Automatic proportion control system for interlocking filling materials in mines

Abstract

The present invention belongs to the field of automatic control technology, and specifically relates to an automated proportioning control system for interlocking filling materials in mines. The system includes: a data acquisition and dynamic monitoring unit, an intelligent control and optimization calculation unit, and an automated execution unit; the data acquisition and dynamic monitoring unit is used to define multiple group proportion constraints and total mass constraints, calculate the real-time local concentration of each component of the filling material slurry, and establish a comprehensive objective function to measure the filling performance; the intelligent control and optimization calculation unit is used to construct a pressure penalty function to quantify the risk of exceeding the limit according to the determined pressure safety upper limit; dynamically solve the optimal proportion; the automated execution unit is used to convert the optimal proportion into the feed flow rate of each component, and execute it through pump and valve control. Under complex mine working conditions, the present invention can adjust the group proportions and pump and valve control instructions in real time to ensure the stability of the filling material performance and the safety of the transportation process.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, and in particular relates to an automatic proportioning control system for interlocking filling materials in a mine. Background Art

[0002] Mine mining is an important link in modern industrial production. With the increase in resource mining depth and the increase in the complexity of ore bodies, the geological environmental problems generated during mine mining are becoming increasingly prominent. Mine filling, as a key technology, is widely used in goaf management, surface subsidence control and mine resource recycling in the later stage of mine mining. Among them, the performance of the filling material is directly related to the stability of the goaf, the safety of mine operations and the effect of environmental protection. However, the currently disclosed mine filling technology still has many technical bottlenecks in terms of material ratio, performance optimization and automatic control, which makes it difficult to meet the high efficiency, safety and sustainability requirements of mine filling operations under complex working conditions. In the prior art, mine filling materials usually use tailings as the main aggregate, supplemented by cement as a binder, and adjust fluidity by water or admixtures. These materials are transported to the underground goaf through pipelines to form a filling body, which supports and stabilizes the goaf. The "three-component" slurry based on tailings, cement and water is a representative of traditional mine filling materials, which has the characteristics of easy availability of raw materials, low cost and simple construction. However, this filling technology has great limitations in performance optimization, especially in long-distance transportation, high-drop pipeline layout and complex geological conditions, where the problems of insufficient slurry fluidity and difficulty in meeting strength requirements are particularly prominent.

[0003] In recent years, in order to improve the performance of traditional slurry filling technology, many research works have focused on the optimization of filling material components and the improvement of transportation technology. For example, the addition of chemical admixtures (such as water reducers, plasticizers or early strength agents) has been widely used to improve the fluidity and strength of slurry. However, this improvement still faces the following problems in practical applications: the existing filling material ratios mostly adopt a fixed scheme, and the proportions of each component are determined based on empirical formulas or laboratory test data. This static ratio scheme lacks the ability to adapt to the dynamic changes of actual working conditions underground, such as pipeline pressure fluctuations, changes in slurry transportation distances, and the complexity of geological conditions, which may lead to deviations between the actual filling effect and the design expectations. In addition, the fixed ratio cannot be adjusted according to real-time monitoring data, resulting in frequent occurrence of insufficient slurry fluidity or substandard strength during underground transportation. During the pipeline transportation process of mine filling, the pressure distribution of slurry is affected by many factors, including slurry viscosity, pipeline length, pipe diameter, and the performance of the delivery pump. If the pressure is too high, it may cause serious problems such as pipeline rupture and slurry leakage; if the pressure is too low, pipeline blockage or transportation interruption may occur. Existing technologies usually deal with this by adjusting the pump speed or manually monitoring pressure changes, but this method has a delayed response and is difficult to achieve precise control. In particular, in the case of long-distance and large-drop transportation, the difficulty of pressure management is further increased. Summary of the invention

[0004] The main purpose of the present invention is to provide an automated proportioning control system for interlocking filling materials in mines, which realizes dynamic optimization of filling material proportioning and precise management of pressure. The system constructs a multi-objective optimization framework based on Lagrangian function, comprehensively incorporates material strength, fluidity and transportation safety into the optimization objectives, and uses the Newton-Raphson method to dynamically solve the optimal proportion. Under complex mine conditions, the system can adjust the group proportioning and pump valve control instructions in real time to ensure the stability of filling material performance and the safety of the transportation process.

[0005] In order to solve the above technical problems, the present invention provides an automated proportioning control system for interlocking filling materials in mines, the system comprising: a data acquisition and dynamic monitoring unit, an intelligent control and optimization calculation unit and an automated execution unit; the data acquisition and dynamic monitoring unit is used to collect the real-time basic data of the pressure of the pipeline or underground space and each component of the filling material slurry through various sensors, define multiple groups of proportioning constraints and total mass constraints, construct the convection-diffusion equation of the filling material slurry in the pipeline or underground space, calculate the real-time local concentration of each component of the filling material slurry in combination with the slurry flow velocity field, and establish a comprehensive objective function for measuring the filling performance; the intelligent control and optimization calculation unit is used to construct a pressure penalty function to quantify the over-limit risk according to the determined pressure safety upper limit; the comprehensive objective function and the pressure penalty function are integrated into a Lagrangian function, the partial derivative of the Lagrangian function is obtained, the first-order condition is obtained, and the Newton-Raphson method is used to dynamically solve the optimal proportion; the automated execution unit is used to convert the optimal proportion into the feed flow rate of each component, and execute it through pump and valve control.

[0006] Furthermore, the components of the filling material slurry include: tailings, cement, water and admixtures; the real-time basic data of each component of the filling material slurry include: mass and slump.

[0007] Furthermore, at the time The total mass of the filling material slurry is The masses of tailings, cement, water and admixture are , , and ; Define the multi-group distribution ratio constraints and total mass constraints as:

[0008] ;

[0009] in, is the symbol subscript index; represents tailings; represents cement; Represents water; represents additives; is the matching vector; ; For components The mass ratio of is dimensionless and has a value range of .

[0010] Furthermore, at the time Time component In Location The real-time local concentration is , satisfying the following flow-diffusion equation:

[0011] ;

[0012] in, is the slurry flow velocity field; is the gradient operator; is the slurry density; For components The relative sedimentation velocity, ; For components density; ; For pre-set components and The interaction resistance coefficient between For at the moment Time component In Location Real-time local concentration of is the acceleration due to gravity; is the slurry viscosity; For components The average particle size of For pre-set components The effective diffusion coefficient.

[0013] Furthermore, the slurry flow velocity field is obtained by solving the following equation:

[0014] ;

[0015] in, For pressure.

[0016] Furthermore, the comprehensive objective function is obtained by adding two parts: the local strength part and the local fluidity part; It is expressed by the following formula:

[0017] ;

[0018] Local liquidity section , which is expressed by the following formula:

[0019] ;

[0020] in, Components The slump of ; then the comprehensive objective function The formula is:

[0021] ;

[0022] in, is the set local strength coefficient.

