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CN116759031B - Design method of sludge ash concrete material mixing ratio based on ANN - Google Patents

Design method of sludge ash concrete material mixing ratio based on ANN Download PDF

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CN116759031B
CN116759031B CN202311002324.4A CN202311002324A CN116759031B CN 116759031 B CN116759031 B CN 116759031B CN 202311002324 A CN202311002324 A CN 202311002324A CN 116759031 B CN116759031 B CN 116759031B
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时金娜
张文秀
李伟
冯欢
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Inner Mongolia University of Technology
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Abstract

The invention discloses a design method of sludge ash concrete material mixing ratio based on ANN, which comprises the following steps: collecting and constructing an initial data set of raw material mixing proportion and mechanical property parameters of sludge ash concrete; randomly dividing an initial data set into a training set and a testing set; performing iterative training construction based on the training set to obtain an ANN model, verifying the ANN model according to the testing set, outputting the constructed ANN model if verification is passed, and re-executing the training process to optimize the ANN model if verification is not passed until the ANN model is passed; and inputting the performance index of the sludge ash concrete material to be prepared into an ANN model which is based on verification, and outputting the mixing ratio of the sludge ash concrete raw materials through the ANN model. The invention can solve the problems of long time consumption, large workload and the like of the existing concrete mixing proportion design method.

Description

一种基于ANN的污泥灰混凝土材料配合比的设计方法An ANN-based design method for sludge ash concrete material mix ratio

技术领域Technical field

本发明涉及混凝土配合比设计技术领域。具体地说是一种基于ANN的污泥灰混凝土材料配合比的设计方法。The invention relates to the technical field of concrete mix proportion design. Specifically, it is a design method of sludge ash concrete material mix ratio based on ANN.

背景技术Background technique

污泥灰是指污水处理过程中产生的污泥经过干化、燃烧等处理后得到的灰烬。污泥灰活性高、颗粒细小,具有一定的水泥活性,可在混凝土中替代部分水泥或骨料,达到资源再利用和减少环境污染的目的。对实现城市固废利用,减少环境污染,减少水泥的使用量,助力“双碳”目标实现具有重要意义。Sludge ash refers to the ash obtained after drying, burning and other treatments of sludge produced during sewage treatment. Sludge ash has high activity, small particles, and certain cement activity. It can replace part of the cement or aggregate in concrete to achieve the purpose of resource reuse and reducing environmental pollution. It is of great significance to realize the utilization of urban solid waste, reduce environmental pollution, reduce the use of cement, and help achieve the "double carbon" goal.

但污泥灰的性质复杂,其对混凝土强度、耐久性等性能的影响与传统混凝土材料具有显著差异。为了保证污泥灰混凝土的稳定性和可靠性,必须进行合理的配合比设计。现行配合比设计方法多为质量法或体积法,但这类方法耗时较长且工作量较大,无法满足污泥灰混凝土配合比设计要求。在此背景下,有必要探索新型、快速、高效的设计方法。However, the properties of sludge ash are complex, and its impact on concrete strength, durability and other properties is significantly different from traditional concrete materials. In order to ensure the stability and reliability of sludge ash concrete, reasonable mix ratio design must be carried out. The current mix proportion design methods are mostly mass method or volume method, but these methods are time-consuming and require a large workload, and cannot meet the mix design requirements of sludge ash concrete. In this context, it is necessary to explore new, fast, and efficient design methods.

发明内容Contents of the invention

为此,本发明所要解决的技术问题在于提供一种基于ANN(Artificial NeuralNetwork,人工神经网络)的污泥灰混凝土材料配合比的设计方法,以解决现有的污泥灰混凝土配合比设计方法耗时长、工作量大等问题。To this end, the technical problem to be solved by the present invention is to provide a design method of sludge ash concrete material mix ratio based on ANN (Artificial Neural Network, artificial neural network), so as to solve the problem of the existing sludge ash concrete mix ratio design method that consumes Issues such as time duration and heavy workload.

为解决上述技术问题,本发明提供如下技术方案:In order to solve the above technical problems, the present invention provides the following technical solutions:

一种基于ANN的污泥灰混凝土材料配合比的设计方法,包括如下步骤:An ANN-based design method for the material mix of sludge ash concrete, including the following steps:

步骤(1)、采集构建污泥灰混凝土原材料配合比和力学性能参数的初始数据集;Step (1): Collect and construct an initial data set of sludge ash concrete raw material mix ratio and mechanical property parameters;

步骤(2)、将初始数据集随机划分为训练集和测试集;Step (2): Randomly divide the initial data set into a training set and a test set;

步骤(3)、使用训练集进行迭代训练构建得到ANN模型,并根据测试集对训练得到的ANN模型进行验证,以测试ANN模型输出的配合比与实际配合比的拟合情况;若验证通过则输出构建的ANN模型,若验证不通过则重新执行训练过程优化ANN模型,直至ANN模型通过验证;Step (3): Use the training set to perform iterative training to construct an ANN model, and verify the trained ANN model based on the test set to test the fit between the mix ratio output by the ANN model and the actual mix ratio; if the verification passes Output the constructed ANN model. If the verification fails, re-execute the training process to optimize the ANN model until the ANN model passes the verification;

步骤(4)、将待配制污泥灰混凝土材料的性能指标输入基于验证通过的ANN模型中,通过ANN模型输出污泥灰混凝土原材料的配合比。Step (4): Input the performance indicators of the sludge ash concrete material to be prepared into the verified ANN model, and output the mix ratio of the sludge ash concrete raw materials through the ANN model.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(3)中,ANN模型的构建方法为:In the above ANN-based design method of sludge ash concrete material mix ratio, in step (3), the ANN model construction method is:

步骤(3-1)、将污泥灰混凝土原材料配合比作为输出变量,力学性能参数作为输入变量,分别对输入变量和输出变量进行归一化处理;Step (3-1), use the sludge ash concrete raw material mix ratio as the output variable and the mechanical property parameters as the input variables, and normalize the input variables and output variables respectively;

