Slope reliability analysis method and related device

Abstract

The invention belongs to the technical field of slope reliability analysis, and discloses a slope reliability analysis method and a related device, and the method comprises the steps: obtaining a state variable of a to-be-analyzed slope; calculating the safety coefficient of the slope to be analyzed, and constructing a performance function; establishing and solving a regional modal optimization model for determining a slope limit state curve by using the performance function of the slope to be analyzed, and obtaining the slope limit state curve of the slope to be analyzed; wherein a normal search particle swarm algorithm is adopted for solving, and the normal search particle swarm algorithm is a particle swarm algorithm in which a normal search mode, a particle whole-process dynamic rejection strategy, a particle memory strategy and a low-density area elite particle reproduction strategy are introduced; according to the slope limit state curve of the to-be-analyzed slope, obtaining a reliability analysis result of the to-be-analyzed slope; according to the method, the slope limit state curve is accurately determined, so that the failure probability calculation based on the slope limit state curve is more reliable, and the accuracy of slope stability evaluation is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of slope reliability analysis, and in particular relates to a slope reliability analysis method and related devices. Background Art

[0002] Reliability analysis, as a core component of slope engineering safety design and disaster warning systems, aims to accurately assess slope stability by quantifying failure probabilities. For complex slope systems with d-dimensional state variables, the calculation of failure probabilities essentially relies on the mathematical representation of the performance function. When the performance function takes zero, the corresponding slope limit state curve constitutes the critical interface between safety and instability of the slope system. Therefore, accurately determining the slope limit state curve is crucial for reliability analysis.

[0003] From the perspective of geometric dimensions, the spatial form of the slope limit state curve shows a strict correspondence with the dimension of the state variable. When the dimension of the state variable is 2, the slope limit state curve appears as a closed or open curve in a plane. When the dimension of the state variable is 3, the slope limit state curve expands into a surface in three-dimensional space. When the dimension of the state variable is n, the slope limit state curve degenerates into a hyperplane in n-dimensional space. The above-mentioned dimensional evolution law transforms the problem of solving the slope limit state curve into a global optimization problem with a continuous solution space. Unlike traditional discrete point optimization, the solution set of this optimization problem constitutes a continuous region rather than isolated extreme points. However, there is currently a lack of effective solution algorithms for global optimization problems with continuous solution spaces. If existing multi-modal optimization algorithms are used for solution, the optimal solution is easily clustered, making it difficult to ensure the uniformity and completeness of the solution set within the continuous region. This leads to large deviations in the slope limit state curve results, seriously restricting the engineering applicability of slope reliability analysis. Summary of the Invention

[0004] In response to the technical problems existing in the prior art, the present invention provides a slope reliability analysis method and related devices to solve the technical problem that when using the existing multi-mode optimization algorithm to solve the global optimization problem with a continuous solution space characteristic, the optimal solution is easily aggregated, resulting in large deviations in the slope limit state curve results, which seriously restricts the engineering applicability of slope reliability analysis.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] The present invention provides a slope reliability analysis method, comprising:

[0007] Obtain the state variables of the slope to be analyzed;

[0008] Calculating the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; and constructing a functional function of the slope to be analyzed based on the safety factor of the slope to be analyzed;

[0009] Using the functional function of the slope to be analyzed, a regional modal optimization model for determining the slope limit state curve is established and solved to obtain the slope limit state curve of the slope to be analyzed. The normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic particle exclusion strategy, a particle memory strategy, and a low-density area elite particle breeding strategy.

[0010] According to the slope limit state curve of the slope to be analyzed, the reliability analysis result of the slope to be analyzed is obtained.

[0011] Furthermore, the state variables of the slope to be analyzed include the soil cohesion, internal friction angle and gravity of the slope to be analyzed.

[0012] Furthermore, the regional modal optimization model used to determine the slope limit state curve is as follows:

[0013] min|G(X)|,subject to:X∈Ω

[0014] X=[X1,X2,…,X d ]

[0015] Ω=[L1,U1]×[L2,U2]×…×[L g ,U g ]×…×[L d ,U d ]

[0016] Where G(X) is the performance function of the slope to be analyzed; X is the state variable of the slope to be analyzed; Ω is the feasible region of the optimization problem; X d is the d-th dimension state variable of the slope to be analyzed, d is the dimension of the state variable of the slope to be analyzed; L g is the maximum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed, g∈[1,d]; U g is the minimum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed.

[0017] Furthermore, the normal search mode is as follows:

[0018]

[0019] Among them, N i (t) is the final normal search vector of the i-th particle at the t-th iteration; n i(t) is the initial normal search vector of the i-th particle in the t-th iteration; is the particle p at the tth iteration i Normal search vector; δ is the freezing factor; f(x i (t)) is the fitness function value of the position of the i-th particle at the t-th iteration; f(p g (t)) is the individual's historical optimal fitness function value at the tth iteration; is the neighborhood hyperplane formed by the neighboring particles of the i-th particle; is the unit vector of the neighborhood hyperplane formed by the i-th particle pointing to the i-th particle's neighboring particles at the t-th iteration; ns is the neighborhood size; is the Euclidean distance between the i-th particle and the neighborhood hyperplane formed by the i-th particle's neighboring particles at the t-th iteration; is the particle p at the tth iteration i The Euclidean distance between the particle and the neighborhood hyperplane formed by the neighboring particles of the i-th particle.

[0020] Furthermore, the dynamic exclusion strategy of particles throughout the entire process is as follows:

[0021]

[0022] Among them, r i (t) is the repulsion vector of the i-th particle at the t-th iteration; is the distance from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; d rep is the repulsion distance; is the unit vector from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; i (t) is the position of the i-th particle at the t-th iteration; is the position of the nearest neighbor particle of the i-th particle at the t-th iteration; ||*|| is the L2 norm.

[0023] Furthermore, the particle memory strategy is as follows:

[0024]

[0025] Among them, p i (t) is the historical optimal position of the i-th particle at the t-th iteration; f(x i (τ)) is the fitness function value of the position of the i-th particle at the τ-th iteration; x i (τ) is the position of the i-th particle at the τ-th iteration; k is the memory step size.

