Method for optimizing mix proportion of pavement bricks based on multi-objective collaborative decision

Abstract

The invention provides a pavement brick mix proportion optimization method based on multi-objective collaborative decision, and relates to the technical field of pavement brick mix proportion optimizing.According to the method, joint probability distribution of environmental parameters is constructed, an accelerated aging test and neural network interpolation are combined, the relation between pavement brick performance and different environments is depicted, and a pavement brick mix proportion optimization result is obtained. The material adaptability can be accurately evaluated under variable environment conditions; then, the component mix proportion, the environmental adaptability and the production cost of the pavement brick are organically combined, an intelligent optimization process is constructed, dynamic coupling of material performance and environmental parameters is achieved, the mix proportion which is most suitable for the target area environment and is economical and efficient is screened out through comprehensive optimization, the durability and the economical efficiency are both considered, and the application prospect is wide. Therefore, the applicability and economic benefits of pavement brick material design are greatly improved.

Description

Technical Field

[0001] This invention relates to the field of paving brick mix ratio optimization technology, specifically to a method for optimizing paving brick mix ratio based on multi-objective collaborative decision-making. Background Technology

[0002] With the advancement of urban stormwater management and ecological environment construction, paving bricks are widely used in roads, squares, and other scenarios due to their excellent permeability and ecological functions. However, environmental conditions in different regions, such as temperature and humidity, place multiple demands on the durability and performance of paving bricks. Simultaneously, fluctuations in raw material costs and the need for mix proportion optimization mean that traditional mix design based on experience or single performance indicators cannot simultaneously consider material adaptability, economy, and long-term service performance, often leading to material waste or fluctuations in project quality. Existing technologies generally employ fixed mix proportions or only conduct material performance testing under limited environmental conditions, lacking systematic analysis of complex environmental parameters and multi-objective optimization, making it difficult to meet the collaborative decision-making needs for the comprehensive performance and cost of paving bricks in practical engineering projects.

[0003] In the prior art, CN121257296A discloses an optimization method and system based on the mix proportion of heavy slag paving bricks, including the following steps: determining the mix proportion parameters of heavy slag paving bricks; establishing a performance dataset of heavy slag paving bricks, and constructing a nonlinear mapping function between the mix proportion parameters of the heavy slag paving bricks and the performance dataset; constructing a multi-objective function based on the nonlinear mapping function, establishing multi-objective constraints, and constructing a multi-objective optimization dataset according to the objective function and multi-objective constraints; performing weighted analysis of each performance using entropy weight TOPSIS, substituting the weight values ​​into the multi-objective optimization dataset, and determining the optimal mix proportion. Although this scheme can optimize the mix proportion, it focuses on emphasizing mechanical strength and durability modeling and weight decision-making, without considering the impact of the environment on paving bricks or material cost factors. This results in weak applicability of the optimization results in actual complex environments and economic aspects, limiting its application breadth and economic benefits.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the mix proportion of paving bricks based on multi-objective collaborative decision-making, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: An optimization method for paving brick mix proportion based on multi-objective collaborative decision-making, the specific steps of which include: S1: Obtain the real-time unit price and proportion range of each component in the paving brick. Based on the orthogonal experimental method, construct several paving brick sample groups with different component distribution ratios within the proportion range, and place each paving brick sample in the paving brick sample group under different test environment parameters for accelerated aging test. S2: Collect crack parameters of each sample after the test to quantify its aging degree. Based on the crack parameters, generate the first fit degree of each sample to each test environment parameter, and use it as the fitting point. Use neural network interpolation method to construct the fit degree function of each sample. S3: Collect historical environmental parameters at the target area where the paving bricks are to be installed, estimate their probability distribution to generate a joint probability distribution of historical environmental parameters, and use the Monte Carlo method to combine the joint probability distribution and the fitness function to obtain the second fitness of each sample to the target area. S4: Based on the second fit degree, select several sets of paving brick samples suitable for the target area, calculate the production cost according to the real-time unit price and the component mix ratio of each sample, combine them with the second fit degree to generate a comprehensive optimization coefficient, and take the component mix ratio corresponding to the paving brick sample with the highest comprehensive optimization coefficient as the optimal mix ratio.

[0007] Preferably, the paving bricks are composed of fine aggregate, coarse aggregate, cementitious material, water-reducing agent, and water; the test environment parameters and historical environment parameters both include ambient temperature and ambient humidity; the crack parameters include the number of cracks and the average crack length.

[0008] Preferably, for each paving brick sample, an aging index is generated by weighting the number of cracks and the average crack length. The degree of aging is quantified based on the aging index, and the degree of aging is positively correlated with the aging index, while the first fit is negatively correlated with the aging index.