步骤(3-2)、确定ANN模型的损失函数,基于梯度下降优化算法对ANN模型内部参数进行调整,并采用贝叶斯优化算法对ANN模型超参数进行自适应调整和选择,使训练迭代中的ANN模型损失函数降低至可接受水平;Step (3-2): Determine the loss function of the ANN model, adjust the internal parameters of the ANN model based on the gradient descent optimization algorithm, and use the Bayesian optimization algorithm to adaptively adjust and select the hyperparameters of the ANN model so that the training iterations are The loss function of the ANN model is reduced to an acceptable level;

在ANN的每一层神经元中都会设置权重w和偏置b;对于已知输入x和输出y,神经网络在训练中不断调整w和b,来拟合现有y与x之间的关系,训练结束时得到y=wx+b这个简化关系式,w和b在是ann模型训练出的庞大的参数矩阵;本发明采用梯度下降算法就是对模型内部参数进行寻优的算法,属于模型参数优化算法,调整的模型参数是模型表达式y=wx+b中的w。贝叶斯超参数优化算法是对ANN模型超参数进行选择和设定的算法,属于自动调参算法,可以替代手动调参、网格搜索等方法,方便、耗时短、可确定最优超参数,能够解决仅靠经验法调的参费时费力且无法获得使模型性能最优的超参数的问题;超参数包括:迭代次数、网络层数等这些需要建模时进行设置的超参数;The weight w and bias b are set in each layer of neurons in the ANN; for the known input x and output y, the neural network continuously adjusts w and b during training to fit the relationship between the existing y and x , the simplified relational expression y=wx+b is obtained at the end of the training, w and b are the huge parameter matrices trained by the ann model; the gradient descent algorithm used in the present invention is an algorithm for optimizing the internal parameters of the model, which belongs to the model parameters Optimization algorithm, the adjusted model parameter is w in the model expression y=wx+b. The Bayesian hyperparameter optimization algorithm is an algorithm for selecting and setting hyperparameters of ANN models. It is an automatic parameter adjustment algorithm and can replace manual parameter adjustment, grid search and other methods. It is convenient, short-time consuming, and can determine the optimal hyperparameter. Parameters can solve the problem that it is time-consuming and laborious to adjust parameters based on empirical methods alone, and it is impossible to obtain hyper-parameters that optimize model performance; hyper-parameters include: the number of iterations, the number of network layers, and other hyper-parameters that need to be set during modeling;

步骤(3-3)、使用测试集对训练好的ANN模型进行验证,将测试集的输入变量输入训练好的ANN模型中,使用Min-Max反归一化算法将输出结果映射到真实区间,并与测试集的输出变量进行对比;Step (3-3), use the test set to verify the trained ANN model, input the input variables of the test set into the trained ANN model, and use the Min-Max denormalization algorithm to map the output results to the real interval. And compare it with the output variables of the test set;

步骤(3-4)、使用均方根误差和决定系数对ANN模型训练结果进行评价,若满足评价目标则输出训练模型为ANN模型,若不满足评价目标,则重新执行训练过程,直至满足评价目标的要求。Step (3-4), use the root mean square error and coefficient of determination to evaluate the ANN model training results. If the evaluation objectives are met, the training model will be output as the ANN model. If the evaluation objectives are not met, the training process will be re-executed until the evaluation is met. Goal requirements.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(3-1)中,采用Min-Max归一化法对输入变量和输出变量进行归一化处理,归一化处理的计算公式为:In the above ANN-based design method of sludge ash concrete material mix ratio, in step (3-1), the Min-Max normalization method is used to normalize the input variables and output variables, and the calculation formula of the normalization process is for:

(1); (1);

式(1)中,x 表示未归一化的数值,表示归一化之后的数值;max表示同一批次数据中的最大值,min表示同一批次数据中的最小值;In formula (1), x represents an unnormalized value, represents the value after normalization; max represents the maximum value in the same batch of data, and min represents the minimum value in the same batch of data;

步骤(3-2)中,ANN模型的损失函数为:In step (3-2), the loss function of the ANN model is:

(2); (2);

式(2)中,n表示训练集样本总数,表示模型给出的配合比预测值,/>表示归一化后的实际配合比;loss值在0~0.05范围内时,表明模型损失函数降低至可接受水平;In formula (2), n represents the total number of samples in the training set, Indicates the predicted value of the mix ratio given by the model,/> Indicates the actual mix ratio after normalization; when the loss value is in the range of 0 to 0.05, it indicates that the model loss function has reduced to an acceptable level;

步骤(3-3)中,Min-Max反归一化算法的计算公式为:In step (3-3), the calculation formula of the Min-Max denormalization algorithm is:

(3); (3);

式(3)中,x表示未归一化的数值,表示归一化之后的数值;max表示同一批次数据中的最大值,min表示同一批次数据中的最小值;In formula (3), x represents an unnormalized value, represents the value after normalization; max represents the maximum value in the same batch of data, and min represents the minimum value in the same batch of data;

步骤(3-4)中,均方根误差RMSE和决定系数R 2的计算公式为:In step (3-4), the calculation formula of the root mean square error RMSE and the coefficient of determination R2 is:

(4); (4);

(5); (5);