[0026] Furthermore, the elite particle breeding strategy in the low-density area is as follows:

[0027] When the number of extreme value points of particles in the population reaches a preset proportion of the total number of current particles, the number of particles within the cutoff radius of each particle is counted with each particle in the population as the center and the cutoff distance as the radius to obtain the density of each particle;

[0028] According to the density of each particle, elite particles are bred in low-density areas; the low-density area is an area where the density of particles is less than a preset density threshold;

[0029] Continue iterating and optimizing until the ratio of the number of new extreme points in the population to the total number of new particles is greater than the reproduction ratio limit;

[0030] Continue to reproduce and optimize until the number of particles in the population reaches the requirement.

[0031] Furthermore, the process of obtaining the reliability analysis result of the slope to be analyzed based on the slope limit state curve of the slope to be analyzed includes:

[0032] According to the slope limit state curve of the slope to be analyzed, a slope limit state curve proxy model of the slope to be analyzed is constructed;

[0033] Using the Monte Carlo simulation algorithm and combining it with the slope limit state curve proxy model of the slope to be analyzed, the response values of several sampling points in the design space of the slope to be analyzed are obtained;

[0034] According to the response values of several sampling points in the design space of the slope to be analyzed, the failure probability of the slope to be analyzed is calculated, that is, the reliability analysis result of the slope to be analyzed is obtained.

[0035] The present invention also provides a slope reliability analysis system, comprising:

[0036] Variable acquisition module, used to obtain the state variables of the slope to be analyzed;

[0037] A function construction module is used to calculate the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; and to construct a functional function of the slope to be analyzed according to the safety factor of the slope to be analyzed;

[0038] The limit state curve solving module is used to establish and solve the regional modal optimization model used to determine the slope limit state curve using the functional function of the slope to be analyzed, thereby obtaining the slope limit state curve of the slope to be analyzed. The normal search particle swarm algorithm is used to solve the regional modal optimization model used to determine the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic particle exclusion strategy, a particle memory strategy, and a low-density area elite particle breeding strategy.

[0039] The reliability analysis module is used to obtain the reliability analysis result of the slope to be analyzed according to the slope limit state curve of the slope to be analyzed.

[0040] The present invention also provides an electronic device, comprising:

[0041] a processor suitable for executing a computer program;

[0042] A computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the slope reliability analysis method is executed.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The slope reliability analysis method provided by the present invention uses the functional function of the slope to be analyzed to establish and solve the regional modal optimization model to obtain the slope limit state curve of the slope to be analyzed; by accurately determining the slope limit state curve, the failure probability calculation based on the slope limit state curve is made more reliable, thereby improving the accuracy of the slope stability assessment, enhancing the accuracy, versatility, flexibility and efficiency of the reliability analysis, and providing a more scientific basis for the safety design and disaster warning of slope projects; wherein, the normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the slope limit state curve, and the normal search particle swarm algorithm is introduced into the normal search particle swarm algorithm. The search mode, particle full-process dynamic exclusion strategy, particle memory strategy and low-density area elite particle breeding strategy enable the algorithm to better search in the continuous solution space, avoid the aggregation of optimal solutions, and ensure the uniformity and completeness of the solution set in the continuous area, thereby improving the solution accuracy of the slope limit state curve and enhancing the engineering applicability of slope reliability analysis; in the present invention, the constructed regional modal optimization model and the adopted normal search particle swarm algorithm have good versatility, can adapt to slope systems with different state variable dimensions, enhance the flexibility and applicability of the analysis method, and provide an effective tool for reliability analysis of various complex slope projects.

[0045] The slope reliability analysis system, electronic equipment, computer-readable storage medium and computer program product provided by the present invention have all the advantages of the above-mentioned slope reliability analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flowchart of the slope reliability analysis method provided in Example 1;

[0047] Figure 2 Schematic diagram comparing the traditional point search mode and the normal search mode in Example 1;

[0048] Figure 3Schematic diagram of the local oscillation effect caused by the normal search mode in Example 1;

[0049] Figure 4 Schematic diagram of the principle of the dynamic particle exclusion strategy throughout the entire process in Example 1;

[0050] Figure 5 Schematic diagram of the principle of individual optimal position memory selection in Example 1;

[0051] Figure 6 Schematic diagram of the principle of the elite particle breeding strategy in the low-density area in Example 1;

[0052] Figure 7 This is a flow chart of the normal search particle swarm algorithm in Example 1;

[0053] Figure 8 Schematic diagram of the extreme value region of the test function in Example 1;

[0054] Figure 9 Schematic diagram of the optimization results of all algorithms in Example 1 on the test function F17;

[0055] Figure 10 Schematic diagram of the optimal solution for different diversity and uniformity in Example 1;

[0056] Figure 11 A structural block diagram of the slope reliability analysis system provided in Example 2;

[0057] Figure 12 This is a structural block diagram of the electronic device provided in Example 3. DETAILED DESCRIPTION

[0058] In order to make the technical problems, technical solutions, and beneficial effects solved by this application more clearly understood, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application; it is obvious that the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of this application.

[0059] The present invention provides a slope reliability analysis method, comprising the following steps:

[0060] Step 100: Obtain the state variables of the slope to be analyzed.

[0061] Step 200: Calculate the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; and construct a functional function of the slope to be analyzed according to the safety factor of the slope to be analyzed.

[0062] Step 300: Using the functional function of the slope to be analyzed, a regional modal optimization model for determining the slope limit state curve is established and solved to obtain the slope limit state curve of the slope to be analyzed; wherein, a normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic particle exclusion strategy, a particle memory strategy, and a low-density area elite particle breeding strategy.

[0063] Step 400: Obtain reliability analysis results of the slope to be analyzed based on the slope limit state curve of the slope to be analyzed.

