Slope safety coefficient probability evaluation and control method fusing uncertainty modeling and multi-objective optimization

Abstract

The invention relates to the technical field of slope stability analysis, and particularly discloses a slope safety coefficient probability evaluation and control method fusing uncertainty modeling and multi-objective optimization, and the method comprises the steps: S01, obtaining disturbance input and parameter samples, and inputting the disturbance input and the parameter samples to obtain a probability distribution function; s02, inputting the probability distribution function as feedback information of strategy optimization into a reinforcement learning strategy optimization module, updating an environment state and continuously optimizing a control strategy; s03, a reinforcement learning strategy optimization module forms a closed loop structure of disturbance-evaluation-control-re-evaluation; s04, a probability inversion feedback module is started to conduct inversion analysis, a parameter sample interval inducing instability is output, and real-time early warning is provided in combination with a monitoring system, and the method aims at achieving deep coupling of dynamic prediction, risk quantification and strategy control of the slope safety state under the multi-source uncertain disturbance condition.

Description

Technical Field

[0001] This application relates to the field of slope stability analysis technology, and specifically discloses a method for probabilistic assessment and control of slope safety factor that integrates uncertainty modeling and multi-objective optimization. Background Technology

[0002] Slope stability analysis, as a crucial research area in geotechnical engineering and geological disaster prevention, has long been a core issue in interdisciplinary research involving soil mechanics, engineering geology, and hydrogeology. With the expansion of urban construction into mountainous and geologically complex regions, and the increasing number of large-scale infrastructure projects such as highways, railways, reservoirs, and mines, geological disasters caused by slope instability are becoming more frequent, sudden, and widespread, seriously threatening the safety of people's lives and property and the stability of engineering operations. Therefore, how to scientifically and accurately assess slope stability and formulate effective control and early warning strategies has become a critical technical problem urgently needing to be solved in this field.

[0003] Traditional slope stability analysis primarily relies on numerical calculation methods such as the limit equilibrium method, finite element method, and finite difference method. These methods offer high computational accuracy under static conditions and can quantitatively analyze the location of the slip surface and the safety factor. However, with increasing uncertainties in engineering environments, such as frequent disturbances like heavy rainfall, earthquakes, and blasting, slope stability assessment is gradually shifting from deterministic calculations to uncertainty analysis. In recent years, probabilistic reliability methods have developed rapidly. Monte Carlo simulation, Latin hypercube sampling, and the first-order second-moment method (FORM / SORM) are widely used to quantitatively calculate the distribution characteristics of slope safety factors and the probability of instability, providing important data for slope risk assessment.

[0004] Meanwhile, with the development of sensing and information processing technologies, slope monitoring data is becoming increasingly comprehensive, prompting slope stability assessment methods to evolve towards intelligence and real-time capabilities. Machine learning-based slope prediction models are constantly emerging, and algorithms such as artificial neural networks, support vector machines, and decision trees have been used for sub-tasks such as landslide identification and deformation trend prediction. However, these methods are mostly based on static data fitting and are insufficient to meet the dynamic control requirements under disturbed environments.

[0005] In recent years, reinforcement learning, as an important branch of artificial intelligence, has gradually attracted attention in the engineering field due to its advantages in control strategy optimization. Although some studies have attempted to apply reinforcement learning to slope slip surface search or hydrological control scheduling, how to effectively integrate it with uncertainty modeling, probabilistic optimization, and parameter inversion is still in the exploratory stage. Therefore, constructing a slope stability analysis and control method oriented towards uncertain disturbances, multi-objective control, and capable of closed-loop feedback will help promote the advancement of slope engineering technology from "assessment" to "active intervention," and has significant theoretical value and engineering application prospects.

[0006] Currently, slope stability analysis technology is gradually evolving from traditional deterministic analysis methods towards uncertainty modeling and intelligent decision control. Among these methods, Monte Carlo simulation is widely used for slope reliability analysis. By randomly sampling uncertain factors such as soil parameters and operational disturbances, it achieves a probabilistic assessment of the slope safety factor. For example, Xu et al. proposed a slope parameter analysis method based on Monte Carlo inversion, combined with sensitivity analysis to interpret the risk distribution. This method integrates parameter inversion and risk modeling, but it still belongs to a forward static evaluation process and lacks strategy output and real-time feedback mechanisms.

[0007] Building upon this foundation, some scholars have attempted to introduce artificial intelligence (AI) technology to improve the efficiency of slope safety prediction and reliability assessment. Mohammad Aminpour et al. proposed replacing traditional limit equilibrium calculation models with random forests and neural networks to accelerate the Monte Carlo simulation process. Mohammad Aminpour et al. further constructed machine learning surrogate models to handle spatial random field problems, achieving rapid estimation of safety factors for batch samples. These methods significantly improve assessment efficiency, but remain limited to "prediction" functions and do not integrate control strategy optimization or closed-loop decision-making mechanisms, thus limiting their application value in practical engineering dynamic management.

[0008] Furthermore, in slope or similar engineering scenarios, some studies have applied reinforcement learning (RL) to auxiliary decision-making tasks. Andriotis et al. used a deep reinforcement learning model to optimize drainage facility control strategies, achieving groundwater level control under specific rainfall disturbance conditions. This study validated the feasibility of RL in complex geological systems, but its applicability is limited to groundwater regulation systems, and the model's objective is the change of state variables, not the optimization of the probability distribution of safety factors, nor does it involve parameter inversion analysis. Review studies such as "Rock Slope Stability Prediction: A Review of Machine Learning Techniques" point out that although ML technology has made progress in slope slip surface identification and deformation trend prediction, the comprehensive application of reinforcement learning in slope control remains a gap.

[0009] Based on the above existing technologies, it can be seen that the current method has the following main shortcomings: (1) Most Monte Carlo and uncertainty modeling methods are only used for assessing the probability of static instability of slopes and lack subsequent strategy adjustment mechanisms; (2) Although machine learning models can improve simulation efficiency, they are mostly limited to building "alternative models" and cannot achieve dynamic interactive optimization; (3) Reinforcement learning applications are mostly focused on single-objective control, such as water level or sliding path search, and have not yet been integrated with probability distribution optimization objectives, perturbation input mechanisms or inversion feedback systems.

