In pumped storage projects, the permeability of rock masses is a crucial parameter in engineering design and construction. The rock mass permeability coefficient (
Due to the heterogeneity and anisotropy of rock masses,
Establishing complex nonlinear relationships involves predicting
Accordingly, this study selects geological parameters that are easy to obtain and crucial in engineering sites to represent the permeability characteristics of rock masses at an engineering site as accurately as possible. The correlation between these parameters and
DELM is an ELMderived method that constructs multilayer network structures by superimposing an extreme learning machine autoencoder (ELMAE) to minimize input information reconstruction errors and improve the representational capability of a network. The output of the ELMAE is expressed as follows:
When
In the training process of the DELM, the original data sample
The SSA is a relatively new swarm intelligence optimization algorithm introduced in 2020 [
If discoverers find food, they instantly leave their present position to compete. The position update equation for joiners is expressed as follows:
When a population forages, sparrows provide alerts. Vigilantes are randomly generated in each group. The initial positions are randomly generated using the following rules:
Mao et al. [
Sine chaotic initialization
Sine and logistic chaos are typically employed to improve the optimization performance of search problems. When the sine chaotic method initializes the population, it ensures that the entire sparrow population is uniformly distributed throughout the search space, thus increasing the probability of determining the globally optimal solution [
The initial value cannot be 0 to prevent immobility and the occurrence of a zero point at [−1, 1].
Dynamic adaptive weights
This study proposes an improved discovery position update strategy to enhance the effectiveness of the search algorithm and avoid prematurely falling into local optimal solutions. The advantage of this method is that the discoverer not only considers their previous position when moving but is also guided by the previously determined optimal solution. This aids the algorithm in breaking out potential local optimal traps determined solely by their current position [
The updated formula for the improved vigilantes is
The improved equation indicates that when a sparrow is in the optimal position in a group, any point between the current optimal and worst positions is selected as the new foothold to avoid potential danger or prevent resource depletion. In other cases, a random point is selected to jump between its current and best positions.
Integration of Cauchy mutation and OBL
The use of Cauchy mutation can introduce more variation into the population to improve the ability of the algorithm to explore the entire search space.
Incorporating Cauchy mutations into the update process of the target search positions further expands the algorithm’s performance in global optimization problems.
The OBL method [
The optimization efficiency of the algorithm is improved through a flexible selection mechanism that dynamically switches between different strategies [
If
Although OBL and Cauchy mutations can help the algorithm avoid falling into local optima, each perturbation or variation is not guaranteed to result in a better solution because they are stochastic. Therefore, the algorithm introduces a greedy rule to overcome the possible degradation of the solutions caused by random disturbances. The greedy rule is a selective updating mechanism that ensures that the algorithm only updates its position when it obtains a higherquality solution. The greedy rule is expressed as follows:
Algorithm performance testing
Four benchmark functions are employed to compare the performance of ISSA with SSA, grey wolf optimization (GWO), and mothflame optimization (MFO) [
Function types  Value ranges  Optimal solution 

Sphere  [−100, 100]  0 
Schwefel’s 2.22  [−10, 10]  0 
Quartic  [−1.28, 1.28]  0 
Ackley  [−32, 32]  0 
Function types  Algorithm  Average value  Standard deviation 

Sphere  GWO  9.568E−28  6.363E−04 
MFO  3.956E+03  1.027E+03  
SSA  1.187E−62  6.496E−62  
ISSA  0.000E+00  0.000E+00  
Schwefel’s 2.22  GWO  9.765E−17  7.336E−17 
MFO  2.601E+01  3.290E+00  
SSA  1.880E−30  8.665E−30  
ISSA  1.140E−244  0.000E+00  
Quartic  GWO  1.247E−51  2.127E−51 
MFO  5.596E−01  3.943E−01  
SSA  1.431E−109  7.839E−109  
ISSA  0.000E+00  0.000E+00  
Ackley  GWO  1.055E−13  1.823E−14 
MFO  1.184E+01  1.144E+00  
SSA  8.882E−16  0.000E+00  
ISSA  8.882E−16  0.000E+00 
The algorithm steps are as follows:
Initialize parameters (Percentage of discoverers (PD), Percentage of vigilantes (SD), warning value (ST), and others) and use
Calculate the fitness values of each sparrow.
Sparrows with better fitness values are selected as discoverers, and their positions are updated according to
Select the Cauchy mutation or OBL strategy based on the
Determine whether to perform position updates based on
Determine whether the end condition is satisfied. If the conditions are satisfied, the optimal position of the output sparrow is used as the optimal input weight for the DELM model. Otherwise, skip to step (2).
The input layer weights and thresholds of the DELM are randomly generated from the orthogonal matrices according to the Johnson–Lindensrauss theorem. This orthogonalized design enhances the generalization ability of the system but also results in high volatility in the prediction results. Therefore, the ISSA is used to optimize the input layer weights and thresholds to reduce the prediction model’s volatility and enhance the prediction results’ stability and accuracy. The optimization process and flowchart are depicted in
A pumpedstorage power station in Shanxi Province is planned to have an installed capacity of 1500 MW with a firstclass engineering grade. The survey and location map of the study area are shown in
The geological engineering conditions are shown in
The burial depth reflects the stress level of the geological environment in which the rock mass is located.
The RQD is a quantitative index of a rock mass’s degree of integrity and weathering. Therefore, several researchers have studied the relationship between the RQD and
Author  Simultaneous equations 

