Optimization of Hydrogeological Parameters Based on Sparrow Search Algorithm in Matlab

Abstract: To improve the accuracy of hydrogeological parameter solutions and expand optimization methods for hydrogeological parameters, this paper utilizes the Theis basic formula and the Sparrow Search Algorithm to optimize the calculation of the Theis formula’s transmissivity and storage coefficient, aiming to verify the feasibility and effectiveness of the Sparrow Algorithm for optimizing hydrogeological parameters.

1. Sparrow Search Algorithm

The specific principles of the Sparrow Search Algorithm can be referenced in the blog: https://blog.csdn.net/u011835903/article/details/108830958

2. Objective Function Modeling

In pumping tests, for aquifer systems that meet the Theis assumption, the drawdown in observation wells can be expressed as:

Where s is the drawdown (m); Q is the pumping well flow rate (m³/h); K is the transmissivity (m²/s); W is the Theis well function, u is a parameter that holds when u or t is satisfied; t is the time from the start of pumping to the calculation moment; r is the distance from the observation hole to the pumping well (m); S is the storage coefficient.

Based on equations (1) and (2), the objective fitness function is constructed:Where s_obs is the measured drawdown (m); s_opt is the optimized drawdown (m); i is the pumping sequence or observation well number, i = 1, 2, …, N; T is the transmissivity to be optimized; S is the storage coefficient.

3. Experimental Testing

Example 1: A multi-well pumping test was conducted in a confined aquifer in a certain area, with a stable flow rate of 60 m³/h for the pumping well. Well 14 is a complete pumping well, while wells 2, 15, 16, 10, and 9 are observation wells. The distance r from observation well 15 to the pumping well is 125 m, and the drawdown at different times during the pumping process is shown in Table 1. This paper uses the observation data from the pumping experiment at observation well 15 as an example, utilizing the Gold-SA algorithm to optimize the transmissivity T and storage coefficient S.

Table 1 Observation Well 15 Pumping Test Data

Serial Number	Time t/min	Drawdown s/m
1	10	0.16
2	20	0.48
3	30	0.54
4	40	0.65
5	60	0.75
6	80	1
7	100	1.12
8	120	1.22
9	150	1.36
10	210	1.55
11	270	1.7
12	330	1.83
13	400	1.89
14	450	1.98
15	645	2.17
16	870	2.38
17	990	2.46
18	1185	2.54

Parameter settings. The search range for the transmissivity T and storage coefficient S is set to [0, 1000];

The results of the Sparrow Search Algorithm experiment are as follows:

From the curves in the above figures, it can be seen that the optimized T and S simulated drawdown is very close to the actual drawdown, indicating that this method has a certain feasibility.

Best T, S obtained by SSA: 9.1354, 0.013582Best fitness value obtained by SSA: 0.0061864

4. References

[1] Zhou Yourong, Li Na, Zhou Fahui. Application of Golden Sine Algorithm in Hydrogeological Parameter Optimization [J]. People’s Pearl River, 2020, 041(006):117-120,128.

5. Matlab Code

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