Multi-Criteria Evaluation of Small-Scale Sprinkler Irrigation Systems Using Grey Relational Analysis

Abstract

The technical and socioeconomic evaluation of small-scale sprinkler irrigation systems is a multi-criteria problem characterized by complexity and uncertainty. In order to solve that, the application of Grey Relational Analysis (GRA) was presented. An evaluation model with ten sub-criteria under four groups, namely, technical, economic, environmental and social, was established. Among the criteria, calculation method of labor use in the small-scale sprinkler systems was originally addressed, and Life Cycle Cost (LCC) was used as an economic indicator. In the design of GRA, a combination weighting method based on Analytical Hierarchy Process (AHP) and entropy measurement was employed to take into account the experts’ knowledge and the inherent information in the experimental data. Six irrigation systems for three field sizes 0.5 ha, 2 ha and 5 ha respectively were considered to verify the model. The systems were optimized with Genetic Algorithms (GAs) first to figure out the optimal combinations of sprinklers and pipes and further, field tests were performed. The discussions show that: the developed approach has successfully provided the ranking of systems for three field sizes. When different types of sprinklers are used, the criteria including atomize index, application efficiency and specific energy consumption change greatly. And the ownership cost, particularly the energy consumption fee, accounts for the largest part of LCC in most of the systems. In comparison, System 5 and System 1 are generally the best. The evaluation model solved by GRA integrated with GAs is effective and can be extended to the comprehensive evaluation and optimization of other irrigation systems.

Appendix

Labor use (Operation time)

The operation time of a small-scale sprinkler irrigation system can be calculated using Eq. (16) in reference to the formula of manufacture time involved in the fire-fighting (Du and Xu 2011) and surgery (Garg et al. 2010).

$$ {T}_p=\left(1+{k}_1\right)\left(1+{k}_2\right)\left(1+{k}_3\right){\displaystyle \sum_{i=1}^p{T}_i} $$

(16)

where, T _p represents the operation time of irrigation system on each location, min; k ₁ is coefficient of experience of workers; k ₂ is coefficient of weather condition, temperature and humidity for instance, influencing the efficiency of workers; k ₃ is the coefficient related to the muddy ground; p is the number of components, or items included; i indicates the i-th part, including the operation time of pump and motor, pipes, sprinklers and walking time in the field; T _i is the operation time for the i-th part, min. All the time is summarized according to experiences and statistical data in field tests and the questionnaire among users.

• (1) Pump and motor

  The operation time spent on the pump and motor T _m includes three items: carrying them to the water source, connecting the suction pipe and checking the parts before start.

• (2) Pipes

  The time for laying and connecting the delivery pipes, T _d shown in Eq. (17) can be divided into two parts: the operation time and walking time for transportation.

  $$ {T}_d= n\left[{T}_{d1}\left(1+{k}_d\right)+{T}_{d2}\right] $$

  (17)
  $$ {T}_{d2}={k}_t{t}_d a $$

  (18)

  where, Td1 is the operation time for each pipe connecting two sprinklers; kd is coefficient related to pipe diameter; Td2 is walking time for allocating and installing the pipes, min; kt is coefficient of walking times, k = 1, 2, for the initial time, k = 2, others, k = 1; td is the walking time per meter, min.

• (3) Sprinklers

  The operation time of sprinklers T _s can be described with Eq. (19).

  $$ {T}_s= n{T}_{s0} $$

  (19)

  where, T _s0 is the operation time for each set of sprinkler, riser pipe and supporter, min.

• (4) Walking time or transportation time

  The walking time or transportation time in distributing the sprinklers, pipes and couplings is related to the area of the field in each irrigation event. Supposing all the facilities are placed at one end of the field while the end sprinkler is arranged at the other end. The walking time T _l is then presented:

  $$ {T}_l={t}_d\frac{n\left( n-1\right)}{2} a $$

  (20)

  The coefficients used in these equations are listed in Table 9 (Du and Xu 2011).

  Table 9 Values of coefficients