[0023] Furthermore, the pressure safety upper limit is expressed using the following formula:

[0024] ;

[0025] in, The set safety upper limit of pressure; Indicates time The maximum pressure that occurs in a pipeline or underground space; pressure penalty function It is expressed by the following formula:

[0026] .

[0027] Furthermore, the comprehensive objective function and pressure penalty function are integrated into a Lagrangian function In the formula, the following is true:

[0028] ;

[0029] in, is the Lagrange multiplier; taking the partial derivative of the Lagrange function, the first-order condition is expressed by the following formula:

[0030] .

[0031] Furthermore, the process of dynamically solving the optimal ratio using the Newton-Raphson method specifically includes:

[0032] Iterate through the following formula:

[0033] ;

[0034] in, Indicates time No. The matching vector of the iteration; Indicates time No. The matching vector of the iteration; is the transpose operation;

[0035] For the moment No. The gradient vector of iteration:

[0036] ;

[0037] in, For the moment No. The Lagrangian function of the iteration;

[0038] For the moment No. The Jacobian matrix of the iteration:

[0039] ;

[0040] The iteration is terminated when the following conditions are met:

[0041] ;

[0042] ;

[0043] in, is the set gradient threshold; is the set iteration threshold.

[0044] The automatic proportioning control system of the mine interlocking filling material of the present invention has the following beneficial effects:

[0045] The present invention realizes accurate optimization of the proportion of filling materials through real-time data collection and dynamic monitoring. The data collection and dynamic monitoring unit in the system can obtain key data such as concentration distribution, pipeline pressure, flow rate, etc. of each component of the slurry (tailings, cement, water, admixture) in real time. Compared with the traditional filling method that relies on empirical formulas or fixed ratios, the present invention constructs a multi-objective optimization framework based on real-time data, and comprehensively incorporates slurry strength, fluidity and transportation safety into the optimization goals. Especially in a mine environment where working conditions change frequently (such as pipeline layout adjustments or increased transportation distances), the present invention can dynamically adjust the component ratios through intelligent algorithms to ensure that the performance of the filling materials always meets the design requirements. This real-time optimization capability significantly improves the adaptability and reliability of filling operations.

[0046] The present invention introduces a pressure penalty function in terms of pressure management, and organically combines the pressure safety upper limit with the ratio optimization through mathematical modeling. The system integrates the comprehensive objective function and the pressure penalty function by constructing a Lagrangian function, and dynamically optimizes the ratio scheme by solving the partial derivative conditions of the Lagrangian function. When the pressure in the pipeline or underground space approaches or exceeds the safety upper limit, the pressure penalty function will quickly amplify the impact of the pressure on the optimization target, and preferentially guide the system to adjust the ratio to reduce the pressure risk. For example, the system can reduce the viscosity of the slurry by reducing the proportion of tailings and increasing the proportion of water and admixtures, thereby alleviating the pressure increase in the pipeline. This mechanism significantly enhances the pressure management capability of the system, avoids accidents such as pipeline rupture and slurry leakage caused by excessive pressure, and can also avoid transportation interruptions or blockages when the pressure is too low.

[0047] In addition, the intelligent control and optimization calculation unit of the present invention uses the Newton-Raphson method to dynamically solve the optimal ratio. This method accurately characterizes the direction and step size of the ratio optimization by calculating the gradient vector and the Jacobian matrix, and can achieve rapid convergence in complex multi-objective optimization problems. Compared with traditional empirical adjustment or single-objective optimization methods, the present invention not only considers the interaction of strength, fluidity and pressure in the ratio optimization process, but also can adaptively adjust the priority of the optimization target according to real-time data. For example, in long-distance transportation scenarios, the system may prioritize the optimization of fluidity to ensure smooth transportation; while in the underground goaf filling stage, the system will pay more attention to the strength performance of the material. Through this dynamic optimization, the present invention can balance multiple demands at different stages and achieve optimal overall performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0049] Figure 1 A schematic diagram of the system structure of an automated proportioning control system for mine interlocking filling materials provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The method of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments of the present invention.

[0051] Example 1, reference Figure 1 : An automated proportioning control system for interlocking filling materials in mines, the system comprising: a data acquisition and dynamic monitoring unit, an intelligent control and optimization calculation unit and an automated execution unit; the data acquisition and dynamic monitoring unit is used to collect the real-time basic data of the pressure of the pipeline or underground space and the various components of the filling material slurry through various sensors, define multiple group proportioning constraints and total mass constraints, construct the convection-diffusion equation of the filling material slurry in the pipeline or underground space, calculate the real-time local concentration of each component of the filling material slurry in combination with the slurry flow velocity field, and establish a comprehensive objective function for measuring the filling performance; the intelligent control and optimization calculation unit is used to construct a pressure penalty function to quantify the risk of exceeding the limit according to the determined pressure safety upper limit; the comprehensive objective function and the pressure penalty function are integrated into a Lagrangian function, the partial derivative of the Lagrangian function is obtained, the first-order condition is obtained, and the Newton-Raphson method is used to dynamically solve the optimal proportion; the automated execution unit is used to convert the optimal proportion into the feed flow rate of each component, and execute it through pump and valve control.

[0052] Specifically, during the mine filling process, the slurry flows and distributes in the pipeline and underground space, and its state is subject to multiple factors such as geological conditions, pipeline layout, and material characteristics. During this process, parameters such as pressure change, slurry flow rate, and concentration of each component will change dynamically, and these changes will directly affect the filling quality and transportation safety. The data acquisition and dynamic monitoring unit collects multiple sets of data including pressure, flow rate, concentration, etc. in real time through multiple types of sensors deployed in key positions of pipelines and underground, forming a full-scale perception of the filling process. The pressure sensor can monitor the pressure distribution of the slurry in the pipeline in real time, detect possible over-limit conditions in time, and avoid the risk of pipeline rupture or slurry backflow due to excessive pressure; the flow rate sensor monitors the flow velocity field of the slurry in the pipeline, providing basic data for analyzing the slurry flow state and transportation efficiency; and the monitoring of component concentration is achieved through density sensors, acoustic sensors or conductivity sensors, which can accurately obtain the local concentration changes of different materials in the slurry (such as cement, fly ash, gangue, admixtures, etc.), so as to evaluate the distribution law of multiple components in the transportation process in real time. The data from these sensors are transmitted to the control center through a digital transmission system, forming a high-frequency, multi-dimensional dynamic monitoring data stream.

