A multi-objective intelligent optimization method for solid waste concrete mix design

Abstract

The application discloses a multi-objective intelligent optimization method for solid waste concrete mix proportion design, and relates to the field of building material engineering and intelligent optimization technology.The method obtains a concrete performance prediction distribution by constructing an uncertainty transmission model from solid waste raw material performance fluctuation characteristic spectrum and mix proportion parameters to concrete performance, and constructs a performance toughness index accordingly.On this basis, a dynamic mapping relationship between a nominal solution space and a toughness solution space is established, a multi-objective toughness equilibrium optimization model in the toughness solution space is formed, and a toughness Pareto frontier is output based on a performance toughness dominance relationship.Furthermore, a final mix proportion scheme is selected from the toughness Pareto frontier, and a corresponding raw material entry performance control interval is generated, so that the unity of solid waste concrete mix proportion design and engineering quality control is realized.

Description

Technical Field

[0001] This invention relates to the fields of building materials engineering and intelligent optimization technology, and in particular to a multi-objective intelligent optimization method for the mix design of solid waste concrete. Background Technology

[0002] Solid waste concrete, as a type of concrete that uses recycled aggregates and industrial solid waste to replace natural materials, is of great significance in terms of resource conservation and environmental protection. However, due to the complex sources, large fluctuations in composition, and strong performance dispersion of solid waste raw materials, solid waste concrete generally suffers from unstable performance and insufficient quality control in engineering applications.

[0003] Existing methods for designing mix proportions for solid waste concrete are mostly based on deterministic design using nominal or statistical average values ​​of raw material performance parameters, and adjustments to the mix proportions are made through a small number of experiments or empirical corrections. These methods fail to systematically reflect the random fluctuations in raw material performance across different sources, batches, time scales, and engineering conditions, leading to performance deviations in the mix proportions during actual production and use.

[0004] With the development of computational methods and data-driven technologies, some studies have attempted to introduce performance prediction models or optimization algorithms to improve concrete mix proportions. However, most existing technologies still use a single performance prediction result as the evaluation basis, ignoring the transmission effect of performance prediction uncertainty in the optimization process; or they only verify the performance stability in the post-optimization stage, lacking a unified mechanism to directly introduce uncertainty into optimization modeling and solution space construction.

[0005] Furthermore, in multi-objective optimization scenarios, existing methods typically use the traditional Pareto dominance relationship to weigh performance indicators, cost indicators, or resource utilization rates. However, these dominance relationships are mostly based on deterministic indicator values, which makes it difficult to reflect the stability differences of solid waste concrete under the condition of random fluctuations in raw material performance. As a result, the optimization results still need to rely on a lot of experience judgment in the engineering implementation stage.

[0006] Therefore, how to systematically characterize the performance fluctuation characteristics of solid waste raw materials in the mix design stage, introduce the uncertainty propagation process into the optimization model, and simultaneously consider performance, resource utilization level and stability requirements in the multi-objective optimization process remains a technical problem that urgently needs to be solved in the field of solid waste concrete mix design. Summary of the Invention

[0007] To address the above problems, this invention proposes a multi-objective intelligent optimization method for mix design of solid waste concrete.

[0008] The present invention achieves the above objectives through the following technical solutions:

[0009] A multi-objective intelligent optimization method for mix design of solid waste concrete, the method comprising:

[0010] The performance fluctuation characteristic spectrum of solid waste raw materials is obtained. The performance fluctuation characteristic spectrum is obtained based on statistical analysis and probability distribution fitting of historical raw material performance data, and is used to characterize the discrete value range and distribution form of each raw material performance parameter.

[0011] Based on the performance fluctuation characteristic spectrum, a transfer function model is constructed between mix proportion parameters and concrete performance uncertainty. The transfer function model is used to input mix proportion parameters and output the predicted distribution of concrete performance.

[0012] Define a performance toughness index based on the predicted distribution of concrete performance, which is used to characterize the probability characteristics and performance degradation rate of the mix design satisfying the concrete performance constraints when the raw material performance parameters fluctuate randomly within the performance fluctuation characteristic spectrum.

[0013] A dynamic two-layer solution space mapping relationship is constructed, including a nominal solution space and a toughness solution space. The nominal solution space is determined based on the mean value of raw material performance parameters and engineering constraints, and the corresponding mix proportion parameters are used as nominal mix proportion parameters. The toughness solution space is dynamically generated by performing local Monte Carlo sampling and stability assessment at the mix proportion parameter value points of the nominal solution space in combination with the transfer function model and performance toughness index, and forms a nonlinear mapping to the nominal solution space.

[0014] A multi-objective toughness equilibrium optimization model is established in the toughness solution space, with the comprehensive performance index of concrete, the resource utilization rate of solid waste and the performance toughness index as optimization objectives. The optimization search process is based on the performance toughness dominance relationship, and the individual fitness evaluation is based on the local stability simulation results in the toughness solution space.

[0015] The multi-objective toughness equilibrium optimization model is executed to output the toughness Pareto front; the non-dominated solutions in the toughness Pareto front are associated with the output of nominal mix proportion parameters, concrete performance prediction distribution, and toughness coefficients calculated based on performance toughness index.

[0016] Based on the engineering risk appetite and resilience requirements, the final mix design is selected from the resilience Pareto front, and the raw material entry performance control range is generated based on the performance fluctuation characteristic spectrum.

[0017] As a preferred embodiment of the present invention, the acquisition of the performance fluctuation characteristic spectrum includes:

[0018] Data were collected on multiple performance parameters of solid waste raw materials from different sources and within different time windows, and statistical analysis was conducted on the fluctuation range and correlation of raw material performance parameters between batches.

[0019] Based on the statistical analysis results, performance parameters that contribute more than a preset threshold to the uncertainty of concrete performance are identified, and a subset of parameters is constructed to characterize the dominant fluctuation mode of raw material performance.

[0020] For the aforementioned parameter subset, corresponding probability distribution models are established under different engineering conditions or mix proportion parameter ranges to form a conditional performance fluctuation description structure associated with the engineering conditions.

[0021] Within the conditional performance fluctuation description structure, a multi-parameter coupled performance fluctuation description model is constructed through joint distribution or correlation constraints. The performance fluctuation description model is then segmented and organized according to different engineering conditions or mix proportion parameter ranges to form a performance fluctuation structure with non-stationary characteristics.

[0022] The performance fluctuation description model is used as the performance fluctuation feature spectrum, and the corresponding performance fluctuation description model is dynamically selected according to the range of the mix proportion parameters in the subsequent optimization process. This is used to constrain the generation of the concrete performance prediction distribution and the calculation process of the performance toughness index.

[0023] As a preferred embodiment of the present invention, the construction of the transfer function model includes:

[0024] Based on the performance fluctuation characteristic spectrum, the mapping relationship between the mix proportion parameter space and the concrete performance space is modeled so that the transfer function model can comprehensively consider the random fluctuation of raw material performance parameters within the range of the performance fluctuation characteristic spectrum under a given set of determined mix proportion parameters, and output the corresponding concrete performance prediction distribution.

