CN111475884A - Optimization method of foundation pit precipitation based on particle swarm optimization and groundwater model - Google Patents

Abstract

The present invention relates to a foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model, comprising the following steps: Step S1: constructing a groundwater flow simulation model to describe the dynamic change process of the groundwater flow field in and around the foundation pit area; Step S2 Step S3: coupling the groundwater flow simulation model and the optimization model; Step S4: using the PSO optimization technology to solve the optimal solution of the coupled model; Step S5: according to the optimal solution, The spatial distribution and pumping flow of optimal dewatering wells are obtained. The spatial distribution and pumping flow of the optimal dewatering well obtained by the invention can not only save a lot of construction time, speed up the construction period, but also greatly improve the dewatering efficiency.

Description

Optimization method of foundation pit precipitation based on particle swarm optimization and groundwater model

technical field

The invention relates to the field of groundwater science and engineering, in particular to a foundation pit precipitation optimization method based on a particle swarm algorithm and a groundwater model.

Background technique

During the construction of the foundation pit, in order to meet the excavation requirements of the foundation pit, the groundwater level at the bottom of the foundation pit needs to be lowered. At present, in the process of foundation pit dewatering, dewatering wells are generally arranged evenly at a certain distance, and analytical solutions are used to calculate the pumping flow of all single wells. This method will generate large construction costs or fail to meet the precipitation requirements of engineering construction. Therefore, it is necessary to use optimization technology to scientifically manage the spatial distribution of dewatering wells, and to reduce the cost of engineering construction as much as possible on the premise of meeting the construction requirements.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model.

To achieve the above object, the present invention adopts the following technical solutions:

A foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model, comprising the following steps:

Step S1: build a groundwater flow simulation model, and describe the dynamic change process of the groundwater flow field in the foundation pit area and its surroundings;

Step S2: based on preset objective function and constraints, establish an optimization model;

Step S3: coupling groundwater flow simulation model and optimization model;

Step S4: adopt PSO optimization technology to solve the optimal solution of the model after coupling;

Step S5: According to the optimal solution, the spatial distribution and pumping flow of the optimal dewatering wells are obtained.

Further, the preset objective function and constraints are specifically:

Objective function:

minimize

Restrictions:

Q _mi ≤Q ^t _i ≤Q _max (3)

Among them, C is the construction cost of the foundation pit dewatering project; _Dw is the number of dewatering wells; y _i is the binary number used for well i; Q _i ^t is the pumping flow of well i in the t-th management period; D _t is the total number of management periods; Δt _t is the duration of the t-th stress period; α _i ( _i =1, 2) represents the price coefficient of well installation and pumping; hi represents the groundwater level in the foundation pit construction area; h _upper represents The required groundwater level during the construction of the foundation pit; h _lower represents the lower limit of the groundwater level reduction during the construction of the foundation pit; R represents the scope of the construction of the foundation pit.

Further, the step S3 is specifically:

Step S31: the target of the coupled model optimization management is a function of decision variables and state variables;

Step S32: continuously update the state variable through the simulation model, calculate the objective function value and judge whether the constraint condition is satisfied; select the decision variable through the optimization model, and return to the simulation model to update the state variable;

The above formula indicates that the state variable w ^t of the system at a certain time t is a function of the decision variable Q ^t of the period and the state variable w ^t-1 of the previous period t-1, and the state transition function is represented by f _w ;

Step S32: The decision variables and state variables in the coupled model satisfy the simulation model at the same time, and are updated synchronously.

Further, the step S4 is specifically:

Step S41: represent the position of the dewatering well and the well flow rate by means of real number coding, set the population size, acceleration factor, and maximum allowable number of iterations of the system, and randomly generate the initial position and initial velocity information of each particle;

Step S42: Judging whether the particle satisfies the constraint, if it does not satisfy the constraint, use the correction function to correct the particle to make it a feasible solution

Step S43: Calculate the fitness value of each particle in the group according to the objective function

Step S44: Determine the most individual in unit history and the optimal individual in group history according to the fitness value of the particle

Step S45: Update the speed and position of the particles:

Step S46: Update the inertia weight to limit the speed and range of the particle swarm

Step S47: judge whether the termination criterion has been reached, if the termination criterion is satisfied, the iteration is terminated and the optimal solution is output; if the termination criterion is not satisfied, return to step S44: continue the search.

Step S48: Display the optimal position in the global, and give the quantitative results of each index.