[0010] Therefore, for the problem of uncertain slope stability caused by disturbances, there is currently no intelligent closed-loop optimization method that takes the probability distribution of the safety factor as the core objective, integrates Monte Carlo simulation, reinforcement learning control strategy output, and parameter inversion feedback. This invention is based on the above-mentioned technological gap and proposes an integrated slope safety factor control method that can dynamically respond to disturbance input, aims at the optimal probability distribution, and has risk inversion and strategy output functions. It makes up for the lack of strategic, feedback, and active intervention capabilities in existing technologies, and has significant engineering practical value and theoretical innovation significance.

[0011] This invention provides a method for probabilistic assessment and control of slope safety factor that integrates uncertainty modeling and multi-objective optimization, in order to solve the above-mentioned problems. Summary of the Invention

[0012] This invention addresses the significant shortcomings of current slope stability analysis methods in terms of disturbance response capability, risk control accuracy, and intelligent regulation mechanisms. It proposes a probabilistic assessment and control method for slope safety factor that integrates uncertainty modeling and multi-objective optimization. The aim is to achieve deep coupling of dynamic prediction, risk quantification, and strategy control of slope safety status under multi-source uncertain disturbance conditions.

[0013] To achieve the above objectives, the present invention provides the following basic solution: A method for probabilistic assessment and control of slope safety factor that integrates uncertainty modeling and multi-objective optimization includes the following approach: a disturbance-driven modeling module that dynamically interacts with data flow and state feedback; a safety factor probability simulation module; a reinforcement learning strategy optimization module; and a probability inversion feedback module. Step S01: Obtain the disturbance input and parameter samples , respectively and parameter samples Input is entered into the disturbance-driven modeling module and the safety factor probability simulation module to obtain the probability distribution function. ; Step S02: Convert the probability distribution function The feedback information is fed into the reinforcement learning policy optimization module as a result of policy optimization, and the reinforcement learning policy optimization module selects the control action in each round of simulation. Update the environment status and continuously optimize the control strategy; Step S03: The control results obtained by the reinforcement learning policy optimization module are reflected in the probability distribution function. In this process, a closed-loop structure of "disturbance-assessment-control-reassessment" is formed; Step S04: Introduce a monitoring system and set a preset threshold. The probability of instability detected is close to the preset threshold. The probability inversion feedback module is activated to perform inversion analysis and output the key parameter combination that induces instability. It also provides real-time early warnings in conjunction with a monitoring system.

[0014] Furthermore, the disturbance-driven modeling module also includes a stability analysis module that simulates external disturbances and inputs the disturbances. The input is fed into the stability analysis module to drive the slope response; Safety factor probability simulation module: receives parameter samples under the influence of disturbances. With disturbance input The safety factor was calculated by simulating a large number of samples using the Monte Carlo method. probability distribution function The output includes the expected value. Standard deviation Instability probability and tail indicators; The reinforcement learning policy optimization module includes a probabilistic simulation module: using the metrics output by the probabilistic simulation module as the basis for the reward function, the agent's policy function is constructed. Training reinforcement learning models to generate control actions This causes the risk indicators of the slope system to converge. Probability inversion feedback module: Probability of target instability or minimum safety threshold Perform constraint optimization on any of the terms, and invert the output to get the corresponding parameter sample interval. It also combines monitoring data to perform closed-loop correction, assisting in risk warning and adaptive updating of control parameters.

[0015] Furthermore, parameter samples ; in: Cohesion (unit: kPa); : Angle of internal friction (unit: °); : Specific density (unit: kN / m³); Elastic modulus (unit: MPa); Poisson's ratio (dimensionless); Disturbance input ,in: Rainfall intensity (unit: mm / h) can be generated based on either the Gumbel distribution or the empirical annual maximum daily rainfall. : Explosive impact intensity, the time domain distribution of which can be obtained by fitting either Poisson process modeling or measured blast records (unit: kPa); Seismic acceleration time history can be generated using either existing standard ground motion input or synthetic seismic wave model (unit: g). : Perturbation time series Disturbance input The effect on the slope seepage-mechanics coupling model is mainly achieved by regulating pore water pressure. The shear strength reduction mechanism affects the slope's strength parameters. Under rainfall disturbance, the seepage field will change the pore pressure distribution, thus affecting the effective stress and shear strength, according to the following formula: ; In the formula, The shear strength at time t (unit: kPa); Effective cohesion (unit: kPa); Total stress (unit: kPa); The pore water pressure caused by the disturbance; The effective internal friction angle (unit: °) is determined by the fact that the increase in pore pressure caused by disturbance will lead to a decrease in effective stress, thereby reducing the effective internal friction angle. This weakens the slope's shear resistance.

[0016] Furthermore, the slope seepage-mechanics coupled model will calculate the time-series safety factor in a time-step manner. : ; in, The length of the potential slip surface (in meters). The sliding surface inclination angle (unit: °); The soil's self-weight (unit: kN) is used as the basis for the safety factor probabilistic simulation module output, which includes the safety factor time series under the influence of the disturbance field. This serves as the input basis for subsequent Monte Carlo probabilistic simulations and reinforcement learning training.

[0017] Furthermore, based on the disturbance-driven modeling module, an uncertainty input sample space is constructed, and the probability distribution of the slope safety factor is estimated using the Monte Carlo method. The specific method is as follows: First: Let the set of random input variables for the slope system to be analyzed be: ; in, Cohesion (unit: kPa). The internal friction angle (unit: °). Severe (unit: kN / m³). Elastic modulus (unit: MPa). The inputs are rainfall intensity, blasting impact intensity, and seismic acceleration (units are mm / h, kPa, and g, respectively) in the disturbance time series, all described by probability density functions. The probability distribution type of the parameters is determined based on field geological surveys or empirical statistics. Secondly: Latin hypercube sampling (LHS) technique is used to sample variables from the variable space. N sets of input samples are generated to form an uncertain input set: ; Each sample group is input into the aforementioned seepage-stress coupling model, and the corresponding safety factor is calculated by considering the effects of disturbance. This forms a sample set. ; Finally, by performing kernel density estimation or histogram statistics on the above sample set, the probability density function of the safety factor can be obtained. Furthermore, its statistical characteristics, including mathematical expectation, are extracted: ; Standard deviation: ; Probability of instability: ; in, The indicator function takes the value 1 if the condition is true and 0 otherwise. Furthermore, to measure extreme risk, the Conditional Value at Risk (CVaR) is introduced as a tail indicator, calculated as follows: ; in, Indicates sorting by ascending order. The set of percentile samples, usually or .

