The formulation of irrigation and nitrogen application strategies under multi-dimensional soil fertility targets based on preference neural network

Study area

Figure 2 shows the location of the study area on a map of China generated by ArcGIS software. This study’s field experiments were carried out in the Shuanghe Town agricultural comprehensive water-saving demonstration area (40°42′ N; 107°24′ E), which is located in the middle reaches of the Hetao Irrigation Area of Inner Mongolia. The duration of the experimental process ranged from April in 2018 to October in 2020. The experimental area was characterized by a mid-temperate semi-arid continental climate. The average annual precipitation was determined to be 138 mm and the average evaporation was approximately 2332 mm. The majority of the rainfall was concentrated during summer and autumn seasons, and the accumulation of salt in the surface soil was considered to be serious in the spring and winter months. The average rainfall during maize growth period was 75.3 mm. The 0 to 40 cm soil layers in the experimental area were categorized as silty loam soil, with an average bulk density ranging from 1.42 to 1.53 g cm⁻³. A maize straw layer with a thickness of 5 cm was buried at a depth of 40 cm, and then the land was leveled. Also, in addition to autumn watering and spring irrigation procedures, water from the Yellow River was used three times for irrigation during the entire growth period of the maize crops. The adopted irrigation method belonged to border irrigation. Urea (46% N) were used as the fertilizer types.

Field trials design and data collection

We carried out experiment 1 from 2018 to 2019, and the data obtained were used for model training and to determine the hyper-parameters. The experimental design is shown in Table 1. The PNN model trained from the data obtained in experiment 1 predicted the optimal range of irrigation amount and nitrogen application rate (N rate) for each growth period of maize. In these ranges, the soil organic matter and total nitrogen could be kept above 20 g/kg and 1.6 g/kg, respectively, the soil salt content was less than 2 g/kg, and the pH value was between 6.5 and 7.5. In order to verify the accuracy and feasibility of the range of irrigation and nitrogen application simulated by PNN, the field experiment 2 was set in 2020 based on the range simulated by PNN and to evaluate the fitting degree between measured and simulated values of soil indicators under the same amount of irrigation and nitrogen application. The experimental design is shown in Table 2.

The experimental design were repeated for three times. The plot area of each treatment measuring 8 × 9 = 72 m². The surrounding area was separated using 1.2 m buried polyethylene plastic film, and 30 cm was left at the top to prevent fertilizer and water from flowing into each other. The field management process was consistent with that used by the local farmers. The film width of maize was 1.1 m, with each film covering two rows. The plant spacing was approximately 45 cm, and the row spacing was 35 cm. In addition, the planting density of the maize was 60,000 plants/hm².

During the entire growth period of the maize crops, soil samples were collected from the 0 to 20 cm, 20 to 40 cm, 40 to 60 cm, 60 to 80 cm, and 80 to 100 cm soil layers using a soil drill and a three-point method was adopted. The soil samples were stored at 4 °C for the determination of total nitrogen, organic matter, total salt content, and pH values. The total nitrogen, organic matter, total salt content, and pH were determined using a KDN-AA double tube azotometer, MWD-2 microwave universal digestion device, TU1810PC ultraviolet–visible spectrophotometer, and a TU18950 double beam ultraviolet–visible spectrophotometer, respectively.

Soil parameters measured include organic matter (SOM), total nitrogen (TN), Salt and pH. The data set includes pre-irrigation and post-irrigation reports from 2018 to 2020. Statistical parameters regarding the soil data are shown in Table 3.

The dataset obtained in Experiment 1 in 2018 to 2019 was 2490 rows in size, the 80/20 principle was used to data into training, and testing sets were required for ML modeling; 80% of data were employed for model training, while the remaining 20% were used for testing. Specifically, the data corresponding to the treatments with the nitrogen application rate (N rate) of 75 kg/hm² (N3) in all the treatments (W1N3, W2N3, W3N3) were used as the test set, and the data of the other treatments were used as the training set. The training set was used to initiate ML parameter training. Subsequently, The test set was employed to assess the model. The dataset size in 2020 was 1080 rows, which was used to verify ML modeling.

Figure 3 shows the changes of soil indexes over time for each treatment in the field test (take the 0–40 cm soil in the main distribution area of maize roots as an example). There are differences under the influence of different irrigation amounts. When irrigation is 90 mm, soil SOM is 13.25% and 7.00% higher than 60 mm and 120 mm, and soil TN is 4.59% and 6.50% higher than 60 mm and 120 mm, respectively. The soil Salt was 23.30% lower than 60 mm, and the pH was 4.16% and 4.36% lower than that of 60 mm and 120 mm, respectively. It can be seen that irrigation of 90 mm is more favorable for increasing soil SOM and TN contents and reducing soil salinity and alkalinity. Soil SOM and TN contents were the highest at n 75 kg/hm², which were 4.38% and 8.34% higher than those at N = 93.3 kg/hm², respectively. Soil Salt was the lowest at N = 60 kg/hm², which was 3.02% lower than those at N = 75 kg/hm², with a small gap with other levels. In conclusion, nitrogen application of 75 kg/hm² was beneficial to increase soil organic matter and nitrogen content, and nitrogen application of 60 kg/hm² was beneficial to controlling soil salt content.

