Manufacturing method of new environmentally friendly and energy-saving materials for roads and bridges based on intelligent algorithms

Abstract

The present invention relates to the technical field of material optimization, and further to a method for manufacturing new environmentally friendly and energy-saving materials for roads and bridges based on intelligent algorithms. The method comprises: step 1: setting the porosity of the material as the key value of the optimization target, taking the porosity as a variable parameter, setting the strength function and thermal conductivity function of the material, and setting the cost function in the material manufacturing process; step 2: defining the weights of the strength function, thermal conductivity function and cost function respectively, calculating the weighted sum of the strength function, thermal conductivity function and cost function to define the target function of material manufacturing; step 3: using an improved particle swarm algorithm to iteratively optimize the porosity until the set number of iterations is reached. The present invention utilizes particle swarm optimization technology to significantly reduce the manufacturing cost while ensuring that the material has excellent mechanical properties.

Description

Technical Field

[0001] The present invention belongs to the technical field of material optimization, and in particular relates to a method for manufacturing new environmentally friendly and energy-saving materials for roads and bridges based on intelligent algorithms. Background Art

[0002] With the continuous advancement of global infrastructure construction, especially the increase in major engineering projects such as roads and bridges, the demand for high-performance, low-cost, environmentally friendly and energy-saving materials is becoming increasingly urgent. Road and bridge engineering materials play a vital role in the construction and maintenance of such infrastructure. Traditional road and bridge materials such as concrete and steel, although they have good mechanical properties and durability, their high energy consumption, high emissions and relatively high manufacturing costs have become bottlenecks restricting their widespread application. Therefore, the development of new materials with excellent performance and environmental protection and energy saving has become an important research direction in the current field of engineering materials. Existing road and bridge materials are mainly high-strength concrete and high-performance steel. High-strength concrete is widely used in bridge construction due to its good compressive properties and long service life. However, the manufacturing process of high-strength concrete requires a large amount of cement, which not only leads to huge energy consumption, but also generates a large amount of carbon dioxide emissions, increasing the environmental burden. In addition, concrete has poor thermal conductivity. Under extreme climatic conditions, cracks are easily formed due to thermal expansion and contraction, affecting the stability and service life of the bridge structure. In order to improve the thermal conductivity of concrete, the prior art attempts to improve its thermal conductivity by adding thermally conductive fillers or admixtures, but these measures often lead to increased material costs and complicated construction processes, making them difficult to promote on a large scale in actual projects.

[0003] The optimization of existing materials often focuses on improving a single performance, such as enhancing mechanical properties or improving durability. However, the performance of materials is multidimensional, especially in road and bridge applications, where materials need to meet multiple requirements such as strength, thermal conductivity, durability and economy at the same time. The existing technology lacks a method that can achieve global optimization among multiple objectives, resulting in the improvement of one performance of the material while other performances are often damaged, making it difficult to meet the needs of comprehensive applications. High performance of materials is often accompanied by high costs. For example, although composite materials have excellent mechanical properties, their high manufacturing costs limit their large-scale application. When optimizing materials, the existing technology often ignores the cost factor, resulting in the optimized materials being difficult to promote in practical applications despite their excellent performance. In addition, there is a lack of a systematic method for balancing cost and performance in the material optimization process, and it is impossible to maximize economy while ensuring material performance. In road and bridge materials, there is often a certain contradiction between thermal conductivity and strength. For example, although concrete materials have high strength, their thermal conductivity is poor, and they are prone to thermal stress during temperature changes, affecting structural stability. The existing technology lacks in-depth research and optimization methods on the relationship between thermal conductivity and strength, which limits the application of materials in extreme environments. Summary of the invention

[0004] The main purpose of the present invention is to provide a method for manufacturing new environmentally friendly and energy-saving road and bridge materials based on intelligent algorithms, which achieves a balance of multi-objective performance by optimizing the porosity, strength, thermal conductivity and manufacturing cost of the material. The method uses particle swarm optimization technology to significantly reduce the manufacturing cost while ensuring that the material has excellent mechanical properties.

[0005] In order to solve the above problems, the technical solution of the present invention is achieved as follows:

[0006] A method for manufacturing new environmentally friendly and energy-saving materials for roads and bridges based on intelligent algorithms, the method comprising:

[0007] Step 1: Set the porosity of the material as the key value of the optimization target, use the porosity as a variable parameter, set the strength function and thermal conductivity function of the material, and set the cost function in the material manufacturing process;

[0008] Step 2: By defining the weights of the strength function, thermal conductivity function and cost function respectively, the weighted sum of the strength function, thermal conductivity function and cost function is calculated to define the objective function of material manufacturing;

[0009] Step 3: Use the improved particle swarm algorithm to iteratively optimize the porosity until the set number of iterations is reached, specifically including: initializing a group of particles representing possible porosity solutions; each particle has an initial position and initial velocity, and a nonlinear function is used to ensure the diversity of the initial solution and cover the entire search space; using the improved particle swarm algorithm to update the position and velocity of each particle, and using the objective function defined in step 2 as the objective function of the improved particle swarm algorithm. During the updating process, the goal is to maximize the value of the objective function; introducing an adaptive mutation mechanism to dynamically adjust the mutation probability and mutation intensity according to the current number of iterations; performing a local search for the current global optimal solution, and using a nonlinear function to adjust the position of the solution.

[0010] Furthermore, in step 3, a group of particles representing possible porosity solutions is initialized by the following formula:

[0011] ;

[0012] ;

[0013] in, For the The initial position of each particle represents the porosity; For the The initial velocity of each particle; is the minimum porosity; is the maximum porosity; is the maximum permissible speed; for A random number in the range.

[0014] Furthermore, in step 3, the position and velocity of each particle are updated using the improved particle swarm algorithm using the following formula:

[0015] ;

[0016] ;

[0017] ;

[0018] in, For the Particles in The speed of the moment; For the Particles in The speed of the moment; For the Particles in The location at the moment; For the Particles in The acceleration of the moment; is the time step; is the global best position; is the dynamic inertia weight; is the first dynamic acceleration coefficient; is the second dynamic acceleration coefficient; and Are all random numbers in the range of 0 to 1.

[0019] Furthermore, in step 3, the maximum porosity and the minimum porosity satisfy the following constraint relationship:

[0020] .

[0021] Furthermore, in step 3, the adaptive mutation mechanism is expressed by the following formula:

[0022] ;

[0023] in:

[0024] ;

[0025] ;

[0026] in, is the variation intensity; is the mutation probability; is the set initial mutation strength; is the set initial mutation probability; is the minimum value of the objective function; is the maximum value of the objective function; Indicates is the value of the objective function of the variable; is a random number ranging from 0 to 1; is the maximum time;

[0027] Furthermore, in step 3, the current global optimal solution is locally searched using the following formula:

[0028] ;

[0029] in:

[0030] ;

[0031] in, is the new global optimal solution after local search; is the local search step size; is the initial local search step size.

[0032] Furthermore, the objective function Use the following formula to express it:

[0033] ;

[0034] in, Strength objective function; is the heat conduction objective function; is the cost objective function; is the intensity weight; is the thermal conductivity weight; is the cost weight.