[0025] When constructing the transfer function model, the mix proportion parameter is used as the first type of input variable, and the raw material performance parameter characterized by the performance fluctuation characteristic spectrum is used as the second type of uncertainty input variable. By jointly modeling the two types of input variables, the mapping relationship between the change of mix proportion parameter and the change of concrete performance prediction distribution is established.

[0026] In the transfer function model, the uncertainty propagation path of raw material performance parameters is modeled in a differentiated manner, so that different types of raw material performance parameters act on different concrete performance indicators through corresponding propagation paths, thereby reflecting the differentiated impact of raw material performance fluctuations on concrete performance results.

[0027] Based on the parameter range or engineering conditions where the mix proportion parameters are located, different uncertainty propagation structures or model parameter configurations are called or switched accordingly to ensure that the transfer function model is consistent with the segmented structure of the performance fluctuation characteristic spectrum.

[0028] The concrete performance prediction distribution generated by the transfer function model is used as a unified input for calculating performance and toughness indices, constructing the toughness solution space, and performing local Monte Carlo sampling and stability assessment.

[0029] As a preferred embodiment of the present invention, the performance toughness index includes at least:

[0030] The performance reliability component is calculated based on the proportion of concrete performance prediction distribution results that meet the target requirements or allowable range of the comprehensive performance index of concrete.

[0031] And the performance degradation sensitivity component calculated based on the variation characteristics of the concrete performance prediction distribution within the judgment threshold range corresponding to the comprehensive performance index of the concrete.

[0032] The performance toughness index is constructed by regularizing or weighting the performance reliability component and the performance degradation sensitivity component. It is used to characterize the ability of the mix proportion scheme to maintain the target requirements of the comprehensive performance index of concrete under the condition of fluctuation of raw material performance, and serves as the evaluation basis for the construction of toughness solution space and multi-objective toughness equilibrium optimization.

[0033] As a preferred embodiment of the present invention, the construction of the nominal solution space includes:

[0034] Based on the mean values ​​of raw material performance parameters and engineering constraints, a nominal mix proportion parameter value space consisting of multiple sets of mix proportion parameters is determined, and the mix proportion parameters are used as value points in the nominal solution space.

[0035] For each nominal mix proportion parameter in the nominal solution space, based on the transfer function model and combined with the performance fluctuation characteristic spectrum, multiple random samplings are performed on the raw material performance parameters to generate the corresponding concrete performance prediction distribution.

[0036] The performance toughness index is calculated based on the predicted distribution of concrete performance, and the performance toughness index is used as a local stability measure of the mix proportion parameter value points in the nominal solution space to characterize the stability difference of different nominal mix proportion parameters under the condition of random fluctuation of raw material performance.

[0037] As a preferred embodiment of the present invention, the toughness solution space is generated based on the nominal solution space and in the following manner:

[0038] Based on the performance toughness index corresponding to each mix proportion parameter value point in the nominal solution space, the toughness of the value points in the nominal solution space is determined, and the value points that meet the preset toughness conditions are mapped to the toughness solution space.

[0039] Based on the distribution level of performance toughness index in different regions of the nominal solution space, the mapping density or search scale of the value points in the region in the toughness solution space is adaptively adjusted so that the nominal solution space region that meets the preset toughness judgment condition has a higher representation resolution in the toughness solution space.

[0040] Based on the changing trend of performance toughness index in nominal solution space, the mapping relationship between nominal solution space and toughness solution space is continuously adjusted so that the boundary shape of toughness solution space exhibits a nonlinear and irregular dynamic structure as performance toughness index changes.

[0041] During the optimization iteration process, the toughness solution space is dynamically updated as the range of values ​​for the mix proportion parameter in the nominal solution space changes.

[0042] As a preferred embodiment of the present invention, the process of establishing a multi-objective toughness equilibrium optimization model in the toughness solution space includes:

[0043] In the toughness solution space, the points corresponding to the nominal mix proportion parameters are used as candidate optimization individuals, and each candidate optimization individual is associated with the concrete performance prediction distribution, solid waste resource utilization rate index and performance toughness index.

[0044] The set of objective functions is composed of the comprehensive performance index of concrete, the resource utilization rate of solid waste, and the performance and toughness index.

[0045] Among them, the comprehensive performance index of concrete is used as the first objective function. Defined as:

[0046] ;

[0047] In the formula, The nominal combination ratio parameter is used to optimize the candidate individuals; This is the mean of the performance predictions calculated based on the aforementioned concrete performance prediction distribution; The results are calculated based on the predicted distribution of concrete performance. Quantile performance value; For performance toughness indicators; These are preset coefficients;

[0048] Solid waste resource utilization rate is used as the second objective function The performance resilience index is used as the third objective function. Together, they constitute a multi-objective resilience equilibrium optimization model.

[0049] In a preferred embodiment of the present invention, the optimization search process is based on the performance resilience dominance relationship, and the fitness evaluation of candidate optimization individuals includes:

[0050] Calculate for each candidate optimization individual , and and within the current iteration candidate set , and Normalize them separately to obtain , , ;

[0051] Constructing a resilience equilibrium deviation function : ;

[0052] Individual fitness values ​​are generated based on the aforementioned resilience equilibrium deviation function and performance resilience index. :

[0053] ;

[0054] In the formula, The preset coefficients are used; during the dominance determination, based on... Perform multi-objective dominance relationship determination, and with The fitness evaluation value of candidate optimization individuals participates in the optimization search.

[0055] As a preferred embodiment of the present invention, the process of executing the multi-objective resilience equilibrium optimization model and outputting the resilience Pareto front includes:

[0056] Within the resilience solution space, the dominance relationship between candidate optimization individuals is determined according to the performance resilience dominance relationship, and candidate optimization individuals that are not dominated by other candidate optimization individuals are selected to form a non-dominated candidate set;

[0057] The non-dominated candidate set is used as a resilient Pareto front, and the non-dominated candidate set is updated during the optimization iteration process;

[0058] For each nondominated solution in the toughness Pareto front, the corresponding nominal mix proportion parameter is output.

[0059] For the non-dominated solution, the transfer function model is invoked to output the corresponding concrete performance prediction distribution;

[0060] The corresponding toughness coefficient is calculated based on the predicted distribution of concrete performance and the toughness index.

[0061] As a preferred embodiment of the present invention, the process of selecting the final mix proportion from the toughness Pareto front and generating the raw material entry performance control range includes:

[0062] In the resilience Pareto front, based on the preset engineering risk preference parameters, the resilience coefficients corresponding to the non-dominated solutions are screened to determine the target non-dominated solutions that meet the resilience requirements.

[0063] The nominal mix proportion parameters corresponding to the target non-dominated solution are used as the final mix proportion scheme;

[0064] For the final mix design, based on the performance fluctuation description model corresponding to the mix design parameter range in the performance fluctuation characteristic spectrum, the conditional probability distribution range of the raw material performance parameters is extracted;

[0065] Based on the conditional probability distribution range, the allowable value range of each raw material performance parameter is determined, forming the raw material entry performance control range.