式(4)和式(5)中,n表示测试集样本总数,表示反归一化后预测值,/>表示实际值,/>表示n个测试集样本的实际值的均值;当均方根误差RMSE小于或等于0.01,且决定系数R 2大于或等于0.95时,表明训练模型满足要求;均方根误差RMSE的数值越接近0,表示模型的拟合效果越好,决定系数R 2的数值越接近1,表示模型的拟合效果越好。因此,若均方根误差RMSE数值较大或者决定系数R 2数值较小,则应调整并重新执行训练过程,直至均方根误差RMSE和决定系数R 2满足要求。In Formula (4) and Formula (5), n represents the total number of samples in the test set, Represents the predicted value after denormalization,/> Represents the actual value,/> Represents the mean of the actual values of n test set samples; when the root mean square error RMSE is less than or equal to 0.01, and the coefficient of determination R2 is greater than or equal to 0.95, it indicates that the training model meets the requirements; the closer the value of the root mean square error RMSE is to 0 , indicating that the better the fitting effect of the model is, the closer the value of the determination coefficient R 2 is to 1, indicating the better the fitting effect of the model. Therefore, if the value of the root mean square error RMSE is large or the value of the coefficient of determination R2 is small, the training process should be adjusted and re-executed until the root mean square error RMSE and the coefficient of determination R2 meet the requirements.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(3-2)中,采用贝叶斯超参数优化算法对ANN模型的超参数进行自适应调整和选择,以提升ANN模型的建模精度,最终获得精确度高的污泥灰混凝土配合比ANN设计模型;具体的调优方法为:In the above ANN-based design method of sludge ash concrete material mix ratio, in step (3-2), the Bayesian hyperparameter optimization algorithm is used to adaptively adjust and select the hyperparameters of the ANN model to improve the construction of the ANN model. mold accuracy, and finally obtain a highly accurate ANN design model of sewage ash concrete mix ratio; the specific tuning method is:

首先,根据经验或模型测试的表现设计或调整ANN模型中各超参数的优化空间Θ,以降低运算复杂度;该优化空间可根据后续模型的预测表现进行调整;First, design or adjust the optimization space Θ of each hyperparameter in the ANN model based on experience or model testing performance to reduce computational complexity; the optimization space can be adjusted based on the prediction performance of subsequent models;

其次,设定超参数调优的目标函数h(θ):Secondly, set the objective function h ( θ ) for hyperparameter tuning:

(6); (6);

式(6)中,n表示样本总数,表示预测值,/>表示实际值,θ表示超参数;In formula (6), n represents the total number of samples, Represents the predicted value,/> represents the actual value, θ represents the hyperparameter;

然后,利用贝叶斯超参数优化法求解得到使h(θ)值最小的超参数;求解过程表示为:Then, the Bayesian hyperparameter optimization method is used to solve to obtain the hyperparameter that minimizes the h ( θ ) value; the solution process is expressed as:

(7); (7);

式(7)中,θ*为贝叶斯超参数优化算法需要寻找的最优超参数,θ为输入的超参数,Θ为设定的参数空间,n表示样本总数,表示预测值,/>表示实际值。In formula (7), θ * is the optimal hyperparameter that the Bayesian hyperparameter optimization algorithm needs to find, θ is the input hyperparameter, Θ is the set parameter space, n represents the total number of samples, Represents the predicted value,/> represents the actual value.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,贝叶斯超参数优化算法寻找最优超参数的方法为:The above-mentioned ANN-based design method of sludge ash concrete material mix ratio and the Bayesian hyperparameter optimization algorithm to find the optimal hyperparameters are:

目标函数h(θ)服从高斯分布,即:The objective function h ( θ ) obeys Gaussian distribution, that is:

(8); (8);

式(8)中,μ(θ)为h(θ)的均值,O(θ,θ´)为h(θ)的协方差矩阵,O(θ,θ’)的初始值表示为:In formula (8), μ ( θ ) is the mean value of h ( θ ), O ( θ , θ ´) is the covariance matrix of h ( θ ), and the initial value of O ( θ , θ' ) is expressed as:

(9); (9);

在贝叶斯超参数优化过程中,协方差矩阵O(θ,θ’)会随着训练的迭代而改变,随着训练迭代的进行,假设在第t+1步输入的超参数为θ t+1,则O(θ,θ’)的值表示为:In the Bayesian hyperparameter optimization process, the covariance matrix O ( θ , θ' ) will change with the iterations of training. As the training iterations proceed, assume that the hyperparameter input at step t+1 is θ t+ 1 , then the value of O ( θ , θ' ) is expressed as:

(10); (10);

因此,目标函数h(θ)的后验概率的计算公式为:Therefore, the calculation formula for the posterior probability of the objective function h ( θ ) is:

(11); (11);

式(11)中,D为观测值,μ t+1(θ)为第t+1步h(θ)的均值,σ2 t+1(θ)为第t+1步h(θ)的方差;In equation (11), D is the observation value, μ t+ 1 ( θ ) is the mean value of h ( θ ) at step t+1, and σ 2 t+ 1 ( θ ) is the variance of h ( θ ) at step t+1;

得到后验概率后,贝叶斯超参数优化算法根据后验分布,在上一次超参数附近空间进行寻找,寻找方法为:After obtaining the posterior probability, the Bayesian hyperparameter optimization algorithm searches for the space near the last hyperparameter according to the posterior distribution. The search method is:

(12); (12);

式(12)中ζt+1是常数,设定为0.01;θ t+1是选取出的第t+1步的超参数;In formula (12), ζ t+1 is a constant, set to 0.01; θ t+1 is the selected hyperparameter of step t+1;