[0018] Furthermore, the state space in the learning strategy optimization module Action space Reward function The Markov decision process (MDF) iterates through a state-action-reward-update mechanism in each learning round, ultimately obtaining the optimal policy function. The state space is defined as follows: ; That is, the current expected value, standard deviation, and conditional risk value of the safety factor, and the current disturbance intensity (rainfall). ,blasting ,earthquake The state input, consisting of the previous control action, can fully reflect the slope's risk level and behavioral response under the current disturbance, and the action space... A set of continuous or discrete adjustable engineering control parameters: ; in This indicates the current pumping rate (unit: L / min). This indicates the anchor bolt density (unit: bolts / m²) or reinforcement stiffness parameter, both of which are engineering-implementable intervention measures. The specific value range is set according to the constraints of the engineering site. , Indicates the reinforcement level, reward function The core of guiding policy learning is designed around the control objective—the characteristics of the probability distribution function. To encourage the agent to reduce the tail risk of the system, the reward function is set as follows: ; In the formula, This represents the conditional risk value (tail mean) under the current distribution. The probability of instability. This is an adjustable weighting coefficient used to balance the proportion of the two in the reward.

[0019] Furthermore, in each round of training, the agent reads the current state. Based on policy function Output Action After the action is applied to the environment model, a new perturbation response and probability distribution function are obtained. The environment then provides a reward based on the reward function. The agent updates the policy network using the policy gradient method; the policy function... Modeling and training are performed using any one of the following algorithms: Deep Deterministic Policy Gradient (DDPG) or Proximal Policy Optimization (PPO). DDPG is suitable for continuous action spaces, while PPO offers stronger convergence and sample utilization efficiency. The reinforcement learning process is integrated with a Monte Carlo simulation module; that is, after each control action is generated, it is embedded into the perturbation input model and parameter sample model to simulate the corresponding probability distribution function and calculate the reward feedback to form a closed loop. After training, the policy function... It can be directly used for optimal control output under new disturbance scenarios to realize the system's dynamic response capability and risk control capability.

[0020] Furthermore, the probability inversion feedback module uses a preset threshold. To achieve the goal, establish the objective function: By solving the above objective function, the combination of input parameters that puts the slope system in a boundary risk state can be determined. ,in The safety factor value, calculated under the combined effects of disturbance and geological input, was obtained using the aforementioned seepage-stress coupling model and Monte Carlo simulation; the details are as follows: First: First, fix the disturbance input. , with parameter samples For the inversion variables, an initial search space is constructed within their known distribution range; then, a genetic algorithm (GA) based on sample selection is used for searching, and the optimal matching parameter set is obtained through iterative convergence. The probability error of meeting the target does not exceed the set tolerance. ,Right now: .

[0021] Then: After the above inversion calculation is completed, the critical parameter combination is output. And construct the corresponding sensitivity range: .

[0022] This parameter range can be regarded as the "risk-sensitive area" when the slope system is in an unstable boundary state. When the monitoring system or subsequent model updates find that the actual parameters fall into this range, risk warnings or enhanced control measures can be triggered.

[0023] The principle and effect of this solution are as follows: 1. Compared with existing technologies, this invention first solves the problem that existing methods cannot effectively model the dynamic impact of natural disturbances (such as rainfall, blasting, or vibration) on slope safety. Most current methods treat disturbances as static inputs or boundary conditions, making it difficult to characterize the continuous effects of disturbance intensity, duration, and temporal fluctuations on slope mechanical behavior. This invention constructs a multi-source disturbance input model, uses stochastic processes to simulate disturbance event sequences, and couples the disturbance field into the stability analysis model, thereby modeling the safety factor response process of slopes driven by the disturbance field, improving the real-world adaptability and dynamic expressiveness of slope state prediction. Secondly, this invention addresses the structural shortcoming of existing technologies that "can only assess, not control." While traditional methods can assess the mean safety factor or instability probability, they cannot directly output executable control strategies based on risk indicators, making it difficult to apply risk prediction results. This invention introduces a reinforcement learning strategy optimization mechanism based on probability distribution characteristics. It uses the statistical characteristics of the safety factor (such as mean, variance, CVaR, etc.) as the objective function for training the agent, enabling it to learn optimal intervention strategies, such as drainage intensity adjustment and anchorage stiffness optimization, through continuous perturbation and feedback. This achieves proactive control with the goal of risk distribution convergence, providing an algorithmic foundation and strategy generation logic for intelligent slope control.

[0024] 2. Compared with existing technologies, this invention also addresses the problem of the disconnect between parameter inversion and risk feedback. Current parameter inversion processes largely rely on manual adjustments and forward simulation matching, making it difficult to form a closed-loop feedback structure within the system. This invention constructs an instability probability inversion module, sets an acceptable risk threshold, and determines the key parameter combinations corresponding to the slope reaching a critical state through optimization search, realizing a reverse identification process from "target risk → input parameters." This module can serve as a pre-diagnostic tool for decision support systems, used to identify potential instability triggers and formulate targeted early warning measures, further enhancing the system's engineering practicality and foresight.

[0025] In summary, this invention mainly addresses the following three key technical problems: 1. Modeling the dynamic impact of multi-source disturbance inputs on slope safety factor in spatial and temporal dimensions.

[0026] 2. The problem of using the probability distribution of the safety factor as a control objective for optimization decision-making and outputting engineering intervention strategies.

[0027] 3. Regarding the problem of constructing a closed loop for system parameter inversion and risk feedback based on reliability indices, this invention overcomes the limitations of the separation of "assessment-control-inversion" in the prior art by systematically solving the above key technical problems. It establishes an integrated intelligent optimization method system for slope safety analysis and control, which has strong engineering adaptability, intelligent level and risk response capability.