[0066] The beneficial effects of this invention are as follows: It introduces a performance fluctuation characteristic spectrum to achieve structured modeling of raw material uncertainties; it constructs a transfer function model to achieve unified propagation of uncertainty to concrete performance; it constructs a performance toughness index based on the predicted distribution of concrete performance, integrating the probability characteristics of meeting performance requirements with the performance degradation change characteristics, making the stability of the mix proportion scheme a technical quantity that can be directly used in optimization evaluation; by introducing local stability assessment and Monte Carlo sampling into the nominal solution space, the solution space structure dynamically changes with the uncertainty characteristics of raw materials, thus forming a toughness solution space different from the traditional deterministic solution space; it introduces a performance toughness dominance relationship in the multi-objective optimization process, enabling the optimization search to not only consider the comprehensive performance of concrete and the utilization rate of solid waste resources, but also reflect the stability differences of different mix proportion schemes under uncertainty conditions; through the structured output of the non-dominated solution, it correlates the nominal mix proportion parameters, the predicted distribution of concrete performance, and the toughness coefficient, and further generates the raw material entry performance control interval, enabling the optimization results to be directly used for quality control in the engineering implementation stage. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0069] like Figure 1 As shown, this is an embodiment of the present invention, which provides a multi-objective intelligent optimization method for mix design of solid waste concrete, including the following steps:

[0070] S1: Obtain the performance fluctuation characteristic spectrum of solid waste raw materials. The performance fluctuation characteristic spectrum is obtained based on the statistical analysis and probability distribution fitting of historical raw material performance data. It is used to characterize the discrete value range and distribution form of each raw material performance parameter.

[0071] In solid waste concrete engineering applications, the physical properties and chemical composition of solid waste raw materials fluctuate significantly due to their complex origins and significant batch-to-batch variations. Using only a single average value or probability distribution to describe the raw material properties will fail to reflect the performance uncertainties under real engineering conditions, thus affecting the accuracy of subsequent concrete performance prediction and toughness assessment. Therefore, this embodiment provides a method for constructing a performance fluctuation characteristic spectrum to systematically describe the fluctuation structure of solid waste raw material performance parameters under different sources, times, and engineering conditions, and to provide a constrained basis for subsequent concrete performance prediction distribution and performance toughness index calculation.

[0072] In this embodiment, data on multiple performance parameters of solid waste raw materials are first collected. The solid waste raw materials may include, but are not limited to, recycled coarse aggregate, recycled fine aggregate, and industrial by-product admixtures. Data sources include, but are not limited to: raw material batches from different suppliers, raw material batches from the same supplier at different time periods, and raw material samples used in different engineering projects. For each batch of raw materials, its corresponding performance parameter data are collected. These performance parameters may include, but are not limited to: density, water absorption rate, particle size distribution, crushing index, mud content, and chemical composition ratio. The above data is organized according to the dimensions of "raw material type—source batch—time window" to form a historical database of raw material performance parameters.

[0073] After obtaining a historical database of raw material performance parameters, statistical analysis is performed on the variations of the same performance parameter across different batches. This includes: calculating the range of values ​​for each performance parameter across different batches; calculating the fluctuation range of each performance parameter, such as the maximum value, minimum value, and standard deviation; and analyzing the correlation between different performance parameters, such as the correlation trend between water absorption rate and density. Through the above analysis, it is possible to identify which performance parameters exhibit significant fluctuations across different batches and time windows, and which parameters show obvious correlations.

[0074] Based on statistical analysis, the influence of each raw material performance parameter on the uncertainty of concrete performance is further evaluated. Specifically, each raw material performance parameter is introduced as an input variable into the concrete performance prediction model; the influence of changes in each input parameter on the fluctuation of the concrete performance prediction results is analyzed; and the raw material performance parameters are ranked according to the magnitude of their influence. When the contribution of a certain raw material performance parameter to the fluctuation of concrete performance prediction exceeds a preset threshold, that parameter is identified as the dominant uncertainty parameter. Through this step, a subset of parameters describing the dominant fluctuation pattern of raw material performance is constructed, thereby avoiding the inclusion of a large number of parameters with relatively small impact on the results in uncertainty modeling and reducing model complexity.

[0075] For the selected parameter subset, performance fluctuation description structures are established under different engineering conditions or different mix proportion parameter ranges. In this embodiment, the engineering conditions or mix proportion parameter ranges may include, but are not limited to: different water-cement ratio ranges, different recycled aggregate replacement rate ranges, and different design strength grade ranges. For example, when the mix proportion parameter is within a certain water-cement ratio range, only the raw material performance data collected within the corresponding range are used to establish probability distribution models for each performance parameter in the parameter subset. In this way, the description of raw material performance fluctuations corresponds to specific engineering conditions or mix proportion parameter ranges, forming a conditional performance fluctuation description structure.

[0076] Within the conditional performance fluctuation description structure, the coupling relationship between multiple raw material performance parameters is further considered. Specifically, this includes: introducing correlation constraints between parameters based on the aforementioned correlation analysis results; and describing the coordinated fluctuation behavior of multiple performance parameters through a joint distribution or correlation constraint model. Simultaneously, the multi-parameter coupled performance fluctuation description model is segmented according to different engineering conditions or mix proportion parameter ranges. For example, different recycled aggregate replacement rate ranges correspond to different fluctuation sub-models. Through this segmented organization, the performance fluctuation description model exhibits non-stationary characteristics, meaning that different parameter ranges correspond to different fluctuation structures.

[0077] The multi-parameter coupled performance fluctuation description model, organized in segments according to engineering conditions or mix proportion parameter ranges, is collectively constituted as a performance fluctuation characteristic spectrum. During subsequent concrete mix proportion optimization, when a specific mix proportion parameter scheme is selected, the parameter range in which that mix proportion parameter lies is first determined. Based on this parameter range, a corresponding fluctuation description model is dynamically selected from the performance fluctuation characteristic spectrum. Based on the selected fluctuation description model, random samples of raw material performance parameters are generated for subsequent calculations of concrete performance prediction distribution and performance toughness indices, enabling the dynamic retrieval of the performance fluctuation characteristic spectrum during the optimization process.

[0078] The method described in this embodiment can construct a performance fluctuation characteristic spectrum that reflects the performance dispersion, conditional correlation, and non-stationary characteristics of solid waste raw materials without relying on a single statistical distribution assumption. This provides a basic data structure for the subsequent generation of concrete performance prediction distribution and the calculation of performance toughness indicators.

[0079] S2: Construct a transfer function model between mix proportion parameters and concrete performance uncertainty based on the performance fluctuation characteristic spectrum. The transfer function model is used to input mix proportion parameters and output the predicted distribution of concrete performance.

[0080] In this embodiment, the transfer function model is constructed using a modular structure, and includes the following:

[0081] The system comprises a mix proportion parameter input module, a raw material performance uncertainty input module, an uncertainty propagation modeling module, and a performance prediction distribution output module. Specifically, the mix proportion parameter input module receives deterministic mix proportion parameters; the raw material performance uncertainty input module receives sampling results of raw material performance parameters constrained by performance fluctuation characteristic spectra; the uncertainty propagation modeling module jointly models the above two types of inputs and distinguishes the uncertainty propagation paths of different raw material performance parameters; and the performance prediction distribution output module statistically summarizes the model output results to form a concrete performance prediction distribution.