[0035] Furthermore, in step 1, the strength function of the material defined is Use the following formula to express it:

[0036] ;

[0037] in, is the initial strength of the solid phase of the material; is the porosity; is the porosity corresponding to the maximum strength of the solid phase of the material; is the strength correction factor, ranging from 0.1 to 0.3; the strength objective function is expressed using the following formula:

[0038] ;

[0039] in, Adjust parameters for intensity; is the minimum strength required;

[0040] Thermal conductivity function of the material defined Use the following formula to express it:

[0041] ;

[0042] in, is the initial thermal conductivity of the solid phase; is the thermal conductivity of air; is the thermal conductivity correction factor, ranging from 0.5 to 2; the thermal conductivity objective function is expressed using the following formula:

[0043] ;

[0044] in, is the optimal thermal conductivity; Adjust parameters for thermal conductivity.

[0045] Furthermore, the cost function of the material manufacturing process is Use the following formula to express it:

[0046] ;

[0047] in, is the initial manufacturing cost of the unit material; is the preset critical porosity;

[0048] ;

[0049] in, is the unit cost of the pore former; is the ideal porosity; Adjust parameters for cost.

[0050] The method for manufacturing new environmentally friendly and energy-saving road and bridge materials based on intelligent algorithms of the present invention has the following beneficial effects: the present invention uses intelligent algorithms, such as particle swarm optimization algorithms, to perform accurate multi-objective optimization on the porosity of the material. In the optimization process, strength, thermal conductivity and manufacturing cost are integrated into a comprehensive objective function, and the optimization direction under different engineering requirements is flexibly adapted by adjusting the weights. This multi-objective optimization strategy effectively solves the problem that it is difficult to balance material performance and cost in the prior art. In practical applications, the material can not only maintain sufficient mechanical strength and good thermal conductivity, but also effectively control the manufacturing cost, thereby improving the economy and market competitiveness of the material. Traditional material design relies on a large number of experiments and experience accumulation, and the optimization process is time-consuming and easily affected by human factors, resulting in low efficiency and unstable results. The present invention introduces intelligent algorithms, and significantly improves the optimization efficiency and accuracy through automated and systematic optimization processes. The intelligent algorithm can quickly find the optimal solution in a complex multidimensional search space, avoiding the local optimal solution trap that may occur in traditional methods. Especially when dealing with multi-objective optimization problems, the intelligent algorithm shows strong adaptability and robustness, making the material design process more scientific and reasonable. The material strength function and thermal conductivity function of the present invention accurately describe the effect of porosity on material performance through a sophisticated mathematical model. The strength function takes into account the nonlinear attenuation effect of increased porosity on the structural integrity and load-bearing capacity of the material, and accurately simulates the mechanical behavior of the material at different porosities through a combination of polynomial and exponential functions. The thermal conductivity function optimizes the performance of the material under extreme temperature conditions by describing the effect of porosity on the thermal conductivity of the material. By optimizing these two performance functions, the present invention achieves fine control of the material's strength and thermal conductivity, ensuring that the material achieves the best balance between high strength and good thermal conductivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A schematic flow chart of a method for manufacturing new environmentally friendly and energy-saving materials for roads and bridges based on an intelligent algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0053] Example 1: Reference Figure 1 , a method for manufacturing new environmentally friendly and energy-saving road and bridge materials based on intelligent algorithms, the method comprising:

[0054] Step 1: Set the porosity of the material as the key value of the optimization target, use the porosity as a variable parameter, set the strength function and thermal conductivity function of the material, and set the cost function in the material manufacturing process;

[0055] The manufacturing method of the new environmentally friendly and energy-saving road and bridge material sets the porosity of the material as the key value of the optimization target, thereby reflecting its significant advantages in structural performance and energy-saving effect in the material design process. Porosity is the ratio of the internal voids of the material to the total volume, and is a key parameter affecting the performance of the material. Especially in road and bridge engineering, the porosity of the material is directly related to its mechanical strength, durability, thermal conductivity and other aspects. The optimization of porosity can not only adjust the density of the material, thereby changing its strength and stiffness, but also affect its thermal conductivity by changing the heat conduction path of the material. The materials in the road and bridge engineering need to have sufficient strength to withstand heavy pressure and good thermal conductivity to cope with temperature changes. Under the requirements of environmental protection and energy saving, the manufacturing cost of the material must also be controlled within a reasonable range. Therefore, the present invention takes porosity as a variable parameter, and sets the strength function, thermal conductivity function and cost function related to it, aiming to achieve the optimal combination of material properties. First, the change of porosity will directly affect the internal structure of the material, thereby changing its mechanical strength. For road and bridge materials, mechanical strength is the basis for ensuring their stability and durability. When setting the strength function of the material, it is necessary to consider the effect of porosity on the arrangement of particles inside the material and its bonding force. A higher porosity usually means that there are more voids inside the material, which may lead to a decrease in the overall strength of the material. However, reasonable control of porosity can optimize the density of the material to a certain extent, so that it can reduce its own weight while ensuring strength, and meet the demand for lightweight materials in road and bridge projects. In addition, the optimization of porosity can also affect the deformation capacity of the material, so that it can better disperse stress under heavy load conditions and avoid local damage, thereby improving the overall stability and service life of the road and bridge structure. Secondly, thermal conductivity is an important factor that must be considered when road and bridge materials cope with changes in ambient temperature. The thermal conductivity of the material directly affects its performance under high or low temperature conditions, especially under extreme climatic conditions, the thermal conductivity of the material will affect the thermal expansion and contraction of the road and bridge structure. Porosity has a significant effect on the thermal conductivity of the material, because the voids inside the material will form air layers, which have lower thermal conductivity, thereby reducing the transfer of heat. Therefore, by optimizing the porosity, the thermal conductivity of the material can be effectively adjusted so that it can maintain stable performance under high temperatures in summer or low temperatures in winter. In addition, the thermal conductivity of the material is closely related to the energy-saving performance. The optimized porosity can not only improve the thermal resistance of the material and reduce heat loss, but also reduce the overall energy consumption of the road and bridge project, thereby achieving the goal of environmental protection and energy saving. Finally, cost control is a factor that cannot be ignored in the material manufacturing process. Road and bridge projects usually involve large-scale material use, so the cost of materials is directly related to the economic benefits of the project. By setting a cost function related to porosity, the manufacturing cost of the material can be effectively predicted and controlled in the design stage. Higher porosity may mean lower material density, which can not only reduce the consumption of raw materials, but also reduce transportation and construction costs.However, too high a porosity may lead to a decline in material performance and increase the cost of subsequent maintenance. Therefore, in the present invention, the cost function, strength function, and thermal conductivity function together constitute the key part of the multi-objective optimization problem. By weighing and balancing the three, it is ensured that the material meets the strength and thermal conductivity requirements while minimizing the cost, and finally produces an environmentally friendly and energy-saving material that meets the needs of road and bridge engineering.