[0064] The slope reliability analysis method described in the present invention adopts a normal search particle swarm algorithm to solve the regional modal optimization model used to determine the limit state curve of the slope, which can obtain a number of discrete points evenly distributed on the limit state curve, thereby realizing the accurate determination of the limit state curve, making the slope reliability analysis result highly accurate and stable; wherein, the normal search mode, the particle full process dynamic exclusion strategy, the particle memory strategy and the low-density area elite particle breeding strategy are introduced into the normal search particle swarm algorithm, so that the algorithm can better search in the continuous solution space, avoid the aggregation of the optimal solution, and ensure that the solution set is in the continuous area. uniformity and completeness; secondly, by introducing multiple strategies into the normal search particle swarm algorithm, it helps to improve the search efficiency and convergence speed of the algorithm, making the solution process of the regional modal optimization model faster, thereby improving the efficiency of the entire slope reliability analysis; specifically, by introducing the normal search mode, particles can be guided to search towards the optimal solution faster; the introduction of the particle full-process dynamic exclusion strategy can prevent particles from falling into the local optimal solution; the introduction of the particle memory strategy can retain the historical information of the particles and accelerate the search process; the introduction of the low-density area elite particle breeding strategy can increase the diversity of the population and improve the global search capability of the algorithm.

[0065] The slope reliability analysis method provided by the present invention is further explained below with some specific examples:

[0066] Example 1

[0067] As attached Figure 1 As shown, this embodiment 1 provides a slope reliability analysis method, including the following steps:

[0068] Step 1: Obtain the state variables of the slope to be analyzed, wherein the state variables of the slope to be analyzed include the soil cohesion, internal friction angle, and gravity of the slope to be analyzed.

[0069] Step 2: Based on the state variables of the slope to be analyzed, calculate the safety factor of the slope to be analyzed; and construct the functional function of the slope to be analyzed based on the safety factor of the slope to be analyzed. Specifically, the process is as follows:

[0070] Step 21: Based on the state variables of the slope to be analyzed, the safety factor of the slope to be analyzed is calculated using the finite element sliding surface stress method.

[0071] Step 22: Construct a functional function of the slope to be analyzed based on the safety factor of the slope to be analyzed; wherein the functional function of the slope to be analyzed is:

[0072] G(X)=FS(X)-1

[0073] Among them, G(X) is the performance function of the slope to be analyzed; FS(X) is the safety factor of the slope to be analyzed; and X is the state variable of the slope to be analyzed.

[0074] Step 3: Using the functional function of the slope to be analyzed, a regional modal optimization model for determining the slope limit state curve is established and solved to obtain the slope limit state curve of the slope to be analyzed; wherein, a normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic exclusion strategy for particles, a particle memory strategy, and a low-density area elite particle breeding strategy.

[0075] In this embodiment 1, the absolute value of the performance function of the slope to be analyzed is taken and the minimum value is obtained, thereby obtaining a regional modal optimization model for determining the limit state curve of the slope. The regional modal optimization model for determining the limit state curve of the slope is as follows:

[0076] min|G(X)|,subject to:X∈Ω

[0077] X=[X1,X2,…,X d ]

[0078] Ω=[L1,U1]×[L2,U2]×…×[L g ,U g ]×…×[L d ,U d ]

[0079] Where Ω is the feasible domain of the optimization problem, which is a d-dimensional hyperrectangular region consisting of the state variable constraint interval of the slope to be analyzed; X d is the d-th dimension state variable of the slope to be analyzed, d is the dimension of the state variable of the slope to be analyzed; L g is the maximum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed, g∈[1,d]; U gis the minimum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed.

[0080] It should be noted that the optimal solution of the regional modal optimization model used to determine the limit state curve of the slope is a continuous region, and the optimization problem with the optimal solution as a continuous region is named regional modal optimization problems (RMOPs); the normal search particleswarm optimization algorithm (NSPSO) is used to try to solve RMOPs by using the idea of discretization of the solution set, that is, using a number of discrete points uniformly distributed on the optimal solution to represent the optimal solution; specifically, the normal search particle swarm algorithm is used to solve the regional modal optimization model used to determine the limit state curve of the slope. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic exclusion strategy for particles, a particle memory strategy, and a low-density area elite particle breeding strategy.

[0081] In this embodiment 1, the normal search mode is to expand the point search in the traditional algorithm to the regional search, taking into full consideration the characteristics of RMOPs. The most essential feature of RMOPs is that the optimal solution has continuity, which makes it very different from traditional optimization problems. When solving existing optimization problems, traditional algorithms make particles converge toward one or more points, such as the following. Figure 2 The normal search mode guides the particles to search in the normal direction of the line connecting their optimal neighbor particles (two-dimensional problems) or the hyperplane formed by the optimal neighbor particles (three-dimensional and above problems), as shown in the attached figure. Figure 2 As shown in area B in the middle; it can be seen that the normal search mode can enable multiple particles to move towards multiple positions in the extreme region, rather than searching within a small range in the extreme region; the normal search mode fully considers the continuity of the optimal solution of RMOPs, which can ensure that the optimization results are better distributed in the entire extreme region, which is conducive to ensuring the diversity of solutions.

[0082] For n-dimensional optimization problems, the normal search mode establishes a new search mode that guides particles to explore in the direction of their neighborhood hyperplane; wherein, the neighborhood hyperplane is composed of the individual extreme positions of neighboring particles, and the selection of neighboring particles is evaluated using Euclidean distance, that is, when the neighborhood size is ns, the ns particles with the closest Euclidean distance to the particle are taken as its neighborhood; specifically, when RMOPs is two-dimensional, the particle searches along the normal direction of the line connecting the individual extreme positions of its two neighboring particles; when it is three-dimensional, the particle searches along the normal direction of the plane formed by the individual extreme positions of the three neighboring particles in its neighborhood; and so on. When the problem is n-dimensional, the particle searches along the normal direction of the hyperplane formed by the individual extreme positions of its n neighboring particles.