[0082] In terms of model hierarchy, the transfer function model includes at least an input layer, an uncertainty propagation layer, and an output statistics layer. Different uncertainty propagation paths are modeled in the uncertainty propagation layer and connected to the corresponding concrete performance output nodes.

[0083] The training process for the transfer function model includes the following steps: First, construct a training sample set based on historical experimental or simulated data, containing mix proportion parameters, raw material performance parameters, and corresponding concrete performance outputs. Second, preprocess the training samples, including parameter normalization, outlier removal, and sample labeling according to performance output type. Third, train the model parameters in the uncertainty propagation modeling module based on the training samples, enabling the model to learn the joint influence of changes in mix proportion parameters and raw material performance parameters on concrete performance output. Fourth, after model training, validate the model prediction results using independent validation samples, and adjust the model structural parameters or propagation weights based on the validation results. Finally, obtain a transfer function model that can be used for performance prediction distribution generation.

[0084] In one embodiment, the transfer function model can be implemented based on random forests and Monte Carlo simulations.

[0085] In this embodiment, a dataset for training the transfer function model is first constructed, and the dataset includes:

[0086] Mix proportion parameter data: The concrete mix proportion schemes obtained from history or simulation are compiled to form a mix proportion parameter sample set. Each sample includes at least the water-cement ratio, the recycled aggregate replacement rate, and the proportion of cement and admixtures.

[0087] Raw material performance parameter samples: Based on the performance fluctuation characteristic spectrum, under the given mix proportion parameters, the raw material performance parameters are randomly sampled to generate multiple sets of raw material performance parameter samples, such as: water absorption rate of recycled aggregate, particle size distribution parameters, and strength-related indicators.

[0088] Concrete performance output data: For each combination of "mix proportion parameters + raw material performance parameters", existing performance prediction methods or test data are used to obtain the corresponding concrete performance results, such as compressive strength, workability index, etc.

[0089] Through the above steps, a joint sample set is formed, which includes "first type of input variable (mix ratio parameter) + second type of input variable (raw material performance parameter) → concrete performance output".

[0090] In this embodiment, to distinguish different uncertainty propagation paths, concrete performance outputs are divided into different types, such as mechanical performance outputs (e.g., compressive strength) and workability-related performance outputs. For each type of performance output, a corresponding random forest model is constructed. For mechanical performance outputs, mechanically relevant raw material performance parameters are primarily used as input features; for workability performance outputs, parameters such as water absorption rate and particle size distribution are primarily used as input features. Through this method, the propagation paths of raw material performance uncertainties are distinguished and modeled at the model structure level.

[0091] After the random forest model is trained, for a given combination ratio parameter scheme, the following steps are performed:

[0092] Based on the parameter range in which the mix proportion parameter is located, select the corresponding raw material performance fluctuation description model from the performance fluctuation characteristic spectrum;

[0093] Based on the selected fluctuation description model, the raw material performance parameters are randomly sampled multiple times;

[0094] Each set of sampling results and mix proportion parameters are input into the random forest model to obtain the corresponding predicted concrete performance values;

[0095] Statistical processing was performed on multiple prediction results to form a predicted distribution of concrete performance.

[0096] Under different mix proportion parameter ranges (e.g., different recycled aggregate replacement rate ranges), corresponding random forest models can be trained separately, or the importance weights of the input features in the model can be adjusted. When the mix proportion parameter scheme changes within a range, the system automatically calls the model configuration corresponding to that range, realizing a range adaptive calling mechanism.

[0097] In another embodiment, a Gaussian process regression model is used as the implementation form of the transfer function model to simultaneously describe the combined effects of mix proportion parameters and raw material performance parameters on concrete performance output, and directly obtain the uncertainty distribution of performance prediction.

[0098] In this embodiment, the input vector consists of mix proportion parameters and raw material performance parameters, and the output is a specific performance index of concrete. The Gaussian process regression model is trained using historical or simulated data, enabling the model to learn the mapping relationship between changes in input parameters and changes in performance output. In the Gaussian process regression model, by constructing a multi-output model or setting different kernel function forms for different performance indices, different types of raw material performance parameters can have different effects on different performance outputs, thereby distinguishing uncertainty propagation paths. Under different mix proportion parameter ranges or engineering conditions, corresponding Gaussian process regression models can be trained separately, or the kernel function parameters of the model can be adjusted. In practical applications, the corresponding model configuration is selected according to the range of mix proportion parameters to achieve a structural switching mechanism.

[0099] Whether using a random forest model or a Gaussian process regression model, the following methods can be used for verification:

[0100] A subset of samples was used as a validation set to compare the model's predictions with actual performance data.

[0101] Check whether the mean and variance of the predicted distribution can reflect the actual performance fluctuation range;

[0102] Verify the prediction stability of different interval models within the corresponding parameter intervals.

[0103] In this embodiment, the inputs to the transfer function model include: a first type of input, which is a deterministic mix proportion parameter vector; and a second type of input, which is a vector of raw material performance parameters randomly sampled under the constraint of performance fluctuation characteristic spectrum. The output of the transfer function model is a set of predicted results for the corresponding concrete performance indicators. After statistical processing, the set of predicted results forms a concrete performance prediction distribution, which is used for subsequent calculation of performance and toughness indicators, construction of the toughness solution space, and multi-objective toughness equilibrium optimization process.

[0104] It should be clearly stated that the random forest model and Gaussian process regression model used in this embodiment are only one of the specific implementation methods for illustrating the transfer function model. The technical solution protected by this invention is as follows:

[0105] The mix proportion parameters are jointly modeled with the uncertainty of raw material properties;

[0106] Distinguish between uncertain propagation paths;

[0107] The model structure or parameters can be adaptively switched according to the parameter range or engineering conditions.

[0108] Output the predicted distribution of concrete properties for subsequent toughness analysis.

[0109] Without deviating from the above technical principles, those skilled in the art can use other modeling methods to achieve the same function, such as support vector regression, multilayer neural networks, or other probabilistic modeling methods.

[0110] S3: Define a performance toughness index based on the predicted distribution of concrete performance. This index characterizes the probability characteristics and performance degradation rate of a mix design satisfying concrete performance constraints when raw material performance parameters fluctuate randomly within the performance fluctuation characteristic spectrum. The performance toughness index includes at least: a performance reliability component calculated based on the proportion of predicted concrete performance distribution results that meet the target requirements or allowable range corresponding to the comprehensive concrete performance index; and a performance degradation sensitivity component calculated based on the variation characteristics of the predicted concrete performance distribution within the judgment threshold range corresponding to the comprehensive concrete performance index.

[0111] In the mix design of solid waste concrete, due to the random fluctuations in the properties of raw materials, even if a certain mix design meets the design requirements of the comprehensive performance index of concrete on average, it may still face the risk of performance failure or rapid deterioration under actual engineering conditions. Therefore, this embodiment provides a method for constructing a performance toughness index based on the predicted distribution of concrete performance. This method is used to quantitatively describe the ability of a mix design to maintain the target requirements or allowable range of the comprehensive performance index of concrete, taking into account the fluctuations in raw material properties, and to provide an evaluation basis for the construction of the toughness solution space and the optimization of multi-objective toughness equilibrium.

