the results showed that drones have certain advantages in straw mulch detection. The mapping relationship established between spectral data and straw dry matter content is one of the simplest methods used to obtain the straw mulch quantity. Yang et al. [16] used a machine learning algorithm combined with a vegetation index approach to estimate the leaf dry matter content. Liu et al. [17] used PCA transform to reconstruct leaf reflectance spectra and retrieve the leaf biochemical composition, which included the leaf mass per area. Machine learning techniques have the advantage of solving nonlinear tasks and have been widely applied to the remote sensing of biochemical composition in recent years. Meanwhile, in the application of remote-sensing technology, machine learning algorithms are considered to be reliable and efficient methods for inverting models; they can greatly improve processing speeds and analysis accuracy [18]. Fu et al. [19], Han et al. [20], Ban et al. [21], and Nasi et al. [22] used machine learning to construct an inversion model for crop performance evaluation under different conditions related to, for example, crop yield estimation and soil salinity. Although machine learning has reached a certain degree of accuracy, the prediction performance is greatly affected by the model parameters [23]. The Meta-Heuristic Algorithm can help models be less likely to fall into a local optimum during the search process and find the global optimal solution with great probability, which is a commonly used optimization method [24]. Zhu et al. [25] and Mo et al. [26] proposed that the hybrid algorithm is superior and can address the shortcomings of a single optimization algorithm well, allowing the model to be further optimized in terms of convergence speed and computational accuracy.

In practical application scenarios, we cannot accurately estimate the global straw mulch quantity using only the inversion model because we can only obtain local samples at each site and are limited by the sampling environment and data quantity. The Monte Carlo method [27], as a flexible and efficient numerical solution, has become a key tool in the field of scientific computing and engineering and plays a crucial role in solving practical problems. The idea of the Monte Carlo method addresses the problem of estimating overall sample distribution by random sampling, which is precisely the problem we wanted to solve. It can approximate the global straw mulch quantity by using local samples [28]. Therefore, to complete the transformation from “with” and “without” to “more” and “less” of the global field straw mulch and return effect, the establishment of an efficient and accurate regional straw mulch quantity estimation model is the most important task.

Aiming at the above problems, this study adopts a UAV carrying a multispectral camera to acquire corn straw mulch remote sensing images of the study areas and simultaneously determines the data of straw mulch quantity at the sampling points. Based on the RF inversion model, we proposed the hybrid GA-HPSO algorithm to improve the performance of the inversion model and optimize the model to obtain the sample data results. The Monte Carlo idea is used to estimate the global straw mulch quantity and complete the detection of straw return to the field, which provides important modern information technology support to effectively solve the hidden dangers and problems of conservation tillage, such as “difficult to verify the area, difficult to monitor the quality, and high risk of subsidy fund issuance”.

2. Materials and Methods

2.1. Overview of the Study Area

To facilitate a comprehensive discussion on straw mulch quantity estimation, the study area was divided into experimental and validation segments. The experimental areas were primarily designed to assess the feasibility of the optimal inversion model and estimation methods, while the validation areas aimed to demonstrate the practical applicability of these methodologies. The study site was located in Changchun City, Jilin Province, China, situated in the temperate semi-humid continental monsoon climate zone, characterized by an average annual temperature of 5.5 °C, average annual precipitation of 558 mm, and an average elevation of approximately 220 m. Jilin Province has actively promoted conservation tillage practices involving straw mulch, with widespread adoption of full straw mulch applications. Details of the study area selection are presented in

Table 1. Description of study area selection.

Study Area	Site	Latitude and Longitude	Area [m2]
Experimental area	Yingjun Town, Erdao (study area 1)	125°29′56″ E 43°52′06″ N	22,500
	Bahao Town, Yushu (study area 2)	126°13′59″ E 45°05′44″ N	20,000
Verification area	Huancheng Town, Yushu (study area 3)	126°28′14″ E 44°51′24″ N	25,000
	Biangang Town, Dehui (study area 4)	125°39′02″ E 44°35′04″ N	15,000
	Tiantai Town, Dehui (study area 5)	125°35′57″ E 44°34′04″ N	22,500
	Kai’an Town, Nong’an (study area 6)	125°11′34″ E 44°07′27″ N	15,000
	Nong’an Town, Nong’an (study area 7)	125°14′44″ E 44°36′20″ N	10,000
	Chaoyangpo Town, Gongzhuling (study area 8)	124°47′45″ E 43°36′54″ N	20,000

.

The experimental fields across the eight study areas employed crop rotation and wide–narrow row planting patterns, predominantly utilizing the Udi 598 maize hybrid (Hongxiang Seed Industry Company Limited, Jilin, China). Spring corn is typically sown in early May and harvested in early October. The terrain within the study area is relatively flat, with rows fully covered by returned straw post-crushing, as illustrated in Figure 1. The return-row plowing method allows for substantial or complete straw return to the field, thereby reducing soil erosion from wind and water while enhancing soil fertility [29]. This setting provides an optimal environment for conducting maize straw mulch detection research.