[0056] Step 2: By defining the weights of the strength function, thermal conductivity function and cost function respectively, the weighted sum of the strength function, thermal conductivity function and cost function is calculated to define the objective function of material manufacturing;

[0057] First, the strength of road and bridge engineering materials is a key factor in determining whether they can withstand huge loads and complex environmental stresses. High-strength materials can provide better durability, extend the service life of roads and bridges, and reduce the frequency of maintenance and repair. Therefore, in the optimization process, the importance of strength is usually given a higher weight. By setting the weights reasonably, it can be ensured that the material will not sacrifice its basic mechanical properties due to excessive pursuit of low cost or thermal conductivity while optimizing other properties. In this way, the material can not only maintain stability under extreme weather and long-term heavy load conditions, but also effectively deal with stress concentration and fatigue damage in the road and bridge structure, thereby ensuring the safety and reliability of the project. Secondly, thermal conductivity is also a performance indicator that cannot be ignored in road and bridge materials, especially in scenarios where the impact of temperature changes on material structures needs to be considered. Road and bridge projects are often exposed to various complex environmental conditions. The thermal conductivity of the material is directly related to its thermal expansion and contraction behavior, which affects the stability of the entire structure. If the thermal conductivity of the material is not designed properly, it may lead to local thermal stress concentration, which in turn causes cracks or other structural problems. Therefore, when setting the objective function, the weight of thermal conductivity must be finely adjusted to ensure that the material can still effectively manage the transfer and diffusion of heat while meeting other performance requirements. In addition, optimizing the thermal conductivity of materials can also help improve the overall energy saving effect, reduce energy loss under extreme temperature conditions, and improve the environmental adaptability of road and bridge structures. Finally, cost is a factor that must be strictly controlled in the manufacturing process of road and bridge materials. Considering that road and bridge projects usually require large-scale use of materials, the manufacturing cost of materials will directly affect the overall budget and economy of the project. Therefore, in the optimization process, the setting of the cost function is crucial, which not only involves the procurement cost of raw materials, but also covers the energy consumption and resource consumption in the manufacturing process. By setting the cost weights reasonably, the various expenditures in material production can be effectively controlled, so that the final material is economically feasible. When setting the weights, cost is usually included in the multi-objective optimization model together with strength and thermal conductivity, and the optimal combination of material performance and cost is achieved by balancing the relationship between the three. The principle of step 2 is to form a weighted sum objective function by assigning appropriate weights to strength, thermal conductivity and cost respectively, so as to consider multiple performance indicators simultaneously in the optimization process of materials. The innovation of this method is that it can not only incorporate different performance indicators into the same optimization framework, but also flexibly adjust the priority of each performance according to engineering needs. This process is particularly important in the manufacture of new environmentally friendly and energy-saving materials for roads and bridges, as it ensures that the materials achieve high performance and high reliability while minimizing the consumption of resources and energy, thereby achieving true energy-saving and environmental protection goals.

[0058] Step 3: Use the improved particle swarm algorithm to iteratively optimize the porosity until the set number of iterations is reached, specifically including: initializing a group of particles representing possible porosity solutions; each particle has an initial position and initial velocity, and a nonlinear function is used to ensure the diversity of the initial solution and cover the entire search space; using the improved particle swarm algorithm to update the position and velocity of each particle, and using the objective function defined in step 2 as the objective function of the improved particle swarm algorithm. During the updating process, the goal is to maximize the value of the objective function; introducing an adaptive mutation mechanism to dynamically adjust the mutation probability and mutation intensity according to the current number of iterations; performing a local search for the current global optimal solution, and using a nonlinear function to adjust the position of the solution.

[0059] As an optimization method based on swarm intelligence, the core idea of ​​particle swarm algorithm comes from the simulation of group behavior in nature, especially the dynamic process of bird flocks foraging and fish schools swimming. Through the iterative update of particle position and velocity, PSO algorithm can gradually approach the optimal solution of the problem. In the present invention, the improved particle swarm algorithm is used to optimize the porosity of road and bridge materials. This is because porosity is an important parameter that directly affects the microstructure and performance of materials. Reasonable porosity optimization can significantly improve the overall performance of materials, while reducing manufacturing costs and energy consumption, thereby achieving the goal of environmental protection and energy saving. First of all, the porosity of materials is an important variable for optimizing material performance in road and bridge engineering. The size of porosity not only affects the strength and thermal conductivity of materials, but is also closely related to the weight and cost of materials. In the optimization process, each particle group needs to be assigned an initial position and initial velocity representing different porosities in the initial stage. These initial particles represent possible solutions for the porosity of the material. Through the distribution of these solutions, the algorithm can fully explore the entire search space, thereby avoiding the trap of falling into the local optimal solution. In order to ensure the diversity of the initial solution, the algorithm introduces a nonlinear function for initialization. This strategy enables the particle swarm to cover a wider search space and enhances the global search capability of the algorithm. In the design of new energy-saving materials for roads and bridges, this initial diversity is particularly important because it ensures that the different performance requirements of the material (such as strength, thermal conductivity and cost) are fully considered, thereby avoiding the neglect of certain key performances due to the limitations of the search space in the early stage. Next, the core step of the particle swarm algorithm is the dynamic update of the particle position and velocity. In each round of iteration, the position update of the particle follows two main mechanisms: one is the approach to its own historical optimal position, and the other is the approach to the global optimal position. This mechanism enables the particles to continuously approach the optimal solution while exploring the unknown solution space. In the material optimization of the present invention, the objective function is the weighted sum objective function defined in step 2. Through this function, the algorithm can dynamically evaluate the pros and cons of the current porosity solution of each particle and adjust the particle's motion trajectory accordingly. Since there is often a complex nonlinear relationship between the strength, thermal conductivity and cost of road and bridge materials, the particle swarm algorithm needs to flexibly adjust the position of the particles during the optimization process to find the best balance between multiple performance indicators. Through multiple iterations, the algorithm gradually converges to a global optimal solution, that is, finding a porosity value that can achieve the best combination between strength, thermal conductivity and cost.

[0060] On this basis, the present invention further introduces an adaptive mutation mechanism to enhance the exploration ability of the particle swarm algorithm. The adaptive mutation mechanism is achieved by dynamically adjusting the mutation probability and mutation intensity. In the early iterations of the algorithm, higher mutation probability and mutation intensity can prompt the particle swarm to explore a wider solution space, thereby increasing the possibility of finding the global optimal solution. In the later iterations of the algorithm, the mutation probability and intensity gradually decrease, so that the particle swarm can converge more stably when approaching the optimal solution, avoiding solution deviation or oscillation caused by excessive mutation. In the design of new energy-saving materials for roads and bridges, this adaptive mutation mechanism ensures that the optimization process of the material porosity is both widely exploratory and can effectively avoid falling into the local optimal solution, thereby minimizing the manufacturing cost and energy consumption while ensuring the strength and thermal conductivity of the material, and truly achieving the design goal of energy saving and environmental protection. Finally, in each round of iteration, the present invention also introduces a local search mechanism to further improve the optimization accuracy of the particle swarm algorithm. The core idea of ​​local search is to make fine adjustments based on the current global optimal solution, and to make small adjustments to the position of the particles by using nonlinear functions, so that the particles can perform more detailed searches near the global optimal. This mechanism is particularly suitable for optimizing complex multi-objective problems, such as the design of road and bridge materials, where the balance between different performance indicators is often very delicate. Through local search, the algorithm can further optimize the porosity of the material based on the global optimal solution, so that the material can achieve a higher level of optimization in multiple performance indicators. In the application scenario of new energy-saving materials for roads and bridges, this refined optimization process ensures that the material achieves the best balance between strength, thermal conductivity and cost, providing high-performance and economically feasible material solutions for engineering applications.

[0061] Example 2: In step 3, a group of particles representing possible porosity solutions is initialized by the following formula:

[0062] ;

[0063] ;

[0064] in, For the The initial position of each particle represents the porosity; For the The initial velocity of each particle; is the minimum porosity; is the maximum porosity; is the maximum permissible speed; for A random number in the range.