通过不断迭代寻找,利用贝叶斯超参数优化算法可以确定在给定的超参数优化空间Θ中的最优超参数,该组超参数能够使ANN模型取得最优的训练结果。Through continuous iterative search, the Bayesian hyperparameter optimization algorithm can be used to determine the optimal hyperparameters in a given hyperparameter optimization space Θ. This set of hyperparameters can enable the ANN model to achieve optimal training results.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,贝叶斯超参数优化算法调优的ANN模型超参数包括隐藏层数量、训练迭代次数、优化器、批量样本量、学习率、激活函数和丢弃法比率。The above-mentioned ANN-based design method of sludge ash concrete material mix ratio, the ANN model hyperparameters tuned by the Bayesian hyperparameter optimization algorithm include the number of hidden layers, the number of training iterations, the optimizer, the batch sample size, the learning rate, and the activation function. and discard ratio.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(1)中,通过收集公开数据资料和/或实验的方式获取污泥灰混凝土原材料配合比和力学性能的初始数据集。In the above ANN-based design method of sludge ash concrete material mix ratio, in step (1), the initial data set of sludge ash concrete raw material mix ratio and mechanical properties is obtained by collecting public data and/or experiments.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(2)中,将初始数据集中的数据按照7:3的比例随机划分为训练集和测试集。In the above ANN-based design method of sludge ash concrete material mix ratio, in step (2), the data in the initial data set are randomly divided into a training set and a test set in a ratio of 7:3.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,步骤(1)中,污泥灰混凝土原材料包括污泥灰、水泥、碎石、砂子、减水剂、增稠剂、膨胀剂和水;力学性能参数包括抗压强度、抗折强度、塌落度和耐久性。In the above ANN-based design method of sludge ash concrete material mix ratio, in step (1), the raw materials of sludge ash concrete include sludge ash, cement, gravel, sand, water reducing agent, thickener, expansion agent and water. ; Mechanical performance parameters include compressive strength, flexural strength, slump and durability.

上述基于ANN的污泥灰混凝土材料配合比的设计方法,耐久性为氯离子渗透系数、抗冻性和碱骨料反应中的一种或两种及两种以上。For the above-mentioned ANN-based design method of sludge ash concrete material mix ratio, the durability is one or two or more of the chloride ion permeability coefficient, frost resistance and alkali aggregate reaction.

本发明的技术方案取得了如下有益的技术效果:The technical solution of the present invention achieves the following beneficial technical effects:

1、由于污泥灰对混凝土性能的影响较为复杂,采用现有的配合比设计手段耗时较长且工作量较大,难以满足污泥灰混凝土这类性质复杂的配合比设计需求。本发明所提出的基于ANN和贝叶斯超参数优化的配合比设计模型不仅预测精度远高于现有技术,且智能化、自动化水平较高,更适合工程实际。1. Since the influence of sludge ash on the performance of concrete is relatively complex, using existing mix proportion design methods is time-consuming and requires a large workload, and it is difficult to meet the complex mix design requirements of sludge ash concrete. The mix ratio design model based on ANN and Bayesian hyperparameter optimization proposed by this invention not only has a much higher prediction accuracy than the existing technology, but also has a higher level of intelligence and automation, making it more suitable for engineering practice.

2、本发明基于污泥灰混凝土的性能指标进行设计,使用ANN人工神经网络方法对污泥灰混凝土多种掺料的配合比及抗压强度等性能参数进行建模,同时使用贝叶斯超参数优化算法对ANN模型的多个超参数进行调优,相比基于经验的手工调优方法可以更充分地发挥ANN模型的拟合能力,获得最优设计模型。2. The present invention is designed based on the performance indicators of sludge ash concrete, uses the ANN artificial neural network method to model the performance parameters such as the mix ratio and compressive strength of various additives of sludge ash concrete, and uses Bayesian super The parameter optimization algorithm tunes multiple hyperparameters of the ANN model. Compared with the manual tuning method based on experience, it can fully utilize the fitting ability of the ANN model and obtain the optimal design model.

3、本发明使用ANN构建污泥灰混凝土各原材料的配合比回归预测模型,替代传统的质量法、体积法和数学关系式等方式,可以对多达14种变量进行建模,更好的拟合污泥灰混凝土性能指标与配合比之间的复杂非线性关系,得到更接近预定性能指标的配合比设计。3. The present invention uses ANN to construct a regression prediction model of the mix ratio of each raw material of sludge ash concrete, replacing the traditional mass method, volume method and mathematical relational expressions. It can model up to 14 variables and better simulate Combining the complex nonlinear relationship between the performance indicators and mix ratio of sludge ash concrete, we can obtain a mix ratio design that is closer to the predetermined performance indicators.

附图说明Description of the drawings

图1本发明实施例中构建ANN模型时的模型训练过程示意图;Figure 1 is a schematic diagram of the model training process when constructing an ANN model in the embodiment of the present invention;

图2本发明实施例中构建ANN模型时的模型测试过程示意图;Figure 2 is a schematic diagram of the model testing process when constructing the ANN model in the embodiment of the present invention;

图3本发明实施例中基于验证集的模型预测值与实际值对比图。Figure 3 is a comparison chart between model prediction values and actual values based on the validation set in the embodiment of the present invention.

具体实施方式Detailed ways

本实施例基于ANN的污泥灰混凝土材料配合比设计方法包括如下步骤:The ANN-based sludge ash concrete material mix design method in this embodiment includes the following steps:

步骤(1)、采集构建污泥灰混凝土原材料配合比和力学性能参数的初始数据集;本实施例通过收集网络公开数据资料和实验采集的方式获取污泥灰混凝土原材料配合比和力学性能数据,构建得到初始数据集。Step (1): Collect and construct an initial data set of sludge ash concrete raw material mix ratio and mechanical property parameters; in this embodiment, the sludge ash concrete raw material mix ratio and mechanical property data are obtained by collecting online public data and experimental collection. Build the initial data set.

步骤(2)、将初始数据集随机划分为训练集和测试集;初始数据集中的抗压强度、抗折强度、塌落度、耐久性(耐久性包括氯离子渗透系数、抗冻性、碱骨料反应)的数值作为输入变量,污泥灰、水泥、碎石、砂子、水、减水剂、增稠剂和膨胀剂的配合比例作为输出变量;将初始数据集按照7:3的比例随机划分为训练集和测试集,训练集用来训练模型以得到最优的拟合效果,测试集用来验证和评价训练模型对污泥灰混凝土配合比的计算效果。Step (2): Randomly divide the initial data set into a training set and a test set; the compressive strength, flexural strength, slump, and durability in the initial data set (durability includes chloride ion permeability coefficient, frost resistance, alkali resistance, etc. The value of aggregate reaction) is used as the input variable, and the mixing ratio of sludge ash, cement, gravel, sand, water, water reducing agent, thickener and expanding agent is used as the output variable; the initial data set is based on the ratio of 7:3 It is randomly divided into a training set and a test set. The training set is used to train the model to obtain the optimal fitting effect. The test set is used to verify and evaluate the calculation effect of the training model on the sludge ash concrete mix ratio.