[0028] 3. Compared with the existing technology, the present invention has the ability to perform dynamic simulation driven by disturbance, the ability to optimize strategies based on probability distribution, and the ability to provide early warning with closed-loop feedback. It can be widely used in engineering scenarios such as mine slope, high slope treatment and geological disaster risk control. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This paper presents a structural framework diagram of a slope safety factor optimization system that integrates uncertainty modeling and multi-objective optimization for probabilistic assessment and control of slope safety factor, as proposed in an embodiment of this application. Figure 2 This illustration shows a disturbance propagation and slope response process of a slope safety factor probabilistic assessment and control method that integrates uncertainty modeling and multi-objective optimization proposed in an embodiment of this application. Figure 3 This paper presents a flowchart illustrating the estimation of the probability distribution of the slope safety factor and the formation of an optimized control strategy, which integrates uncertainty modeling and multi-objective optimization in a slope safety factor probability assessment and control method proposed in an embodiment of this application. Figure 4 This paper presents a system execution flow and module integration diagram illustrating a slope safety factor probabilistic assessment and control method that integrates uncertainty modeling and multi-objective optimization, as proposed in an embodiment of this application. Figure 5 The figure shows the slope stability response change curve under rainfall disturbance adaptation of a slope safety factor probabilistic assessment and control method that integrates uncertainty modeling and multi-objective optimization proposed in this application. Detailed Implementation

[0031] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structure, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0032] Implementation, for example Figures 1-5 As shown: A method for probabilistic assessment and control of slope safety factor that integrates uncertainty modeling and multi-objective optimization includes the following approach: a disturbance-driven modeling module that dynamically interacts with data flow and state feedback; a safety factor probability simulation module; a reinforcement learning strategy optimization module; and a probability inversion feedback module. Step S01: Obtain the disturbance input and parameter samples , respectively and parameter samples Input is entered into the disturbance-driven modeling module and the safety factor probability simulation module to obtain the probability distribution function. .

[0033] The disturbance-driven modeling module, the safety factor probability simulation module, the reinforcement learning strategy optimization module, and the probability inversion feedback module are hardware components, serving as the hardware support for implementing this project.

[0034] Specifically as follows: The disturbance-driven modeling module also includes a stability analysis module that simulates external disturbances and inputs the disturbances. The input is fed into the stability analysis module to drive the slope response.

[0035] Safety factor probability simulation module: receives parameter samples under the influence of disturbances. With disturbance input The safety factor was calculated by simulating a large number of samples using the Monte Carlo method. probability distribution function The output includes the expected value. Standard deviation Instability probability And tail indicators.

[0036] The reinforcement learning policy optimization module includes a probabilistic simulation module: using the metrics output by the probabilistic simulation module as the basis for the reward function, the agent's policy function is constructed. Training reinforcement learning models to generate control actions This causes the risk indicators of the slope system to converge.

[0037] Probability inversion feedback module: Probability of target instability or minimum safety threshold Perform constraint optimization on any of the terms, and invert the output to get the corresponding parameter sample interval. It also combines monitoring data to perform closed-loop correction, assisting in risk warning and adaptive updating of control parameters.

[0038] Regarding disturbance input and parameter samples : Slope parameter sample set: ; in: Cohesion (unit: kPa); : Angle of internal friction (unit: °); : Specific density (unit: kN / m³); Elastic modulus (unit: MPa); Poisson's ratio (dimensionless); External disturbance input: ; in: Rainfall intensity (unit: mm / h); : Explosive impact strength (unit: kPa); Earthquake acceleration time history (unit: g); : Perturbation time series ; The perturbation input is represented by the perturbation input vector W(t), where t is the perturbation time series, and its value ranges from 1 to 10. The complete expression is: .

[0039] in, The rainfall intensity per unit time (unit: mm / h) can be generated based on the Gumbel distribution or empirical annual maximum daily rainfall statistics. The blasting impact intensity (unit: kPa) can be represented by its time domain distribution, which can be obtained by modeling a Poisson process or by fitting measured blasting records. The earthquake acceleration time history (unit: g) can be generated using existing standard ground motion inputs or synthetic seismic wave models.

[0040] The disturbance input will act on the slope seepage-mechanics coupled model, mainly by adjusting the pore water pressure. The shear strength reduction mechanism affects the strength parameters of the slope. Under rainfall disturbance, the seepage field will change the pore pressure distribution, thus affecting the effective stress and shear strength, according to the following formula: ; In the formula, The shear strength at time t (unit: kPa); Effective cohesion (unit: kPa); Total stress (unit: kPa); The pore water pressure caused by the disturbance; The effective internal friction angle (unit: °) is determined by the fact that the increase in pore pressure caused by disturbance will lead to a decrease in effective stress, thereby reducing the effective internal friction angle. This weakens the slope's shear resistance.

[0041] As time progresses, different disturbance sources will superimpose and dynamically alter the mechanical response of the slope. The slope seepage-mechanical coupling model will calculate the time-series safety factor in a time-step manner. Its expression is based on the simplified limit equilibrium method as follows: ; in, The length of the potential slip surface (in meters). The sliding surface inclination angle (unit: °); The soil's self-weight (unit: kN) is used as the basis for the safety factor probabilistic simulation module output, which includes the safety factor time series under the influence of the disturbance field. This serves as the input basis for subsequent Monte Carlo probabilistic simulations and reinforcement learning training.

[0042] Figure 2 The diagram shows the overall structure of disturbance modeling and slope response mechanism. It includes a disturbance input module, a seepage-mechanical model, a dynamic parameter update path, and the evolution path of the safety factor, which ultimately affects the slope. Each disturbance signal acts on key parameters in the slope model through function mapping, forming a direct coupling link between disturbance input and response analysis.

[0043] The output of the disturbance-driven modeling module includes the time series of the safety factor under the action of the disturbance field. This serves as the input foundation for subsequent Monte Carlo probabilistic simulations and reinforcement learning training. Based on this, a tight connection is achieved between disturbance simulation and slope response calculation, constructing a risk transmission channel that matches actual slope conditions. This is the first step in achieving closed-loop optimization of the system.

[0044] Step S02: Convert the probability distribution function The feedback information is fed into the reinforcement learning policy optimization module as a result of policy optimization, and the reinforcement learning policy optimization module selects the control action in each round of simulation. Update the environment status and continuously optimize the control strategy.

[0045] probability distribution function Essentially, it is a statistical representation of slope response results under numerous disturbance scenarios, and its essence stems from multiple simulation outputs of the disturbance driving model and the slope response model over the time dimension. The safety factor time series mentioned earlier... The response trajectory, obtained under a single disturbance path, evolves over time and reflects the stability of the slope system over time under a specific disturbance condition. However, under the Monte Carlo sampling framework with uncertain inputs, the system's response to disturbance inputs... Multiple independent simulations were performed, and multiple time series of safety factors were obtained. For each simulated trajectory, safety factor values ​​(such as the lowest point, the steady state after the disturbance response, the difference before and after the disturbance, or the average value over a period of time) are extracted from key moments or representative segments to form a statistically valid sample set. The sample set, after kernel density estimation or histogram statistical processing, can be used to construct the probability density function of the safety factor. This is used to characterize the global distribution features of slope system stability under given disturbance uncertainty. Therefore, the safety factor time series is a generation probability distribution function. Based on this data foundation, a clear connection is established between the two through structured extraction and statistical estimation. Specifically, a single time series reflects the trajectory of a single disturbance response, while... This falls under the category of population distribution modeling, and the two are not contradictory; rather, they form a probabilistic integrated expression through multi-trajectory statistics. This connection mechanism not only ensures the rationality of the physical origin of the distribution function but also provides theoretical support and a closed-loop data logic for subsequent control optimization using distribution characteristics as the objective function.