[0065] Specifically, the initial position of the particle represents the possibility of different porosities, which will directly affect the microstructure and macroscopic properties of the material. In order to avoid the singleness and limitation of the initial solution, the formula is transformed into a random number by Introduced into the exponential function, the nonlinear distribution of the initial position is realized. Specifically, The calculation is not just a simple linear interpolation, but through a nonlinear function Redistributing the porosity range increases the dispersion of particles in the search space, ensuring that more possible solution areas are covered in the initial stage. This is particularly important for the optimization of road and bridge materials, because different porosities may have significant differences in the performance of materials. Through this nonlinear initialization method, the algorithm can better capture the potential optimal solution. In addition, the initial velocity The setting of also introduces randomness and nonlinear changes. The sine function is used in the formula to calculate the initial velocity, which makes the particle velocity have a periodic distribution in different ranges. Such a velocity distribution enables particles to quickly cover a large search space in the early exploration stage, and also provides better convergence conditions for the later fine search. In the design of new energy-saving materials for roads and bridges, there is often a complex nonlinear relationship between material properties. A reasonable initial velocity distribution can help the algorithm quickly find potential solutions in the early stage of exploration, and then gradually reduce the speed when approaching the optimal solution to improve the accuracy, thereby achieving the best balance between strength, thermal conductivity and cost. More importantly, this initialization method not only enhances the global search capability of the particle swarm algorithm, but also avoids particles from falling into local optimal solutions too early in the search process by introducing nonlinearity and randomness. This is particularly critical in the optimization of road and bridge engineering materials, because the global optimal solution of material performance is often hidden in a complex, multi-peak performance space, and it is difficult to effectively explore these areas by relying solely on linear methods. Through this initialization strategy, the algorithm can find the performance balance point in different areas of the search space, and finally provide a material design solution that combines strength, thermal conductivity and cost-effectiveness.

[0066] Embodiment 3: In step 3, the position and velocity of each particle are updated using the improved particle swarm algorithm using the following formula:

[0067] ;

[0068] ;

[0069] ;

[0070] in, For the Particles in The speed of the moment; For the Particles in The speed of the moment; For the Particles in The location at the moment; For the Particles in The acceleration of the moment; is the time step; is the global best position; is the dynamic inertia weight; is the first dynamic acceleration coefficient; is the second dynamic acceleration coefficient; and Are all random numbers in the range of 0 to 1.

[0071] Specifically, the basis of the speed update formula is to determine the next direction and speed of each particle by comparing the particle's own historical optimal position with the global optimal position. This process is the key to the particle swarm algorithm, which uses the idea of ​​swarm intelligence, that is, each particle not only relies on its own experience, but also improves the overall search efficiency through collaboration with other particles. In the formula, the speed update term is divided into three main parts: inertia term, self-acceleration term, and global acceleration term. The inertia term reflects the inertia of the particle, that is, at the previous moment Speed This inertia term is composed of a dynamic weight Adjustment, dynamic weights are designed to implement different optimization strategies at different stages of the algorithm. In the early stages of the algorithm, the inertia weight is large, which allows particles to move freely in a larger search space, thereby increasing the possibility of exploring unknown areas. This is particularly important in material optimization, because different porosities may lead to significant changes in material properties, and extensive searches can help discover these potential optimal solutions. In the later stages of the algorithm, the inertia weight gradually decreases, and the movement of particles becomes more stable and concentrated, with the aim of enabling them to finely search areas near the optimal solution and avoid missing the optimal solution due to large movements. This dynamic adjustment mechanism ensures that the algorithm can perform at its best in different optimization stages and provides strong technical support for material design.

[0072] The first part of the acceleration term is the self-acceleration term, which is obtained through a dynamic acceleration coefficient Adjust the particle to its best historical position This acceleration term reflects the particle's reliance on its own experience, that is, when searching for the optimal solution, the particle will adjust according to the best position it has reached. This mechanism simulates the process of individual learning. In material design, this means that particles will tend to keep those solutions that have been proven to achieve good performance at a specific porosity, thereby improving the efficiency of optimization. The second part is the global acceleration term, which is expressed by another dynamic acceleration coefficient Adjust particles to the global optimal position The global acceleration term reflects the advantage of swarm intelligence, that is, each particle not only learns from its own experience, but also draws on the best experience of the entire particle group. This mechanism ensures that the algorithm can effectively avoid falling into a local optimal solution, but constantly moves closer to the optimal solution of the entire group. In the design of new environmentally friendly and energy-saving materials for roads and bridges, the role of the global acceleration term is particularly critical, because the multi-objective optimization of materials often involves complex nonlinear relationships. Through global learning, the algorithm can more quickly find the optimal porosity combination that takes into account strength, thermal conductivity and cost. The position update formula combines the particle's velocity change and acceleration, so that the particle moves not only according to the current velocity in each iteration, but also considers the influence of acceleration. Acceleration term The introduction of adds additional momentum to the movement of particles, which is determined by the relationship between the distance between the particle's current position and the global optimal position and the objective function value. In material optimization, the objective function value represents the performance of the material at a specific porosity, such as strength and thermal conductivity. The direction of the acceleration points to the global optimal position, and the magnitude is proportional to the objective function value, which means that when the particle approaches the global optimal solution, the acceleration will become larger, thereby accelerating its convergence to the optimal solution. This design not only improves the convergence speed of the algorithm, but also enables particles to make more refined adjustments when approaching the optimal solution, further optimizing material properties.

[0073] Specifically, the acceleration term in the formula is related to the density function of the material The density function reflects the physical properties of the material at different porosities. By considering the relationship between density and the objective function value, the algorithm can dynamically adjust the acceleration of the particles so that they can move towards the optimal solution more effectively while taking into account the physical properties of the material. This mechanism is of great significance in the optimization of road and bridge materials because it ensures the balance between strength and thermal conductivity of the material while also taking into account the constraints of manufacturing costs, so that the final optimization result not only has excellent performance but also has economic feasibility. In addition, the time step The introduction of simulates the continuous movement of particles on the time axis, making the trajectory of particles smoother and more natural. The design of this time step plays a regulatory role in the optimization process, allowing particles to update their positions at an appropriate pace, avoiding the convergence of the algorithm affected by too fast or too slow updates. In practical applications, a reasonable time step can improve the efficiency of the algorithm, make the optimization process more in line with actual engineering needs, and ultimately provide a more accurate and reliable material design solution. In the manufacturing process of new energy-saving materials for roads and bridges, this improved particle swarm algorithm dynamically adjusts the position and speed of particles, making the porosity optimization process of the material both extensively exploratory and highly accurate when converging to the optimal solution. This process ensures the best balance between strength, thermal conductivity and cost of the material, and ultimately produces road and bridge materials with superior performance and meeting energy-saving and environmental protection standards. This material can not only withstand harsh engineering conditions, but also bring significant economic and environmental benefits to engineering practice through optimized thermal conductivity and reasonable cost control. The innovation of this method is that it closely combines intelligent algorithms with material science, providing a powerful tool for future road and bridge construction, making the design and manufacturing of new environmentally friendly and energy-saving materials more efficient and feasible.

[0074] Example 4: In step 3, the maximum porosity and the minimum porosity satisfy the following constraint relationship:

[0075] .