2.2. Data Acquisition and Analysis

2.2.1. Determination of Straw Mulch Quantity

To provide a better understanding of the study areas, the weather information under sunny skies, including wind direction, wind speed, and temperature, was collected and shown in

Table 2. The weather information used for collecting data on different study areas.

Study Area	Site	Collection Time	Collecting Weather	Sample Size
Experimental area	Study area 1	23 April 2022	Sunny, West wind, 3.4–5.4 m/s, 12–3 °C	54
		1 November 2022	Sunny, West wind, 3.4–5.4 m/s, 12–4 °C	54
		23 April 2023	Sunny, Northwest wind, 3.4–5.4 m/s, 11–3 °C	54
		26 October 2023	Sunny, Northwest wind, 3.4–5.4 m/s 10–4 °C	54
	Study area 2	25 April 2022	Sunny, West wind, 5.5–7.9 m/s, 13–4 °C	48
		2 November 2022	Sunny, West wind, 3.4–5.4 m/s, 6–4 °C	48
		11 May 2023	Sunny, Southwest wind, 3.4–5.4 m/s, 14–1 °C	48
		27 October 2023	Sunny, West wind, 0.3–1.5 m/s, 12–3 °C	48
Verification area	Study area 3	28 October 2023	Sunny, Southeast wind, 5.5–7.9 m/s, 12–2 °C	60
	Study area 4	2 November 2023	Sunny, Southeast wind, 5.5–7.9 m/s, 16–4 °C	36
	Study area 5	3 November 2023	Sunny, Northeast wind, 3.4–5.4 m/s, 2–7 °C	54
	Study area 6	24 October 2023	Sunny, Northeast wind, 3.4–5.4 m/s, 19–1 °C	36
	Study area 7	25 October 2023	Sunny, Southwest wind, 5.5–7.9 m/s, 19–1 °C	24
	Study area 8	29 October 2023	Sunny, Southwest wind, 3.4–5.4 m/s, 18–7 °C	48

. The experimental data were collected after harvesting in the autumn but before planting in the spring of the second year concerning the timeliness and diversity of the data. Meanwhile, the locations and number of sampling points were determined based on the size of the area. The corn straw mulch quantity parameters were measured at the sampling points.

We defined each sampling unit as approximately 2500 m², randomly selecting six 0.5 m × 0.5 m squares within each unit as sampling points. After measuring straw mulch quantity within these points, we assessed thickness at five designated corners and the center for error verification, utilizing an electronic scale (Hengzi KC-833, accuracy: 0.001 kg). A total of 408 sampling points were collected during the experimental phase and 258 during the validation phase, with the sampling process illustrated in Figure 2. For example, in Study Area 1, the area was divided into nine sampling units, each containing six randomly distributed sampling points. The UAV captured multispectral images above these points to measure straw mulch quantity.

2.2.2. UAV Remote Sensing Data

The DJI Matric 300 RTK drone (DJI Technology Company Limited, Shenzhen, China) was equipped with an AQ600 PRO multispectral camera (Changguang Yuchen Information Technology and Equipment Company Limited, Qingdao, China). The AQ600 PRO sensor collects data across discrete spectral bands: blue (450 ± 35 nm), green (555 ± 25 nm), red (660 ± 20 nm), red edge (720 ± 10 nm), and near-infrared (840 ± 35 nm), with a pixel resolution of 2048 × 1536. Real-time radiometric correction was supported, with radiometric calibration images captured prior to each flight. Aerial image acquisition was conducted during the optimal timeframe of 10:00 to 15:00.

To ensure comprehensive data collection from the study area plots, we utilized a high-altitude UAV flight pattern. The UAV followed a pre-planned route at a speed of 3 m/s, maintaining an 80% overlap for both bypass and heading. After conducting several trial flights, an optimal flight altitude of 40 m was determined. Additionally, to guarantee the accuracy of spectral images, we employed a fixed-point manual control mode, hovering at a determined altitude of 12 m for image capture above each sampling point.

The multispectral images acquired via UAV were processed and analyzed using Yusense Map V 2.2.3 software, which is specifically designed for the multispectral camera. Initially, we employed the band alignment function within Yusense Map V 2.2.3 software. Subsequently, geometric and radiometric corrections were applied to eliminate potential noise and interference. The corrected UAV multispectral images were then imported into ENVI 5.3 software, where the corresponding spectral image portions were cropped according to the predefined sampling points. Finally, we calculated the average reflectance spectra for the straw mulch samples within the region of interest, yielding the spectral reflectance data.

2.3. Spectral Reflectance Measurement

The objective of the spectral reflectance measurements was to simulate and analyze variations in spectral reflectance associated with different straw mulch quantities within the same area, thereby assessing the impact of these variations on remote sensing estimates of straw mulch quantity and validating the feasibility of this study.