Machine learning (ML) models used for irrigation and nitrogen application strategies

Five ML frames were used to estimate the irrigation and N rate. These models are preference Neural Network (PNN), Support Vector Regression (SVR), Linear Regression (LR), Logistic Regression (LOR), and traditional BP Neural Networks (BPNN). Among them, the prediction effects of linear, Poly, and rbf kernel functions are respectively tried in SVR framework. The torch framework was used to train and test machine learning models in Python.

Development of preference neural network

Model framework

The preference neural network (PNN) which was proposed for the first time in this study was a typical deep learning model. PNN can be regarded as an approximate natural function in order to describe the complete dependence of the soil fertility indexes, including the effects of soil total nitrogen, organic matter, total salt content, and pH values on irrigation and nitrogen applications. More specifically, PNN has the ability to optimize the function by constructing the mapping y = f (x, θ) and learning parameter θ.

First, the input end of PNN model was defined as matrix X ∈ ℝ^n×d (in which n is the sample size, n = 2490; and d is the dimension of each input vector, d = 6), where {x_i} _{i=1, …, n} ∈ X represents the vectorized set of total nitrogen, organic matter, salt content, and pH used for measuring the soil fertility, as well as the nitrogen application and irrigation durations (expressed by days after sowing). At the same time, the output end of the model was defined as the matrix Y ∈ ℝ^n×2, which represented the levels of the irrigation and nitrogen fertilizer applications. The goal of the proposed PNN model was to learn the fixed mapping Y′ = f (X; θ) ⇒Y through the given input matrix X, where θ is the well optimized learnable parameters which can be obtained via PNN training. Meanwhile, the predicted value Y′ will infinitely approach the measured value Y. The structure and the algorithm of this study’s PNN model is shown in Fig. 4 and Table. 4.

Layer-by-layer affine transformation

A good definition of the affine transformation of the information flow between layers is considered to be the key to neural network model training. Generally speaking, the learnable parameter θ of each layer of a model includes the weight parameter w and the preference parameter b. The hidden representation h_l of the l-th layer in PNN is defined as follows:

where W_l and b_l represent the learnable weight and bias variables of the l layer, respectively, and h_l-1 is the hidden representation of the upper layer. Therefore, when l = 1, then h₀ = X.

In the present study, using the hierarchical update rules, a given input data stream was allowed to pass through each hidden layer with intermediate operations, and then finally reached the output end.

Preference structure

The correlation between different production behavior factors (e.g., irrigation levels) and different natural factors (e.g., soil organic matter) differs in agricultural production. However, the traditional fully connected neural network has the characteristic that nodes of one layer are fully connected with all nodes of subsequent layers, resulting in the neurons between production behavior factors and natural factors with very weak correlation still all being connected. Conversely, connections between neurons corresponding to factors with solid correlations are not strengthened.

Therefore, in this study the preference value module was specially developed. By first calculating the correlation and significance between different production behavior factors (irrigation amount, N rate) and different soil fertility factors (organic matter, total nitrogen, total salt and pH), the preference value between the above two types of variables was calculated, and the preference matrix was constructed. Then the Hadamard product of the weight matrix and preference matrix was used to realize the artificial intervention and guidance to the neural network’s learning process.

In order to reduce the adverse impact of non-normality of data on correlation analysis as much as possible, this study rank-based inverse normal (RIN) transformations (i.e., conversion to rank score) methods were used to normally process the data²⁸. The RIN transformation function used here is as follows:

where Φ^–1 is the inverse normal cumulative distribution function, and n is the sample size.

The normal cumulative distribution function is represented as follows: for discrete variables, the sum of probabilities of all values less than or equal to a, and its formula is as shown below:

The RIN normalized conversion values meet the requirements of normal distribution, Pearson correlation analysis and t-test can be directly performed, and the formula used was as follows:

where r (X, Y) is the Pearson Correlation Coefficient, Var [X] is the variance of X, and Var [Y] is the variance of Y, Cov (X, Y) is the covariance of X and Y, which represents the overall error of the two variables. The t-test is performed on the normalized data after rank-based inverse normal (RIN) transformation method, and the formula is as follows:

where n is the number of samples, and r represents the Pearson Correlation Coefficient. Preference value is the concentrated embodiment of correlation and significance between variables, and the calculation formula is as follows:

where PV_ij represents the preference values between the variables X_i and Y_j, X_i represents the ith production behavior factor (e.g., irrigation amount), and Y_j represents the jth soil fertility factor (e.g., soil organic matter content), ({P}_{ij}) is obtained by looking up the table based on the t, and e is a constant, taking 0.001 in order to prevent the denominator of the formula from being 0.

In order to make the preference values of the various indicators in the same order of magnitude more stable, the preference values were normalized:

where N represents the number of variables related to the experimental treatments, PV_i –PV_avg takes the absolute value, while the positive or negative values of the PV_normal were determined by the positive or negative values of the correlation r.