[0076] Specifically, the core of this formula is to constrain the porosity update through the sine function, so that the updated porosity Always fluctuates within the specified range. The sine function in the formula Designed as a periodic function, its output range is By adding 1 and dividing by 2, the formula normalizes this output to interval, thereby ensuring that the updated porosity is within and This constraint is critical because it not only limits the physical upper and lower limits of porosity, but also allows the algorithm to adjust the porosity in a smooth and controlled manner during the optimization process, thus avoiding excessive fluctuations that lead to unstable material properties. Second, the nonlinear nature of the porosity update in the formula comes from the use of a sine function. This nonlinear adjustment makes the rate of change of porosity vary with the current value. For example, when the porosity is close to or When the porosity is in the middle value, the derivative of the sine function is small, and the change amplitude of the updated porosity will be small, maintaining a relatively stable adjustment process; when the porosity is in the middle value, the derivative of the sine function is large, and the change speed will be correspondingly accelerated. This design can ensure that the optimization process becomes more refined when the material is close to the optimal solution, and the optimization speed is faster when it is far from the optimal solution, which improves the overall efficiency of the algorithm. In the manufacturing process of new environmentally friendly and energy-saving materials for roads and bridges, this precise control of porosity is crucial. The porosity of the material directly affects its physical properties, such as strength and thermal conductivity. Too high porosity may lead to insufficient material strength, while too low porosity may lead to excessive thermal conductivity of the material, which cannot effectively isolate heat, thus affecting the energy-saving effect of the material. Through this formula, the optimization algorithm can dynamically adjust the porosity so that the material can perform optimally in different application scenarios. In addition, the control of porosity also directly affects the density of the material, which is also of great significance to the structural design and construction cost in road and bridge projects. Reasonable density can reduce the dead weight of the material, thereby reducing the load on the bridge foundation and improving the overall safety and stability of the project. The introduction of this constraint relationship also has certain physical significance. The smooth changes and periodic fluctuations of the sine function are similar to the way many physical phenomena in nature manifest themselves, such as fluctuations and oscillations. By simulating these natural phenomena, the algorithm can better adapt to the physical properties of the material, thereby improving the actual effect of optimization. In the actual application of road and bridge materials, this method can not only improve the scientificity and rationality of material design, but also optimize the overall performance of the material through precise porosity control, ultimately achieving the goal of energy conservation and environmental protection.

[0077] Example 5: In step 3, the adaptive mutation mechanism is represented by the following formula:

[0078] ;

[0079] in:

[0080] ;

[0081] ;

[0082] in, is the variation intensity; is the mutation probability; is the set initial mutation strength; is the set initial mutation probability; is the minimum value of the objective function; is the maximum value of the objective function; Indicates is the value of the objective function of the variable; is a random number ranging from 0 to 1; is the maximum time.

[0083] Specifically, the core of the adaptive mutation mechanism lies in the mutation intensity and mutation probability Dynamic adjustment of the variation intensity It is through the formula to determine, among which is the initial mutation intensity, It represents the maximum time step of the algorithm. As time goes by, the mutation intensity gradually weakens. The logic behind this design is that a stronger mutation intensity is usually required in the early stages of the optimization process in order to explore a wider search space. This high-intensity mutation can help the particle swarm quickly jump out of the local optimal solution in the early stages, ensuring that the algorithm can cover the entire search space and find the potential global optimal solution. In material optimization, this mechanism is particularly important because the relationship between material properties is often complex and nonlinear, and relying solely on local search may not fully explore the best performance combination of materials. By increasing the mutation intensity, the algorithm can find more possible solutions in different porosity combinations, thereby improving the diversity and performance potential of material design. However, as time goes by, the optimization process gradually enters the stage of fine adjustment, at which time the mutation intensity needs to be reduced to prevent the solution from being unstable due to excessive disturbance. By allowing the mutation intensity to weaken over time, the algorithm can converge more stably to the vicinity of the optimal solution and avoid missing the global optimal solution due to frequent mutations. This dynamic adjustment strategy is very critical in the optimization of road and bridge materials, because the strength, thermal conductivity and cost of materials often need to be precisely balanced in a smaller solution space. At this stage, reducing the variation intensity can ensure that the final design of the material is more accurate and can fully reflect the optimization advantages of the material. is another key part of the adaptive mutation mechanism. Formula

[0084] By combining the objective function value of the current particle position and the global optimal objective function value and , to dynamically adjust the mutation probability. When approaching the global optimal solution, the objective function value Gradually approaching , at this time, the probability of mutation will be significantly reduced, and the possibility of mutation will be reduced. This design logic is to protect the particle position close to the global optimal solution to avoid breaking the state that is close to the optimal solution due to mutation. On the contrary, when the particle position is far away from the global optimal solution, the probability of mutation will increase, thereby increasing the possibility of particle mutation, which enables the particle to jump out of the dilemma of the local optimal solution and continue to approach a better solution. Random variables in the mutation mechanism The value range is between 0 and 1, and is used to determine whether the particle will mutate in each iteration. By introducing randomness, the algorithm can maintain a certain degree of uncertainty in the overall optimization process, thereby increasing the coverage of the search space. Specifically, when the random number Less than the mutation probability When , the position of the particle will change, the formula

[0085] Describes the specific process of mutation operation. In this formula, the tangent function The introduction of adds nonlinear characteristics to the variation amplitude, which makes the variation not limited to simple linear adjustment, but can produce disturbances in a larger range. This nonlinear variation is particularly beneficial to break the equilibrium state of particles and expand the search space during the optimization process, especially in the early stage, it can significantly increase the possibility of finding the global optimal solution. In the design process of new energy-saving materials for roads and bridges, the application of this adaptive variation mechanism can significantly improve the flexibility and accuracy of the optimization process. For example, in the early design stage of the material, the algorithm can explore various porosity combinations through high variation intensity and variation probability to find possible strength and thermal conductivity optimal points; in the later optimization stage, as the variation intensity and probability gradually decrease, the algorithm can make fine adjustments near the optimal solution to find a porosity combination with optimal performance and cost. This dynamic adjustment mechanism ensures the overall efficiency of material design, so that the final material not only has good physical properties, but also can achieve the goal of energy conservation and environmental protection in the manufacturing process. Modern road and bridge construction has higher and higher requirements for materials, not only to meet the basic strength and durability requirements, but also to consider the energy conservation and environmental protection characteristics of the material. Improving the thermal conductivity of the material and reducing the manufacturing cost by optimizing the porosity is an effective way to achieve these goals. However, the optimization of porosity involves complex problems with multiple objectives and multiple constraints, which traditional optimization algorithms may not be able to effectively solve. Through the adaptive mutation mechanism, the particle swarm algorithm can more flexibly deal with complex constraints in multi-objective optimization and find the best solution that takes into account both performance and cost, which plays an important role in promoting the development of new energy-saving materials for roads and bridges. In addition, the adaptive mutation mechanism can also be adjusted according to different optimization requirements to adapt to different material design tasks. For example, by adjusting the initial mutation intensity and the initial mutation probability , which can make the algorithm more adaptable to different material performance targets and engineering requirements, thereby providing more personalized optimization solutions. This flexibility makes the adaptive variation mechanism not only suitable for the design of road and bridge materials, but can also be extended to the optimization of other types of engineering materials, providing technical support for a wider range of engineering applications.

