Coupled online sequential extreme learning machine model with ant colony optimization algorithm for wheat yield prediction

Abstract

Inadequate agricultural planning compounded by inaccurate predictions results in an inflated local market rate and prompts higher importation of wheat. To tackle this problem, this research has designed two-phase universal machine learning (ML) model to predict wheat yield (W_pred), utilizing 27 agricultural counties' data within the Agro-ecological zone. The universal model, online sequential extreme learning machines coupled with ant colony optimization (ACO-OSELM) is developed, by incorporating the significant annual yield data lagged at (t - 1) as the model's predictor to generate future yield at 6 test stations. In the first phase, ACO is adopted to search for suitable, statistically relevant data stations for model training, and the corresponding test station by virtue of a feature selection strategy. An annual wheat yield time-series input dataset is constructed utilizing data from each selected training station (1981-2013) and applied against 6 test stations (with each case modelled with 26 station data as the input) to evaluate the hybrid ACO-OSELM model. The partial autocorrelation function is implemented to deduce statistically significant lagged data, and OSELM is applied to generate W_pred. The two-phase hybrid ACO-OSELM model is tested within the 6 agricultural districts (represented as stations) of Punjab province, Pakistan and the results are benchmarked with extreme learning machine (ELM) and random forest (RF) integrated with ACO (i.e., hybrid ACO-ELM and hybrid ACO-RF models, respectively). The performance of the ACO-OSELM model was proven to be good in comparison to ACO-ELM and ACO-RF models. The hybrid ACO-OSELM model revealed its potential to be implemented as a decision-making system for crop yield prediction in areas where a significant association with the historical agricultural crop is well-established.

Figure 1

Map of the study region. (a) Provinces of Pakistan. (b) Districts of Punjab where the present study was undertaken.

Figure 2

The selected training stations in red and the corresponding test stations in yellow are (a), (b), (c), (d), (e), and (f) respectively. Note that the stations shown in green have ‘no available wheat yield data’ and those in blue were not selected by the ant colony optimisation algorithm.

Figure 3

Bar graphs of the root mean squared error (RMSE) encountered by the ant colony optimisation algorithm in the selection of training study stations for each testing study station: Station 1: Rahimyar Khan, Station 2: D. G. Khan, Station 3: Kasur, Station 4: Sialkot, Station 5: Rawalpindi, and Station 6: Jhang.

Figure 4

Time series of the annual wheat yield data for the training stations selected by the ant colony optimisation algorithm for each testing study station: Station 1: Rahimyar Khan, Station 2: D. G. Khan, Station 3: Kasur, Station 4: Sialkot, Station 5: Rawalpindi, and Station 6: Jhang.

Figure 5

Partial autocorrelation function correlation coefficient (PACF) of the historical annual wheat yield time series for each testing study station: Station 1: Rahimyar Khan, Station 2: D. G. Khan, Station 3: Kasur, Station 4: Sialkot, Station 5: Rawalpindi, and Station 6: Jhang.

Figure 6

Flow chart of the proposed hybrid two-phase Ant Colony Optimization algorithm integrated with the Online Sequential Extreme Learning Machine (OSELM) model.

Figure 7

Scatterplots of the predicted (W_pred) and observed wheat yield (W_obs) (kg ha⁻¹) in the testing phase of the ACO-OSELM versus ACO-ELM and ACO-RF models including the coefficient of determination (r²) and a linear fit inserted in each panel for the tested study zones. Note: Each point represents each year’s data in the testing period.

Figure 8

Boxplots of the prediction error |PE| (kg ha⁻¹) of ACO-OSELM versus ACO-ELM and ACO-RF models between the predicted and observed wheat yield for Station 1: Rahimyar Khan, Station 2: D. G. Khan, Station 3: Kasur, Station 4: Sialkot, Station 5: Rawalpindi, and Station 6: Jhang.

Figure 9

Vector field evaluation (VFE) diagram showing Willmott’s agreement between the observed and predicted wheat yield and standard deviation (SD) of ACO-OSELM versus ACO-ELM and ACO-RF models for all tested stations.

Figure 10

Empirical cumulative distribution function (ECDF) of the prediction error, |PE| (kg ha⁻¹) for the testing stations using ACO-OSELM versus ACO-ELM and ACO-RF models.

Figure 11

Polar plots showing the prediction error |PE| in each year generated from the ACO-OSELM versus ACO-ELM and ACO-RF models in predicting wheat yield for all stations.