Modeling and prediction of CO2 exchange response to environment for small sample size in cucumber

• We develop an effective crop model for small sample size, which has high accuracy.
• The intelligent algorithm is compared with classical regression model.
• Factor analysis including path analysis and cross validation is used to select independent variables from monitored variables.
• An improved relative error is used for comprehensive error analysis.

The crop model for estimating the CO2 exchange in response to environment is constructed for cucumber, in order to develop an efficient model for small sample size and predict the growth accurately. The factor analysis consists of path analysis and cross validation. Path analysis is used to quantify the relationship among factors so as to obtain the variables with significant influence on the CO2 exchange from the monitored environmental factors. Cross validation is used to determine the independent variables. A BPNN (Back propagation neural network) is trained and optimized by genetic algorithm to model the CO2 exchange. The predicted results are compared with that of the classical regression. Factor analysis selects the following environmental characteristics as the correlated independent variables: air temperature, relative humidity, radiation, and CO2 concentration in the air. In the comparison of three models, GA–BPNN (Genetic Algorithm Based Back propagation Neural Network) had the best accuracy followed by BPNN. Although GA–BPNN has a disadvantage of slow operating speed, it has high accuracy, which is the key factor limiting the application of the model for small sample size. Consequently, GA–BPNN is an efficient crop model for small sample size. And it can also be used in modeling other ecological and physiological characteristics for other crops.