[0086] Embodiment 6: In step 3, the current global optimal solution is locally searched using the following formula:

[0087] ;

[0088] in:

[0089] ;

[0090] in, is the new global optimal solution after local search; is the local search step size; is the initial local search step size.

[0091] Specifically, the core of this local search mechanism is to use the step size Controls the adjustment range of the global optimal solution. The definition is ,in is the initial local search step size, is the maximum time step. Advancement, step length The purpose of this design is to allow a larger adjustment range in the early stages of optimization so as to fully explore the area near the global optimal solution; in the later stages of optimization, the step size is reduced to make the adjustment more precise to avoid missing the optimal solution due to excessive disturbance. This gradually decreasing step size ensures that the algorithm can make more precise fine-tuning when approaching the global optimal solution, thereby improving the accuracy of the optimization results. Next is the nonlinear perturbation function in the formula , which introduces a complex nonlinear adjustment by combining the logarithmic function and the sine function. This nonlinear adjustment helps to introduce moderate disturbances near the global optimal solution to prevent the algorithm from falling into the local optimal solution, while also avoiding the instability of the solution caused by excessive disturbances. Specifically, the logarithmic function The randomness of the adjustment process is increased, so that the adjustment amplitude is no longer linear, but is related to the random number. The sine function Periodic changes are introduced to make the adjustment process present a fluctuating characteristic. This fluctuating characteristic can be fine-tuned multiple times in the local area, which helps to better capture the global optimal solution. In the manufacturing process of new energy-saving materials for roads and bridges, this local search mechanism can significantly improve the refinement of optimization. The porosity of the material directly affects its physical properties, including strength, thermal conductivity, and manufacturing cost. Therefore, when the optimization is nearing the end, any slight adjustment may have a significant impact on the final material performance. By introducing this local search mechanism, the algorithm can perform further optimization on the basis of the global optimal solution to ensure that the final configuration of the material is optimal in terms of various performance indicators. For example, between the strength and thermal conductivity of the material, the fine-tuned porosity may bring better thermal insulation effect without significantly reducing the mechanical strength of the material, which is of great significance to the safety and long-term performance of road and bridge projects. In addition, the local search step length The gradual reduction of the step size can also ensure the stability of the solution in the final stage of optimization. This means that when the algorithm is very close to the global optimal solution, the solution will not deviate from the optimal point due to excessive adjustments, resulting in optimization failure. By gradually reducing the control step size, the algorithm can make adjustments in smaller steps when approaching the optimal solution, thereby steadily converging to the global optimal solution. This stability is crucial in material optimization, because small differences in material properties can have a significant impact on practical applications. Through this refined adjustment, the final designed material not only has superior performance, but also can show better reliability and stability in actual engineering.

[0092] Example 7: Objective Function Use the following formula to express it:

[0093] ;

[0094] in, Strength objective function; is the heat conduction objective function; is the cost objective function; is the intensity weight; is the thermal conductivity weight; is the cost weight.

[0095] Specifically, in material optimization, strength and thermal conductivity are often two important indicators that influence each other. Mechanical strength is the ability of a material to withstand external loads. For key components in road and bridge construction, the material must have sufficient strength to withstand external forces such as vehicle loads, wind pressure, and seismic forces. The strength objective function in the optimization process reflects the strength performance of the material under different porosity configurations, and the goal is to maintain the mechanical strength of the material at the highest possible porosity. This not only helps to reduce the weight of the material and improve the safety of the structure, but also saves material costs. Thermal conductivity is also crucial in road and bridge engineering. Road and bridge structures are exposed to the external environment all year round. The thermal conductivity of the material directly affects its reaction speed to temperature changes, and then affects its ability to manage thermal expansion and contraction effects. The setting of the thermal conductivity objective function aims to optimize the porosity of the material so that it can still effectively manage heat conduction under extreme temperature conditions and reduce structural damage caused by temperature differences. This is especially important in road and bridge construction in extremely cold or high temperature areas, because in these areas, the temperature changes are drastic and frequent, and the thermal conductivity of the material will directly affect the long-term service life of the bridge. However, while optimizing the strength and thermal conductivity of the material, cost is also a factor that cannot be ignored. Road and bridge projects usually involve the use of a large amount of materials. If the cost is not controlled, the economic efficiency of the entire project will be greatly reduced. Therefore, the cost objective function plays an important balancing role in the formula. By incorporating cost into the optimization goal, it ensures that the economic efficiency of the manufacturing process is reasonably controlled while improving the material performance. This cost function not only takes into account the price of raw materials, but also the complexity of the processing technology and energy consumption, aiming to find the best balance between performance and cost. The weighted design of the objective function provides flexibility for multi-objective optimization. By adjusting the weights of strength, thermal conductivity and cost, the optimization direction can be flexibly adjusted according to specific engineering needs. For example, in the design of bridge main beams that require extremely high strength, the weight of strength can be increased to ensure that the mechanical properties of the material are in the optimal state; while in areas with extreme climates, thermal conductivity may occupy a higher weight to ensure that the material has sufficient tolerance when facing temperature changes. The weight of cost is flexibly adjusted according to the project budget to ensure that the material design is both high-performance and economically feasible. This weighted optimization strategy not only improves the scientificity and rationality of material design, but also provides technical support for multi-objective decision-making in road and bridge construction. By taking into account the different performance indicators of the material, the objective function helps the optimization algorithm find the optimal solution in a complex multi-objective environment, thereby designing materials that meet engineering needs. This method greatly improves the adaptability of the material, enabling it to perform well in different application scenarios. In addition, the design of this objective function also takes into account the performance conflicts that may be encountered in actual engineering. Generally, improving the strength of the material may lead to a decrease in thermal conductivity, and vice versa. Cost control may limit the improvement of material performance.By introducing weights into the objective function, the priority of each performance indicator can be dynamically adjusted during the optimization process to ensure that the final material design is optimized overall. This method provides an effective solution for the development of new energy-saving materials for roads and bridges, helping engineers to flexibly adjust the material design strategy under different conditions, and ultimately produce environmentally friendly and energy-saving materials that meet high performance and low cost requirements.

[0096] Example 8: In step 1, the strength function of the material defined is Use the following formula to express it:

[0097] ;

[0098] in, is the initial strength of the solid phase of the material; is the porosity; is the porosity corresponding to the maximum strength of the solid phase of the material; is the strength correction factor, ranging from 0.1 to 0.3; the strength objective function is expressed using the following formula:

[0099] ;

[0100] in, Adjust parameters for intensity; is the minimum strength required;

[0101] Thermal conductivity function of the material defined Use the following formula to express it:

[0102] ;

[0103] in, is the initial thermal conductivity of the solid phase; is the thermal conductivity of air; is the thermal conductivity correction factor, ranging from 0.5 to 2; the thermal conductivity objective function is expressed using the following formula:

[0104] ;

[0105] in, is the optimal thermal conductivity; Adjust parameters for thermal conductivity.