To facilitate this, we collected straw samples from the experimental area across four datasets in 2022 and 2023, placing approximately 0.7 kg of straw into black bags. The experimental environment was maintained under natural light conditions. A square area measuring 0.5 m × 0.5 m was designated for sampling, with a layer of black soil (0.01 m thick) spread evenly. The multispectral camera (AQ600 PRO) was fixed at a height of 1 m above the black soil. We collected multispectral data corresponding to varying straw mulch quantities, starting with 0.1 kg of straw evenly distributed across the sampling area and increasing in 0.1 kg increments up to 0.5 kg. This acquisition process is illustrated in Figure 3, and we captured radiometric calibration target images prior to each set of measurements.

2.4. Spectral Index Construction

Spectral indices serve as metrics for analyzing and characterizing spectral data, enabling the study of the composition, structure, and properties of substances. By enhancing the separability of targets, spectral indices improve the accuracy of feature detection. Given their sensitivity to feature characteristics, we selected 12 widely used spectral indices for our experiments, with their calculation formulas detailed in

Table 3. Spectral index and its formula.

Spectral Index	Abbreviation	Formula	Reference
Normalized difference vegetation index	NDVI	NDVI = (NIR − R)/(NIR + R)	[30]
Difference vegetation index	DVI	DVI = NIR − R	[31]
Enhanced vegetation index	EVI	EVI = 2.5(NIR − R)/(NIR + 6R − 7.5B + 1)	[32]
Brightness index	BI	BI = (R + NIR)0.5	[33]
Simple ratio index	SR	SR = NIR/R	[34]
Green-light normalized difference vegetation index	GNDVI	GNDVI = (NIR − G)/(NIR + G)	[35]
Green-light ratio vegetation index	GRVI	GRVI = NIR/G	[36]
Straw multiplier index	SMI	SMI = NIR × (NIR − G) × (R − G)	[37]
Red edge ratio index	RERI	RERI = RE/NIR	[38]
Near-infrared normalized index	NRNI	NRNI = NIR/(NIR + R + G)	[39]
Normalized difference red edge index	NDRE	NDRE = (NIR − RE)/(NIR + RE)	[40]
Red-light normalized difference index	RNDI	RNDI = (RE − R)/(RE + R)	[41]

B, G, R, RE, and NIR are the spectral reflectance at 450, 555, 660, 720, and 840 nm wavelengths, respectively.

.

2.5. Optimization of the Inverse Model for Straw Mulch Quantity

Previously, our team compared various inversion models in the context of straw mulch quantity estimation, concluding that the Random Forest (RF) algorithm yielded the most effective inversion model [42]. Therefore, we employed the RF algorithm in this study [43]. This algorithm integrates ensemble learning with decision trees, utilizing resampling methods to enhance the prediction accuracy and convergence speed. However, empirical evidence suggests that hyperparameters—specifically, the number of decision trees (n_estimators), maximum tree depth (max_depth), and maximum number of leaf nodes (max_leaf_nodes)—significantly influence RF performance. Consequently, it is essential to balance accuracy and computational efficiency in parameter selection.

To address this, we introduced a hybrid optimization approach combining Genetic Algorithm (GA) [44] and Particle Swarm Optimization (PSO) [45], resulting in the GA-HPSO optimization algorithm. This method enables the RF model to autonomously identify optimal solutions, mitigating the subjectivity associated with manual parameter tuning and alleviating issues related to parameter sensitivity in model prediction performance.

The GA is advantageous due to its population diversity and global search capabilities; however, it lacks individual memory and exhibits slower convergence. Conversely, the PSO benefits from memory and rapid convergence but is susceptible to premature convergence and diminished diversity. By merging these two algorithms, we aim to leverage their complementary strengths. Parameter values such as inertia weights and learning factors in the PSO significantly affect convergence performance. Conventional approaches to these parameters can hinder convergence speed and overall efficiency. Additionally, initialization plays a critical role in accuracy and speed; uneven solution space distribution may lead to local optima.

Traditional PSO algorithms typically employ random initialization to determine initial population distributions. This method can result in uneven initial particle distribution within the solution space, adversely affecting early convergence and increasing the likelihood of local optima. To overcome this, we adopted chaotic initialization to replace the conventional random method. Chaotic initialization incorporates randomness, traversal, and regularity, allowing the search space to be traversed systematically without repetition, thereby enhancing both solution accuracy and convergence speed. In this study, we employed the Logistic Chaos Model for initialization [46], as represented in Equation (1):

$$X_{n+1}=\mu \times X_n\times \left(1-X_n\right), \mu ϵ\left[0,4\right]$$

(1)

where $\mu$ is the chaotic model mapping parameter. When $\mu ϵ\left[\mathrm{3.57,4}\right]$, the system exhibits chaotic behavior; at $\mu =4$, it reaches a fully chaotic state, which we employed in this study.