[0053] The data acquisition and dynamic monitoring unit not only relies on the hardware functions of the sensor, but also needs to complete the analysis and modeling of the dynamic monitoring data through a systematic data processing algorithm. During the filling process, the distribution law of the concentration of each component is not only affected by the initial ratio, but also constrained by the convection and diffusion effects that occur during the flow of the slurry in the pipeline. Convection causes the slurry to displace along the flow direction, and diffusion stems from the interaction of the component particles in the fluid medium, resulting in a trend of uniform concentration in the direction of low gradient. In order to accurately describe these dynamic processes, the unit combines sensor data to construct a convection-diffusion mathematical model to solve the local concentration distribution of each component in the slurry in real time. Through this modeling process, the distribution changes of the slurry in the pipeline and underground space can be grasped in real time, thereby providing a basic basis for subsequent optimization decisions. For example, when the cement concentration at a certain location is detected to be low, the system can predict that the strength of the filling material at that location may be insufficient, thereby providing forward-looking information for the intelligent optimization unit to adjust the feed ratio. In addition, the data acquisition and dynamic monitoring unit also shows a high degree of advantage in real-time and dynamic adaptability. The mine operating environment is complex, and the uncertainty of geological conditions and transportation conditions poses a challenge to the continuity and stability of the filling process. For example, pressure fluctuations caused by local bends or drops in the pipeline layout may have a significant impact on the flow state and distribution pattern of the slurry. Traditional methods often operate through preset fixed ratio schemes and lack the ability to respond to these dynamic changes. The data acquisition and dynamic monitoring unit uses a real-time feedback mechanism to form a rapid response to changes in operating conditions. When the pressure is detected to be too high, the system can make safe adjustments by adjusting the feed amount or reducing the flow rate; when the flow rate is found to be low, the transportation efficiency can be improved by optimizing the slurry rheology or increasing the pump pressure. In addition, the real-time performance of the unit is also reflected in the dynamic adjustment of multiple groups of distribution ratio constraints. For example, when the slurry concentration deviates from the preset target, the system can quickly identify the cause and provide a basis for the adjustment plan.

[0054] In mine filling operations, the performance and effect of filling materials are affected by many factors, including the pressure in the pipeline, the fluidity of the slurry, the concentration distribution of each component, and the coagulation properties of the material. These factors are not only interrelated, but also constantly change as the operation progresses, so the traditional static proportioning method is difficult to cope with complex working conditions. The intelligent control and optimization calculation unit introduces the idea of ​​dynamic optimization to convert the real-time collected pressure, flow rate, concentration and other data into an accurate representation of the system state, and calculates the best proportioning scheme under the current working conditions based on the optimization algorithm. Specifically, the unit first defines a comprehensive objective function for measuring filling performance. The objective function not only includes the requirements for the strength and fluidity of the filling material, but also combines the constraints of material cost and operational safety, and strives to achieve global optimization under multi-objective conditions. The core of the optimization calculation is to convert the comprehensive goal of the filling operation into a mathematical problem for solution. In mine filling, safety is always the primary consideration, so the system defines a pressure penalty function by setting a pressure safety upper limit to quantify the risk of pipeline overpressure. If the pressure at a certain location of the pipeline is close to or exceeds the safety threshold, the pressure penalty function will rise rapidly, thereby imposing stronger constraints on the working conditions in the high-pressure zone during the optimization process, forcing the system to adjust the ratio or reduce the feed amount to ensure safety. At the same time, the unit introduces the Lagrangian optimization method to integrate the comprehensive objective function of filling performance with the pressure penalty function and the ratio constraint function into a unified optimization framework. Through the construction of the optimization framework, the system can find the optimal solution among a variety of mutually exclusive or mutually constrained objectives. For example, when pursuing material strength, it may be necessary to increase the proportion of cement; and to reduce costs, it is necessary to reduce the feed of high-priced components. The intelligent control and optimization calculation unit dynamically weighs these objectives to provide a globally optimal ratio scheme.

[0055] In the specific solution process, the intelligent control and optimization calculation unit uses advanced numerical algorithms, such as the Newton-Raphson method, for iterative calculations. This method can quickly approach the optimal solution, and is particularly suitable for a large number of nonlinear constrained optimization problems involved in mine filling operations. In each iteration, the system first calculates the gradient information of the objective function and the constraint function based on the real-time monitoring data and the current proportioning scheme, and then uses the gradient descent or second-order derivative information to correct the current proportioning scheme until the objective function converges to the optimal value. This process is highly adaptable in a dynamic environment: when the sensor detects changes in the underground working conditions, such as a sudden increase in pipeline pressure or a decrease in slurry flow rate, the system will quickly reconstruct the optimization problem and recalculate the optimal proportion to ensure that the adjustment can immediately reflect the actual situation. In addition, the system also combines machine learning technology to continuously optimize model parameters through the accumulation and analysis of historical data, so that the accuracy and efficiency of the optimization calculation gradually improve over time. Another key function of the intelligent control and optimization calculation unit is to convert the optimization results into executable feeding instructions in real time. This process relies on the closed-loop control mechanism of the system, that is, through the dynamic feedback of real-time monitoring data, the optimization parameters and execution schemes are continuously adjusted. For example, when it is detected that the concentration of a certain component deviates from the target value, the system will dynamically adjust the feed flow rate of the component according to the optimization results and correct the error in time. In addition, the unit also has emergency response capabilities for emergencies in mine operations, such as pipeline blockage or changes in geological conditions. It can quickly analyze the causes of abnormalities and propose optimization and adjustment strategies to ensure the continuity and safety of operations. It is worth mentioning that the unit has also incorporated the concept of predictive control on the basis of optimization calculation. By modeling and simulating the flow state and concentration distribution of the slurry in the pipeline, the system can predict changes in operating conditions in the future and adjust the proportioning scheme in advance. For example, in long-distance transportation, due to the convection and diffusion effect of the slurry, the concentration of different components at the end of the transportation may change significantly. The intelligent control and optimization calculation unit simulates the convection and diffusion process to predict the actual concentration distribution of each component in the underground filling space, thereby ensuring that the filling material achieves the best performance at the target location.

[0056] The working principle of the automatic execution unit is based on the comprehensive application of industrial automation technology, including pump and valve control, flow regulation and execution accuracy optimization. Its core component is the pump and valve system, which is responsible for adjusting the delivery rate of filling materials such as cement, fly ash, coal gangue, and water. In the interlocking filling of mines, the ratio of each component not only affects the physical properties of the filling materials, but also affects the fluidity and safety of the pipeline during the transportation process. Therefore, the precise control of the pump and valve system is crucial. The automatic execution unit receives the instructions of the optimization calculation unit, converts the optimal ratio into the specific feeding flow of each component, and realizes independent control of different components through real-time adjustment of electric valves or servo control pumps. For example, when the system calculates that the cement ratio needs to be increased under the current conditions, the automatic execution unit will increase the cement feeding flow rate and coordinate the flow changes of other components to ensure the balance of the total ratio and the stability of the target concentration. In order to meet the high dynamics and complexity of mine filling operations, the automatic execution unit introduces a closed-loop control mechanism in the flow regulation process. This mechanism relies on real-time feedback data provided by the data acquisition and dynamic monitoring unit, such as the current slurry pressure, flow rate and component concentration. When the pump and valve system is adjusted, the sensor will immediately collect the latest operating status data and transmit it back to the control center to compare it with the target value predicted by the optimization calculation unit. If there is a deviation, the system will adjust the pump and valve parameters again through the automated execution unit until the actual state is consistent with the target value. Such closed-loop control enables the system to maintain a high degree of stability and adaptability under complex working conditions. For example, when the pressure in a section of the underground pipeline increases due to the drop, the system can relieve the pressure by reducing the feed flow rate of that section or slowing down the total flow rate, and ensure the continuous flow and safe transportation of the filling material.