[0106] Specifically, the intensity function It describes the porosity of materials at different It takes into account the effect of porosity on the structural integrity and load-bearing capacity of the material, which is a crucial aspect in the design of road and bridge materials. Road and bridge structures usually require materials to have extremely high mechanical strength to withstand various external stresses such as vehicle loads, wind pressure, earthquakes, etc. Therefore, the design of the strength function directly affects the actual application effect of the material. Represents the initial strength of the material in the solid phase, that is, the theoretical maximum strength of the material when the porosity is zero. This parameter provides a benchmark for the entire formula and describes the mechanical properties of the material under ideal conditions. However, as the porosity increases, voids gradually form inside the material, which weakens the bonding force between the particles inside the material, thereby reducing the overall strength of the material. This effect is expressed in the formula through the exponential function To describe. Exponential function part This reflects the nonlinear attenuation effect of the increase in porosity on the material strength. Specifically, as the porosity increases, As the porosity increases, the volume ratio of the solid part of the material decreases, resulting in a rapid decrease in strength. The exponential function is particularly suitable for describing this rapid decay process, because the characteristic of the exponential function is that it changes rapidly when the variable is small, and as the variable increases, the change tends to be gentle. This characteristic is consistent with the actual situation, that is, when the porosity of the material is low, the decrease in strength is more obvious, and when the porosity is large, the rate of strength decrease gradually slows down, because the material structure has become very fragile, and the effect of further increasing the porosity on the strength becomes no longer significant. The coefficients in the exponential function This decay rate is further modified. When it is close to 3, the coefficient The value of increases rapidly, causing the value of the exponential function to decrease rapidly, indicating that when the porosity approaches the limit value, the strength of the material is almost completely lost. This design is to capture the brittle behavior of the material under high porosity conditions, because in practical applications, the material often exhibits sudden failure when the porosity approaches the limit value. This nonlinear attenuation model can more accurately reflect the physical properties of the material and provide a more reliable basis for material optimization. The second term in the strength function This further modifies the material strength attenuation curve. Unlike the exponential function, this term describes the effect of porosity on material strength in the form of a polynomial, especially adjusting the strength performance in the medium porosity range. Specifically, when the porosity When smaller, The value of is also small, so Close to 1, the effect on strength is small; but as the porosity increases, The value of increases, causing this term to drop rapidly, reflecting the further weakening of the material strength at medium and high porosity. The physical significance of this polynomial term is that it reflects the gradual weakening of the material's porosity on strength, rather than sudden failure. For road and bridge materials, this gradual weakening is particularly important because it determines whether the material can maintain a certain safety margin at high porosity during construction and use. This term is expressed in the form of a quadratic power (i.e. ) emphasizes the sharp drop in strength at medium and high porosity, reminding designers to pay special attention to avoid configurations that will significantly reduce material strength when selecting material porosity. The third part of the strength function is a correction factor , which expresses the nonlinear characteristics of material strength through a supplement in the formula. Correction factor The value range is between 0.1 and 0.3. By adjusting this factor, it can be optimized according to the specific characteristics of different materials. Further description of the quadratic effect of porosity on strength, especially when the porosity is close to a certain value Specifically, is the porosity corresponding to the maximum strength of the solid phase of the material, which means that when the porosity is close to The material strength exhibits a specific peak or inflection point when . This correction factor captures this effect and describes the influence of porosity on the material strength near this special point through a combination of an exponential function and a quadratic term. This makes this term in porosity keep away When the porosity is close to When This effect is enhanced, making the material strength show significant changes in this area. The introduction of this correction term enables the strength function to more accurately describe the strength changes of materials at different porosities, providing more information for the optimization algorithm, helping designers find a porosity configuration that can ensure material strength while taking into account other properties.

[0107] Strength objective function Through the intensity function The standardization process compares the actual strength of the material with the minimum strength required by the design, thereby evaluating the applicability of the material under different porosities. The design of this objective function is directly related to the selection of material porosity by the optimization algorithm, because it uses mathematical expressions to clarify which porosity combinations can meet engineering requirements and which combinations need to be excluded during the optimization process. The standardization part in the objective function Compare the actual strength of the material with the required minimum strength. Higher than the minimum required strength , the normalized value will be greater than 1, indicating that the material has a high safety margin at this porosity; conversely, a normalized value less than 1 indicates that the material is not strong enough and is not suitable for use in practical applications. Gaussian attenuation term The value of the objective function is further adjusted, especially for porosity combinations close to the minimum required strength. This item is designed to prevent the optimization algorithm from selecting only those configurations that are slightly higher than the required strength, because although these configurations can meet the minimum requirements, they may show instability in actual use. By introducing this attenuation term, the optimization algorithm can pay more attention to selecting those configurations that are significantly higher than the required strength, thereby improving the safety and long-term performance of the material. The design of this objective function ensures that the selection during the optimization process is more rigorous and precise, helping designers to exclude those porosity configurations that do not have sufficient strength, while giving priority to those configurations that have significant advantages in strength. This is crucial for the design of road and bridge materials because it directly affects the safety and service life of the structure.

[0108] The thermal conductivity function describes the effect of porosity on the thermal conductivity of a material. Thermal conductivity is also critical in road and bridge materials, especially when temperature changes need to be managed. The thermal conductivity of a material determines how it behaves under external temperature changes, affecting the thermal expansion and contraction effects of the bridge structure. and Represent the thermal conductivity of the solid phase and air of the material respectively. These two parameters are the basis for defining the thermal conductivity of the material. The thermal conductivity of the solid phase is usually higher, while the thermal conductivity of air is lower, which means that as the porosity increases, the proportion of air in the material increases and the thermal conductivity decreases. The first term in the thermal conductivity function Represents the thermal conductivity contribution of the solid part. As the porosity increases, the value of this term decreases gradually because the volume proportion of the solid phase decreases. describes the thermal conductivity contribution of the air part. As the porosity increases, the value of this term gradually increases. The correction factor in the formula Through the quadratic Adjust the nonlinear effect of air thermal conductivity. For some materials, when the porosity increases to a certain level, the presence of air may cause a sharp drop in thermal conductivity. This nonlinear behavior is described by the introduction of quadratic terms. The introduction of this correction factor allows the thermal conductivity function to more accurately reflect the thermal conductivity characteristics of the material at different porosities, helping the optimization algorithm find the porosity configuration with the best thermal conductivity. Thermal conductivity objective function The thermal conductivity function The value of and the optimal thermal conductivity The thermal conductivity objective function is similar to the strength objective function, which helps the optimization algorithm make the best choice in thermal conductivity through a combination of normalization and Gaussian attenuation terms. Compare the thermal conductivity of the material with the optimal thermal conductivity. If the thermal conductivity of the material is close to or reaches the optimal value, the value of the objective function will be higher; conversely, if the thermal conductivity deviates far from the optimal value, the value of the objective function will drop significantly. The introduction of further refines the evaluation of thermal conductivity, especially those configurations that slightly deviate from the optimal value. With this design, the optimization algorithm can more accurately select those porosity configurations with superior thermal conductivity, thus achieving the dual goals of performance and energy saving in material design.

[0109] Example 9: Cost function in material manufacturing process Use the following formula to express it:

[0110] ;

[0111] in, is the initial manufacturing cost of the unit material; is the preset critical porosity;

[0112] ;

[0113] in, is the unit cost of the pore former; is the ideal porosity; Adjust parameters for cost.