Next, the inertia weight parameter in the PSO algorithm significantly influences convergence performance. A larger inertia weight favors global exploration, while a smaller weight accelerates local convergence. To balance these capabilities, we introduced a dynamic weight factor (ω) to enhance both convergence speed and accuracy. The formulation of ω is shown in Equation (2):

$$\omega =\left\{\begin{array}{c}{\omega }_{min}-{\displaystyle \frac{\left({\omega }_{max}-{\omega }_{min}\right)\times \left(f-f_{min}\right)}{f_{avg}-f_{min}}},f\le f_{avg}\\ {\omega }_{max},f>f_{avg}\end{array}\right.$$

(2)

where $f$ represents the real-time objective function value of the particle. $f_{avg}$ and $f_{min}$ denote the average and minimum objective value of all current particles, respectively. A larger weight at the search’s initial phase promotes global exploration, while a smaller weight in later phases fosters local optimization.

Furthermore, the learning factors $c_1$ and $c_2$ in the PSO algorithm impact overall performance and are typically fixed. In this study, to prevent rapid convergence around local optima during the initial stages, we allowed $c_1$ to be larger and $c_2$ to be smaller. Conversely, in the later stages, we adjusted $c_1$ to be smaller and $c_2$ to be larger to facilitate quick and accurate convergence to the global optimum. Thus, $c_1$ and $c_2$ are represented in Equations (3) and (4) as follows:

$$c_1=c_{1i}+t\times \left(c_{1f}-c_{1i}\right)/T_{max}$$

(3)

$$c_2=c_{2i}+t\times \left(c_{2f}-c_{2i}\right)/T_{max}$$

(4)

where $t$ is the current iteration number. $T_{max}$ is the maximum iteration number of the particle swarm. $c_{1i}$, $c_{2i}$ are the $c_1$, $c_2$ initial values and $c_{1f}$, $c_{2f}$ are the $c_1$, $c_2$ final values. When $c_{1i}\ne c_{2f}$ and $c_{2i}\ne c_{1f}$, it is an asymmetric learning factor method.

Lastly, we incorporated crossover and mutation operators from GA into the PSO framework. These operations enhance population diversity and broaden the algorithm’s search range, thereby aiding in the attainment of a global optimum. The computational flow of the GA-HPSO algorithm is illustrated in Figure 4.

The research environment utilized MATLAB 2018a, running on a Windows 10 operating system with an Intel (R) Core (TM) i7-8550U [email protected] GHz 2.00 GHz processor and an NVIDIA GeForce 940MX graphics card.

2.6. Global Estimation Methods

To relate sample point data to global straw mulch quantity, this study employed the Monte Carlo method. This method’s fundamental principle involves obtaining desired results through random sampling and statistical averaging. The steps typically include defining the problem and required data; calculating necessary functions and probability distributions; designing a random sampling approach (e.g., utilizing pseudo-random numbers); and deriving statistical quantities from the sampled data, such as sums, averages, and variances. Conclusions are drawn based on these results.

Utilizing the Monte Carlo method, the straw mulch quantities obtained from sampling points via the optimal inversion model are treated as known samples. From these samples, an empirical distribution is established, leading to the formulation of a Gaussian mixture model. The probability density function of this model, constituted by the superposition of $k$ Gaussian distributions, is expressed in Equation (5):

$$p\left(x|\theta \right)=\sum _{k=1}^k{\pi }_{k}p\left(x,{\mu }_k,{\sum }_k\right)$$

(5)

where $\theta$ is the full Gaussian model parameter, $\sum _{k=1}^k{\pi }_k$ is 1, ${\pi }_k$ is the weight, $x$ is the sample, $\mu$ is the model expectation, and $\sum$ is the model variance.

The parameters for each class in the hybrid model are derived using an Expectation-Maximization (EM) algorithm with an iterative optimization strategy, comprising an Expectation step (E step) and a maximization step (M step). The E step is represented in Equation (6):

$$Q\left(\theta ,{\theta }^i\right)=E_Z\left[log\left(X,Z|\theta \right)X,{\theta }^i\right]=\sum logp\left(X,Z|\theta \right)P\left(Z|X,{\theta }^i\right)$$

(6)

where $Z$ denotes the hidden variable associated with the unknown straw mulch quantity data. $\theta =\left({\mu }_k,{\sum }_k,{\pi }_k\right)$ is the parameter estimate of the initial Gaussian model. $\left({\mu }_k^i,{\sum }_k^i,{\pi }_k^i\right)$ is the parameter estimate of the Gaussian model with i iterations. The joint distribution is $P\left(Z|X,\theta \right)$. Given the observed data $X$ and parameter estimates ${\theta }^i$, the conditional probability distribution of the hidden variable $Z$ is sought $P\left(Z|X,{\theta }^i\right)$.

The M step is shown in Equation (7):

$${\theta }^{i+1}=argmaxQ\left(\theta ,{\theta }^i\right)$$

(7)

This involves maximizing $Q\left(\theta ,{\theta }^i\right)$ to determine the parameter estimates for the subsequent iteration.

Employing the Monte Carlo principle, the global estimation method entails n random draws from a known distribution function, yielding n known sample data. Given the unknown probability distribution formula and normalization constant of the Gaussian mixture model, direct sampling from the distribution function proves infeasible. Thus, we employed the choice algorithm for random sampling, employing the accept–reject principle. In this process, a random point is accepted if it lies within the designated region; otherwise, it is rejected.