[0057] Embodiment 2: The components of the filling material slurry include: tailings, cement, water and admixture; the real-time basic data of each component of the filling material slurry include: mass and slump.

[0058] Specifically, the components of the filling material slurry have their own characteristics and functions, and even a slight change in their proportions may have a profound impact on the final effect of the filling operation. Tailings, as the main aggregate, provides the basic skeleton of the filling material, and its particle size and quality directly affect the stability and filling strength of the slurry; cement, as a binder, is the core that determines the final solidification strength of the material, and changes in the amount of cement will significantly affect the performance of the slurry; water is not only a guarantee of fluidity in the entire slurry, but also directly related to the water-cement ratio, thus affecting the rheology, setting time and strength development of the slurry; admixtures are added in small amounts to achieve directional regulation of slurry properties, such as plasticizers to improve fluidity, early strength agents to accelerate setting speed, and water reducers to reduce water consumption but maintain slump. These components complement each other in the filling process. Only through accurate real-time proportioning can the multiple requirements of mine filling for strength, fluidity and safety be met. Quality and slump are two key variables, which provide an intuitive reflection of the slurry state from a quantitative and rheological perspective, respectively. Real-time quality monitoring enables the system to accurately control the feed amount of each component, thereby ensuring the realization of the target mix ratio. The feed quality of tailings, cement, water and admixtures is not only the basis for the initial mix ratio setting, but also the basis for dynamic adjustment. When the quality of a component is detected to be deviated in real time, the system can immediately issue an adjustment instruction, adjust the corresponding pump valve output, and correct the feed rate. For example, if the tailings quality is lower than the set value, the system will automatically increase the feed amount of tailings to compensate for the deficiency, and adjust the proportion of other components to maintain the balance of the overall mix ratio. The slump directly reflects the fluidity and anti-separation of the slurry. By monitoring the slump in real time, the system can evaluate the operability of the slurry in transportation and filling. When the slump is too high, it may mean that the slurry is too thin, which is easy to cause separation or water seepage; while the slump is too low, it may cause insufficient fluidity of the slurry and increase the risk of pipeline blockage. Through real-time feedback on the slump, the system can quickly adjust the feed ratio of water and admixture to keep the slurry in the optimal rheological state.

[0059] Example 3: Assuming at time The total mass of the filling material slurry is The masses of tailings, cement, water and admixture are , , and ; Define the multi-group distribution ratio constraints and total mass constraints as:

[0060] ;

[0061] in, is the symbol subscript index; represents tailings; represents cement; Represents water; represents additives; is the matching vector; ; For components The mass ratio of is dimensionless and has a value range of .

[0062] Specifically, in the automatic proportioning control system of the mine filling material of the present invention, the core principle of the formula of Example 3 is to establish the constraint relationship between the proportion of the components and the total mass by defining the total mass that changes with time and the dynamic mass of each component, thereby providing a clear mathematical framework for real-time proportioning optimization. The total filling material slurry mass is , and the masses of tailings, cement, water and admixtures are , , and , at this time, the mass conservation is expressed by a constraint, namely is equal to the sum of the masses of each component, and on this basis the ratio vector Defined as ,in Characterizes the proportion of each component in the total mass. In this way, it is possible to avoid losing control of the relative ratio due to dynamic fluctuations in absolute mass, especially when the mine filling process is constantly changing and flow rate and pressure fluctuations may occur in each pipeline section. Effective monitoring and control of key ratio parameters can still be maintained. Since the strength, fluidity and setting time requirements of such filling material slurries under different working conditions are often different, only by accurately controlling the relative mass ratio of tailings, cement, water and admixtures within an appropriate range can the safety and efficiency of the pipeline transportation process be taken into account while meeting the needs of underground void support or surrounding rock stability. Define the ratio vector The advantage of is that its value range is constant between zero and one, and the sum of its components is always one, which provides a concise feasible domain for the optimization algorithm: when the system is in operation, the real-time sensor data collected will characterize the current pressure, flow rate and corresponding slurry characteristics, and the algorithm will calculate the new optimal solution based on this information combined with the above-mentioned ratio constraints. In this way, the mathematical optimization process can be used to balance safety, economy and performance requirements at every moment to ensure the actual amount of filling material (i.e. Whether it is the imbalance of the ratio caused by insufficient tailings supply or the cost increase and rapid coagulation risk caused by excessive cement ratio, the corresponding In addition, the time variable is introduced This gives the model good scalability: when the mine operating environment or pipeline operating conditions change, it is not necessary to completely overturn the original ratio design, but only to continuously correct the ratio vector based on real-time monitoring, so that the system has the ability to adapt to various complex working conditions. Through this joint constraint of mass and ratio, Example 3 theoretically clarifies the quantitative connection and dynamic evolution mode between the components of the filling material, provides a rigorous and flexible numerical basis for the entire set of automated ratio control systems, and also provides a mathematical interface for coupling for subsequent solutions based on convection-diffusion equations or other physical models.

[0063] Example 4: Assuming at time Time component In Location The real-time local concentration is , satisfying the following flow-diffusion equation:

[0064] ;

[0065] in, is the slurry flow velocity field; is the gradient operator; is the slurry density; For components The relative sedimentation velocity, ; For components density; ; For pre-set components and The interaction resistance coefficient between For at the moment Time component In Location Real-time local concentration of is the acceleration due to gravity; is the slurry viscosity; For components The average particle size of For pre-set components The effective diffusion coefficient.

[0066] Specifically, in the formula, the components At the moment and location The concentration change It is determined by the combined action of multiple physical processes. These processes include convective transport caused by slurry flow, diffusion effect driven by concentration gradient, gravity effect of particle sedimentation, and interaction between multiple components. First, the time variation of concentration directly reflects the temporal trend of local concentration, while the convection term This reflects the effect of slurry flow on concentration distribution. Obtained from actual monitoring or simulation, it describes the flow characteristics of slurry in pipelines or underground spaces. The combination of these two parts reveals the overall migration law of slurry during transportation. In addition to convection transport, diffusion effect is a key factor affecting slurry uniformity. Diffusion term The diffusion coefficient in Determined by the physical properties of the components and the characteristics of the medium, it controls the diffusion rate of concentration from high concentration areas to low concentration areas. In mine filling material systems, this mechanism helps to alleviate the local concentration unevenness that may occur during transportation, thereby improving the uniformity of the slurry. At the same time, the gravity effect cannot be ignored in slurry transportation. Sedimentation term Describes the process by which particles settle downward due to gravity. The size depends on the particle density, particle size and slurry viscosity. The calculation formula is This relationship is directly revealed. The larger the particle size and the greater the difference between the density and the slurry density, the faster the sedimentation rate. This process is particularly significant in long-distance transportation or large drop pipelines, which may cause slurry separation or sedimentation. Through the introduction of the model, the system can dynamically adjust the flow rate and ratio according to the monitored concentration distribution to reduce the adverse effects of sedimentation.