The PNN integrated the preference matrixes into the neural network structures by identifying the Hadamard products of the learnable weights between the preference matrixes and the input and output data. By referring to Eq. (1) in the hierarchical affine transformation, the preference constraint of PNN could be expressed as follows:

where P is the preference matrix calculated by Eq. (8), and ⊙ represents the Hadamard product of the corresponding elements of the matrix. The structure of preference neural network and preference value are shown in Figs. 5 and 6.

Hyper-parameters of PNN

We conducted experiments on the datasets with varying the hyper-parameters (such as the number of PNN layers and hidden layers, the number of nodes in each layer, learning rate, dropout rate and batch size) to understand that how the Hyper-parameters impact on the performance of PNN.

We select the activation function and learning rate by referring to the neural network structure commonly used in similar fields (1 hidden layer and 64 hidden nodes)^29,30. It is found that ReLU has better performance than other activation functions (sigmoid, tanh). The performance is best when the learning rate is around 0.005. It is generally believed that neural networks with more hidden layers are able, with the same number of resources, to address more complex problems³¹, but excessively increasing network depth will easily lead to overfitting³². Since there is no direct method to select the optimal number of hidden layers and nodes³³, this study first calculated the structure of one hidden layer and 64 nodes in each layer, and found that the combined effect was poor (R² of irrigation and nitrogen application were 0.3971 and 0.4124, respectively). Therefore, the trial-and-error method is adopted. The number of hidden layers starts from 1 and is incremented by 1 to test the maximum number of 10 hidden layers. The number of nodes in each layer were tested with a maximum number of 100 hidden neurons, starting with 5 and increasing by 5.

We found that when the number of hidden layers of PNN exceeds 6, and the number of nodes in each layer exceeds 65, the performance will drop significantly. The reason behind this phenomenon could be the current dataset size is insufficient for larger scale of the PNN model. In the consideration of that the size of new dataset we can obtain very year is similar to the current dataset size, we believe that current hyper-paramter settings of PNN is in a reasonable condition.

After that, the number of layers was fixed as 6, and the number of nodes in each layer were tested 10 times with 60 as the starting point and 1 as the increment, we found that when the number of nodes was 64, the improvement of the fit degree was no longer noticeable. On this basis, we changed different activation functions and learning rate again, and found that PNN still has the best performance when the activation function is ReLU and the learning rate is 0.005. Then, different batch sizes and dropout rates were tried. The two parameters had weaker effects on the performance than the other parameters, and the performance was optimal at 256 and 0.1, respectively.

The hyper-parameters include:

1. 1.

   number of PNN layers;

2. 2.

   number of hidden layers;

3. 3.

   types of activation function;

4. 4.

   percentage of dropout;

5. 5.

   learning rate;

6. 6.

   loss function;

7. 7.

   optimizer;

8. 8.

   batch size;

9. 9.

   number of epochs;

10. 10.

    number of workers.

The ideal PNN structure for the study comprises these layers:

1. 1.

   number of PNN layers is 8;

2. 2.

   number of hidden layers is 6;

3. 3.

   Fully connected layers with 64 nodes and ReLU activation function

4. 4.

   dropout with 0.1.

5. 5.

   the learning rate is 0.005;

6. 6.

   loss function is Huber Loss Methods (HLM);

7. 7.

   optimizer: ADAM;

8. 8.

   epochs is 500;

9. 9.

   the batch size is 256;

10. 10.

    number of workers is 6.

Hyper-parameters of other models

LR algorithms and LOR do not have hyper-parameters that need to be adjusted. A part of the hyper-parameters of the SVR model was determined by referring to Guan Xiaoyan’s research³⁴, and a part of the hyper-parameters of the BPNN model was determined by referring to Gu Jian’s research²⁷. RMLP takes the same hyperparameters as PNN. The hyperparameters of SVR and BPNN models are shown in Table 5.

Model performance evaluation

The proposed PNN model was trained and validated using the field measured data from 2020 and the performance achievements of PNN were evaluated by the root mean square errors, mean square errors, and mean absolute errors as follows:

Model multidimensional fertility targets

The soil fertility grade classification of soil organic matter, soil total nitrogen content and salt content in this study was based on the soil fertility grade classification results by the Agriculture and Animal Husbandry Bureau of Bayannur City, along with the local standard Technical Specifications for the Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), as the shown in Tables 6 and 7.

In the evaluation system of soil fertility referencing the Technical Specifications for Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), the pH was divided into four grades according to the membership degrees of the land productivity evaluations, as detailed in Table 8.

Based on the classification standard of soil fertility obtained by the Bureau of Agriculture and Animal Husbandry of Bayannur City, when the farmland soil is at the high fertility level, the soil organic matter and total nitrogen content should be more than 20 g/kg and 1.6 g/kg, respectively. Soil salt content was less than 2 g/kg. Meanwhile, the pH value is kept between 6.5 and 7.5.

Source: Ecology - nature.com