[0083] It should be noted that, although the algorithm optimization mode described above can be used for fast search, when the particle has reached the extreme value, a small oscillation may still occur. This phenomenon occurs mainly because when the particle reaches the extreme value, the normal search strategy will still drive the particle to move in the normal direction of its neighborhood hyperplane, that is, the algorithm's guidance position is inconsistent with the expected convergence position. Figure 3 As shown; To solve the local oscillation problem caused by the normal search mode, an adaptive activation-freeze strategy is introduced into the normal search mode, that is, before the iterative convergence, the normal search mode is activated, and after convergence, the normal search mode is frozen; Therefore, the implementation method of the normal search mode with the adaptive activation-freeze strategy introduced in this embodiment 1 is as follows:

[0084]

[0085] Among them, N i (t) is the final normal search vector of the i-th particle at the t-th iteration; n i (t) is the initial normal search vector of the i-th particle in the t-th iteration; is the particle p at the tth iteration i Normal search vector; δ is the freezing factor; f(x i (t)) is the fitness function value of the position of the i-th particle at the t-th iteration; f(p g (t)) is the individual's historical optimal fitness function value at the tth iteration; is the neighborhood hyperplane formed by the neighboring particles of the i-th particle; is the unit vector of the neighborhood hyperplane formed by the i-th particle pointing to the i-th particle's neighboring particles at the t-th iteration; is the Euclidean distance between the i-th particle and the neighborhood hyperplane formed by the i-th particle's neighboring particles at the t-th iteration; is the particle p at the tth iteration iThe Euclidean distance between the particle and the neighborhood hyperplane formed by the neighboring particles of the i-th particle.

[0086] It should also be noted that the normal search mode of the adaptive activation-freeze strategy is mainly introduced by adding a counter-term after the normal search term; the counter-term includes a coefficient and the product of the normal search term of the individual extreme position of the particle; the observation coefficient It can be seen that when the function value at the location of particle i differs greatly from the global extreme value, the coefficient is very small, that is, the offset term is very small, so that the normal search is not affected by the offset term, and it is in the normal search activation stage; when particle i approaches the extreme value area through multiple updates, the difference between the function value at its location and the global extreme value will gradually decrease, and the offset term coefficient will gradually increase, which will reduce the normal search term of particle i until particle i reaches the extreme value area, that is, f(x i (t))=f(p g (t)), the normal search term is completely offset and is in the normal search freezing stage. At this time, particle i will converge to a point on the extreme value region.

[0087] In this embodiment 1, by introducing a dynamic exclusion strategy for particles throughout the entire process, a certain distance can be maintained between particles, effectively avoiding the aggregation of particles during the optimization process, and ensuring that the solution set density is controllable and the diversity of solutions is achieved; the idea of discrete extreme points approximating continuous regions is adopted to solve RMOPs; therefore, the distribution breadth of the algorithm solution set is crucial, that is, the solution set must be able to well cover the entire optimal solution; and for different actual optimization problems, the required solution density is different; the particle full-process dynamic exclusion strategy adopts the method of, during the entire iterative process, when the distance between a particle and its nearest neighbor particle is less than the exclusion distance d rep When the particle is given a component velocity that repels the particles outside the line connecting the two particles, so that a certain distance is maintained between the particles. Figure 4 As shown; from the attached Figure 4 It can be seen that particles a and b are each other's nearest neighbor particles. When the Euclidean distance between them is less than the repulsive distance d rep When the velocity of particles a and b increases along the direction of the arrow, the same applies to particles c and d. Correspondingly, the Euclidean distance between particles a and f, and d and e is greater than the repulsive distance d. rep , it will not be affected by the repulsion between particles; the implementation of the dynamic repulsion strategy of the whole particle process can be achieved by controlling the repulsion distance d rep To control the density of the final solution set, on-demand optimization is achieved, which greatly saves the computational overhead of the optimization process; in addition, the implementation of the exclusion strategy can further avoid the problem of solution aggregation.

[0088] Specifically, the dynamic particle exclusion strategy for the entire process is as follows:

[0089]

[0090] Among them, r i (t) is the repulsion vector of the i-th particle at the t-th iteration; is the distance from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; d rep is the repulsion distance; is the unit vector from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; i (t) is the position of the i-th particle at the t-th iteration; is the position of the nearest neighbor particle of the i-th particle at the t-th iteration; ||*|| is the L2 norm.

[0091] It should be noted that the introduction of the dynamic exclusion strategy for particles throughout the entire process makes it possible for particles to adjust their positions after reaching the extreme value area. Therefore, particles need to find extreme values in new areas without being disturbed by the previous extreme value positions. To this end, a particle memory strategy is introduced in this embodiment 1 to achieve the forgetting of particles' older information, thereby improving the convergence of the algorithm.

[0092] The selection of the optimal position of an individual particle in the neighborhood is the key to determining the search direction of the particle. The implementation of the exclusion strategy makes it possible for the particle to adjust its position after reaching the extreme value area. Therefore, the particle needs to find the extreme value in the new area without being disturbed by the previous extreme value position. In the past, the time span considered in the selection of the optimal position of an individual particle was from the beginning of the iteration to the current iteration, which made it impossible for the particle to forget the older information, making it difficult to find a new extreme value position in the new area. Figure 5 As shown; from the attached Figure 5 As can be seen in the figure, particle a selects neighboring particles b1 and b2. The optimal positions before particles b1 and b2 are c1 and c2, and the closest optimal positions are c3 and c4. In fact, particles c1 and c2 move to c3 and c4 under the influence of the exclusion strategy. If the selection of individual optimal positions is based on the individual optimal positions throughout the entire iterative history, particle a will move along the normal direction of the line connecting c1 and c2 (indicated by the green arrow), which is obviously incorrect. This is because extreme points already exist at the positions of c1 and c2, and if new extreme points appear, the particle will also move to other locations to seek optimal solutions under the exclusion strategy. However, if the memory step size k is considered in the selection of individual optimal positions, that is, the individual optimal position is selected from iteration tk to iteration t, then the particle can move toward the normal direction of the line connecting the more recent individual optimal positions c3 and c4 in its neighborhood (indicated by the yellow arrow) to explore other optimal solution locations.

[0093] In this embodiment 1, a particle memory strategy is introduced, that is, the historical optimal position of the particle is selected within the memory step size k, so as to assist the particle iterative convergence process and continuously adjust the individual optimal position under the action of the particle repulsion strategy, thereby facilitating the search for new extreme points by particles in the population; wherein, if k is too large, the possibility of particle aggregation is greater; on the contrary, if k is too small, the particle optimization search and exploration capabilities are weaker.

[0094] Specifically, the particle memory strategy is as follows:

[0095]

[0096] Among them, p i (t) is the historical optimal position of the i-th particle at the t-th iteration; f(x i (τ)) is the fitness function value of the position of the i-th particle at the τ-th iteration; x i (τ) is the position of the i-th particle at the τ-th iteration; k is the memory step size.