步骤(3)、使用训练集进行迭代训练构建得到ANN模型,并根据测试集对训练得到的ANN模型进行验证,若验证通过则输出构建的ANN模型,若验证不通过则重新执行训练过程优化ANN模型,直至ANN模型通过验证;即:构建ANN模型,基于训练集迭代训练模型,使模型能够根据训练集输入变量的数值,输出越来越接近输出变量的结果。为了得到使ANN模型性能更优的超参数组合,本实施例使用贝叶斯超参数优化算法对迭代次数、学习率等模型超参数进行自适应调优。使用测试集对基于最优参数组合下的ANN模型进行验证,使用均方根误差和决定系数作为评价指标对模型的训练效果进行评价。Step (3): Use the training set to perform iterative training to build an ANN model, and verify the trained ANN model based on the test set. If the verification passes, the constructed ANN model will be output. If the verification fails, the training process will be re-executed to optimize the ANN. model until the ANN model passes the verification; that is, construct the ANN model and iteratively train the model based on the training set so that the model can output results that are closer and closer to the output variable based on the values of the input variables in the training set. In order to obtain a hyperparameter combination that improves the performance of the ANN model, this embodiment uses the Bayesian hyperparameter optimization algorithm to adaptively tune model hyperparameters such as the number of iterations and the learning rate. Use the test set to verify the ANN model based on the optimal parameter combination, and use the root mean square error and coefficient of determination as evaluation indicators to evaluate the training effect of the model.

具体的,ANN模型的构建方法为:Specifically, the construction method of the ANN model is:

步骤(3-1)、将污泥灰混凝土原材料配合比作为输出变量,力学性能参数作为输入变量,分别对输入变量和输出变量进行归一化处理;采用Min-Max归一化法对输入变量和输出变量进行归一化处理,归一化处理的计算公式为:Step (3-1): Use the sludge ash concrete raw material mix ratio as the output variable and the mechanical property parameters as the input variables. Normalize the input variables and output variables respectively; use the Min-Max normalization method to normalize the input variables. And the output variables are normalized. The calculation formula of normalization is:

(1); (1);

式(1)中,x表示未归一化的数值,表示归一化之后的数值;max表示同一批次数据中的最大值,min表示同一批次数据中的最小值。In formula (1), x represents an unnormalized value, represents the normalized value; max represents the maximum value in the same batch of data, and min represents the minimum value in the same batch of data.

步骤(3-2)、确定ANN模型的损失函数,基于梯度下降优化算法对ANN模型内部参数进行调整,并采用贝叶斯优化算法对ANN模型超参数进行自适应调整和选择,使训练迭代中的ANN模型损失函数降低至可接受水平;ANN模型的损失函数为:Step (3-2): Determine the loss function of the ANN model, adjust the internal parameters of the ANN model based on the gradient descent optimization algorithm, and use the Bayesian optimization algorithm to adaptively adjust and select the hyperparameters of the ANN model so that the training iterations are The loss function of the ANN model is reduced to an acceptable level; the loss function of the ANN model is:

(2); (2);

式(2)中,n表示训练集样本总数,表示模型给出的配合比预测值,/>表示归一化后的实际配合比;loss值在0~0.05范围内时,表明模型损失函数降低至可接受水平;In formula (2), n represents the total number of samples in the training set, Indicates the predicted value of the mix ratio given by the model,/> Indicates the actual mix ratio after normalization; when the loss value is in the range of 0 to 0.05, it indicates that the model loss function has reduced to an acceptable level;

贝叶斯超参数优化算法调优的ANN模型超参数包括隐藏层数量、训练迭代次数、优化器、批量样本量、学习率、激活函数和丢弃法比率;贝叶斯超参数优化算法对ANN模型的内部超参数进行调优的方法为:The ANN model hyperparameters tuned by the Bayesian hyperparameter optimization algorithm include the number of hidden layers, the number of training iterations, the optimizer, the batch sample size, the learning rate, the activation function and the dropout ratio; the Bayesian hyperparameter optimization algorithm has a positive impact on the ANN model. The method for tuning the internal hyperparameters is:

首先,根据经验或模型测试的表现设计或调整ANN模型中各超参数的优化空间Θ;First, design or adjust the optimization space Θ of each hyperparameter in the ANN model based on experience or model test performance;

其次,设定超参数调优的目标函数h(θ):Secondly, set the objective function h ( θ ) for hyperparameter tuning:

(6); (6);

式(6)中,n表示样本总数,表示预测值,/>表示实际值,θ表示超参数;In formula (6), n represents the total number of samples, Represents the predicted value,/> represents the actual value, θ represents the hyperparameter;

然后,利用贝叶斯超参数优化法求解得到使h(θ)值最小的超参数;求解过程表示为:Then, the Bayesian hyperparameter optimization method is used to solve to obtain the hyperparameter that minimizes the h ( θ ) value; the solution process is expressed as:

(7); (7);

式(7)中,θ*为贝叶斯超参数优化算法需要寻找的最优超参数,θ为输入的超参数,Θ为设定的参数空间,n表示样本总数,表示预测值,/>表示实际值。In formula (7), θ * is the optimal hyperparameter that the Bayesian hyperparameter optimization algorithm needs to find, θ is the input hyperparameter, Θ is the set parameter space, n represents the total number of samples, Represents the predicted value,/> represents the actual value.