[0112] For any mix design to be evaluated Based on the transfer function model and combined with the performance fluctuation characteristic spectrum, the performance parameters of raw materials are randomly sampled multiple times. Under each random sampling condition, the corresponding concrete performance prediction result is calculated, thus forming a sample set of concrete performance prediction results. ,in Indicates the number of random samples. Indicates the first The predicted concrete performance values ​​obtained under the sub-sampling conditions are statistically processed on the predicted result sample set to obtain the corresponding predicted concrete performance distribution.

[0113] Based on engineering design requirements, target requirements or allowable ranges are set for the comprehensive performance indicators of concrete: ,in This represents the lower limit threshold of the comprehensive performance index of concrete. This represents the upper limit threshold of the comprehensive performance index of concrete. When only one-sided constraints are set for the comprehensive performance index of concrete, only one threshold can be set, and the other side can be set to infinity or infinitesimal.

[0114] The performance reliability component characterizes the proportion of concrete performance predictions that meet the target requirements or allowable range of the comprehensive performance index of concrete under conditions of random fluctuations in raw material performance parameters. The specific calculation process is as follows:

[0115] For each predicted value in the sample set of concrete performance prediction results Determine whether it satisfies: The number of prediction results that meet the criteria is counted, and the number of prediction results that meet the criteria is added to the total number of prediction results. The ratio of these values ​​is used as a performance reliability component. The expression is: ,in This represents an interval indicator function.

[0116] To characterize the changes in concrete performance prediction distribution as it approaches the threshold for judging the comprehensive performance index of concrete, a preset threshold range is constructed in this embodiment. When the comprehensive performance index of concrete is set to a lower limit threshold... At that time, construct the judgment threshold range When the comprehensive performance index of concrete is set to an upper limit threshold At that time, construct the judgment threshold range: ,in This indicates the preset interval width parameter, which can be set according to the allowable deviation of the project or the dispersion of the predicted distribution of concrete performance.

[0117] In this embodiment, the performance degradation sensitivity component is used to characterize the concentration or tendency of concrete performance predictions to exceed a judgment threshold range. One implementation method is to judge the concrete performance prediction result sample. Whether the prediction falls within the threshold range; count the prediction results that fall within the threshold range; and compare the count with the total number of prediction results. The ratio of these values ​​is used as a component of performance degradation sensitivity. The expression is: ,in This represents the corresponding threshold range. Another equivalent implementation is: .

[0118] In obtaining the performance reliability component With performance degradation sensitivity component Then, a performance resilience index is constructed through rule-based integration or weighted mapping. In this embodiment, the performance resilience index... It can be built in the following ways:

[0119] Weighted mapping method: ;

[0120] Ratio mapping method: ;

[0121] in , and These are parameters set based on the project's risk appetite.

[0122] The performance toughness index constructed in the above manner is used to characterize the ability of the mix design to maintain the target requirements of the comprehensive performance index of concrete under the condition of fluctuation in raw material performance. In this embodiment, the performance toughness index is used for:

[0123] Determine whether the mix design meets the entry conditions for the toughness solution space;

[0124] As an optimization objective or constraint in a multi-objective resilience equilibrium optimization model;

[0125] It is used in the determination of the dominance relationship of toughness to compare the merits of different mix proportion schemes.

[0126] The method described in this embodiment can construct a performance toughness index with a clear structure and well-defined calculation path based on the predicted distribution of concrete performance. This index is used to quantitatively describe the ability of a mix design to maintain the target requirements or allowable range of the comprehensive performance index of concrete under random fluctuations in raw material performance parameters, providing a reliable basis for subsequent toughness solution space construction and multi-objective toughness equilibrium optimization.

[0127] S4: Construct a dynamic two-layer solution space mapping relationship, including a nominal solution space and a toughness solution space. The nominal solution space is determined based on the mean value of raw material performance parameters and engineering constraints, and the corresponding mix proportion parameters are used as nominal mix proportion parameters. The toughness solution space is dynamically generated by performing local Monte Carlo sampling and stability assessment at the mix proportion parameter value points of the nominal solution space in combination with the transfer function model and performance toughness index, and forms a nonlinear mapping to the nominal solution space.

[0128] The construction of the nominal solution space includes:

[0129] Based on the engineering design requirements and the statistical average of raw material performance parameters, the allowable range of mix proportion parameters is determined. For example, the range of water-cement ratio, the range of recycled aggregate replacement rate, and the range of cementitious material composition ratio. Within this range, multiple sets of mix proportion parameter combinations are generated according to a preset parameter step size or sampling rule. Each set of mix proportion parameters is defined as a nominal mix proportion parameter, and the parameter set composed of these nominal mix proportion parameters forms the nominal solution space.

[0130] For each nominal mix proportion parameter in the nominal solution space, the following steps are performed: Based on the transfer function model and combined with the performance fluctuation characteristic spectrum, the raw material performance parameters are randomly sampled multiple times. Under each random sampling condition, the corresponding concrete performance prediction result is calculated, thereby obtaining the concrete performance prediction distribution corresponding to the nominal mix proportion parameter. Based on the performance toughness index calculation method, the performance reliability component and performance degradation sensitivity component are calculated respectively, and the corresponding performance toughness index is constructed through regular integration or weighted mapping. In this embodiment, the performance toughness index is used as a local stability measure of each nominal mix proportion parameter value point in the nominal solution space to reflect the stability differences of different nominal mix proportion schemes under the condition of random fluctuation of raw material performance.

[0131] The local stability evaluation results of each value point in the nominal solution space are stored, and a corresponding performance toughness index label is attached to each nominal mix proportion parameter. The labeling result serves as the input data for the subsequent construction of the toughness solution space.

[0132] In the nominal solution space, the values ​​of the mix proportion parameters in different regions exhibit varying levels of stability under conditions of random fluctuations in raw material properties. This embodiment provides a method for generating a toughness solution space based on performance toughness indices, enabling the solution space structure to dynamically adjust according to uncertainty characteristics.

[0133] Methods for generating the toughness solution space include:

[0134] Based on the nominal solution space and its corresponding performance toughness index, toughness determination is performed on the value points in the nominal solution space. In this embodiment, according to preset toughness determination conditions, the value points of the nominal mix ratio parameter that satisfy the determination conditions are screened and mapped to the toughness solution space as the initial set of value points of the toughness solution space.

[0135] During the generation of the toughness solution space, the mapping density or search scale is adaptively adjusted according to the distribution of performance toughness indicators in different regions of the nominal solution space: for nominal solution space regions that meet the preset toughness judgment conditions, the mapping density is increased or the search scale is adjusted so that the nominal solution space regions have higher representation resolution in the toughness solution space; for nominal solution space regions that do not meet the toughness judgment conditions, the mapping density is reduced or the search scale is restricted accordingly; in this way, the toughness solution space pays more attention to high toughness regions in terms of structure.