[0067] In addition, the formula also takes into account the interaction between the components. Describes the interaction resistance effect between different components. This effect manifests itself as collision, adhesion or agglomeration between particles in multi-component slurries, and plays an important role in the evolution of concentration distribution. For example, when the concentration difference between tailings and cement particles is large, the interaction resistance will cause the particles to redistribute, thereby improving the overall uniformity. Through this term, the formula can effectively capture the complex interactions in multi-component systems and provide accurate input for optimization calculations. It is worth noting that the gravity effect in the formula is not only reflected in the sedimentation velocity, but also through The term further affects the concentration distribution. This term indicates that when the local density of a component exceeds the overall density of the slurry, gravity will drive it to settle downward, and vice versa. The coupling of this density gradient and the gravity field has an important influence on the concentration distribution in vertical transportation. By solving this model in real time, the system can predict possible concentration deviations in the pipeline and correct them by adjusting the ratio or flow rate.

[0068] Example 5: The slurry flow velocity field is obtained by solving the following equation:

[0069] ;

[0070] in, For pressure.

[0071] Specifically, in the automated proportioning control system of mine interlocking filling materials, Example 5 reveals the flow behavior of complex multi-component slurry in pipelines or underground spaces and its dynamic change mechanism under the action of multiple forces by solving the equation of slurry flow velocity field. The principles of each part of the formula start from different physical effects, covering inertial force, pressure gradient, viscous force, gravity and interaction force between multiple components, and establish a complete mathematical framework to describe the dynamic evolution of slurry velocity field. By solving this equation, the flow state during slurry transportation can be accurately controlled, providing key numerical support for the entire automated proportioning control system.

[0072] The left side of the formula contains , describes the inertial effect of the slurry. The first term It represents the time variation of the velocity field and reflects the dynamic variation of the velocity at different time points, which is the core of the transient characteristics of slurry flow. For multi-component slurries in pipelines, the change of the velocity field is usually unstable due to the changes in component concentrations and flow conditions, so this term is crucial to describe the dynamic characteristics of the slurry. It is the convection term of the velocity field, reflecting the velocity change caused by flow. In the process of conveying mine filling materials, the change of flow velocity may be affected by pipe bending, pressure gradient change or change of slurry component characteristics. This term can capture these complex changes. The first term on the right side of the formula is is the pressure gradient term, which represents the driving force of pressure on slurry flow. In the process of mine filling, the flow of slurry mainly depends on the pressure difference provided by the delivery pump, so the pressure gradient is the key parameter for controlling the flow rate. By real-time monitoring and calculation of pressure distribution, the uniformity of flow rate can be ensured to avoid pipeline rupture due to excessive pressure or flow stagnation due to insufficient pressure. The distribution of pressure gradient terms can also reflect local flow anomalies in the pipeline, such as flow blockage areas caused by local settlement. The second term is the viscous force term, which describes the regulating effect of the slurry viscosity on the velocity field. It is a function of multi-component concentrations and is affected by water content, tailings concentration, cement ratio, and admixture type. This term reflects the relationship between velocity gradient and viscosity, ensuring that the slurry maintains stable flow in the pipeline. Especially in long-distance transportation or complex pipeline layouts, viscosity is crucial to suppress the instability of the velocity field. When the slurry viscosity is too high, the viscosity will limit the increase in velocity; when the viscosity is too low, it may cause flow turbulence and concentration separation. The third term is the gravity term, which describes the physical effect of the slurry under the action of gravity. The effect of gravity on the velocity distribution is particularly obvious for vertical pipes or conveying pipes with drops in mine filling. The greater the density of the slurry, the more significant the effect of gravity. This term is crucial to describing the velocity changes in vertical flow. For example, in a pipeline with a large drop, the slurry may be accelerated by gravity, which will cause a sharp increase in downstream pressure. This phenomenon must be alleviated by real-time control of the pump speed or adjustment of the ratio. The last term It reflects the coupling effect between multiple components, especially the influence of sedimentation effect on the velocity field. It is a component The formula for the sedimentation velocity is This formula shows that the sedimentation velocity is proportional to the square of the particle size and is closely related to the particle density and slurry viscosity. The greater the sedimentation velocity, the more significant the effect of the particles on the velocity field. The concentration gradient in this term is It represents the spatial distribution of the concentrations of different components in the slurry, and its coupling effect reflects the adjustment of the migration behavior of particles to the flow velocity. For example, when the tailings concentration in a certain area is high, particle sedimentation will slow down the local flow velocity and may cause flow turbulence. This equation couples the flow inertia, pressure drive, viscous resistance, gravity effect and multi-component interaction of the slurry as a whole, forming a mathematical framework that comprehensively describes the slurry velocity field. In the automated proportioning control system, real-time solution of this equation can accurately predict the velocity distribution of the slurry at different locations, and adjust the pump speed and proportion in combination with real-time monitoring data. For example, when the velocity field shows that the flow velocity of a certain section of the pipeline decreases, it may be due to local blockage caused by sedimentation. At this time, the viscosity can be reduced by increasing the proportion of water or admixtures, or the risk of sedimentation can be eliminated by increasing the flow rate. Conversely, when the flow rate is too high and causes pressure fluctuations, the flow state can be optimized by reducing the pump speed or adjusting the pressure distribution.

[0073] Example 6: The comprehensive objective function is obtained by adding two parts: the local strength part and the local fluidity part; wherein the local strength part It is expressed by the following formula:

[0074] ;

[0075] In the formula, the core of the local strength depends on the concentration of cement This is because cement is the main bonding component of the filling material, and its content directly determines the strength of the support body formed after the slurry solidifies. The higher the cement concentration, the greater its strength contribution, but this relationship is not linear. It reflects the square root dependence of cement concentration on strength, which means that the strength contribution of cement increases rapidly at low concentrations and gradually approaches saturation at high concentrations. This nonlinear relationship reflects the actual law of cement use in mine filling: increasing cement content within a certain range can indeed significantly increase strength, but beyond a certain ratio, the bonding properties of the material reach an upper limit, and the cost-effectiveness of continuing to increase cement decreases. Therefore, this part is designed in square root form, which is a mathematical abstraction of this physical phenomenon. and admixtures The concentration is also incorporated into the formula through the denominator to constrain the relative contribution of cement concentration. This treatment method ensures that all solid components jointly affect the final strength during the multi-component mixing process of the slurry. Tailings, as the main aggregate of the filling material, provides physical support and filling effect for the slurry, but its strength contribution is limited, mainly through the combination with cement to form an integral structure. Therefore, the increase in tailings concentration will dilute the strength contribution of cement to a certain extent, and the formula cleverly reflects this point through the design of the denominator. In addition, admixtures The introduction of enhances the universality of the formula, allowing the system to adjust the type and amount of admixtures according to actual needs to further optimize strength performance. Then The form of water affects the local strength. Water is an important medium for forming slurry, but its increase may dilute the proportion of cementing components, thereby weakening the strength. The design with a negative index directly reflects this negative effect, and the size of the index value This indicates that water weakens strength slowly. This treatment method fully considers the balance between paste fluidity and strength: in actual filling operations, an appropriate amount of water is necessary, which not only ensures the fluidity of the paste, but also promotes the hydration reaction of cement, but too much water will lead to a decrease in the cohesion of the paste. Therefore, the negative impact of water concentration on strength is expressed in power form, which reasonably captures this complex relationship. The multiplication structure of the entire formula It is an overall expression of local strength. This form combines the strengthening effect of cement with the weakening effect of water, showing a dynamic balance of the strength characteristics of the filling material. is a set local strength coefficient used to adjust the applicability of the formula under different working conditions. For example, in mines with high support requirements, The value of is used to increase the weight of the strength part in the comprehensive objective function, so that the system is more inclined to improve the material strength when optimizing the ratio.