The ultimate goal of this research is to assess straw mulch quantity in the field and evaluate the effectiveness of straw return in conservation tillage. To achieve this, we need to establish the theoretical straw resources to facilitate subsequent calculations of straw volume return rates. The grass-to-grain ratio method [47], as outlined in NY/T 1701–2009 [48], was utilized to obtain the theoretical straw resources. The grass-to-grain ratio $\mu$ is defined in Equation (8):

$$\mu ={\displaystyle \frac{m_s\left(1-A_s\right)/\left(1-15\%\right)}{m_G\left(1-A_G\right)/\left(1-12.5\%\right)}}$$

(8)

where $m_s$ is the mass of straw, $m_G$ is the mass of grain, $A_s$ is the moisture content of straw, and $A_G$ is the moisture content of grain. The standard moisture content of air-dried straw is 15%, while the national standard moisture content for grain crops is 12.5%. The theoretical corn straw resource $P$ is articulated in Equation (9):

$$P=\sum {\mu }_i{G}_i$$

(9)

where $G_i$ is the maize yield. The straw collectible resource $P_c$ is shown in Equation (10):

$$P_c=\sum \delta {\mu }_i{G}_i$$

(10)

where $\mathsf{\delta }$ is the straw collection coefficient, as shown in Equation (11):

$$\delta =\left[\left(1-{\displaystyle \frac{L_{i,j}}{L_i}}\right)J_i+\left(1-{\displaystyle \frac{L_{i,r}}{L_i}}\right)\left(1-J_i\right)\right]\left(1-Z_i\right)/100$$

(11)

where $L_i$ is the average plant height of maize, $L_{i,j}$ is the stubble height of mechanically harvested crops, $L_{i,r}$ is the stubble height of manually harvested crops, $J_i$ is the mechanised harvesting rate of the crop, and $Z_i$ is the rate of loss of the crop stalks during harvesting and transportation. The theoretical straw resources and collectible straw resources were calculated based on relevant data obtained from the study area, with results presented in

Table 4. Research data related to straw in the study area.

Study Areas	Periods	μ [%]	P [t]	$\mathsf{\delta }$ [%]	Pc [t]
Study area 1	Spring 22	0.90	21.552	0.93	20.043
	Autumn 22	0.91	21.930	0.92	20.176
	Spring 23	0.91	21.930	0.92	20.176
	Autumn 23	0.89	22.001	0.92	20.241
Study area 2	Spring 22	0.91	16.542	0.92	15.219
	Autumn 22	0.92	17.027	0.93	15.835
	Spring 23	0.92	17.027	0.93	15.835
	Autumn 23	0.90	16.476	0.91	14.993
Study area 3	Autumn 23	0.90	21.807	0.91	19.844
Study area 4		0.89	12.091	0.93	11.245
Study area 5		0.89	18.335	0.92	16.868
Study area 6		0.89	12.166	0.92	11.193
Study area 7		0.89	8.291	0.90	7.462
Study area 8		0.90	17.070	0.93	15.875

.

3. Results and Analysis

3.1. Spectral Reflectance Analysis

In this study, spectral reflectance data corresponding to varying straw mulch quantities were processed, with the results presented in Figure 5. A positive correlation was observed between straw mulch quantity and spectral reflectance across four data groups. Notably, the spectral reflectance differences between bands diminished as the mulch quantity increased. Additionally, it was evident that spectral reflectance in spring was lower than in fall, with a slower decrease at 450 nm compared to other wavelengths. This analysis suggests that utilizing spectral indices to differentiate spectral characteristics, followed by inverse modeling to simulate reflectance under various mulch amounts, can effectively estimate the corn straw mulch quantity.

3.2. Correlation Analysis

In remote sensing image processing, efficient spectral index screening algorithms significantly reduce data dimensionality, streamline processing, and enhance computational efficiency while minimizing storage needs. The Elastic-net (ENET) algorithm [49], a linear regression model that integrates Lasso’s L1 and Ridge’s L2 regularization terms, serves to balance model sparsity and non-sparsity [50].

To evaluate the relationship strength between spectral variables and straw mulch quantity, this study employed the ENET algorithm to screen 12 spectral index variables. The findings are summarized in

Table 5. Spectral variable screening based on ENET.

Study Areas	Periods	NDVI	DVI	EVI	BI	SR	GNDVI	GRVI	SMI	RERI	NRNI	NDRE	RNDI
Study area 1	Spring 22	0.39	0	0	0	0.47	0.43	0	0	0.56	0	0.54	0
	Autumn 22	0.56	0.53	0	0	0.57	0.50	0	0	0.61	0	0.55	0
	Spring 23	0.38	0	0	0	0.45	0.42	0	0	0.56	0	0.50	0
	Autumn 23	0.58	0.49	0	0	0.55	0.51	0	0	0.60	0	0.54	0
Study area 2	Spring 22	0.38	0	0	0	0.46	0.42	0	0	0.57	0	0.54	0
	Autumn 22	0.55	0.53	0	0	0.57	0.50	0	0	0.60	0	0.55	0
	Spring 23	0.41	0	0	0	0.46	0.40	0	0	0.58	0	0.54	0
	Autumn 23	0.55	0.50	0	0	0.56	0.53	0	0	0.61	0	0.55	0

, where regression coefficients indicate the valid spectral information conveyed by each index and its explanatory power in the model [51]. Coefficients nearing zero were eliminated, and the remaining spectral variables were selected as input for the model.