[0136] In this embodiment, mapping is not only based on the performance resilience index of a single value point, but also combined with the changing trend of the performance resilience index in the nominal solution space to continuously adjust the mapping relationship between the nominal solution space and the resilience solution space. When the performance resilience index shows significant changes between adjacent nominal solution space values, the mapping relationship is adjusted accordingly to cause nonlinear deformation of the boundary shape of the resilience solution space.

[0137] In subsequent optimization iterations, as the range of values ​​for the mix proportion parameters changes or the search region is adjusted, the toughness determination, mapping density adjustment, and boundary continuous adjustment processes are repeatedly executed, so that the toughness solution space is dynamically updated with the local changes in the nominal solution space.

[0138] The generated and dynamically updated toughness solution space is used for:

[0139] Limit the search region of the multi-objective resilience equilibrium optimization model;

[0140] Provides the candidate solution space required for generating resilient Pareto fronts;

[0141] During the optimization and iteration process, the search is guided to converge towards regions with high resilience.

[0142] Using the above methods, the nominal solution space and the toughness solution space form a hierarchical and dynamically related two-layer solution space structure, which allows the uncertainty of raw material performance to directly affect the solution space morphology through performance toughness indicators, providing an executable and scalable engineering implementation path for multi-objective toughness equilibrium optimization.

[0143] S5: Establish a multi-objective toughness equilibrium optimization model in the toughness solution space with the comprehensive performance index of concrete, the resource utilization rate of solid waste and the performance toughness index as optimization objectives. The optimization search process is based on the performance toughness dominance relationship, and the individual fitness evaluation is based on the local stability simulation results in the toughness solution space.

[0144] In this embodiment, the toughness solution space is used as the optimization search space. For each candidate optimization individual in the toughness solution space, there is a corresponding set of nominal mix ratio parameters, and the following data is associated with that candidate optimization individual:

[0145] Predicted distribution of concrete performance generated by transfer function model;

[0146] The solid waste resource utilization rate index is calculated based on the proportion of solid waste materials in the mix proportion.

[0147] The calculated performance toughness index.

[0148] The above data serves as the basic input for the multi-objective resilience equilibrium optimization model.

[0149] For each candidate optimization individual, based on its corresponding concrete performance prediction distribution, the following statistical calculations are performed:

[0150] Calculate the statistical mean of the predicted distribution of concrete performance. This is used to characterize the average performance level of the mix design under random fluctuation conditions;

[0151] The predicted distribution of concrete performance is calculated at a preset quantile level. quantile performance values , used to characterize the conservative performance level at the tail of the performance distribution.

[0152] Based on this, a comprehensive performance index of concrete is constructed as the first objective function. Defined as:

[0153] ;

[0154] In the formula, The nominal combination ratio parameter is used to optimize the candidate individuals; This is the mean of the performance predictions calculated based on the aforementioned concrete performance prediction distribution; The results are calculated based on the predicted distribution of concrete performance. Quantile performance value; For performance toughness indicators; This is a preset coefficient used to adjust the degree of performance risk penalty;

[0155] Solid waste resource utilization rate is used as the second objective function The performance resilience index is used as the third objective function. Together, they constitute a multi-objective resilience equilibrium optimization model.

[0156] The three objectives mentioned above all originate from the same concrete performance prediction distribution and its derived indices, but they differ at the statistical representation level, thus constituting the set of objective functions for the multi-objective toughness equilibrium optimization model. During the optimization process, no single objective is used as a deterministic constraint; instead, a multi-objective trade-off approach guides the evolution of candidate optimization individuals within the toughness solution space.

[0157] In this embodiment, the determination of the dominance relationship between candidate optimization individuals in the toughness solution space is performed in the following order:

[0158] Phase 1 Assessment: Based on Performance Resilience Indicators The candidate optimization individuals are compared, and the next stage of judgment is only entered when the first candidate optimization individual meets the dominance condition in terms of performance resilience index.

[0159] The second stage of judgment: Provided the performance and toughness index is deemed valid, further judgment is made based on the comprehensive performance target of concrete. and solid waste resource utilization rate indicators Determine the multi-objective dominance relationship.

[0160] Through the above hierarchical judgment process, the performance resilience index is used as a prerequisite judgment condition in the construction of the dominance relationship during the optimization search process.

[0161] In the current optimization iteration, calculations are performed on each candidate optimization individual within the toughness solution space. , and And based on the extreme value range of the current candidate set, for , and Normalize them separately to obtain , , To eliminate the influence of different dimensions on fitness evaluation;

[0162] After normalization, a resilience equilibrium deviation function is constructed. This characterizes the degree of equilibrium among multiple optimization objectives for a candidate optimization individual, and is expressed as:

[0163] ;

[0164] Individual fitness values ​​are generated based on the resilience equilibrium deviation function and performance resilience index. :

[0165] ;

[0166] In the formula, The preset coefficients are used; during the dominance determination, based on... Perform multi-objective dominance relationship determination, and with The fitness evaluation value of candidate optimization individuals participates in the optimization search.

[0167] S6: Execute the multi-objective toughness equilibrium optimization model and output the toughness Pareto front; the non-dominated solutions in the toughness Pareto front are associated with the output of nominal mix proportion parameters, concrete performance prediction distribution, and toughness coefficients calculated based on performance toughness indices.

[0168] In this embodiment, based on the multi-objective resilience equilibrium optimization model and the performance resilience dominance relationship, the following steps are performed on candidate optimization individuals in the resilience solution space:

[0169] In the current optimization iteration, the nominal mix proportion parameters, concrete comprehensive performance target value, solid waste resource utilization rate index, and performance toughness index corresponding to all candidate optimization individuals are obtained. According to the performance toughness dominance relationship, the dominance relationship between candidate optimization individuals is determined one by one.

[0170] Candidate optimization individuals that are not dominated by other candidate optimization individuals in the current iteration are selected to form a non-dominated candidate set, which serves as the resilient Pareto front for the current optimization stage.

[0171] In subsequent optimization iterations, as the set of candidate optimization individuals is updated, the dominance determination and screening steps described above are repeated to update the resilience Pareto front, so that the resilience Pareto front reflects the distribution of non-dominated solutions in the resilience solution space under different optimization stages.

[0172] For each nondominated solution in the toughness Pareto front, perform the following associated output step:

[0173] Output the nominal mix proportion parameters corresponding to the non-dominated solution;

[0174] Call the transfer function model and output the corresponding predicted distribution of concrete performance under the nominal mix proportion parameters;

[0175] Based on the predicted distribution of concrete properties, the corresponding toughness coefficient is calculated and output.

[0176] In this embodiment, the toughness coefficient is calculated based on two types of input data: the concrete performance prediction distribution corresponding to the non-dominated solution and the performance toughness index. The concrete performance prediction distribution is obtained by multiple random samplings and can be represented as a sample set or equivalent probability distribution of performance random variables.

[0177] For each non-dominated solution, perform the following computation steps:

[0178] In the concrete performance prediction distribution, the proportion of samples that meet the target requirements or allowable ranges corresponding to the comprehensive performance index of concrete is statistically analyzed to obtain the performance reliability component. .