[0114] Specifically, the cost function The relationship between material manufacturing cost and porosity is described. The multiple parameters involved in the formula jointly determine the complex trend of cost. Initial manufacturing cost The material is free of pores (i.e., porosity ), which is the starting point for the entire manufacturing process. As porosity increases, the manufacturing cost of the material changes due to multiple factors, including changes in the material itself, adjustments to the manufacturing process, and changes in energy consumption during production. The first term in the cost function It shows the effect of increasing porosity on the volume of the solid part of the material. As the volume of the solid part of the material increases, it decreases, which directly reduces the manufacturing cost because less raw material is needed. However, this reduction is not a linear relationship, but rather a quadratic term It is described that at lower porosity, the manufacturing cost decreases faster, but as the porosity increases further, the cost decrease tends to be slow. This further describes the nonlinear effect of porosity on cost. This function form shows that when the porosity approaches 1, the cost will drop rapidly. The physical meaning behind this is that when the porosity is close to 1, the material is almost entirely composed of pores, and the proportion of the solid part is extremely small, so the manufacturing cost approaches zero. However, in actual engineering, extremely high porosity usually leads to a significant decrease in material performance, so this function also reflects the undesirability of material performance when the porosity is too high. The hyperbolic tangent function in the formula Introduced the critical porosity effect during material manufacturing . Critical porosity It is a key turning point in the relationship between manufacturing cost and porosity during the manufacturing process of materials. The form of this function shows that when the porosity near When the manufacturing cost changes significantly, is a smooth nonlinear function. near increases rapidly when This reflects the increased sensitivity of manufacturing costs as the porosity approaches a critical value, because at this point the material’s microstructure changes significantly and may require adjustments to the manufacturing process or material mix, which in turn affects costs. This effect is further described. When the porosity is far from the critical porosity, the manufacturing cost changes more slowly, but when the porosity approaches or exceeds the critical value, the manufacturing cost will show obvious nonlinear changes. This design can accurately reflect the impact of material structure changes on cost during the manufacturing process, especially at high porosity, the manufacturing difficulty and process complexity of the material may increase significantly, resulting in a significant increase in cost. Cost objective function The actual manufacturing cost of the material is compared with the cost under the ideal porosity through normalization and Gaussian attenuation. The design of this function directly affects the optimization algorithm's choice of material porosity because it clarifies the advantages and disadvantages of material manufacturing costs under different porosities.

[0115] The normalized part of the objective function Represents the comparison between the actual manufacturing cost of the material and the benchmark cost. In this expression, is the unit cost of the pore former, which becomes a larger proportion as the porosity increases during the manufacturing process. As the porosity increases, the cost of the pore former becomes the main part of the total manufacturing cost. The standardized expression describes the linear trend of the manufacturing cost with the increase of porosity. Through the standardized processing, the optimization algorithm can directly compare the cost advantages and disadvantages under different porosity configurations. Gaussian attenuation term The cost objective function is further modified, especially for the ideal porosity The physical significance of this attenuation term is that it focuses the optimization algorithm's attention on configurations that are close to the ideal porosity, because these configurations can usually achieve the best balance between performance and cost. By introducing this Gaussian attenuation term, the optimization algorithm will be more inclined to those configurations with low manufacturing cost and porosity close to the optimal value when selecting material porosity. Ideal porosity It is a target value set in advance during the design phase. It represents the optimal porosity of the material in terms of cost and performance under current technical conditions. This parameter plays an important guiding role in the optimization process, especially in the design of the objective function. The introduction of the Gaussian attenuation term enables the optimization algorithm to converge to the ideal porosity more accurately in actual operation. Cost adjustment parameter It reflects the sensitivity of cost changes in the manufacturing process. It determines the width of the Gaussian attenuation term, thus affecting the response speed of the objective function to cost changes. When it is larger, the objective function has a higher tolerance to cost changes, and the optimization algorithm can accept larger porosity changes; on the contrary, when When it is smaller, the optimization algorithm will control the porosity more strictly, making the manufacturing cost as close to the minimum as possible. The introduction of this parameter enables the cost objective function to adapt more flexibly to different design requirements and engineering conditions, providing strong support for the economic optimization of materials.

[0116] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for manufacturing new environmentally friendly and energy-saving materials for roads and bridges based on intelligent algorithms, characterized in that: The method comprises: Step 1: Set the porosity of the material as the key value of the optimization target, use the porosity as a variable parameter, set the strength function and thermal conductivity function of the material, and set the cost function in the material manufacturing process; Step 2: By defining the weights of the strength function, thermal conductivity function and cost function respectively, the weighted sum of the strength function, thermal conductivity function and cost function is calculated to define the objective function of material manufacturing; Step 3: Use the improved particle swarm algorithm to iteratively optimize the porosity until the set number of iterations is reached, specifically including: initializing a group of particles representing possible porosity solutions; each particle has an initial position and initial velocity, and a nonlinear function is used to ensure the diversity of the initial solution and cover the entire search space; using the improved particle swarm algorithm to update the position and velocity of each particle, and using the objective function defined in step 2 as the objective function of the improved particle swarm algorithm. During the updating process, the goal is to maximize the value of the objective function; introducing an adaptive mutation mechanism to dynamically adjust the mutation probability and mutation intensity according to the current number of iterations; performing a local search for the current global optimal solution, and using a nonlinear function to adjust the position of the solution; In step 3, a group of particles representing possible porosity solutions is initialized using the following formula: ； ； in, For the The initial position of each particle represents the porosity; For the The initial velocity of each particle; is the minimum porosity; is the maximum porosity; is the maximum permissible speed; for A random number in a range; In step 3, the position and velocity of each particle are updated using the improved particle swarm algorithm using the following formula: ； ； ； in, For the Particles in The speed of the moment; For the Particles in The speed of the moment; For the Particles in The location at the moment; For the Particles in The acceleration of the moment; is the time step; is the global best position; is the dynamic inertia weight; is the first dynamic acceleration coefficient; is the second dynamic acceleration coefficient; and are all random numbers in the range of 0 to 1. Indicates is the value of the objective function of the variable, is the density function of the material, For its best historical position, For the Particles in The location at the moment, For the Particles in The location at the moment; In step 3, the maximum porosity and the minimum porosity satisfy the following constraints: ； In step 3, the adaptive mutation mechanism is expressed by the following formula: ； in: ； ； in, is the variation intensity; is the mutation probability; is the set initial mutation strength; is the set initial mutation probability; is the minimum value of the objective function; is the maximum value of the objective function; is a random number ranging from 0 to 1; is the maximum time; is the minimum value of porosity, is the maximum value of porosity; In step 3, the current global optimal solution is locally searched using the following formula: ； in: ； in, is the new global optimal solution after local search; is the local search step size; is the initial local search step length; Objective Function Use the following formula to express it: ； in, Strength objective function; is the heat conduction objective function; is the cost objective function; is the intensity weight; is the thermal conductivity weight; is the cost weight; In step 1, define the strength function of the material Use the following formula to express it: ； in, is the initial strength of the solid phase of the material; is the porosity; is the porosity corresponding to the maximum strength of the solid phase of the material; is the strength correction factor, ranging from 0.1 to 0.3; the strength objective function is expressed using the following formula: ； in, Adjust parameters for intensity; is the minimum strength required; Thermal conductivity function of the material defined Use the following formula to express it: ； in, is the initial thermal conductivity of the solid phase; is the thermal conductivity of air; is the thermal conductivity correction factor, ranging from 0.5 to 2; the thermal conductivity objective function is expressed using the following formula: ； in, is the optimal thermal conductivity; Adjust parameters for thermal conductivity; Cost function in material manufacturing process Use the following formula to express it: ； in, is the initial manufacturing cost of the unit material; is the preset critical porosity; ； in, is the unit cost of the pore former; is the ideal porosity; Adjust parameters for cost.

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