3.3. Evaluation of Inversion Models

To demonstrate the superiority of the proposed GA-HPSO algorithm over GA and PSO algorithms, we evaluated three standard test functions from the CEC: Sphere, Griewank, and Rastrigin. The Sphere function is articulated in Equation (12):

$$f\left(X\right)=\sum _i^N{X}_i^2$$

(12)

where the range of values of the independent variable $X_i$: −100 < $X_i$ < 100. The Griewank function is shown in Equation (13):

$$f\left(X\right)={\displaystyle \frac{1}{4000}}\sum _i^N{X}_i^2-\prod _i^N\mathit{cos}\left({\displaystyle \frac{X_i}{\sqrt{i}}}\right)+1$$

(13)

where the range of values of the independent variable $X_i$: −600 < $X_i$ < 600. The Rastrigin function is shown in Equation (14):

$$f\left(X\right)=\sum _i^N\left[X_i^2-10\mathit{cos}\left(2\pi X_i\right)+10\right]$$

(14)

where the range of values of the independent variable variable $X_i$: −5.12 < $X_i$ < 5.12.

The results depicted in Figure 6 show that PSO exhibited the least effective convergence, while GA-HPSO demonstrated superior convergence performance, efficiently identifying optimal individual fitness with fewer iterations while maintaining stability. This indicates that the GA-HPSO algorithm significantly enhances global optimization performance and convergence speed compared to standalone GA and PSO algorithms.

To comprehensively assess the straw mulch quantity inversion model, spectral variables filtered by the ENET algorithm were utilized as input variables for models based on RF, GA-RF, PSO-RF, and GA-HPSO-RF algorithms. Model accuracy was evaluated using R² and RMSE metrics. Higher R² values (closer to 1) and lower RMSE values (closer to 0) indicate better model accuracy. The results displayed in

Table 6. Model inversion results based on different data.

Periods	Modeling Algorithm	Study Area 1				Study Area 2
		Modeling Set		Validation Set		Modeling Set		Validation Set
		R2c	RMSEc	R2v	RMSEv	R2c	RMSEc	R2v	RMSEv
Spring 22	RF	0.65	0.0665	0.62	0.0679	0.65	0.0650	0.63	0.0651
	GA-RF	0.71	0.0583	0.69	0.0614	0.74	0.0462	0.68	0.0542
	PSO-RF	0.71	0.0601	0.67	0.0630	0.73	0.0467	0.67	0.0571
	GA-HPSO	0.78	0.0415	0.71	0.0596	0.76	0.0451	0.70	0.0515
Autumn 22	RF	0.69	0.0596	0.67	0.0631	0.70	0.0528	0.67	0.0564
	GA-RF	0.74	0.0449	0.73	0.0462	0.77	0.0424	0.72	0.0447
	PSO-RF	0.75	0.0451	0.71	0.0466	0.79	0.0415	0.71	0.0454
	GA-HPSO	0.77	0.0408	0.75	0.0453	0.79	0.0427	0.75	0.0441
Spring 23	RF	0.69	0.0626	0.63	0.0667	0.69	0.0634	0.64	0.0640
	GA-RF	0.71	0.0578	0.69	0.0597	0.73	0.0513	0.68	0.0630
	PSO-RF	0.71	0.0601	0.67	0.0624	0.72	0.0547	0.66	0.0676
	GA-HPSO	0.77	0.0474	0.72	0.0574	0.76	0.0474	0.70	0.0544
Autumn 23	RF	0.71	0.0587	0.68	0.0604	0.72	0.0543	0.68	0.0637
	GA-RF	0.75	0.0481	0.71	0.0523	0.75	0.0458	0.73	0.0482
	PSO-RF	0.74	0.0482	0.72	0.0501	0.75	0.0471	0.71	0.0511
	GA-HPSO	0.78	0.0432	0.74	0.0485	0.78	0.0435	0.75	0.0453

reveal that the inversion model constructed using the ENET algorithm, with spectral indices as input variables, achieved substantial accuracy and stability. The closeness of R²_c and R²_v values indicates that the models are not “overfitted” while maintaining high accuracy. Notably, the GA-HPSO-RF algorithm outperformed the others, achieving the highest R²_c and R²_v values exceeding 0.70, with both RMSE_c and RMSE_v below 0.061. Comparatively, GA-RF and PSO-RF models showed improved accuracy over the original model, with R²_v values exceeding 0.66. Thus, the GA-HPSO-RF algorithm demonstrated the best accuracy among the four models.