[0179] In the concrete performance prediction distribution, for samples falling within the performance judgment threshold range, the degree of deviation from the target requirement is calculated, and the degree of deviation is normalized to obtain the performance degradation sensitivity component. ;

[0180] A performance resilience index is constructed based on the performance reliability component and the performance degradation sensitivity component, and the resilience coefficient is calculated based on the performance resilience index. : ;in It is a monotonic mapping function used to convert performance resilience indices into resilience coefficients for the resilience Pareto front correlation output.

[0181] In this embodiment, the mapping function can take the following form: or , This represents the set of nondominated solutions corresponding to the current resilience Pareto front.

[0182] S7: Based on the engineering risk preference and toughness requirements, select the final mix design from the toughness Pareto frontier, and generate the raw material entry performance control range based on the performance fluctuation characteristic spectrum.

[0183] In this embodiment, according to the engineering design requirements, an engineering risk preference parameter is preset to limit the requirements for the stability level of the mix proportion scheme. The engineering risk preference parameter is given in the form of an allowable range of the toughness coefficient or a screening threshold.

[0184] Based on the toughness Pareto front obtained in step S6, the following screening steps are performed on each non-dominated solution in the Pareto front:

[0185] Read the toughness coefficient corresponding to each non-dominated solution;

[0186] The toughness coefficient is compared with the preset engineering risk preference parameter;

[0187] Select non-dominated solutions whose toughness coefficients meet the toughness requirements to form the target set of non-dominated solutions.

[0188] Within the target non-dominated solution set, the final implementation scheme is determined according to preset scheme selection rules. In this embodiment, the scheme selection rules include, but are not limited to, one or more of the following:

[0189] After sorting by toughness coefficient, select the nondominated solution that ranks first.

[0190] Under the premise of meeting the resilience requirements, the ranking and selection are combined with the solid waste resource utilization rate index.

[0191] The nominal mix proportion parameters corresponding to the selected non-dominated solution of the objective are used as the final mix proportion scheme.

[0192] For the final mix design, based on the range of the mix design parameters, a performance fluctuation description model corresponding to that range is selected from the performance fluctuation characteristic spectrum. This performance fluctuation description model is part of the conditional performance fluctuation description structure constructed in step S1. Based on the performance fluctuation description model, the conditional probability distribution of each raw material performance parameter under the conditions of the final mix design is extracted. The raw material performance parameters include, but are not limited to, particle size distribution, moisture content, density, or other performance parameters already defined in the performance fluctuation characteristic spectrum.

[0193] Based on the conditional probability distribution of the raw material performance parameters, the corresponding allowable value range is determined. The allowable value range is determined by one of the following methods:

[0194] The range of values ​​for the conditional probability distribution is truncated according to a pre-set confidence interval;

[0195] The upper and lower limits are determined by the quantile intervals of the conditional probability distribution.

[0196] For each raw material performance parameter, a corresponding incoming performance control range is generated. The control range serves as the basis for raw material incoming quality control during the project implementation phase.

[0197] The method described in this embodiment ultimately outputs the following:

[0198] A set of nominal mix proportion parameters for final implementation;

[0199] The performance control range of each raw material entering the site corresponding to the final mix design.

[0200] The above output results are used to guide the selection of raw materials and quality control in the subsequent concrete production process.

[0201] In summary, this invention systematically integrates the performance uncertainty of solid waste raw materials into the mix design and multi-objective optimization process by introducing performance fluctuation characteristic spectrum, transfer function model and performance toughness index. It constructs an optimization framework that combines nominal solution space and toughness solution space, and on this basis, realizes multi-objective toughness equilibrium optimization and direct generation of engineering implementation parameters. Thus, it provides a calculable, optimizable and implementable technical solution for the mix design of solid waste concrete.

[0202] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-objective intelligent optimization method for mix design of solid waste concrete, characterized in that, The method includes: The performance fluctuation characteristic spectrum of solid waste raw materials is obtained. The performance fluctuation characteristic spectrum is obtained based on statistical analysis and probability distribution fitting of historical raw material performance data, and is used to characterize the discrete value range and distribution form of each raw material performance parameter. Based on the performance fluctuation characteristic spectrum, a transfer function model is constructed between mix proportion parameters and concrete performance uncertainty. The transfer function model is used to input mix proportion parameters and output the predicted distribution of concrete performance. Define a performance toughness index based on the predicted distribution of concrete performance, which is used to characterize the probability characteristics and performance degradation rate of the mix design satisfying the concrete performance constraints when the raw material performance parameters fluctuate randomly within the performance fluctuation characteristic spectrum. A dynamic two-layer solution space mapping relationship is constructed, including a nominal solution space and a toughness solution space. The nominal solution space is determined based on the mean value of raw material performance parameters and engineering constraints, and the corresponding mix proportion parameters are used as nominal mix proportion parameters. The toughness solution space is dynamically generated by performing local Monte Carlo sampling and stability assessment at the mix proportion parameter value points of the nominal solution space in combination with the transfer function model and performance toughness index, and forms a nonlinear mapping to the nominal solution space. A multi-objective toughness equilibrium optimization model is established in the toughness solution space, with the comprehensive performance index of concrete, the resource utilization rate of solid waste and the performance toughness index as optimization objectives. The optimization search process is based on the performance toughness dominance relationship, and the individual fitness evaluation is based on the local stability simulation results in the toughness solution space. The multi-objective toughness equilibrium optimization model is executed to output the toughness Pareto front; the non-dominated solutions in the toughness Pareto front are associated with the output of nominal mix proportion parameters, concrete performance prediction distribution, and toughness coefficients calculated based on performance toughness index. Based on the engineering risk appetite and resilience requirements, the final mix design is selected from the resilience Pareto front, and the raw material entry performance control range is generated based on the performance fluctuation characteristic spectrum.

2. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 1, characterized in that, The acquisition of the performance fluctuation characteristic spectrum includes: Data were collected on multiple performance parameters of solid waste raw materials from different sources and within different time windows, and statistical analysis was conducted on the fluctuation range and correlation of raw material performance parameters between batches. Based on the statistical analysis results, performance parameters that contribute more than a preset threshold to the uncertainty of concrete performance are identified, and a subset of parameters is constructed to characterize the dominant fluctuation mode of raw material performance. For the aforementioned parameter subset, corresponding probability distribution models are established under different engineering conditions or mix proportion parameter ranges to form a conditional performance fluctuation description structure associated with the engineering conditions. Within the conditional performance fluctuation description structure, a multi-parameter coupled performance fluctuation description model is constructed through joint distribution or correlation constraints. The performance fluctuation description model is then segmented and organized according to different engineering conditions or mix proportion parameter ranges to form a performance fluctuation structure with non-stationary characteristics. The performance fluctuation description model is used as the performance fluctuation feature spectrum, and the corresponding performance fluctuation description model is dynamically selected according to the range of the mix proportion parameters in the subsequent optimization process. This is used to constrain the generation of the concrete performance prediction distribution and the calculation process of the performance toughness index.

3. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 1, characterized in that, The construction of the transfer function model includes: Based on the performance fluctuation characteristic spectrum, the mapping relationship between the mix proportion parameter space and the concrete performance space is modeled so that the transfer function model can comprehensively consider the random fluctuation of raw material performance parameters within the range of the performance fluctuation characteristic spectrum under a given set of determined mix proportion parameters, and output the corresponding concrete performance prediction distribution. When constructing the transfer function model, the mix proportion parameter is used as the first type of input variable, and the raw material performance parameter characterized by the performance fluctuation characteristic spectrum is used as the second type of uncertainty input variable. By jointly modeling the two types of input variables, the mapping relationship between the change of mix proportion parameter and the change of concrete performance prediction distribution is established. In the transfer function model, the uncertainty propagation path of raw material performance parameters is modeled in a differentiated manner, so that different types of raw material performance parameters act on different concrete performance indicators through corresponding propagation paths, thereby reflecting the differentiated impact of raw material performance fluctuations on concrete performance results. Based on the parameter range or engineering conditions where the mix proportion parameters are located, different uncertainty propagation structures or model parameter configurations are called or switched accordingly to ensure that the transfer function model is consistent with the segmented structure of the performance fluctuation characteristic spectrum. The concrete performance prediction distribution generated by the transfer function model is used as a unified input for calculating performance and toughness indices, constructing the toughness solution space, and performing local Monte Carlo sampling and stability assessment.

4. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 1, characterized in that, The performance resilience indicators include at least: The performance reliability component is calculated based on the proportion of concrete performance prediction distribution results that meet the target requirements or allowable range of the comprehensive performance index of concrete. And the performance degradation sensitivity component calculated based on the variation characteristics of the concrete performance prediction distribution within the judgment threshold range corresponding to the comprehensive performance index of the concrete. The performance toughness index is constructed by regularizing or weighting the performance reliability component and the performance degradation sensitivity component. It is used to characterize the ability of the mix proportion scheme to maintain the target requirements of the comprehensive performance index of concrete under the condition of fluctuation of raw material performance, and serves as the evaluation basis for the construction of toughness solution space and multi-objective toughness equilibrium optimization.

5. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 1, characterized in that, The construction of the nominal solution space includes: Based on the mean values ​​of raw material performance parameters and engineering constraints, a nominal mix proportion parameter value space consisting of multiple sets of mix proportion parameters is determined, and the mix proportion parameters are used as value points in the nominal solution space. For each nominal mix proportion parameter in the nominal solution space, based on the transfer function model and combined with the performance fluctuation characteristic spectrum, multiple random samplings are performed on the raw material performance parameters to generate the corresponding concrete performance prediction distribution. The performance toughness index is calculated based on the predicted distribution of concrete performance, and the performance toughness index is used as a local stability measure of the mix proportion parameter value points in the nominal solution space to characterize the stability difference of different nominal mix proportion parameters under the condition of random fluctuation of raw material performance.

6. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 5, characterized in that, The toughness solution space is based on the nominal solution space and is generated in the following manner: Based on the performance toughness index corresponding to each mix proportion parameter value point in the nominal solution space, the toughness of the value points in the nominal solution space is determined, and the value points that meet the preset toughness conditions are mapped to the toughness solution space. Based on the distribution level of performance toughness index in different regions of the nominal solution space, the mapping density or search scale of the value points in the region in the toughness solution space is adaptively adjusted so that the nominal solution space region that meets the preset toughness judgment condition has a higher representation resolution in the toughness solution space. Based on the changing trend of performance toughness index in nominal solution space, the mapping relationship between nominal solution space and toughness solution space is continuously adjusted so that the boundary shape of toughness solution space exhibits a nonlinear and irregular dynamic structure as performance toughness index changes. During the optimization iteration process, the toughness solution space is dynamically updated as the range of values ​​for the mix proportion parameter in the nominal solution space changes.

7. The multi-objective intelligent optimization method for solid waste concrete mix design according to claim 1, characterized in that, The process of establishing a multi-objective resilience equilibrium optimization model in the resilience solution space includes: In the toughness solution space, the points corresponding to the nominal mix proportion parameters are used as candidate optimization individuals, and each candidate optimization individual is associated with the concrete performance prediction distribution, solid waste resource utilization rate index and performance toughness index. The set of objective functions is composed of the comprehensive performance index of concrete, the resource utilization rate of solid waste, and the performance and toughness index. Among them, the comprehensive performance index of concrete is used as the first objective function. Defined as: ； In the formula, The nominal combination ratio parameter is used to optimize the candidate individuals; This is the mean of the performance predictions calculated based on the aforementioned concrete performance prediction distribution; The results are calculated based on the predicted distribution of concrete performance. Quantile performance value; For performance toughness indicators; These are preset coefficients; Solid waste resource utilization rate is used as the second objective function The performance resilience index is used as the third objective function. Together, they constitute a multi-objective resilience equilibrium optimization model.

8. A multi-objective intelligent optimization method for solid waste concrete mix design according to claim 7, characterized in that, The optimization search process is based on the performance resilience dominance relationship, and the fitness evaluation of candidate optimization individuals includes: Calculate for each candidate optimization individual , and and within the current iteration candidate set , and Normalize them separately to obtain , , ; Constructing a resilience equilibrium deviation function : ; Individual fitness values ​​are generated based on the aforementioned resilience equilibrium deviation function and performance resilience index. : ； In the formula, The preset coefficients are used; during the dominance determination, based on... Perform multi-objective dominance relationship determination, and with The fitness evaluation value of candidate optimization individuals participates in the optimization search.

9. A multi-objective intelligent optimization method for solid waste concrete mix design according to claim 8, characterized in that, The process of executing the multi-objective resilience equilibrium optimization model and outputting the resilience Pareto front includes: Within the resilience solution space, the dominance relationship between candidate optimization individuals is determined according to the performance resilience dominance relationship, and candidate optimization individuals that are not dominated by other candidate optimization individuals are selected to form a non-dominated candidate set; The non-dominated candidate set is used as a resilient Pareto front, and the non-dominated candidate set is updated during the optimization iteration process; For each nondominated solution in the toughness Pareto front, the corresponding nominal mix proportion parameter is output. For the non-dominated solution, the transfer function model is invoked to output the corresponding concrete performance prediction distribution; The corresponding toughness coefficient is calculated based on the predicted distribution of concrete performance and the toughness index.

10. A multi-objective intelligent optimization method for solid waste concrete mix design according to claim 9, characterized in that, The process of selecting the final mix design from the toughness Pareto front and generating the raw material entry performance control range includes: In the resilience Pareto front, based on the preset engineering risk preference parameters, the resilience coefficients corresponding to the non-dominated solutions are screened to determine the target non-dominated solutions that meet the resilience requirements. The nominal mix proportion parameters corresponding to the target non-dominated solution are used as the final mix proportion scheme; For the final mix design, based on the performance fluctuation description model corresponding to the mix design parameter range in the performance fluctuation characteristic spectrum, the conditional probability distribution range of the raw material performance parameters is extracted; Based on the conditional probability distribution range, the allowable value range of each raw material performance parameter is determined, forming the raw material entry performance control range.

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