[0009] Preferably, the neural network interpolation method is a radial basis function network, the environmental parameters are represented in vector form, and the fitness function is used to reflect the mapping relationship between the environmental parameters and the fitness.

[0010] Preferably, the radial basis function network includes: The input layer receives an environment parameter vector and sends it to the hidden layer. The hidden layer comprises several groups of neurons, each group of neurons corresponding to a radial basis function. The hidden layer is used to calculate the distance between the environmental parameter vector and the center of each radial basis function, and then sends it to the output layer after mapping through the radial basis functions. The output layer is used to linearly combine the mapping results of the hidden layer to generate the corresponding first fitness.

[0011] Preferably, the number of neurons is the same as the number of experimental environment parameters and corresponds one-to-one. All of them use Gaussian functions as radial basis functions, and the experimental environment parameters are determined with the center of each radial basis function as the corresponding fitting point.

[0012] Preferably, the logic for obtaining the second fit is as follows: Based on the Monte Carlo method, several sets of sampling points are randomly collected from the joint probability distribution of the target region; Substitute the environmental parameter vectors of each sampling point into the fitness function to calculate the corresponding first fitness prediction value; The average of the first fitness prediction values ​​for each sampling point is taken and calibrated as the second fitness.

[0013] Preferably, step S4 includes: S401: Sort the second fit of each paving brick sample to the target area in descending order, and consider the top 20% of the paving brick samples to be suitable for the target area. S402: For paving brick samples applicable to this target area, calculate the corresponding production cost according to their component mix ratio and the real-time unit price of each component. S403: The production cost and the second fit are weighted and summed to generate a comprehensive optimization coefficient. The paving brick sample with the largest comprehensive optimization coefficient is considered to be the most suitable for the target area, and the component mix ratio corresponding to the paving brick sample is taken as the optimal mix ratio.

[0014] Preferably, the calculation logic for the production cost is as follows: Calculate the weight of each component based on the composition ratio and weight of the paving brick sample. Calculate the real-time total price of each component based on its weight and real-time unit price. The total cost of the paving brick sample is obtained by summing the real-time total prices of each component.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a joint probability distribution of environmental parameters, combines accelerated aging tests and neural network interpolation to characterize the relationship between paving brick performance and different environments, achieving accurate assessment of material adaptability under varying environmental conditions. Furthermore, it organically integrates paving brick component ratios, environmental adaptability, and production costs to construct an intelligent optimization process, realizing dynamic coupling between material performance and environmental parameters. Through comprehensive optimization, it selects the most suitable and cost-effective mix ratio for the target area environment, balancing durability and economy, thereby significantly improving the applicability and economic benefits of paving brick material design. Attached Figure Description

[0016] Fig. 1 This is a schematic diagram of the overall method flow of the present invention; Fig. 2 This is a flowchart illustrating step S4 of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figs. 1-2 The present invention provides a technical solution: An optimization method for paving brick mix proportion based on multi-objective collaborative decision-making, the specific steps of which include: S1: Obtain the real-time unit price and proportion range of each component in the paving brick. Based on the orthogonal experimental method, construct several paving brick samples with different component proportions within the proportion range, and conduct accelerated aging tests under different test environmental parameters. The components of the paving brick include fine aggregate, coarse aggregate, cementitious material, water-reducing agent, and water. The test environmental parameters and subsequent historical environmental parameters include ambient temperature and ambient humidity, but they are different types collected under different scenarios, and all environmental parameters are expressed in vector form.

[0020] The common proportion range of each component of paving bricks is determined by relevant standards or engineering requirements. Generally, it is as follows: coarse aggregate 30%~45%, used to improve permeability; fine aggregate 15%~25%, used to fill the structure and improve the density of paving bricks; cementing materials (such as cement and fly ash) 15%~25%, used to ensure the adhesion between the components of paving bricks; water 6%~10%; and water-reducing agent 0.2%~0.5%.

[0021] For orthogonal experimental methods, the factors to consider are the proportions of each component of the paving brick and different test environmental parameters. Based on the factors and the number of levels, a suitable orthogonal array is selected to ensure that the level combinations of each factor are representative and minimize the number of tests. Then, the orthogonal array is arranged row by row, with each row representing a unique combination of proportions and environmental parameters. Different samples are prepared, numbered, and then subjected to accelerated aging tests (such as freeze-thaw cycles, wet-dry cycles, etc.) under corresponding temperature and humidity conditions. Using orthogonal experimental methods to systematically combine the various component ranges not only covers a wide parameter space but also significantly reduces the number of tests, improves experimental efficiency, reduces experimental resource consumption, and can realistically simulate the impact of different climatic conditions on the performance of paving bricks, ensuring the wide applicability and scientific validity of the experimental data.