[0046] Based on the disturbance-driven modeling module, an uncertainty input sample space is constructed, and the probability distribution of the slope safety factor is estimated using the Monte Carlo method. The specific method is as follows: First: Let the set of random input variables for the slope system to be analyzed be: ; in, Cohesion (unit: kPa). The internal friction angle (unit: °). Severe (unit: kN / m³). Elastic modulus (unit: MPa). The inputs are rainfall intensity, blasting impact intensity, and seismic acceleration (units mm / h, kPa, and g, respectively) in the disturbance time series, all described by probability density functions. The probability distribution type of the parameters is determined based on field geological surveys or empirical statistics.

[0047] Secondly: Latin hypercube sampling (LHS) technique is used to sample variables from the variable space. N sets of input samples are generated to form an uncertain input set: ; Each sample group is input into the aforementioned seepage-stress coupling model, and the corresponding safety factor is calculated by considering the effects of disturbance. This forms a sample set. .

[0048] Finally, by performing kernel density estimation or histogram statistics on the above sample set, the probability density function of the safety factor can be obtained. Furthermore, its statistical characteristics, including mathematical expectation, are extracted: ; Standard deviation: ; Probability of instability: ; in, The indicator function takes the value 1 if the condition is true and 0 otherwise. Furthermore, to measure extreme risk, the Conditional Value at Risk (CVaR) is introduced as a tail indicator, calculated as follows: ; in, Indicates sorting by ascending order. The set of percentile samples, usually or .

[0049] To achieve the above steps, an uncertainty input and safety factor probability distribution estimation module is set up: the output of the uncertainty input and safety factor probability distribution estimation module is a probability distribution function. ,expect Standard deviation Instability probability and tail indicators This constitutes a complete quantitative result of the safety status. Among them, Used to assess trends in risk changes Used to identify tail instability risk It can be used as a trigger threshold condition for the reinforcement learning control and parameter inversion module.

[0050] Step S03: The control results obtained by the reinforcement learning policy optimization module are reflected in the probability distribution function. In this process, a closed-loop structure of "disturbance-assessment-control-reassessment" is formed.

[0051] Specifically, to achieve dynamic control and risk distribution optimization of slope safety under uncertain disturbance conditions, this invention constructs a policy optimization module based on reinforcement learning (RL). The probability distribution function characteristics are used as the feedback target for policy learning, guiding the agent to form the optimal scheduling strategy for engineering control variables through interactive learning. This module receives the output of the safety factor probability simulation module as environmental feedback, aiming to minimize the instability probability, reduce the tail risk index, and improve the system's adaptability to disturbance changes.

[0052] In this invention, the state space of the reinforcement learning agent Action space Reward function A Markov Decision Process (MDP) is constructed, which iterates through a state-action-reward-update mechanism in each learning round to ultimately obtain the optimal policy function. The state space is defined as follows: ; That is, the current expected value, standard deviation, and conditional risk value of the safety factor, and the current disturbance intensity (rainfall). ,blasting ,earthquake The state input, consisting of the previous control action, can fully reflect the risk level and behavioral response of the slope under the current disturbance.

[0053] Action space A set of continuous or discrete adjustable engineering control parameters, such as: ; in This indicates the current pumping rate (unit: L / min). This indicates the anchor bolt density (unit: bolts / m²) or reinforcement stiffness parameter, both of which are engineering-implementable intervention measures. The specific value range is set according to the constraints of the engineering site, for example... , Indicates the level of reinforcement.

[0054] reward function This is the core of guiding policy learning, and in this invention, it is designed around the control objective—the characteristics of the probability distribution function. To encourage the agent to reduce the tail risk of the system, the reward function is set as follows: ; In the formula, This represents the conditional risk value (tail mean) under the current distribution. The probability of instability. This is an adjustable weighting coefficient used to balance the proportion of both in the reward. This setting ensures that the reward is negatively correlated with system risk, encouraging the strategy to seek safer control behaviors under the influence of disturbances.

[0055] In each round of training, the agent reads the current state. Based on policy function Output Action After the action is applied to the environment model, a new perturbation response and probability distribution function are obtained. The environment then provides a reward based on the reward function. The agent updates the policy network using the policy gradient method. The policy function... Modeling and training can be performed using either the Deep Deterministic Policy Gradient (DDPG) algorithm or the Proximal Policy Optimization (PPO) algorithm. DDPG is suitable for continuous action spaces, while PPO has stronger convergence and sample utilization efficiency.

[0056] The reinforcement learning process will operate in conjunction with the Monte Carlo simulation module. That is, after each control action is generated, it is embedded into the perturbation input model and the parameter sample model to simulate the corresponding probability distribution function and calculate the reward feedback to form a closed loop. After training, the policy function... It can be directly used for optimal control output under new disturbance scenarios to realize the system's dynamic response capability and risk control capability.

[0057] Figure 4 The diagram illustrates the closed-loop operation logic of state acquisition, strategy reasoning, action execution, disturbance feedback, safety factor simulation, and reward calculation. This module constitutes the only intelligent unit in the system with autonomous learning and strategy output capabilities, providing an intelligent control path that differs from traditional parameter optimization methods.

[0058] Through the training and deployment of this module, this invention can dynamically output the optimal combination of engineering measures under the conditions of disturbance field changes and parameter fluctuations, so that the probability distribution function is stabilized within the expected range, effectively reducing the risk level of the slope system under high uncertainty, and realizing the active, precise and intelligent slope control function.

[0059] Step S04: Introduce a monitoring system and set a preset threshold. The probability of instability detected is close to the preset threshold. The probability inversion feedback module is activated to perform inversion analysis and output the parameter sample range that induces instability. It also provides real-time early warnings in conjunction with a monitoring system.

