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Water balance is measured by transpiration, which has a significant impact on the performance of geotechnical infrastructure (vegetated slopes), ecological infrastructure (wetlands), urban infrastructure (green roof, biofiltration units) and agricultural infrastructure. Past studies have formulated models using analytical modeling to evaluate the transpiration index based on energy balance and suction. In circumstance of impartial and uncertain information about the root and shoot properties and its effect on the transpiration index, the present work aims to introduce the new optimization algorithm of genetic programming (GP) to quantify and optimize the transpiration index of plant.

The GP framework, having objective function of structural risk minimization, is used for formulating the transpiration index model. The statistical metrics with 2D and 3D analyses of the models are conducted to determine its accuracy and understand the transpiration process.

The model analysis reveals that the proposed model extrapolates the transpiration index values accurately based on five inputs. 2D and 3D relationships between the transpiration index and the five inputs suggest that the total root area has the highest impact on the transpiration index followed by shoot length and root biomass. There is not much impact of the shoot mass and stem basal diameter on the transpiration index. It was also found that the transpiration index increases with an increase in total root area and root biomass.

This work is a first-of-its-kind study involving the extensive computation analysis for quantifying and optimizing the transpiration index of the soil for the complex civil systems.

For measuring the effect of crop root content on soil water retention curves (SWRC), a simulation approach (multi-gene genetic programming (MGGP)), which develops the model structure and its coefficients automatically can be applied. However, it does not perform well due to two vital issues related to its generalization: inappropriate formulation procedure of the multi-gene model and the difficulty in model selection. The purpose of this paper is to propose a heuristic-based-MGGP (N-MGGP) to formulate the functional relationship between the water content and two input parameters (soil suction and volumetric crop root content).

A new simulation approach (heuristic-based-MGGP (N-MGGP)), was proposed to formulate the functional relationship between the water content and two input parameters (soil suction and volumetric crop root content). The proposed approach makes use of a statistical approach of stepwise regression and classification methods (Bayes naïve and artificial neural network (ANN)) to tackle the two issues. Simulated data obtained from the models was evaluated against the experimental data.

The performance of proposed approach was found to better than that of standardized MGGP. Sensitivity and parametric analysis conducted validates the robustness of model by unveiling dominant input parameters and hidden non-linear relationships.

To the best of authors’ knowledge, an empirical model is developed that measures the effect of crop root content on the SWRCs. The authors also proposed a new genetic programming approach in simulating the crop root content dependent SWRCs.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.