[0022] S2: Collect crack parameters of each sample after the test to quantify its aging degree. Crack parameters include the number of cracks and the average crack length. Based on the crack parameters, generate the first fitness of each sample to different test environment parameters in the test and use it as the fitting point. Use a neural network interpolation method to construct the fitness function of each sample. The neural network interpolation method is a radial basis function network, and the fitness function is used to reflect the mapping relationship between the environmental parameters and the first fitness.

[0023] For each paving brick sample, an aging index is generated by weighting the number of cracks and the average crack length. The degree of aging is then quantified based on this index, and the degree of aging is positively correlated with the aging index. The formula for calculating the aging index can be set as follows: In the formula , , They represent the first Group of paving brick samples in the first Aging indexes, number of cracks, and average crack length under the environmental parameters of the group test. , These represent the normalized weights for the number of cracks and the average crack length, respectively. The initial weights are 0.5 and 0.5, meaning they are set equally. These weights can be adjusted based on expert experience or actual needs. , These represent the indexes for the paving brick samples and the test environment parameters, respectively.

[0024] The first fitness level is negatively correlated with the aging index, and its expression can be set as: In the formula The first fit is defined by the expression. It can be seen from this expression that the lower the aging index of the paving brick sample under the test environment, the higher the first fit, and the more suitable it is for use in this environment.

[0025] It is understandable that, since the actual environment of the target area may differ from the test environment, the corresponding historical environmental parameters may not fall within the set of test environmental parameters. Therefore, it is necessary to construct an fitness function to reflect the true fitness of each group of paving brick samples under different environmental parameters in order to improve adaptability to different environments.

[0026] Radial basis function networks (RBFNNs) include: The input layer receives the environment parameter vector and sends it to the radial basis function hidden layer. The hidden layer consists of several groups of neurons, each group of neurons corresponding to a radial basis function. The hidden layer is used to calculate the distance between the environmental parameter vector and the center of each radial basis function, and then sends it to the output layer after mapping through the radial basis function. The number of neurons is the same as the number of experimental environmental parameters and they correspond one-to-one. Gaussian functions are used as radial basis functions, and the center of each radial basis function is determined by the experimental environmental parameters of the corresponding fitting point. The output layer is used to linearly combine the mapping results of the hidden layers to generate the fitness function, the expression of which is: In the formula Indicates the first The environmental parameter vector for the group of paving brick samples is The first fitness prediction value at that time, , Let represent the environmental parameter vector received by the input layer and the experimental environmental parameter vector, respectively. By inputting the historical environmental parameter vector of the target area into the input layer of the radial basis function network, the predicted fit of the paving brick sample to the target area can be obtained. This represents the total number of sets of experimental environment parameter vectors, which is also equivalent to the total number of neurons. Indicates for the first For a set of paving brick samples, the first element in its fit function is... The weights of each neuron are determined during training, and can be obtained through linear algebra or regularization. The Euclidean distance is represented by . Let represent the radial basis functions, which in this scheme are Gaussian functions, i.e.: To avoid confusion between the natural logarithm and the environment parameter vector, the expression exp is used here. The kernel width parameter, which is greater than 0, is typically taken as the average distance between the centers of all radial basis functions. The ratio value, for example: RBFNN has local response characteristics, which can handle the nonlinear and locally varying fitness distribution in the environmental parameter space. It is not only simple to train and suitable for situations with limited but irregularly distributed sample points, but also has good generalization ability. It is suitable for interpolation and prediction in multidimensional input spaces, thereby enabling the prediction of fitness for any environmental parameter and improving the accuracy of the overall prediction results.

[0027] S3: Collect historical environmental parameters of the target area where the paving bricks are to be installed, including historical environmental temperature and historical environmental humidity, estimate their probability distribution to generate a joint probability distribution of historical environmental parameters, and obtain the second fitness of each sample to the target area based on the joint probability distribution and fitness function.

[0028] Since factors such as temperature and humidity also roughly follow a Gaussian distribution, a Gaussian kernel can also be used as the kernel function when constructing the joint probability distribution. The multivariate kernel density estimation (KDE) method is then employed to construct the joint probability distribution of the target region, and its expression is as follows: In the formula This represents the joint probability distribution of the target region. This represents the kernel function, in this case, the Gaussian kernel. This indicates the value within the parentheses in the environment parameter vector, representing the first value in that environment parameter vector. One element, This represents the index of an element, which is also the dimension of the vector. The total number of elements in the environmental parameter vector is 2. In this embodiment, the experimental environmental parameters and historical environmental parameters in the environmental parameters only include temperature and humidity. However, the types of elements in the environmental parameters (such as rainfall, wind speed, etc.) can be increased according to actual needs. Indicates the first Group historical environment parameter vector, Index representing historical environmental parameters, This represents the total number of historical environmental parameters. Indicates the first The bandwidth parameter corresponding to each element is determined by the Silverman method, cross-validation, or expert experience. It can be seen that the core of KDE is to estimate the probability density under any given environmental parameter using a known vector of historical environmental parameters. This reflects the probability of the occurrence of the environmental parameter vector.