[0060] Specifically, a probability inversion feedback module is set up: based on the probability distribution of the safety factor, it inversely derives the sample combination of key parameters under a given instability risk threshold. This module works in conjunction with the aforementioned reinforcement learning module to provide parameter constraints for policy output and connects to the monitoring system to achieve proactive early warning.

[0061] Specifically as follows: In actual engineering operations, slope instability events are often caused by multiple uncertain factors, and the probability of instability is... With input variables Fluctuations are caused by disturbances. When this probability exceeds a preset safety threshold... (For example, 10% or industry standard requirements) means that the slope system is in a high-risk state. Therefore, this module uses... To achieve the inversion objective, the following optimization problem is established: ; By solving the objective function described above, the combination of input parameters that puts the slope system in a boundary risk state can be determined. .in The safety factor value, calculated under the combined effects of disturbance and geological input, is obtained by using the aforementioned seepage-stress coupling model and Monte Carlo simulation.

[0062] To improve computational efficiency and convergence stability, this invention employs a staged inversion strategy: first, the perturbation input is fixed. , with parameter samples For the inversion variables, an initial search space is constructed within their known distribution range; then, a genetic algorithm (GA) or simulated annealing method based on sample selection is used for searching, and the optimal matching parameter set is obtained through iterative convergence. The probability error of meeting the target does not exceed the set tolerance. ,Right now: ; After the above inversion calculation is completed, the critical parameter combination is output. And construct the corresponding sensitivity intervals. For better engineering readability, this invention outputs the variation range of each inversion parameter in the form of upper and lower boundaries, for example: ; Specifically, this interval represents the range of soil shear strength parameters obtained through probabilistic inversion under the condition that the slope safety factor reaches a certain preset probability distribution state (e.g., the instability probability is less than a set threshold). Where, It represents cohesion, with the unit kPa, reflecting the cohesive properties of soil under undrained shear. It represents the internal friction angle, with the unit being °, and reflects the frictional characteristics between soil particles; It is the minimum and maximum cohesion inversion interval that satisfies the target stability probability. This corresponds to the inversion range of the internal friction angle. This range reflects the factors ensuring the slope safety factor under disturbance and uncertainty. The range of input parameters that satisfy the distribution constraints can be used for dynamic correction of design parameters or for feedforward early warning analysis. The asterisk * indicates that this interval is the result after optimization through safety distribution target inversion, not the original measured value. This interval represents the range of soil shear strength parameters obtained through probabilistic inversion under the condition that the slope safety factor reaches a certain preset probability distribution state (e.g., the instability probability is less than a set threshold). In the formula, It represents cohesion, with the unit kPa, reflecting the cohesive properties of soil under undrained shear. It represents the internal friction angle, with the unit being °, and reflects the frictional characteristics between soil particles; It is the minimum and maximum cohesion inversion interval that satisfies the target stability probability. This corresponds to the inversion range of the internal friction angle. This range reflects the factors ensuring the slope safety factor under disturbance and uncertainty. The range of input parameters that satisfy the distribution constraints can be used for dynamic correction of design parameters or for feedforward early warning analysis. The asterisk * indicates that the interval is the result after inversion optimization based on the safety distribution target, not the original measured value. This parameter interval can be considered as the "risk-sensitive region" of the slope system under instability boundary conditions. When the monitoring system or subsequent model updates detect that the actual parameters fall within this interval, risk warnings or enhanced control measures can be triggered. The probabilistic inversion feedback module can run independently to provide a basis for risk review, or it can serve as a priori condition for the strategy constraints of the reinforcement learning module, thereby preventing the strategy from evolving to an uncontrollable or out-of-bounds state. Figure 4 The entire process, including target setting, input parameter selection, safety factor probability simulation, risk error judgment, and inversion parameter output, forms a closed-loop feedback mechanism with "risk control target → parameter identification → early warning response" as the main line. This module, as the system's reverse diagnostic mechanism, further enhances the predictability and robustness of the invention, enabling slope risk control to move from "simulation analysis" to "intelligent identification" and "proactive intervention." While meeting engineering safety requirements, it also provides technical support for resource conservation and management decision-making.

[0063] The method described in this invention is embodied in the overall system architecture as an intelligent optimization system with multi-module coupling, a clearly defined functional closed loop, and a clear control path. This system uses disturbance field drive as the input source, slope safety factor probability distribution as the evaluation core, and reinforcement learning strategy optimization and parameter inversion as the output feedback, realizing an adaptive control process of "disturbance—evaluation—decision—feedback—re-evaluation".

[0064] The overall system's operational logic and module integration methods, such as Figure 1 As shown: The system operation begins in the disturbance-driven modeling module. Based on field monitoring or historical statistics, the system first generates a disturbance input sequence W(t)={R(t),P(t),A(t)}, representing the rainfall intensity, blast impact intensity, and seismic acceleration as they change over time, respectively. After modeling, the disturbance input acts on the coupled seepage-mechanical model, dynamically driving changes in pore water pressure u(t) and shear stress field, thereby affecting the shear strength τ(t) and safety factor FS(t). This disturbance-response path is implemented in the disturbance-driven modeling module and forms a simulateable time-series mechanical process.

[0065] Subsequently, the system enters the uncertainty input and probability simulation stage. Using the Latin hypercube sampling method (LHS), a large number of input samples are generated from the variable space X={c,φ,γ,E,R(t),P(t),A(t)}, and input into the stability model to obtain the corresponding FS sample set {FS¹,FS²,...,FS}. N Then, the probability density function f_FS(x) of FS is estimated, and statistical indicators such as expected value E[FS], standard deviation σ_FS, instability probability P (FS<1.0) and tail indicators are calculated. This process is undertaken by the safety factor probability simulation module, which is the central hub for risk quantification in the system.

[0066] The system then proceeds to the reinforcement learning strategy optimization module. The system uses the reward function as follows: ; Assess the current control effectiveness and guide strategy updates. This module... Figure 5 This is manifested as a closed-loop path integrating "strategy training - action execution - distributed feedback," which is a key link in the intelligent regulation of the system.

[0067] When the system detects that the instability probability is close to the upper limit threshold P* or the long-term strategy no longer converges, the system activates the probability inversion feedback module and sets the objective function as follows: ; The search identifies the input parameter combination G* most likely to cause instability, and outputs its upper and lower bounds to assist in operational early warning. This inversion result can also serve as a policy constraint, preventing reinforcement learning policies from migrating to high-risk regions, thus achieving a two-way mechanism combining feedforward control and reverse adjustment.