Further, the velocity and position of the calculated particle can be calculated according to the following formula

ν _id ^k+1 =ω*ν _id ^k +c ₁ r ₁ (p _id ^k -x _id ^k )+c ₂ r ₂ (p _gd ^k -x _id ^k )

x _id ^k+1 =x _id ^k +ν _id ^k+1 .

where:

k——(times), the number of program iterations;

ω - inertia weight;

c ₁ , c ₂ - learning factors, also known as acceleration constants, according to experience, usually take c ₁ =c ₂ =2;

r ₁ , r ₂ — uniform random numbers in the range of [0, 1];

p _id ^k - the optimal solution searched by the current individual;

p _gd ^k ——the optimal solution searched by the entire population;

ν _id ^k ——the speed of the particle, v _id ^k ∈[-v _max ,v _max ], v _max is a constant, set by the user to limit the speed of the particle;

x _id ^k - the individual parameters of the particle, that is, the decision variable value.

Further, the updated inertia weight can be calculated by the following formula:

where:

ω _max ——Inertia weight initial inertia value;

ω _min ——the inertia weight when iterating to the maximum algebra;

k——current iteration number;

k _max - maximum number of iterations.

The velocity and range of the confinement particle swarm can be calculated as follows:

ν _max =(x _id,max -x _id,min )*P.

In the formula: x _id,max ——the upper limit value of the control variable;

x _id,min ——the lower limit value of the control variable, P=20%

Compared with the prior art, the present invention has the following beneficial effects:

The invention can not only save a lot of construction time and speed up the construction period, but also can greatly improve the precipitation efficiency.

Description of drawings

FIG. 1 is a flow chart of simulation optimization in an embodiment of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

Please refer to FIG. 1, the present invention provides a foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model, including:

Step 1, establish a groundwater flow model to describe the dynamic change process of the groundwater flow field in the foundation pit area and its surroundings;

Step 2: Determine the management objectives and establish an optimization model, as follows:

Objective function:

minimize

Restrictions:

Q _min ≤Q ^t _i ≤Q _max

Among them, C represents the construction cost of the foundation pit dewatering project; _Dw is the number of dewatering wells; when y _i =1, the binary number used for well i, y _i =0, well i does not use binary numbers; Q ^t _i is the well i The pumping flow of i in the t-th management period; D _t is the total number of management periods; Δt _t is the duration of the t-th stress period; α _i represents the price coefficient of well installation and pumping, i=1 or 2; h _i Indicates the groundwater level in the foundation pit construction operation area; h _upper represents the required groundwater level during the foundation pit construction process; h _lower represents the lower limit of the groundwater level reduction during the foundation pit construction process; R represents the foundation pit construction operation scope, objective function and constraints The conditions constitute the mathematical model of the optimal management of foundation pit precipitation;

Step 3, coupling the simulation model and the optimization model;

Step 4, select PSO optimization technology to solve the solution of foundation pit dewatering engineering management problem;

Step 5, output the optimization result.

In this embodiment, the solving step of step 4 is:

1) System initialization

The position and flow rate of the dewatering well are represented by real number coding; the population size, acceleration factor, and maximum allowable iterations of the system are set, and the initial position and initial velocity information of each particle are randomly generated.

It is judged whether the particle satisfies the constraint, and if the constraint is not satisfied, the correction function is used to correct the particle to make it a feasible solution.

2) Calculate the fitness value of each particle in the group according to the objective function

3) According to the fitness value of the particle, determine the most individual in the unit history and the optimal individual in the group history

4) Update the speed and position of the particle

The velocity and position of the calculated particle can be calculated according to the following formula

ν _id ^k+1 =ω*ν _id ^k +c ₁ r ₁ (p _id ^k -x _id ^k )+c ₂ r ₂ (p _gd ^k -x _id ^k )

x _id ^k+1 = x _id ^k +ν _id ^k+1

5) Update the inertia weight to limit the speed and range of the particle swarm

The updated inertia weight can be calculated as:

The velocity and range of the confinement particle swarm can be calculated as follows:

ν _max =(x _id,max -x _id,min )*P

6) Determine whether the termination criterion has been reached. If the termination criterion is satisfied (the maximum number of iterations is reached or a good enough fitness value is obtained), the iteration is terminated and the optimal solution is output. If the termination criterion is not met, return to 3 to continue the search.

7) Display the optimal position in the whole world, and give the quantitative results of various indicators.

For step 1) in step 4, it is judged whether the particle satisfies the constraint, and if the constraint is not satisfied, the particle is corrected by the correction function to make it a feasible solution.

In this embodiment, the function of the decision well flow rate and the state variable water level needs to continuously update the state variable through the simulation model, calculate the objective function value and judge whether the constraint condition is satisfied

The above formula indicates that the state variable w ^t of the system at a certain time t is the decision variable Q ^t of the period and the state of the previous period t-1

The function of variable w ^t-1 , the state transition function is represented by f _w .