Qureshi et al. [ 

ElNaqa [ 

Öge [ 

Jiang et al. [ 
The permeability properties of rock masses are influenced by the fracture filling and their developmental characteristics [
The RID represents the integrity index of a rock mass through its longitudinal wave velocity index, as shown in
Indexes  Significance ( 

Burial depth  <0.01 
RQD  <0.01 
Fracture density  <0.01 
Steep dip ratio  <0.01 
RID  <0.01 
K  <0.01 
Spearman correlation explores the correlation between continuous variables in the range of [−1, 1].
Due to the limited proportion of steepdip ratios in the sample data, some deviations can be occurred in the correlation analysis. The lithology of this project area was primarily composed of metamorphic rocks, and the weight of the fracture steepdip ratio significantly impacted
In summary, the permeability of rock masses is closely related to the burial depth, RQD, and degree of fracture development. This study indexes selected geological parameters such as the burial depth, RQD, FD, and RID as the modeling indexes to ensure the model’s accuracy. Hence, a prediction model of the rock mass permeability based on a multiindex was developed to mitigate the problems of inflexible parameter selection and unreasonable model construction.
Based on the above analysis, four independent and one dependent variables were selected to form a database. A total of 527 valid samples were collected through field tests, with 88% of the rock mass being slightly weathered. The specific information is presented in
Indexes  Min  Max  Average value  Coefficient of variation 

Burial depth (m)  14  770  224  1.1 
RQD (%)  2.8  99.9  65  0.37 
FD (strips/m)  0.08  1.34  0.55  0.36 
RID  0.34  0.92  0.70  0.20 
K (m/d)  0.003  0.07  0.018  0.74 
Region  Number of boreholes drilled  Number of test sections 

Upper reservoir  13  137 
Water conveyance system  15  197 
Lower reservoir  25  193 
The data were divided into two independent datasets: 440 for simulation and 87 for testing the model, as shown in
The final requirement was the predicted values of the parameter variables to verify the model’s predictive performance. Therefore, the normalized data must be converted to the original data scale during the training process, and antinormalization must be performed.
Based on the literature [
The coefficient of determination (
Generally, the smaller the value of
The results of the comparison between the measured and predicted
This study quantitatively evaluated all models using the three evaluation metrics described in
Item  DELM  SSA–DELM  ISSA–DELM 

0.0078  0.0073  0.0072  
0.6900  0.7970  0.8268  
0.0096  0.0090  0.0089  
1.7962  2.2197  2.4029 
This study constructs a dataset of characteristic variables for rock mass permeability by selecting four geological indexes that are easy to obtain and have precise physical meanings on sites. Aiming at the disadvantage that the traditional SSA algorithm easily falls into local optimum at the end of training, Sine chaotic mapping, dynamic adaptive weights, Cauchy mutation, and OBL are adopted to improve the basic SSA algorithm. In addition, the improved algorithm is combined with the DELM algorithm to establish a prediction model of the rock mass permeability coefficient based on various geological indexes in the pumped storage power station project area. The main conclusions are shown below:
The Spearman correlation analysis method successfully identifies the main geological indexes affecting the rock mass permeability in the project area, revealing the correlation between these indexes and
The diversity of solutions is expanded and enriched by adopting multiple learning strategies to improve the SSA algorithm. At the same time, the mutation and update of the optimal solution position is achieved, reducing the probability of the algorithm falling into local extremes. Compared to similar algorithms, the effectiveness and superiority of the ISSA algorithm are verified.
The ISSADELM model can make a rapid and relatively accurate prediction of the rock mass permeability in the pumped storage power station project area. The model has a good application prospect and popularization value in the analysis of seepage stability and can provide a specific reference basis for the support design of hydraulic structures.
Improved sparrow search algorithm
Deep extreme learning machine
Rock quality designation
Fracture density characteristic index
Rock mass integrity designation
Rock mass permeability coefficient
The authors are very grateful to other professors from the School of Engineering and Technology for their theoretical support of this paper.
The authors received no specific funding for this study.
The authors confirm their contribution to the paper as follows: study conception and design: Yingdong Wang; analysis and interpretation of results: Chen Xing; draft manuscript preparation: Leihua Yao. All authors reviewed the results and approved the final version of the manuscript.
The details of the original database are presented in the manuscript in the form of a bar chart. For further information, please contact the corresponding author.
The authors declare that they have no conflicts of interest to report regarding the present study.