[0097] Since the optimal solution of RMOPs is continuous, there must be extreme points near the extreme points. Based on this, this embodiment 1 designs a low-density area elite particle breeding strategy to improve the optimization efficiency of the algorithm. That is, a part of the particles is first used for optimization, and then the better particles (i.e., elite particles) are selected and bred near them to generate new particles for optimization.

[0098] The continuity of the RMOPs optimal solution determines that there must be extreme points near the extreme points. If a part of the particles are used for optimization first, the distribution of the extreme area can be roughly explored; then the extreme point particles (elite particles) are reproduced, the entire optimization process can be completed more quickly; at the same time, if a local extreme area is not searched, the elite reproduction method can make up for the blind spot of the original search in time, and at the same time ensure the efficiency of the NSPSO algorithm optimization process and the distribution breadth of the optimization results.

[0099] As attached Figure 6 As shown, attached Figure 6 The schematic diagram of the principle of the elite particle breeding strategy in the low-density area is given in ; specifically, the elite particle breeding strategy in the low-density area is as follows:

[0100] When the number of extreme value points of particles in the population reaches the preset ratio of the total number of current particles, each particle in the population is taken as the center and the cutoff distance R is used to calculate the number of extreme value points of particles in the population. cut As the radius, count the number of particles within the cutoff radius of each particle to obtain the density of each particle; according to the density of each particle, perform elite particle reproduction in the low-density area; wherein, the low-density area is the area where the density of particles is less than the preset density threshold; specifically, with the low-density area particle as the center, randomly generate n particles within the cutoff radius. bparticles (i.e., the reproduction intensity is n b ); continue iterating and optimizing until the ratio of the number of new extreme points in the population to the total number of new particles is greater than the reproduction ratio limit; continue breeding and optimizing until the number of particles in the population reaches the requirement.

[0101] As attached Figure 7 As shown in FIG, the implementation process of the normal search particle swarm algorithm is as follows:

[0102] Step 1. Initialize relevant variables, including the basic parameters of the particle swarm algorithm, neighborhood size, memory step, repulsion distance and reproduction parameters; among them, each particle in the particle swarm algorithm represents a set of possible values of the slope state variable X to be analyzed.

[0103] Step 2: Calculate the fitness value of each particle (i.e., the objective function value) and determine the global optimal particle position p of the population. g (t).

[0104] Step 3. Calculate the Euclidean distance between particles, determine the particle neighborhood based on the neighborhood size, and implement a normal search strategy to guide the particles to move in the normal direction of their neighborhood hyperplane, so that the particles evenly cover the entire optimal solution area instead of gathering in certain locations.

[0105] Step 4. Determine the size of the repulsion distance during the particle optimization process and implement a particle repulsion strategy to ensure the diversity and uniformity of the solution. When there are close neighboring particles near a particle, the implementation of the repulsion strategy will cause the two to bounce off each other, thereby avoiding the problem of particle aggregation.

[0106] Step 5: Implement the particle memory strategy to determine the individual optimal position of each iteration; the implementation of the particle memory strategy can help particles forget older information, which is beneficial for particles to find extreme points in new areas.

[0107] Step 6. Update the particle velocity and position. The update formula for particle velocity and position is as follows:

[0108]

[0109] x i (t+1)=x i (t)+v i (t+1)

[0110] Among them, v i (t+1) is the velocity of the i-th particle at the t+1th iteration; χ is the inertia weight, -0.16199<χ<0.78540; v i (t) is the velocity of the i-th particle at the t-th iteration; is the individual learning factor; is the group learning factor, r1 and r2 are random numbers in the interval [0,1]; p i (t) is the historical optimal position of the i-th particle at the t-th iteration; N i (t) is the final normal search vector of the i-th particle at the t-th iteration; r i (t-1) is the repulsion vector of the i-th particle at the t-1th iteration; r i (t) is the repulsion vector of the i-th particle at the t-th iteration; (·) N When the tth iteration reaches N i The projection vector of (t); When the tth iteration reaches N i The length of the projection vector of (t); N i The unit vector of (t); x i (t+1) is the position of the i-th particle at the t+1-th iteration.

[0111] Step 7. Determine whether the particle speed and position are out of bounds. When the particle speed is out of bounds, reset the out-of-bounds speed of the particle according to the speed reset formula. If the particle position is out of bounds, reset the out-of-bounds position of the particle using the position reset formula.

[0112] The speed reset formula is as follows:

[0113]

[0114] Among them, v i (t+1)' is the velocity of particle i after reset at the t+1th iteration; v max The maximum limit of particle velocity.

[0115] Among them, the position reset formula is as follows:

[0116]

[0117] Among them, x i (t+1)' is the position of particle i after reset at the t+1th iteration; x max is the maximum position limit of the particle; x min is the minimum position limit of the particle.

[0118] Step 8. When the particle density is lower than the minimum allowed density Ma, the low-density area elite particle strategy is implemented to achieve the optimization of the algorithm using a small number of particles in the initial stage, and fix the final number of particles for optimization, and perform multiple reproductions in the middle to ensure the high efficiency of the NSPSO algorithm in optimization.

[0119] Step 9. Set the iteration termination condition to: the minimum particle density is greater than the breeding density limit and 95% of the particles have converged. When the iteration termination condition is met or the maximum number of iterations is reached, the algorithm ends and the results are output; otherwise, return to Step 2.

[0120] Step 4: Obtain the reliability analysis results of the slope to be analyzed based on the slope limit state curve of the slope to be analyzed. The specific process is as follows:

[0121] Step 41: construct a proxy model of the slope limit state curve of the slope to be analyzed based on the slope limit state curve of the slope to be analyzed. Specifically, when the slope limit state curve is determined using the normal search particle swarm algorithm, the particle positions and corresponding fitness function values of the entire optimization history are used to construct the proxy model of the slope limit state curve of the slope to be analyzed.

[0122] Step 42: Using the Monte Carlo simulation algorithm and combining it with the slope limit state curve proxy model of the slope to be analyzed, the response values of several sampling points in the design space of the slope to be analyzed are obtained; wherein, N is generated in the design space based on the Latin cube sampling method. MCS sampling points and adopting a proxy model Calculate its response value.