[0076] Local liquidity section , which is expressed by the following formula:

[0077] ;

[0078] The viscosity term in the formula It is the basis of local fluidity and directly reflects the core driving force of slurry fluidity. The viscosity of the slurry is determined by the concentration and physical properties of each component and is a key indicator of the overall rheological properties of the slurry. Lower viscosity means higher fluidity and easier transportation in pipelines, while higher viscosity increases flow resistance and reduces transportation efficiency. In mine filling systems, viscosity control is crucial because the slurry needs to maintain a stable flow state in long-distance, high-drop and complex curved pipelines. Through real-time monitoring and calculation , the system can dynamically adjust the component ratio so that the flow properties of the slurry always meet the transportation requirements. The formula further corrects the flowability by the ratio and slump of each component, reflecting the relative contributions of tailings, water, cement and admixtures respectively. This shows that tailings have an inhibitory effect on fluidity. Tailings are the main aggregate in the slurry. Although they play an important role in improving filling strength, due to their large particle size and high density, the increase of tailings tends to significantly increase the viscosity of the slurry and reduce its fluidity. The influence of tailings is restricted within a certain range, and the index The design shows that this inhibitory effect is nonlinear: changes in tailings proportion in a lower range have little effect on fluidity, while changes in tailings proportion in high concentration areas significantly aggravate the decrease in fluidity.

[0079] The effect of water on fluidity is designed to be positive, manifested as Water is the main lubricating medium of the slurry. The increase of its proportion can significantly reduce the viscosity of the slurry and improve the fluidity. However, this positive effect also has certain saturation characteristics, so the index is The power form of effectively captures this nonlinear relationship: in the low water ratio range, the increase of water significantly improves fluidity; while in the high water ratio area, the improvement of fluidity by water gradually weakens. In addition, the slump parameter of water Used as a correction factor to reflect the influence of the physical properties of water on the fluidity, such as temperature, impurity content, etc. Correction term for admixtures It shows that admixtures significantly enhance fluidity. There are many types of admixtures, including plasticizers, water reducers, etc. Their main function is to improve the rheological properties of the slurry. In the formula, the effect of admixtures is set as an exponent The square relationship shows that the admixture has a weak effect on enhancing fluidity at low proportions, but this effect increases rapidly as the proportion increases. This design is consistent with the actual use characteristics of admixtures, because admixtures can significantly improve the uniformity and anti-separation performance of the slurry within a certain proportion range, thereby effectively reducing the viscosity. By segmenting the modeling of the effects of each component, the formula fully reflects the nonlinear contribution of different components to the fluidity of the slurry. This design is particularly suitable for complex conditions of mine filling, because different pipeline layouts and transportation distances have different requirements for slurry fluidity. The system can monitor the group ratio in real time And the slump of each component , dynamically calculate the liquidity part In actual operation, when insufficient fluidity leads to increased transport resistance, the system can increase the proportion of water Or adjust admixture When the fluidity is too high and may cause separation or sedimentation, the system can appropriately increase the tailings or cement ratio to improve the consistency of the slurry.

[0080] in, Components The slump of ; then the comprehensive objective function The formula is:

[0081] ;

[0082] in, is the set local strength coefficient.

[0083] Example 7: The pressure safety upper limit is expressed using the following formula:

[0084] ;

[0085] in, The set safety upper limit of pressure; Indicates time The maximum pressure that occurs in a pipeline or underground space; pressure penalty function It is expressed by the following formula:

[0086] .

[0087] Specifically, the core of this embodiment is to ensure that the maximum pressure of the slurry during pipeline transportation and downhole filling is Always below the set safety threshold At the same time, through the pressure penalty function With the introduction of pressure limit formula, when the pressure approaches or exceeds the safety range, the system can impose strong constraints on the optimization target, thereby dynamically adjusting the ratio and delivery parameters to reduce safety risks. It is the basic constraint of the system and clarifies the mathematical expression of pressure safety. During the mine filling process, the flow state of the slurry is jointly affected by the pipeline layout, flow rate, component ratio and underground geological conditions. Since the pressure directly determines the carrying capacity of the pipeline and equipment, excessive pressure may cause a series of safety problems such as pipeline rupture, slurry leakage and even equipment damage, so it is very important to keep the pressure within the set range. It is a process-related fixed parameter, which is determined by the strength of the pipeline material, the design limit of the conveying equipment and the safety factor. By real-time monitoring of the pressure distribution in the system, especially calculating the maximum pressure at a certain moment , which can ensure that the pressure changes in each link during the transportation process are within the tolerable range of the system.

[0088] In actual operation, the pressure is not constant, but changes dynamically with the flow rate, concentration distribution and pipeline characteristics of the slurry. Therefore, setting a static pressure upper limit is not enough to achieve comprehensive control of the system. Therefore, this embodiment further introduces a pressure penalty function This function imposes a nonlinear constraint on the optimization objective by quantifying the extent to which the pressure is exceeded. Make sure that only When the pressure exceeds the safety threshold, the penalty function will be activated. , will not affect the optimization objective. This design avoids unnecessary constraints and enables the system to fully utilize its delivery efficiency during normal operation. However, once the pressure exceeds the limit, the exponential nature of the penalty function will cause its value to rise rapidly, forcing the system to take necessary adjustments through the optimization algorithm. The mathematical structure of the pressure penalty function reflects the nonlinear sensitivity to pressure exceeding the limit. When Just over When , the value of the penalty function is slightly higher than 1, which has little impact on system optimization, but as the limit exceeds the limit, It grows exponentially. This feature causes the risk of pressure overlimit to be rapidly amplified in the optimization goal, and the optimization algorithm will give priority to reducing the pressure risk of the system. For example, when the pressure of a certain section of the pipeline is monitored to be close to the safety upper limit, the system may alleviate the trend of pressure increase by reducing the slurry flow rate or adjusting the group ratio (such as increasing the water ratio to reduce viscosity). If the degree of overlimit is large, the effect of the penalty function will be further enhanced, forcing the system to take more drastic countermeasures, such as temporarily reducing the pump pressure or adjusting the transportation path to ensure safety. This dynamic pressure management mechanism is particularly important in complex working conditions in mines. Mine filling systems usually face the challenges of long-distance transportation, large-drop pipelines and complex geological conditions, which may lead to significant changes in the pressure distribution in the pipeline. Through the pressure penalty function, the system can respond to these changes in real time and adjust the optimization plan according to the actual distribution of pressure. For example, in a large-drop pipeline, gravity may cause a sudden increase in local pressure. At this time, the system can use pressure distribution prediction to include the pressure risk of the high-pressure area into the optimization goal in advance, thereby avoiding the actual overlimit. In addition, the parameters in the penalty function Controls the sensitivity of penalty growth. The design of this parameter needs to strike a balance between fast response and numerical stability. Larger parameter values ​​will increase the sensitivity of the penalty function to over-limit pressure, but may introduce over-constraints during the optimization process, resulting in a decrease in system performance; while smaller parameter values ​​may make the system not respond quickly enough to over-limit pressure. In practical applications, by adjusting this parameter, the sensitivity of the system can be adjusted according to the specific working conditions and safety requirements of the mine, so as to achieve the optimal balance between safety and efficiency.