步骤(3-3)、使用测试集对训练好的ANN模型进行验证,将测试集的输入变量输入训练好的ANN模型中,使用Min-Max反归一化算法将输出结果映射到真实区间,并与测试集的输出变量进行对比;Min-Max反归一化算法的计算公式为:Step (3-3), use the test set to verify the trained ANN model, input the input variables of the test set into the trained ANN model, and use the Min-Max denormalization algorithm to map the output results to the real interval. And compare it with the output variables of the test set; the calculation formula of the Min-Max denormalization algorithm is:

(3); (3);

式(3)中,x表示未归一化的数值,表示归一化之后的数值;max表示同一批次数据中的最大值,min表示同一批次数据中的最小值;In formula (3), x represents an unnormalized value, represents the value after normalization; max represents the maximum value in the same batch of data, and min represents the minimum value in the same batch of data;

步骤(3-4)、使用均方根误差和决定系数对ANN模型训练结果进行评价,若满足评价目标则输出训练模型为ANN模型,若不满足评价目标,则重新执行训练过程,直至满足评价目标的要求。均方根误差RMSE和决定系数R 2的计算公式为:Step (3-4), use the root mean square error and coefficient of determination to evaluate the ANN model training results. If the evaluation objectives are met, the training model will be output as the ANN model. If the evaluation objectives are not met, the training process will be re-executed until the evaluation is met. Goal requirements. The calculation formula of the root mean square error RMSE and the coefficient of determination R2 is:

(4); (4);

(5); (5);

式(4)和式(5)中,n表示测试集样本总数,表示反归一化后预测值,/>表示实际值,/>表示n个测试集样本的实际值的均值;当均方根误差RMSE小于或等于0.01,且决定系数R 2大于或等于0.95时,表明训练模型满足要求。In Formula (4) and Formula (5), n represents the total number of samples in the test set, Represents the predicted value after denormalization,/> Represents the actual value,/> Represents the mean of the actual values of n test set samples; when the root mean square error RMSE is less than or equal to 0.01, and the coefficient of determination R2 is greater than or equal to 0.95, it indicates that the training model meets the requirements.

贝叶斯超参数优化算法寻找最优超参数的方法为:The method for finding optimal hyperparameters using the Bayesian hyperparameter optimization algorithm is:

目标函数h(θ)服从高斯分布,即:The objective function h ( θ ) obeys Gaussian distribution, that is:

(8); (8);

式(8)中,μ(θ)为h(θ)的均值,O(θ,θ´)为h(θ)的协方差矩阵,O(θ,θ’)的初始值表示为:In formula (8), μ ( θ ) is the mean value of h ( θ ), O ( θ , θ ´) is the covariance matrix of h ( θ ), and the initial value of O ( θ , θ' ) is expressed as:

(9); (9);

随着训练迭代的进行,假设在第t+1步输入的超参数为θ t+1,则O(θ,θ’)的值表示为:As the training iteration proceeds, assuming that the hyperparameter input at step t+1 is θ t+ 1 , the value of O ( θ , θ' ) is expressed as:

(10); (10);

因此,目标函数h(θ)的后验概率的计算公式为:Therefore, the calculation formula for the posterior probability of the objective function h ( θ ) is:

(11); (11);

式(11)中,D为观测值,μ t+1(θ)为第t+1步h(θ)的均值,σ2 t+1(θ)为第t+1步h(θ)的方差;In equation (11), D is the observation value, μ t+ 1 ( θ ) is the mean value of h ( θ ) at step t+1, and σ 2 t+ 1 ( θ ) is the variance of h ( θ ) at step t+1;

得到后验概率后,贝叶斯超参数优化算法根据后验分布,在上一次超参数附近空间进行寻找,寻找方法为:After obtaining the posterior probability, the Bayesian hyperparameter optimization algorithm searches for the space near the last hyperparameter according to the posterior distribution. The search method is:

(12); (12);

式(12)中ζt+1是常数,设定为0.01;θ t+1是选取出的第t+1步的超参数;In formula (12), ζ t+1 is a constant, set to 0.01; θ t+1 is the selected hyperparameter of step t+1;

通过不断迭代寻找,确定在给定的超参数优化空间Θ中的最优超参数。Through continuous iterative search, the optimal hyperparameters in the given hyperparameter optimization space Θ are determined.

在构建ANN模型过程中,ANN模型的隐藏层数量、迭代次数、学习率等超参数均不需预先设定,由贝叶斯超参数优化算法在训练过程中自适应确定,只需要预先给出超参数的优化空间;本实施例给出的优化空间如表1所示。In the process of building an ANN model, the number of hidden layers, number of iterations, learning rate and other hyperparameters of the ANN model do not need to be set in advance. They are adaptively determined by the Bayesian hyperparameter optimization algorithm during the training process and only need to be given in advance. Optimization space of hyperparameters; the optimization space given in this embodiment is shown in Table 1.

表1 超参数优化空间Table 1 Hyperparameter optimization space

数据输入模型前,先经过Min-Max归一化处理;模型输出结果后,也需经过反归一化计算处理,才能得到真实值域内的预测数值。Before the data is input into the model, it must first undergo Min-Max normalization processing; after the model outputs the results, it must also undergo denormalization calculation processing to obtain the predicted value within the true value range.