[0123] Step 43: Calculate the failure probability of the slope to be analyzed based on the response values of several sampling points within the design space of the slope to be analyzed, that is, obtain the reliability analysis result of the slope to be analyzed. The process of calculating the failure probability of the slope to be analyzed is as follows:

[0124]

[0125] Among them, P f,s is the failure probability of the slope to be analyzed; N MCS is the number of sampling points; I[*] is the indicator function, when When I[*] is equal to 1, otherwise it is 0; For the proxy model When the input is X τ The response value when .

[0126] Performance verification of normal search particle swarm algorithm:

[0127] The algorithm performance is tested using test functions to verify the effectiveness of the NSPSO algorithm in solving RMOPs. In Example 1, 20 test functions are constructed based on the CEC2013 standard test function set for multimodal optimization problems, including 10 binary test functions and 10 ternary test functions. Based on a sensitivity analysis of the key control parameters of the NSPSO algorithm, recommended values of the parameters are given. Although there is currently no relevant algorithm for solving RMOPs, when the solution set discretization idea is used to solve RMOPs, multimodal optimization algorithms can also be used to solve such problems. Therefore, the optimization effects of 9 advanced multimodal optimization algorithms and the NSPSO algorithm on the 20 test functions are compared to verify the superiority of the NSPSO algorithm in solving RMOPs.

[0128] (1) Test function construction

[0129] Current optimization algorithms are mainly used to solve single-mode, multi-mode, and multi-objective optimization problems. There are no algorithms or test functions related to RMOPs. Therefore, in Example 1, ten binary and ten ternary test functions were constructed to test the performance of the algorithm.

[0130] Specifically, test functions F1-F20 are designed to verify the optimization effect of the algorithm in different dimensions and complexities; among them, test functions F1-F10 are two-dimensional problems, and test functions F11-F20 are three-dimensional problems; test functions F1-F5 and test functions F11-F15 have a single optimal solution region, while test functions F6-F10 and test functions F16-F20 have multiple optimal solution regions; the basic information and extreme value regions of the test functions are shown in Table 1 and Appendix. Figure 8 It is worth noting that the attached Figure 8 The optimal solution obtained by minimizing the test function is the extreme value region, not the image of the test function itself.

[0131] Table 1 Basic information of test function

[0132]

[0133]

[0134] (2) Performance evaluation indicators

[0135] In this embodiment 1, the inverse generation distance standard deviation (IGD_S) is proposed to measure the diversity and convergence of the regional modal optimization algorithm. It should be noted that IGD_S is a comprehensive indicator. The smaller the value of this indicator, the better the convergence and diversity of the algorithm solution. Specifically, the inverse generation distance standard deviation is as follows:

[0136] IGD_S(O,P)=std(∑ v∈Pd(v,O))

[0137] Where IGD_S(*) is the standard deviation of the inverse generation distance; p is a set of uniformly distributed reference points, and O represents the optimal solution obtained by the regional modal optimization algorithm. d(v,O) is the minimum distance between any point v in p and any point in the set O; std(·) is the standard deviation.

[0138] In this embodiment 1, a Hausdorff distance standard deviation (Δps) suitable for evaluating the regional modal optimization algorithm is proposed. Specifically, the Hausdorff distance standard deviation is as follows:

[0139] Δ ps (O,P,q)=max(GD_S(O,P,q),IGD_S(P,O,q))

[0140]

[0141] Among them, Δ ps (*) is the standard deviation of the Hausdorff distance; q is the outlier penalty parameter. The larger q is, the greater the penalty for outliers. q = 1.5 is taken; GD_S(*) is the standard deviation of the generational distance.

[0142] In this embodiment 1, the performance evaluation indicators also include spacing (SP) and effective optimal solution rate (EOR); spacing (SP) is a measure of the uniformity of the solution obtained by calculating the standard deviation of the distance between each solution obtained by the algorithm optimization and its nearest solution; the effective optimal solution rate (EOR) is used to measure the convergence of the algorithm.

[0143] Specifically, the calculation formula for the spacing (SP) is as follows:

[0144]

[0145] Wherein, SP is the spacing; is the average of the Euclidean distances between all solutions and their nearest solution, dis i is the Euclidean distance between particle i and its nearest solution.

[0146] The calculation formula for the effective optimal solution rate (EOR) is as follows:

[0147]

[0148] Among them, EOR is the effective optimal solution rate; N eop Np is the number of effective optimal solutions obtained by the algorithm. Points gathered in one place are regarded as an effective optimal solution. end is the final population size.

[0149] (3) Comparative experiment

[0150] Ten advanced multi-mode optimization algorithms are used to compare with the NSPSO algorithm; among them, the ten advanced multi-mode optimization algorithms include al-1:NMMSO, al-2:LIPS, al-3:FERPSOLS, al-4:NCDE, al-5:r2pso-lhc, al-6:RS-CMSA-ESII, al-7:DP-MSCC-ES, al-8:MAMO and al-9:MMFOA.

[0151] (4) The main parameter settings of the NSPSO algorithm include: neighborhood size ns = d + 4; memory step k = 25; exclusion distance d rep =A; the reproduction ratio limit Bp = 50%; the reproduction intensity nb is 1 when the optimization problem is two-dimensional and 2 when the optimization problem is three-dimensional.

[0152] To ensure the fairness of the comparison, the NSPSO parameter values of all test functions are fixed. In addition, the fixed parameter values can further verify the robustness and robustness of the NSPSO algorithm in solving various RMOPs. The final population size (Np end ), the maximum number of function evaluations (MFE) and the allowable error (ε f ) settings, as shown in Table 2; among them, the initial population size (NP ini ) and the final population size (Np end ) are equal; all algorithms are optimized 50 times independently on 20 test functions.

[0153] Table 2 Basic parameter settings of all algorithms

[0154]

[0155] (5) Test result description:

[0156] As attached Figure 9 As shown, attached Figure 9 A schematic diagram of the optimization results of all algorithms on the test function F17 is given in Figure 3; the rank sum test at the confidence level p = 0.05 is used to compare the optimization results of each algorithm. The symbols "+", "-" and "~" respectively indicate that the optimization effect of the NSPSO algorithm is significantly better than, significantly worse than, and similar to the comparison algorithm; the performance index calculation results of the NSPSO algorithm and the comparison algorithm after optimization are shown in Tables 3 to 6, and the calculation results of the algorithm with the best performance on each test function are displayed in bold.