[0089] Example 8: Integrating the comprehensive objective function and the pressure penalty function into a Lagrangian function In the formula, the following is true:

[0090] ;

[0091] in, is the Lagrange multiplier; taking the partial derivative of the Lagrange function, the first-order condition is expressed by the following formula:

[0092] .

[0093] Specifically, the introduction of the Lagrangian function solves the problem of how to balance material performance and pressure safety in complex working conditions in mines. As the core goal of system optimization, it directly describes the local strength and fluidity characteristics of the filling material, while the pressure penalty function It is used to constrain the behavior of the optimization objective when the pressure exceeds the limit. and The combination is in fractional form, that is , the system achieves dynamic coordination between performance and pressure. When the pressure is lower than the safety upper limit, , the optimization objective is mainly composed of The optimization direction of the system is to improve the performance of the filling material; when the pressure approaches or exceeds the safety threshold, the penalty function The value of increases rapidly, the optimization target is significantly suppressed, and the system will give priority to adjusting the ratio to reduce the pressure risk. This design allows the system to optimize material performance as much as possible without sacrificing safety, thereby achieving dual guarantees of performance and safety in the complex filling environment of the mine. Lagrange multiplier In this framework, it plays a key role. By introducing the ratio normalization constraint, the optimization process can maintain the conformity with physics and actual operation. The sum must be 1, which is the basic requirement of mass conservation in physics and a necessary constraint for feeding in actual operation. Dynamically adjust the impact of constraints on optimization variables to ensure that the optimization process does not deviate from this basic condition. For example, at a certain moment, when the system optimization needs to increase the proportion of water When , the Lagrangian function is Adjust other components (such as tailings and cement ) to maintain the overall balance of the ratio. This mechanism makes the optimization result of the system not only mathematically reasonable, but also can be efficiently executed in actual filling operations.

[0094] The partial derivative condition of the Lagrangian function reveals the interaction between the comprehensive objective function and the pressure penalty function in the optimization process. The conditional form obtained by taking the partial derivative of the Lagrangian function is It contains three key parts. Directly reflects the comprehensive objective function Ratio of components Through this part, the system can identify the contribution of different components to strength and fluidity. For example, when the increase in cement proportion at a certain moment significantly improves the material strength, the optimization algorithm will prioritize the adjustment of cement feed to achieve strength optimization. However, as the pressure gradually approaches the safety upper limit, the second The influence of begins to emerge. This term originates from the pressure penalty function and describes the constraint effect of pressure exceeding the limit on the optimization process. Since the penalty function grows rapidly in a nonlinear manner, The inverse of The weight of the Lagrange multiplier is used to reduce the pressure first. For example, when the pressure rises sharply due to the increase in the tailings ratio, this part will quickly guide the system to reduce the tailings ratio and increase the proportion of water or admixtures to alleviate the problem of excessive pressure. The dynamic adjustment of further enhances the flexibility and adaptability of the system. Its role is to maintain the strictness of the ratio constraints and ensure the rationality of the optimization direction by exerting a balanced influence on the optimization variables. For example, when the ratio adjustment of a certain component is large, the multiplier It will be fed back to the optimization variable through the constraint term to balance the changes in the proportion of other components and avoid the instability of system performance due to excessive adjustment of a single component. This optimization framework has significant application value in practice. In mine filling operations, the complexity of pipeline layout and the dynamic changes in slurry characteristics often lead to challenges in multi-objective optimization. For example, in long-distance transportation scenarios, drastic changes in pipeline pressure may cause safety hazards. The system needs to dynamically adjust the component ratio to control the pressure by solving the partial derivative conditions of the Lagrangian function in real time. At the same time, in order to meet the support strength requirements of the underground filling space, the system must also take into account the strength target in the ratio optimization. The Lagrangian function enables the system to achieve precise control in complex and changeable working conditions through the synergy of the comprehensive objective function and the pressure penalty function.

[0095] Embodiment 9: The process of dynamically solving the optimal ratio using the Newton-Raphson method specifically includes:

[0096] Iterate through the following formula:

[0097] ;

[0098] in, Indicates time No. The matching vector of the iteration; Indicates time No. The matching vector of the iteration; is the transpose operation;

[0099] For the moment No. The gradient vector of iteration:

[0100] ;

[0101] in, For the moment No. The Lagrangian function of the iteration;

[0102] For the moment No. The Jacobian matrix of the iteration:

[0103] ;

[0104] The iteration is terminated when the following conditions are met:

[0105] ;

[0106] ;

[0107] in, is the set gradient threshold; is the set iteration threshold.

[0108] Specifically, in this method, the matching vector It is defined as the dynamic state of multiple component distribution ratios, including the ratio of tailings, cement, water and admixtures. , the system constructs the Lagrangian function based on the optimization objectives and constraints , combining the comprehensive objective function (such as the trade-off between strength and fluidity) with the pressure penalty function to form a complete optimization framework. The core idea of ​​the Newton-Raphson method is to use the gradient of the Lagrangian function and the Jacobian matrix Accurately characterize the change of function value, so as to quickly converge to the global optimal ratio during the iteration process. It is the key in the optimization process, and its components are the partial derivatives of the Lagrangian function with respect to each component in the ratio vector. The physical meaning of the gradient is how a small change in the proportion of each component under the current ratio will affect the optimization objectives and constraints. For example, when an increase in the tailings ratio may lead to an increase in pressure, the gradient component related to the tailings will reflect this risk, which is manifested as an increase in negative values. This information is used to guide the reduction of the tailings ratio in the next iteration, thereby balancing the pressure risk and material properties. Jacobian matrix It describes the rate of change of the gradient to the ratio vector, which is the matrix form of the second-order derivative, reflecting the interaction between the components in the system. For example, increasing the tailings ratio will not only affect the pressure, but may also indirectly affect the effects of water and admixtures. This coupling effect is reflected by the non-diagonal terms of the Jacobian matrix. Using the inverse of the Jacobian matrix, the system can construct a quadratic approximation of the function in the neighborhood of the current solution and calculate a more accurate update direction and step size.