Preferably, in this embodiment, h _upper is between 0.5m-1.5m below the bottom plate of the foundation pit.

Preferably, in this embodiment, MODFLOW-2005 is used to establish a groundwater flow simulation model.

The above descriptions are only preferred embodiments of the present invention, and all equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope of the present invention.

Claims (6)

1. a foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model, is characterized in that, comprises the following steps: Step S1: build a groundwater flow simulation model, and describe the dynamic change process of the groundwater flow field in the foundation pit area and its surroundings; Step S2: based on preset objective function and constraints, establish an optimization model; Step S3: coupling groundwater flow simulation model and optimization model; Step S4: adopt PSO optimization technology to solve the optimal solution of the model after coupling; Step S5: According to the optimal solution, the spatial distribution and pumping flow of the optimal dewatering wells are obtained. 2. the foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model according to claim 1, is characterized in that, described preset objective function and constraint condition are specifically: Objective function: minimize

Restrictions:

Q _mi ≤Q ^t _i ≤Q _max (3) Among them, C is the construction cost of the foundation pit dewatering project; _Dw is the number of dewatering wells; y _i is the binary number used for well i; Q _i ^t is the pumping flow of well i in the t-th management period; D _t is the total number of management periods; Δt _t is the duration of the t-th stress period; α _i ( _i =1, 2) represents the price coefficient of well installation and pumping; hi represents the groundwater level in the foundation pit construction area; h _upper represents The required groundwater level during the construction of the foundation pit; h _lower represents the lower limit of the groundwater level reduction during the construction of the foundation pit; R represents the scope of the construction of the foundation pit. 3. the foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model according to claim 1, is characterized in that, described step S3 is specifically: Step S31: the target of the coupled model optimization management is a function of decision variables and state variables; Step S32: continuously update the state variable through the simulation model, calculate the objective function value and judge whether the constraint condition is satisfied; select the decision variable through the optimization model, and return to the simulation model to update the state variable;

The above formula indicates that the state variable w ^t of the system at a certain time t is a function of the decision variable Q ^t of the period and the state variable w ^{t -1} of the previous period t-1, and the state transition function is represented by f _w ; Step S32: The decision variables and state variables in the coupled model satisfy the simulation model at the same time, and are updated synchronously. 4. the foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model according to claim 1, is characterized in that, described step S4 is specifically: Step S41: represent the position of the dewatering well and the well flow rate by means of real number coding, set the population size, acceleration factor, and maximum allowable number of iterations of the system, and randomly generate the initial position and initial velocity information of each particle; Step S42: Judging whether the particle satisfies the constraint, if it does not satisfy the constraint, use the correction function to correct the particle to make it a feasible solution Step S43: Calculate the fitness value of each particle in the group according to the objective function Step S44: Determine the most individual in unit history and the optimal individual in group history according to the fitness value of the particle Step S45: Update the speed and position of the particles: Step S46: Update the inertia weight to limit the speed and range of the particle swarm Step S47: judge whether the termination criterion has been reached, if the termination criterion is satisfied, the iteration is terminated and the optimal solution is output; if the termination criterion is not satisfied, return to step S44: continue the search. Step S48: Display the optimal position in the global, and give the quantitative results of each index. 5. the foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model according to claim 4, is characterized in that, the speed and position of described calculation particle can be calculated according to the following formula ν _id ^k+1 =ω*ν _id ^k +c ₁ r ₁ (p _id ^k -x _id ^k )+c ₂ r ₂ (p _gd ^k -x _id ^k ) x _id ^k+1 =x _id ^k +ν _id ^k+1 . In the formula: k is the number of program iterations; ω is the inertia weight; c ₁ , c ₂ are learning factors; r ₁ , r ₂ are uniform random numbers in the range of [0, 1]; p _id ^k is the search result of the current individual The optimal solution of ; p _gd ^k is the optimal solution searched by the entire population; ν _id ^k is the motion speed of the particle, v _id ^k ∈[-v _max ,v _max ], v _max is a constant, set by the user Limit the speed of the particle; x _id ^k is the individual parameter of the particle, that is, the decision variable value. 6. the foundation pit precipitation optimization method based on particle swarm algorithm and groundwater model according to claim 4, is characterized in that, described update inertia weight can be calculated by following formula:

The velocity and range of the confinement particle swarm can be calculated as follows: ν _max =(x _id,max -x _id,min )*P.

Images