[0157] Table 3 Mean and standard deviation of IGD_S of each algorithm after running 50 times

[0158]

[0159]

[0160] Table 4 Mean and standard deviation of Δps of each algorithm after running 50 times

[0161]

[0162]

[0163] Table 5 Mean and variance of SP of each algorithm after running 50 times

[0164]

[0165]

[0166] Table 6 Mean and variance of EOR of each algorithm after running 50 times

[0167]

[0168]

[0169] As shown in Tables 3-4, Tables 3 and 4 give the mean and standard deviation of the performance indicators IGD_S and Δps respectively. The smaller the values of the performance indicators IGD_S and Δps, the better the diversity of the algorithm optimization. Figure 10 As shown, attached Figure 10 The schematic diagram of the optimal solution for different diversity and uniformity in Example 1 is given in FIG. Figure 10 (a) has good diversity and uniformity, while the attached Figure 10 (b) shows that the uniformity of the solution is good but the diversity is poor; from the above Tables 3 and 4 and the attached Figure 10 It can be seen that the performance indicators IGD_S and Δps calculated by the optimization results of the NSPSO algorithm described in Example 1 are significantly better than those of the comparison algorithms, indicating that the NSPSO algorithm can well cover the optimal solution area of ROMPs; the standard deviations of the performance indicators IGD_S and Δps calculated by the NSPSO are small, indicating that the NSPSO algorithm is highly robust, thanks to the normal search mode and particle dynamic exclusion strategy of the algorithm.

[0170] As shown in Table 5, the mean and variance of the performance index SP are given in Table 5. The index SP is used to indicate the uniformity of the distribution of the optimal solutions obtained by each algorithm. A better uniformity indicates that the particles can be more evenly distributed in the optimal solution area. Figure 10 As shown, attached Figure 10 The schematic diagram of the optimal solution for different diversity and uniformity in Example 1 is given in FIG. Figure 10 (a) has good uniformity and diversity, and Figure 10(c) has good diversity but poor uniformity; from Table 5 and the attached Figure 10 As can be seen from the figure, the poor uniformity of the algorithm's optimization results indicates that the distribution of particles in the extreme value regions is uneven, meaning that some extreme value regions are still uncovered. In the NSPSO algorithm, the implementation of the dynamic exclusion strategy acts on all particles throughout the entire iteration process, which can maintain a relatively fixed distance between particles. The density-based elite reproduction strategy can release new particles to areas with low particle density. The former ensures that particles do not aggregate locally, while the latter improves the optimization effect of particles in low-density areas. The combined implementation of the two ensures the uniformity of the solution obtained by the NSPSO. In comparison, the results obtained by the comparison algorithm are unsatisfactory and unstable.

[0171] As shown in Table 6, Table 6 shows the EOR mean and variance calculated from the optimization results of each algorithm. It can be seen from Table 6 that the EOR of most comparison algorithms is low, which is caused by the clustering phenomenon caused by the point search mode of the multi-mode optimization algorithm. At the same time, it can be seen that the optimization effect of the NSPSO algorithm is significantly better than that of other comparison algorithms. Its excellent effect is attributed to the fact that the NSPSO algorithm grasps the essence of the continuity of the RMOPs solution set and adopts the normal search mode for optimization. This is the most essential difference between it and other multi-mode optimization algorithms.

[0172] Example 2

[0173] As attached Figure 11 As shown, this embodiment 2 provides a slope reliability analysis system, including a variable acquisition module, a function construction module, a limit state curve solving module and a reliability analysis module.

[0174] The variable acquisition module is used to obtain the state variables of the slope to be analyzed; the function construction module is used to calculate the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; and the functional function of the slope to be analyzed is constructed according to the safety factor of the slope to be analyzed; the limit state curve solving module is used to use the functional function of the slope to be analyzed to establish and solve the regional modal optimization model for determining the limit state curve of the slope to be analyzed, and obtain the slope limit state curve of the slope to be analyzed; among them, the normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the limit state curve of the slope. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic exclusion strategy of particles, a particle memory strategy, and a low-density area elite particle breeding strategy; the reliability analysis module is used to obtain the reliability analysis results of the slope to be analyzed according to the slope limit state curve of the slope to be analyzed.

[0175] Example 3

[0176] As attached Figure 12As shown, this embodiment 3 provides an electronic device, including: a memory for storing a computer program; a processor for implementing the steps of the slope reliability analysis method when executing the computer program; or, when the processor executes the computer program, implementing the functions of each module in the above-mentioned slope reliability analysis system.

[0177] Exemplarily, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to implement the present invention. The one or more modules / units may be a series of computer program instruction segments capable of implementing preset functions, and the instruction segments are used to describe the execution process of the computer program in the electronic device.

[0178] The electronic device may be a computing device such as a desktop computer, laptop, PDA, or cloud server. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will appreciate that the above are examples of electronic devices and do not constitute a limitation on electronic devices. The electronic device may include more components than those described above, or a combination of certain components, or different components. For example, the electronic device may also include input and output devices, network access devices, buses, etc.

[0179] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the electronic device, connecting various parts of the entire electronic device using various interfaces and lines.

[0180] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the electronic device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0181] The memory may mainly include a program storage area and a data storage area. The program storage area may store an operating system and at least one application required for a function (such as a sound playback function, an image playback function, etc.); the data storage area may store data created based on the use of the mobile phone (such as audio data, a phone book, etc.). In addition, the memory may include a high-speed random access memory and may also include a non-volatile memory, such as a hard disk, internal memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0182] The slope reliability analysis method described in the present invention uses a normal search particle swarm algorithm to solve a regional modal optimization model used to determine the slope limit state curve. This method can obtain a number of discrete points evenly distributed on the limit state curve, achieve accurate determination of the limit state curve, and ensure that the obtained slope reliability analysis results are highly accurate and stable. The normal search particle swarm algorithm has high convergence, diversity, and uniformity when solving the regional modal optimization problem, thereby improving the accuracy of solving the slope limit state curve and enhancing the engineering applicability of slope reliability analysis.