[0109] In each iteration, the Newton-Raphson method completes the update of the matching vector through a formula. This update formula is based on the idea of ​​Taylor expansion, which decomposes the change of the function value into a first-order gradient term and a second-order correction term. The first term Shows the current ratio state, minus the gradient vector The inverse of the Jacobian matrix is ​​used to point to the direction in which the objective function is decreasing; and the update step size and direction are precisely adjusted through the inverse of the Jacobian matrix, thereby improving the convergence speed. It is worth noting that the termination condition of the Newton-Raphson method ensures the efficiency and accuracy of the iteration. Less than the preset threshold When , it means that the optimization target is close to the extreme value point; and when the ratio of two consecutive iterations changes Less than another threshold , the system considers that the proportion adjustment has stabilized. These two types of conditions together ensure that the iteration process will not continue unnecessarily, which not only improves the ability to respond in real time, but also avoids suboptimal solutions caused by premature stopping. The physical meaning of the formula is particularly significant in the dynamic environment of mine filling. For example, when real-time monitoring shows that the pressure in a certain section of the pipeline is close to the safety upper limit, the components related to tailings and cement in the gradient vector will increase significantly, indicating that these two components contribute more to the pressure. In the next iteration, the second-order information calculated by the Jacobian matrix further indicates that appropriately increasing the proportion of water or admixture can not only reduce the pressure, but also improve the fluidity of the slurry. This adjustment strategy is automatically implemented through the Newton-Raphson method, which enables the system to maintain efficient operation under dynamic conditions. In addition, the calculation and inversion of the Jacobian matrix is ​​the computational bottleneck of the algorithm and the key guarantee of system performance. The multi-component coupling characteristics in mine filling make the Jacobian matrix usually a complex asymmetric matrix, whose value depends on the current proportion state and pressure distribution. In the actual solution, the system will use numerical methods to approximate the inversion of the Jacobian matrix, such as Gaussian elimination or preconditioned conjugate gradient method, to balance the calculation accuracy and time cost. The performance of this formula in practical applications reflects the intelligent characteristics of the present invention. Under complex working conditions, the operating conditions of the mine filling system are constantly changing, such as pipeline layout, downhole pressure fluctuations, and dynamic changes in slurry performance requirements. The Newton-Raphson method calculates the gradient and Jacobian matrix of the Lagrangian function in real time, so that the system can respond quickly to these changes and generate the optimal ratio scheme that meets current needs. Especially in long-distance transportation or complex geological conditions, the dynamic changes in pressure risk will significantly affect the priority of ratio optimization, and this method can adjust the ratio at the fastest speed to adapt to changes in working conditions by accurately capturing gradients and second-order information.

[0110] Although the specific embodiments of the present invention are described above, it should be understood by those skilled in the art that these specific embodiments are only illustrative, and those skilled in the art may omit, replace, and change the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, merging the above method steps so as to perform substantially the same functions in substantially the same manner to achieve substantially the same results is within the scope of the present invention. Therefore, the scope of the present invention is limited only by the appended claims.

Claims

1. An automated proportioning control system for mine filling materials, characterized in that: The system includes: a data acquisition and dynamic monitoring unit, an intelligent control and optimization calculation unit and an automatic execution unit; the data acquisition and dynamic monitoring unit is used to collect the real-time basic data of the pressure of the pipeline or underground space and each component of the filling material slurry through various sensors, define multi-group distribution ratio constraints and total mass constraints, construct the convection-diffusion equation of the filling material slurry in the pipeline or underground space, calculate the real-time local concentration of each component of the filling material slurry in combination with the slurry flow velocity field, and establish a comprehensive objective function for measuring the filling performance; the intelligent control and optimization calculation unit is used to construct a pressure penalty function to quantify the over-limit risk according to the determined pressure safety upper limit; the comprehensive objective function and the pressure penalty function are integrated into a Lagrangian function, the partial derivative of the Lagrangian function is obtained, the first-order condition is obtained, and the Newton-Raphson method is used to dynamically solve the optimal ratio; the automatic execution unit is used to convert the optimal ratio into the feed flow rate of each component, and execute it through pump valve control; The comprehensive objective function is obtained by adding two parts: local strength part and local fluidity part. It is expressed by the following formula: ； Among them, at the time Time component In Location The real-time local concentration is ; is the symbol subscript index; represents tailings; represents cement; Represents water; represents additives; is the set local strength coefficient; Local liquidity section , which is expressed by the following formula: ； in, For components The slump of ; is the slurry viscosity; For components The mass ratio of is dimensionless and has a value range of ; then the comprehensive objective function The formula is: ； The pressure safety upper limit is expressed using the following formula: ； in, The set safety upper limit of pressure; Indicates time The maximum pressure that occurs in a pipeline or underground space; pressure penalty function It is expressed by the following formula: 。 2. The automatic proportioning control system for mine interlocking filling materials according to claim 1, characterized in that: The components of the filling material slurry include: tailings, cement, water and admixtures; the real-time basic data of each component of the filling material slurry includes: quality.

3. The automatic proportioning control system for mine interlocking filling materials according to claim 2, characterized in that: Set at time The total mass of the filling material slurry is The masses of tailings, cement, water and admixture are , , and ; Define the multi-group distribution ratio constraints and total mass constraints as: ； in, is the matching vector; .

4. The automatic proportioning control system for mine interlocking filling materials according to claim 3, characterized in that: Set at time Time component In Location The real-time local concentration is , satisfying the following flow-diffusion equation: ； in, is the slurry flow velocity field; is the gradient operator; is the slurry density; For components The relative sedimentation velocity, ; For components density; ; For pre-set components and The interaction resistance coefficient between For at the moment Time component In Location Real-time local concentration of is the acceleration due to gravity; For components The average particle size of For pre-set components The effective diffusion coefficient.

5. The automatic proportioning control system for mine interlocking filling materials according to claim 4, characterized in that: The slurry flow velocity field is obtained by solving the following equation: ； in, For pressure.

6. The automatic proportioning control system for mine interlocking filling materials according to claim 1, characterized in that: Integrate the comprehensive objective function and pressure penalty function into a Lagrangian function In the formula, the following is true: ； in, is the Lagrange multiplier; taking the partial derivative of the Lagrange function, the first-order condition is expressed by the following formula: 。 7. The automatic proportioning control system for mine interlocking filling materials according to claim 6, characterized in that: Using the Newton-Raphson method, the process of dynamically solving the optimal ratio includes: Iterate through the following formula: ； in, Indicates time No. The matching vector of the iteration; Indicates time No. The matching vector of the iteration; is the transpose operation; For the moment No. The gradient vector of iteration: ； in, For the moment No. The Lagrangian function of the iteration; For the moment No. The Jacobian matrix of the iteration: ； The iteration is terminated when the following conditions are met: ； ； in, is the set gradient threshold; is the set iteration threshold.

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