本实施例中采集的初始数据集中的训练数据共84组,剩余的36组作为测试集,用来验证模型训练后的性能(由于数据较多,本实施例不再对各数据进行列举)。模型训练过程中,使用训练数据中的抗压强度(X 1)、抗折强度(X 2)、塌落度(X 3)、氯离子渗透系数(X 4)、抗冻性(X 5)、碱骨料反应(X 6)共六组变量作为模型的输入变量,训练模型输出污泥灰(Y 1)、水泥(Y 2)、碎石(Y 3)、砂子(Y 4)、水(Y 5)、减水剂(Y 6)、增稠剂(Y 7)、膨胀剂(Y 8)共八组变量。There are 84 sets of training data in the initial data set collected in this embodiment, and the remaining 36 sets are used as test sets to verify the performance of the model after training (due to the large amount of data, this embodiment does not list each data). During the model training process , the compressive strength ( X 1 ), flexural strength ( X 2 ), slump ( , alkali aggregate reaction ( _ _ _ _ _ ( Y 5 ), water reducing agent ( Y 6 ), thickener ( Y 7 ), and expansion agent ( Y 8 ), a total of eight groups of variables.

训练结束后,可以查看本次训练中贝叶斯超参数优化得到的超参数组。本实施例中超参数组如表2所示。After training, you can view the hyperparameter group obtained by Bayesian hyperparameter optimization in this training. The hyperparameter set in this embodiment is shown in Table 2.

表2 贝叶斯超参数优化获得的超参数组Table 2 Hyperparameter groups obtained by Bayesian hyperparameter optimization

最后,使用36组测试数据对模型的性能进行验证,并使用均方根误差(RMSE)和决定系数(R 2)两个评价指标进行模型拟合效果的评价。经计算得知,RMSE=0.00263,R2=0.98221。模型给出的预测值与实际值的对比结果如图3所示。Finally, 36 sets of test data were used to verify the performance of the model, and two evaluation indicators, root mean square error ( RMSE ) and coefficient of determination ( R 2 ), were used to evaluate the model fitting effect. After calculation, it is found that RMSE =0.00263 and R 2 =0.98221. The comparison results between the predicted values given by the model and the actual values are shown in Figure 3.

本实施例的污泥灰混凝土配合比建模在测试集中取得了RMSE=0.00263,R2=0.98221的测试结果。据RMSE和R2的公式及含义可知,RMSE的值越接近0,R2的值越接近1,说明模型给出的预测值与实际值的拟合程度越高。因此,由上述评价指标可知,本实施例构建的ANN模型对污泥灰混凝土性能指标与配合比拟合的很好,说明该ANN模型对污泥灰混凝土性能指标与配合比之间的规律进行了充分的学习,可以根据预期的性能指标数值,给出所需的配合比。由图2预测值与实际值的对比结果也可得出:ANN结合贝叶斯超参数优化方法给出了非常贴近实际值的配合比回归预测结果。The sludge ash concrete mix proportion modeling in this embodiment achieved test results of RMSE =0.00263 and R 2 =0.98221 in the test set. According to the formulas and meanings of RMSE and R 2 , it can be seen that the closer the value of RMSE is to 0, the closer the value of R 2 is to 1, indicating that the predicted value given by the model is closer to the actual value. Therefore, it can be seen from the above evaluation indicators that the ANN model constructed in this embodiment fits the performance index and mix ratio of sludge ash concrete very well, indicating that the ANN model can accurately predict the relationship between the performance index and mix ratio of sludge ash concrete. With sufficient learning, the required mix ratio can be given based on the expected performance index values. It can also be concluded from the comparison between the predicted values and actual values in Figure 2: ANN combined with the Bayesian hyperparameter optimization method gives mix ratio regression prediction results that are very close to the actual values.

步骤(4)、将通过验证的ANN模型进行保存,在工程应用时,首先输入预期要达到的污泥灰混凝土性能指标数值,然后该ANN模型将根据已训练好的参数进行计算,从而输出配合比。根据该配合比进行污泥灰混凝土的配制。Step (4): Save the verified ANN model. During engineering application, first enter the expected sludge ash concrete performance index value, and then the ANN model will be calculated based on the trained parameters to output the matching Compare. The sludge ash concrete is prepared according to this mix ratio.

本实施例对按照ANN模型输出的配合比配制好的污泥灰混凝土进行污泥灰混凝土性能指标的实验测试,结果发现,采用ANN模型输出的配合比配置的污泥灰混凝土其性能与预期要达到的性能指标基本吻合,完全满足工程应用需求。In this embodiment, the sludge ash concrete prepared according to the mix ratio output by the ANN model was experimentally tested on the performance indicators of the sludge ash concrete. The results found that the performance of the sludge ash concrete configured according to the mix ratio output by the ANN model was in line with the expected requirements. The achieved performance indicators are basically consistent and fully meet the needs of engineering applications.

在其他一些实施例中,也可以根据实际情况调整污泥灰混凝土原材料的种类作为输出变量,或者根据污泥灰混凝土的应用指标调整力学性能数据的指标种类作为输入变量,构建新的ANN模型。In some other embodiments, the type of sludge ash concrete raw material can be adjusted as an output variable according to the actual situation, or the index type of mechanical property data can be adjusted as an input variable according to the application indicators of sludge ash concrete to construct a new ANN model.

显然,上述实施例仅仅是为清楚地说明所作的举例,而并非对实施方式的限定。对于所属领域的普通技术人员来说,在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引伸出的显而易见的变化或变动仍处于本专利申请权利要求的保护范围之中。Obviously, the above-mentioned embodiments are only examples for clear explanation and are not intended to limit the implementation. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. An exhaustive list of all implementations is neither necessary nor possible. The obvious changes or modifications derived therefrom are still within the protection scope of the claims of this patent application.