[0068] During system operation, each module follows Figure 5The path shown is executed sequentially: disturbance input → probability distribution function simulation → strategy output → action implementation → evaluation feedback → parameter inversion → system adaptive update. This process forms a dynamic self-circulating mechanism of coordinated operation of the three elements of technology, data, and control, enabling the present invention to achieve proactive control of slope stability in highly uncertain environments.

[0069] Figure 5 The document clearly demonstrates the sequential operation logic of each module and its feedback coupling relationship. Modules communicate logically through variable flow, evolve strategies through indicator feedback, and achieve system self-updating capabilities through external monitoring data interfaces. This integrated structure possesses a clear input-decision-output path, with closed logic and a clear structure, making it directly deployable in scenarios such as mine slope protection, landslide control, and high slope management, demonstrating significant engineering practical value.

[0070] Example as follows: This embodiment, based on the technical solution proposed in this invention, constructs a "probabilistic optimization control system for slope stability considering rainfall disturbance," and applies it to an intelligent control simulation experiment of a typical soil slope. This slope is located in a quarry area in southern China, with a height of 30m and a slope angle of 45°. It is a mixed structure of silty clay and sandy fill, significantly affected by torrential rain erosion year-round, exhibiting significant disturbance sensitivity. The experiment aims to optimize the drainage control scheme and reduce the probability of system instability through the integrated operation of disturbance modeling, reinforcement learning control, and probabilistic inversion modules.

[0071] (1) Input parameters and slope physical model settings: The slope physical model is constructed based on a simplified two-dimensional plane limit equilibrium model, and the parameter settings are shown in Table 1 below:

[0072]

[0073] Table 1

[0074] The perturbation input is simulated using the Gumbel extreme value distribution to model rainfall events with return periods of 10, 30, and 50 years, forming... The perturbation input varies over time. Parameter samples are generated from 1000 samples following a normal distribution. Seepage calculations are based on a simple saturated unsteady Darcy flow model, with pore pressure variations used as input for limit equilibrium calculations. The output is the safety factor corresponding to each sample. .

[0075] (2) Integration of probabilistic simulation and reinforcement learning strategies: Using the Monte Carlo method to simulate all samples, with no initial control measures, the results of 1000 simulations show: Average safety factor: ; Probability of instability: ; CVaR : ; The system then activates the reinforcement learning module, using the PPO algorithm to train the policy network. The state input includes the current rainfall intensity. The average safety factor and tail index, with the action being the drainage rate. The reward function is: ; After 2000 rounds of strategy training, the system strategy converged, and the optimal strategy was: to activate the maximum pumping rate at the initial stage of rainfall (rainfall intensity > 50 mm / h). During the rest of the time, it maintains low-power drainage.

[0076] (3) Evaluation and inversion results of control effectiveness: After deploying the strategy, another 1000 sets of samples were simulated, and the output is as follows: The average safety factor has increased to ; The probability of instability has decreased to ; Down to .

[0077] The system automatically determines that the probability of instability is close to the engineering threshold. Start the inversion module and set the objective function: ;

[0078] The results showed that: when , When the probability of instability approaches 5%, the system uses this as a risk-sensitive threshold and outputs the following warning range: as shown in Table 2 below.

[0079]

[0080] Table 2

[0081] If monitoring detects that the soil strength parameters fall into this range, the system will automatically suggest upgrading the drainage level or adding support.

[0082] (4) Equipment and operating conditions: The simulation experiment platform is a high-performance host with a 16-core CPU and 64GB of memory, and the training time for a single round of reinforcement learning is approximately 2.5 hours. The parameters of the drainage facility model are derived from actual engineering equipment, with a maximum drainage flow rate not exceeding 400L / min. Control commands can be linked to the slope monitoring system via a PLC interface.

[0083] This invention addresses the significant shortcomings of current slope stability analysis methods in terms of disturbance response capability, risk control accuracy, and intelligent regulation mechanisms. It proposes a probabilistic assessment and control method for slope safety coefficient that integrates uncertainty modeling and multi-objective optimization, achieving deep coupling of dynamic prediction of slope safety status, risk quantification, and strategy control.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any indirect modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for probabilistic assessment and control of slope safety factor integrating uncertainty modeling and multi-objective optimization, characterized in that, The following methods are formed by a perturbation-driven modeling module that dynamically interacts with data flow and state feedback, a security factor probability simulation module, a reinforcement learning policy optimization module, and a probability inversion feedback module: Step S01: Obtain the disturbance input and parameter samples , respectively and parameter samples Input is entered into the disturbance-driven modeling module and the safety factor probability simulation module to obtain the safety factor distribution. ; Step S02: Convert the probability distribution function The feedback information is fed into the reinforcement learning policy optimization module as a result of policy optimization, and the reinforcement learning policy optimization module selects the control action in each round of simulation. Update the environment status and continuously optimize the control strategy; Step S03: The control results obtained by the reinforcement learning policy optimization module are reflected in the probability distribution function. In this process, a closed-loop structure of "disturbance-assessment-control-reassessment" is formed; Step S04: Introduce a monitoring system and set a preset threshold. The probability of instability detected is close to the preset threshold. The probability inversion feedback module is activated to perform inversion analysis and output the parameter sample range that induces instability. It also provides real-time early warnings in conjunction with a monitoring system.

2. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization as described in claim 1, characterized in that, The disturbance-driven modeling module also includes a stability analysis module that simulates external disturbances and inputs the disturbances. The input is fed into the stability analysis module to drive the slope response; Safety factor probability simulation module: receives parameter samples under the influence of disturbances. With disturbance input The safety factor was calculated by simulating a large number of samples using the Monte Carlo method. probability distribution function The output includes the expected value. Standard deviation Instability probability and tail indicators; The reinforcement learning policy optimization module includes a probabilistic simulation module: using the metrics output by the probabilistic simulation module as the basis for the reward function, the agent's policy function is constructed. Training reinforcement learning models to generate control actions This causes the risk indicators of the slope system to converge. Probability inversion feedback module: Probability of target instability or minimum safety threshold Perform constraint optimization on any of the terms, and invert the output to get the corresponding parameter sample interval. It also combines monitoring data to perform closed-loop correction, assisting in risk warning and adaptive updating of control parameters.

3. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization according to claim 2, characterized in that, Parameter Samples ; in: Cohesion (unit: kPa); Internal friction angle (unit: °); : Specific density (unit: kN / m³); Elastic modulus (unit: MPa); Poisson's ratio (dimensionless); Disturbance input ,in: Rainfall intensity (unit: mm / h) can be generated based on either the Gumbel distribution or the empirical annual maximum daily rainfall. : Explosive impact intensity, the time domain distribution of which can be obtained by fitting either Poisson process modeling or measured blast records (unit: kPa); Seismic acceleration time history can be generated using either existing standard ground motion input or synthetic seismic wave model (unit: g). : Perturbation time series Disturbance input The effect on the slope seepage-mechanics coupling model is mainly achieved by regulating pore water pressure. The shear strength reduction mechanism affects the slope's strength parameters. Under rainfall disturbance, the seepage field will change the pore pressure distribution, thus affecting the effective stress and shear strength, according to the following formula: ； In the formula, The shear strength at time t (unit: kPa); Effective cohesion (unit: kPa); Total stress (unit: kPa); The pore water pressure caused by the disturbance; The effective internal friction angle (unit: °) is determined by the fact that the increase in pore pressure caused by disturbance will lead to a decrease in effective stress, thereby reducing the effective internal friction angle. This weakens the slope's shear resistance.

4. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization according to claim 3, characterized in that, The slope seepage-mechanics coupled model will calculate the time-series safety factor in a time-step manner. : ； in, The length of the potential slip surface (in meters). The sliding surface inclination angle (unit: °); The soil's self-weight (unit: kN) is used as the basis for the safety factor probabilistic simulation module output, which includes the safety factor time series under the influence of the disturbance field. This serves as the input basis for subsequent Monte Carlo probabilistic simulations and reinforcement learning training.

5. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization according to claim 4, characterized in that, Based on the disturbance-driven modeling module, an uncertainty input sample space is constructed, and the probability distribution of the slope safety factor is estimated using the Monte Carlo method. The specific method is as follows: First: Let the set of random input variables for the slope system to be analyzed be: ； in, Cohesion (unit: kPa). The internal friction angle (unit: °). Severe (unit: kN / m³). Elastic modulus (unit: MPa). The inputs are rainfall intensity, blasting impact intensity, and seismic acceleration (units are mm / h, kPa, and g, respectively) in the disturbance time series, all described by probability density functions. The probability distribution type of the parameters is determined based on field geological surveys or empirical statistics. Secondly: Latin Hypercube Sampling (LHS) technique is used to extract data from the variable space. N sets of input samples are generated to form an uncertain input set: ； Each sample group is input into the aforementioned seepage-stress coupling model, and the corresponding safety factor is calculated by considering the effects of disturbance. This forms a sample set. ； Finally, by performing kernel density estimation or histogram statistics on the above sample set, the probability density function of the safety factor can be obtained. Furthermore, its statistical characteristics, including mathematical expectation, are extracted: ； Standard deviation: ； Probability of instability: ； in, The indicator function takes the value 1 if the condition is true and 0 otherwise. Furthermore, to measure extreme risk, the Conditional Value at Risk (CVaR) is introduced as a tail indicator, calculated as follows: ； in, Indicates sorting by ascending order. The set of percentile samples, usually or .

6. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization according to claim 5, characterized in that, The state space in the reinforcement learning strategy optimization module Action space Reward function The Markov decision process (MDF) iterates through a state-action-reward-update mechanism in each learning round to ultimately obtain the optimal policy function. The state space is defined as follows: ； That is, the current expected value, standard deviation, and conditional risk value of the safety factor, and the current disturbance intensity (rainfall). ,blasting ,earthquake The state input, consisting of the previous control action, can fully reflect the slope's risk level and behavioral response under the current disturbance, and the action space... A set of continuous or discrete adjustable engineering control parameters: ； in This indicates the current pumping rate (unit: L / min). This indicates the anchor bolt density (unit: bolts / m²) or reinforcement stiffness parameter, both of which are engineering-implementable intervention measures. The specific value range is set according to the constraints of the engineering site. , Indicates the reinforcement level, reward function The core of guiding policy learning is designed around the control objective—the characteristics of the probability distribution function. To encourage the agent to reduce the tail risk of the system, the reward function is set as follows: ； In the formula, This represents the conditional risk value, or tail mean, under the current distribution. The probability of instability. This is an adjustable weighting coefficient used to balance the proportion of the two in the reward.

7. The slope safety factor probabilistic assessment and control method integrating uncertainty modeling and multi-objective optimization according to claim 6, characterized in that, In each round of training, the agent reads the current state. Based on policy function Output Action After the action is applied to the environment model, a new perturbation response and probability distribution function are obtained. The environment then provides a reward based on the reward function. The agent updates the policy network using the policy gradient method; the policy function... Modeling and training are performed using either the Deep Deterministic Policy Gradient (DDPG) algorithm or the Proximal Policy Optimization (PPO) algorithm. DDPG is suitable for continuous action spaces, while PPO has stronger convergence and sample utilization efficiency. The reinforcement learning process is linked with the Monte Carlo simulation module; that is, after each control action is generated, it is embedded into the perturbation input model and the parameter sample model to simulate the corresponding probability distribution function and calculate the reward feedback to form a closed loop. After training, the policy function... It can be directly used for optimal control output under new disturbance scenarios to realize the system's dynamic response capability and risk control capability.

8. The method for probabilistic assessment and control of slope safety factor integrating uncertainty modeling and multi-objective optimization according to claim 7, characterized in that, The probability inversion feedback module uses a preset threshold. To achieve the goal, establish the objective function: By solving the above objective function, the combination of input parameters that puts the slope system in a boundary risk state can be determined. ,in The safety factor value calculated under the combined effects of disturbance and geological input was obtained by using the aforementioned seepage-stress coupling model and Monte Carlo simulation. Specifically as follows: First: First, fix the disturbance input. , with parameter samples For the inversion variables, an initial search space is constructed within their known distribution range; then, a genetic algorithm (GA) based on sample selection is used for searching, and the optimal matching parameter set is obtained through iterative convergence. The probability error of meeting the target does not exceed the set tolerance. ,Right now: ； Then: After the above inversion calculation is completed, the critical parameter combination is output. And construct the corresponding sensitivity range: This parameter range can be regarded as the "risk-sensitive area" when the slope system is in an unstable boundary state. When the monitoring system or subsequent model update finds that the actual parameters fall into this range, risk warning or enhanced control measures can be triggered.

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