[0183] The above embodiment is only one of the implementation methods that can realize the technical solution of the present invention. The scope of protection claimed by the present invention is not limited only to this embodiment, but also includes changes, replacements and other implementation methods that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention.

Claims

1. A slope reliability analysis method, characterized in that: include: Obtain the state variables of the slope to be analyzed; Calculate the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; And according to the safety factor of the slope to be analyzed, the functional function of the slope to be analyzed is constructed; Using the functional function of the slope to be analyzed, a regional modal optimization model for determining the slope limit state curve is established and solved to obtain the slope limit state curve of the slope to be analyzed. The normal search particle swarm algorithm is used to solve the regional modal optimization model for determining the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic particle exclusion strategy, a particle memory strategy, and a low-density area elite particle breeding strategy. According to the slope limit state curve of the slope to be analyzed, the reliability analysis result of the slope to be analyzed is obtained.

2. A slope reliability analysis method according to claim 1, characterized in that: The state variables of the slope to be analyzed include the soil cohesion, internal friction angle and gravity of the slope to be analyzed.

3. A slope reliability analysis method according to claim 1, characterized in that: The regional modal optimization model used to determine the slope limit state curve is as follows: min|G(X)|,subject to:X∈Ω X=[X1,X2,…,X d ] Ω=[L1,U1]×[L2,U2]×…×[L g ,And g ]×…×[L d ,And d ] Where G(X) is the performance function of the slope to be analyzed; X is the state variable of the slope to be analyzed; Ω is the feasible region of the optimization problem; X d is the d-th dimension state variable of the slope to be analyzed, d is the dimension of the state variable of the slope to be analyzed; L g is the maximum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed, g∈[1,d]; U g is the minimum value limit of the g-th dimension state variable in the state variables of the slope to be analyzed.

4. A slope reliability analysis method according to claim 1, characterized in that: Normal search mode, as follows: Among them, N i (t) is the final normal search vector of the i-th particle at the t-th iteration; n i (t) is the initial normal search vector of the i-th particle in the t-th iteration; is the particle p at the tth iteration i Normal search vector; δ is the freezing factor; f(x i (t)) is the fitness function value of the position of the i-th particle at the t-th iteration; f(p g (t)) is the individual's historical optimal fitness function value at the tth iteration; is the neighborhood hyperplane formed by the neighboring particles of the i-th particle; is the unit vector of the neighborhood hyperplane formed by the i-th particle pointing to the i-th particle's neighboring particles at the t-th iteration; ns is the neighborhood size; is the Euclidean distance between the i-th particle and the neighborhood hyperplane formed by the i-th particle's neighboring particles at the t-th iteration; is the particle p at the tth iteration i The Euclidean distance between the particle and the neighborhood hyperplane formed by the neighboring particles of the i-th particle.

5. A slope reliability analysis method according to claim 1, characterized in that: The dynamic exclusion strategy for particles throughout the entire process is as follows: Among them, r i (t) is the repulsion vector of the i-th particle at the t-th iteration; is the distance from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; d rep is the repulsion distance; is the unit vector from the position of the nearest neighbor particle of the i-th particle at the t-th iteration to the position of the i-th particle at the t-th iteration; i (t) is the position of the i-th particle at the t-th iteration; is the position of the nearest neighbor particle of the i-th particle at the t-th iteration; ||*|| is the L2 norm.

6. A slope reliability analysis method according to claim 1, characterized in that: The particle memory strategy is as follows: Among them, p i (t) is the historical optimal position of the i-th particle at the t-th iteration; f(x i (τ)) is the fitness function value of the position of the i-th particle at the τ-th iteration; x i (τ) is the position of the i-th particle at the τ-th iteration; k is the memory step size.

7. A slope reliability analysis method according to claim 1, characterized in that: The elite particle breeding strategy in the low-density area is as follows: When the number of extreme value points of particles in the population reaches a preset proportion of the total number of current particles, the number of particles within the cutoff radius of each particle is counted with each particle in the population as the center and the cutoff distance as the radius to obtain the density of each particle; According to the density of each particle, elite particles are bred in low-density areas; the low-density area is an area where the density of particles is less than a preset density threshold; Continue iterating and optimizing until the ratio of the number of new extreme points in the population to the total number of new particles is greater than the reproduction ratio limit; Continue to reproduce and optimize until the number of particles in the population reaches the requirement.

8. A slope reliability analysis method according to claim 1, characterized in that: The process of obtaining the reliability analysis result of the slope to be analyzed based on the slope limit state curve of the slope to be analyzed includes: According to the slope limit state curve of the slope to be analyzed, a slope limit state curve proxy model of the slope to be analyzed is constructed; Using the Monte Carlo simulation algorithm and combining it with the slope limit state curve proxy model of the slope to be analyzed, the response values of several sampling points in the design space of the slope to be analyzed are obtained; According to the response values of several sampling points in the design space of the slope to be analyzed, the failure probability of the slope to be analyzed is calculated, that is, the reliability analysis result of the slope to be analyzed is obtained.

9. A slope reliability analysis system, characterized in that: include: Variable acquisition module, used to obtain the state variables of the slope to be analyzed; A function construction module for calculating the safety factor of the slope to be analyzed based on the state variables of the slope to be analyzed; And according to the safety factor of the slope to be analyzed, the functional function of the slope to be analyzed is constructed; The limit state curve solving module is used to establish and solve the regional modal optimization model used to determine the slope limit state curve using the functional function of the slope to be analyzed, thereby obtaining the slope limit state curve of the slope to be analyzed. The normal search particle swarm algorithm is used to solve the regional modal optimization model used to determine the slope limit state curve. The normal search particle swarm algorithm is a particle swarm algorithm that introduces a normal search mode, a full-process dynamic particle exclusion strategy, a particle memory strategy, and a low-density area elite particle breeding strategy. The reliability analysis module is used to obtain the reliability analysis result of the slope to be analyzed according to the slope limit state curve of the slope to be analyzed.

10. An electronic device, characterized in that: include: a processor suitable for executing a computer program; A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the slope reliability analysis method according to any one of claims 1 to 8 is executed.

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