Claims (4)

1. The design method of the sludge ash concrete material mixing ratio based on the ANN is characterized by comprising the following steps of:
step (1), collecting and constructing an initial data set of raw material mixing proportion and mechanical property parameters of sludge ash concrete; the sludge ash concrete raw materials comprise sludge ash, cement, broken stone, sand, a water reducing agent, a thickening agent, an expanding agent and water; mechanical properties include compressive strength, flexural strength, slump and durability;
step (2), randomly dividing the initial data set into a training set and a testing set;
performing iterative training by using a training set to construct an ANN model, verifying the ANN model obtained by training according to a test set, outputting the constructed ANN model if verification is passed, and re-executing the training process to optimize the ANN model if verification is not passed until the ANN model is passed;
step (4), inputting performance indexes of the sludge ash concrete material to be prepared into an ANN model passing verification, and outputting the mixing ratio of the sludge ash concrete raw materials through the ANN model;
in the step (3), the construction method of the ANN model comprises the following steps:
step (3-1), taking the mixing ratio of sludge ash concrete raw materials as an output variable and taking mechanical property parameters as an input variable, and respectively carrying out normalization treatment on the input variable and the output variable;
in the step (3-1), a Min-Max normalization method is adopted to normalize the input variable and the output variable, and a calculation formula of the normalization is as follows:
(1);
in the formula (1), the components are as follows,indicating non-normalized values, ++>Representing the value after normalization; />Represents the maximum value in the same batch of data, +.>Representing the minimum value in the same batch of data;
step (3-2), determining a loss function of the ANN model, adjusting internal parameters of the ANN model based on a gradient descent optimization algorithm, and adopting a Bayesian optimization algorithm to adaptively adjust and select the super parameters of the ANN model so as to reduce the loss function of the ANN model in training iteration to an acceptable level;
in step (3-2), the loss function of the ANN model is:
(2);
in the formula (2), the amino acid sequence of the compound,representing the total number of training set samples, +.>Representing the predicted value of the mix given by the model, < + >>Representing the normalized actual mix ratio;lossvalues in the range of 0 to 0.05 indicate that the model loss function is reduced to an acceptable level;
step (3-3), verifying the trained ANN model by using the test set, inputting the input variable of the test set into the trained ANN model, mapping the output result to a real interval by using a Min-Max inverse normalization algorithm, and comparing the output result with the output variable of the test set;
in the step (3-3), the Min-Max inverse normalization algorithm has a calculation formula:
(3);
in the formula (3), the amino acid sequence of the compound,indicating non-normalized values, ++>Representing the value after normalization; />Represents the maximum value in the same batch of data, +.>Representing the minimum value in the same batch of data;
step (3-4), evaluating the training result of the ANN model by using root mean square error and a decision coefficient, outputting the training model as the ANN model if the evaluation target is met, and re-executing the training process if the evaluation target is not met until the requirement of the evaluation target is met;
in step (3-4), root mean square errorRMSEDetermining coefficientsR 2 The calculation formula of (2) is as follows:
(4);
(5);
in the formulas (4) and (5),representing the total number of test set samples, +.>Representing the inverse normalized predicted value,/->Representing the actual value +.>Representation->An average of actual values of the individual test set samples; when root mean square errorRMSELess than or equal to 0.01 and determining coefficientsR 2 When the training model is more than or equal to 0.95, the training model is shown to meet the requirements;
in the step (3-2), adopting a Bayes super-parameter optimization algorithm to carry out self-adaptive adjustment and selection on the super parameters of the ANN model; the ANN model super parameters optimized by the Bayesian super parameter optimization algorithm comprise the number of hidden layers, the training iteration times, an optimizer, batch sample size, learning rate, activation function and discarding method ratio; the specific tuning method comprises the following steps:
firstly, designing or adjusting an optimization space Θ of each super parameter in an ANN model according to the performance of experience or model test;
secondly, setting an objective function of super parameter tuningh(θ):
(6);
In the formula (6), the amino acid sequence of the compound,representing the total number of samples->Representing predicted values +.>The actual value is represented by a value that is,θrepresenting the super-parameters;
then, solving by using a Bayes super-parameter optimization method to obtain the leadh(θ) Super-parameters with minimum values; the solving process is expressed as:
(7);
in the formula (7), the amino acid sequence of the compound,θ* The optimal super-parameters to be searched for by the Bayes super-parameter optimization algorithm,θfor the input hyper-parameters, Θ is the set parameter space,representing the total number of samples->Representing predicted values +.>Representing the actual value;
the method for searching the optimal super-parameters by the Bayes super-parameter optimization algorithm comprises the following steps:
objective functionh(θ) Obeys gaussian distribution, i.e.:
(8);
in the formula (8), the amino acid sequence of the compound,μ(θ) Is thath(θ) Is used for the average value of (a),O(θ,θ(v) ish(θ) Is used for the co-variance matrix of (a),O(θ,θ’) The initial value of (2) is expressed as:
(9);
as training iterations progress, assume that the super-parameters entered at step t+1 areθ t+1 ThenO(θ,θ’) The values of (2) are expressed as:
(10);
thus, the objective functionh(θ) The posterior probability of (2) is calculated by the following formula:
(11);
in the formula (11), the amino acid sequence of the compound,Din order to observe the value of the value,μ t+1 (θ) Is t+1st steph(θ) Mean, sigma of 2 t+1 (θ) Is t+1st steph(θ) Is a variance of (2);
after posterior probability is obtained, searching the space near the last super parameter according to posterior distribution by a Bayes super parameter optimization algorithm, wherein the searching method comprises the following steps:
(12);
zeta in (12) t+1 Is a constant, set to 0.01;θ t+1 is the super parameter of the selected t+1 step;
by constant iterative search, the optimal superparameter in a given superparameter optimization space Θ is determined.
2. The method for designing the mix proportion of sludge ash concrete materials based on ANN according to claim 1, wherein in the step (1), the initial data set of the mix proportion of sludge ash concrete raw materials and mechanical properties is obtained by collecting public data and/or experimental means.
3. The method for designing a mix ratio of sludge ash concrete materials based on ANN according to claim 1, wherein in step (2), the data in the initial data set is randomly divided into a training set and a test set according to a ratio of 7:3.
4. The method for designing the mix ratio of the ANN-based sludge ash concrete material according to claim 1, wherein the durability is one or two or more of chloride ion permeability coefficient, freezing resistance and alkali aggregate reaction.
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