For a more intuitive comparison of model inversion effects across different periods and regions, the scatter plot of the validation set is illustrated in Figure 7. The GA-HPSO-RF algorithm yielded the best inversion accuracy, with autumn data from both years displaying similar results significantly higher than those obtained in spring. This finding aligns with correlation analysis outcomes and reflects real-world conditions, confirming that the GA-HPSO-RF inversion model based on autumn data is the most effective.

3.4. Assessment of Estimation Models

To assess the empirical distribution of the samples, we analyzed the acquired data presented in Figure 8. The histogram illustrates the initial distribution, and the QQ plot suggests that the samples conform closely to a normal distribution. Therefore, we assumed the global straw distribution to be a mixture of multiple Gaussian distributions, leading to the conclusion that its probability model can be represented as a Gaussian mixture model. Under this assumption, we employed the Expectation-Maximization algorithm to determine each parameter within the Gaussian mixture model. The total data samples were fitted into a mixture distribution to establish the global straw distribution probability model, enabling the global straw mulch quantity to be derived through random sampling from the Gaussian mixture model.

During the experimental phase, eight data sets were collected to determine the straw mulch quantity. To evaluate the effectiveness and feasibility of the proposed Monte Carlo method, we utilized both accuracy assessment mean methods and Monte Carlo estimation. The core concept of the Monte Carlo approach relies on random sampling; as more sample values are obtained, the accuracy increases. We recommended a distribution range of y = 0.6, which encompasses the entire Gaussian mixture model, to facilitate random sampling. The number of iterations was determined based on the total area of the study site and the sampling area, ultimately yielding total sample values that align with the probability distribution model as the global straw mulch quantity solution. Estimated results derived from the GA-HPSO-RF inversion model are summarized in

Table 7. Estimation results based on the different data.

Study Areas	Periods	Pc [t]	Mean Value Method		Monte Carlo Method
			Estimated Value [t]	Accuracy [%]	Estimated Value [t]	Accuracy [%]
Study area 1	Spring 22	20.043	15.983	74.60	17.798	87.39
	Autumn 22	20.176	16.184	75.33	18.014	88.00
	Spring 23	20.176	16.328	76.43	17.968	87.71
	Autumn 23	20.241	16.796	79.49	18.337	89.62
Study area 2	Spring 22	15.219	12.376	77.03	13.579	87.92
	Autumn 22	15.835	12.747	75.77	14.376	89.85
	Spring 23	15.835	13.107	79.19	14.085	87.58
	Autumn 23	14.993	12.661	81.58	13.494	88.89

.

As shown in the table, the Monte Carlo method demonstrated superior estimation accuracy, fluctuating between 87.39% and 89.85%. In contrast, the mean method yielded lower accuracy, ranging from 74.60% to 81.58%. The accuracy of the estimated results based on autumn data was notably higher, between 88.00% and 91.61%, while estimates derived from spring data were lower, with accuracy rates between 87.39% and 87.92%. This discrepancy can be attributed to the limitations of the Gaussian mixture model in handling large data values, resulting in higher estimation accuracy during the autumn season. The comparative experiments validate the feasibility of employing Monte Carlo methods for calculating global straw mulch quantities.

3.5. Global Estimation Validation

To further assess the applicability of the proposed global straw mulch quantity estimation method, we collected validation area data, resulting in 258 samples obtained during the autumn of 2023. The validation process is illustrated in Figure 9.

We utilized six spectral indices—SRER, NDVI, SR, NDRE, GNDVI, and DVI—selected by the ENET algorithm as model input variables. The inversion results for the validation area based on the GA-HPSO-RF algorithm, shown in Figure 10, aligned closely with the measured results, achieving an average R² of 0.74 and RMSE of 0.0483. These results were consistent with those from the experimental phase, confirming the effectiveness of the proposed optimization algorithm in estimating straw mulch quantities.

Using the inversion model results from the GA-HPSO-RF algorithm, the Monte Carlo estimation method was applied to assess global straw mulch quantity in the validation phase, as summarized in

Table 8. Estimation results of global straw mulch quantity.

Study Areas	Μ [%]	Pc [t]	Monte Carlo Method
			Estimated Value [t]	Accuracy [%]
Study area 3	0.90	19.844	17.857	88.87
Study area 4	0.89	11.245	10.059	88.21
Study area 5	0.89	16.868	15.234	89.27
Study area 6	0.89	11.193	10.016	88.25
Study area 7	0.89	7.462	8.375	89.10
Study area 8	0.90	15.875	14.467	90.27

. The estimation accuracy across six validation areas reached a commendable level, ranging from 88.25% to 90.27%. These results were stable and comparable to those obtained in the experimental areas, further demonstrating the method’s robustness and applicability.

Detecting the straw return rate is essential, as some straw is buried during the plowing process, making only surface straw detectable in image acquisition. Data from the experimental area over two years indicated that approximately 0.05 kg/m² of straw is buried in the soil. The straw return quantity and return rate, calculated from the results in

Table 9. Estimation results of the straw return rate in the validation area.

Study Areas	P [t]	Straw Return Quantity to The Field [t]	Straw Return Rate [%]
Study area 3	21.807	17.982	82.46
Study area 4	12.091	10.134	83.81
Study area 5	18.335	15.347	83.70
Study area 6	12.166	10.091	82.94
Study area 7	8.291	6.825	82.32
Study area 8	17.07	14.567	85.34

, revealed return rates ranging from 82.32% to 85.34%. This method proves feasible for estimating both straw mulch and return quantities, providing valuable insights for global straw return estimations.

4. Discussion

4.1. Methodology for Estimation of Global Straw Mulch Quantity

In conservation tillage practices, the intelligent detection of straw mulch quantity remains undeveloped, relying on traditional field measurements that are time-consuming and labor-intensive [52]. By integrating multispectral data with model inversion and employing the Monte Carlo method, we reduced the need for extensive sampling, thus saving time and labor while accurately reflecting regional straw mulch quantities. This approach offers a scientific reference for estimating straw mulch in conservation tillage.

Reflectance data analysis revealed changes in the spectral reflectance of corn straw at varying mulch quantities. Although the straws all showed similar spectral profiles, their spectral profiles were within a range and regular. Light interaction with crops is complex; incident light is partly reflected while the remainder penetrates, leading to absorption and diffuse reflection within the plant structure. Light absorption is primarily influenced by the chemical composition, while diffuse reflection is affected by the physical properties of the straw. Variations in straw thickness and structure result in differing light attenuation [53]. Consequently, establishing a statistical relationship between straw mulch quantity and its optical properties facilitates accurate estimations.

Seasonal changes also impact reflectance spectra, likely related to straw decomposition, akin to findings by Daughtry et al. [13]. The observed higher accuracy of global estimations in fall compared to spring stems from the probabilistic model’s reliance on initial sample quality. While fewer samples might yield smaller errors, the accuracy of global straw estimations improves with higher-quality inversion model results. Over time, changes in the chemical and physical properties of straw during decomposition affect spectral features, weakening remote sensing assessments of straw mulch [54]. Therefore, the fall data yielded more accurate inversion model assessments. Additionally, the uneven global distribution of straw due to environmental factors, such as prolonged exposure to bare conditions and erosion, further complicates global straw mulch quantity estimations.

4.2. Advantages of Algorithms

The RF algorithm demonstrated improved performance in estimating straw mulch quantities; however, its predictive accuracy was significantly influenced by model parameters. The GA and PSO algorithms, as established optimization techniques, can address some of the RF algorithm’s limitations, yet each has its specific applicability and constraints [55,56]. In this study, we employed embedded hybridization to integrate the strengths of both algorithms, enhancing the initial population’s solution accuracy and convergence speed. This complementary approach mitigated the risk of local optima during the search process, resulting in a straw mulch quantity inversion model that effectively extracted features and enhanced detection accuracy.

4.3. Deficiency and Prospect

The methodology yielded promising results in global straw mulch quantity estimation, indicating broad applicability across most of the Corn Belt. However, it also has limitations and may not directly apply to regions with different crops, cropping patterns, or weather conditions. The field data were collected over two years (2022 and 2023), encompassing varied climatic conditions, yet did not account for all potential weather variations and soil moisture levels. Further research is essential for a comprehensive understanding of these dynamics. Additionally, integrating multi-sensor fusion techniques could enhance the accuracy of conservation tillage detection and support sustainable agricultural practices.

5. Conclusions

This study combined remote sensing imagery with ground-measured straw mulch quantity data to establish an inversion model specific to the study area by selecting relevant straw spectral indices. We proposed an optimization algorithm to enhance model performance and employed Monte Carlo methods to estimate global straw mulch quantities. The following conclusions were drawn from the experimental analysis:

(1)

Reflectance changes of corn straw in relation to varying mulch quantities were observed, revealing corresponding shifts in spectral composition. The reflectance spectra across different mulch scenarios were simulated using an inverse model, allowing for the estimation of corn straw mulch quantity based on optimal spectral indices.

(2)

The GA-HPSO-RF inversion model achieved an R² of 0.75 and RMSE_v of 0.044, demonstrating strong nonlinear fitting capability, the highest among the four models, and fulfilling local estimation requirements. The GA-HPSO algorithm addressed the RF model’s sensitivity to parameters, thereby enhancing inversion performance and facilitating more effective corn straw mulch quantity estimations.

(3)

The Monte Carlo method attained an average accuracy of 89.61% for global straw mulch quantity estimation, with relatively stable resultant errors, validating its applicability for large-scale mulch quantity detection.

In the context of global corn straw mulch quantity estimation, the precise application of the inversion model and estimation methods provides a scientific foundation for estimating the volume of corn straw returned to the field. This approach also achieves the quantitative goals of straw return detection, offering scientific and efficient automated means for promoting conservation tillage.