[0029] After obtaining the fit function of each paving brick sample and the joint probability distribution of the target area, the second fit of each sample to the target area can be calculated. This second fit is equal to the probability-weighted average of the fit function in the environmental parameter space of the target area, and its definition is: In the formula Indicates the first The second fit of the paving brick sample to the target area. It is understandable that the environmental parameters of the target area where paving bricks need to be installed are not fixed values ​​but fluctuate. The definition of the second fit is the average value of the sample fit function within the target environmental parameter space, weighted according to the environmental distribution probability. It reflects the expected adaptability level of the paving brick sample under varying environmental conditions, that is, the comprehensive performance of the sample in all possible environments in the actual service area. Its integration space is a multidimensional space containing all environmental parameter vectors, and the specific range is determined by historical environmental parameters combined with expert experience.

[0030] Since the environmental parameter vector has many dimensions, its integration is quite complex. Therefore, the second fitness degree can be approximated using the Monte Carlo method, the logic of which is as follows: Based on the Monte Carlo method, several sets of sampling points are randomly collected from the joint probability distribution of the target region; Substitute the environmental parameter vectors of each sampling point into the fitness function to calculate the corresponding first fitness prediction value; The average of the first fitness prediction values ​​for each sampling point is taken and calibrated as the second fitness.

[0031] When randomly sampling from the joint probability distribution of the target region, commonly used Monte Carlo methods include resampling and kernel density-based sampling. Resampling involves directly sampling randomly from existing historical environmental parameters (with replacement), and the sample points themselves approximately follow a certain probability distribution. The advantage of this method is that the sampling process is simple and it is suitable for situations where the sample size of historical environmental parameters is large. Kernel density-based sampling, on the other hand, takes each sample in the historical environmental parameters as the center and generates sampling points according to the bandwidth parameter of the Gaussian kernel. The overall sample set simulates the multivariate KDE distribution. This sampling method more realistically reflects the estimated continuous probability density and avoids the bias caused by the discrete sample points. It is more suitable for situations where the sample size of historical environmental parameters is small.

[0032] After approximating the result using the Monte Carlo method, the formula for calculating the second fitness is: In the formula This represents the index of the sampling point obtained by the Monte Carlo method. This indicates the total number of sampling points.

[0033] In this step, the second fit integrates the diversity of the target area environment and the actual occurrence frequency through probability distribution, making the evaluation of each paving brick sample more realistic and accurate, thereby enabling better screening of paving brick samples and corresponding component ratios suitable for the target area.

[0034] S4: Based on the second fit degree, select several sets of paving brick samples suitable for the target area, calculate the production cost according to the real-time unit price and the component mix ratio of each sample, combine them with the second fit degree to generate a comprehensive optimization coefficient, and take the component mix ratio corresponding to the paving brick sample with the highest comprehensive optimization coefficient as the optimal mix ratio.

[0035] Step S4 includes: S401: Sort the second fit of each paving brick sample to the target area in descending order, and consider the top 20% of the paving brick samples to be suitable for the target area. S402: For paving brick samples applicable to this target area, calculate the corresponding production cost according to their component mix ratio and the real-time unit price of each component. S403: The production cost and the second fit are weighted and summed to generate a comprehensive optimization coefficient. The paving brick sample with the largest comprehensive optimization coefficient is considered to be the most suitable for the target area, and the component mix ratio corresponding to the paving brick sample is taken as the optimal mix ratio.

[0036] The calculation logic for production costs is as follows: Calculate the weight of each component based on the composition ratio and weight of the paving brick sample. Calculate the real-time total price of each component based on its weight and real-time unit price. The total cost of the paving brick sample is obtained by summing the real-time total prices of each component.

[0037] In this step, the top 20% of samples with excellent performance are first screened out through the second fit, which can narrow the scope of subsequent calculations and decisions, reduce the computational complexity and decision difficulty, and not only rely solely on performance indicators (second fit) to screen samples, but also incorporate production costs into the decision, forming a comprehensive optimization of performance and economy, meeting the dual needs of actual engineering, and enhancing the adaptability of the solution to the environmental conditions of the target area and its actual economy.

[0038] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0039] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0040] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0041] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making, characterized in that, The specific steps include: S1: Obtain the real-time unit price and proportion range of each component in the paving brick. Based on the orthogonal experimental method, construct several paving brick sample groups with different component distribution ratios within the proportion range, and place each paving brick sample in the paving brick sample group under different test environment parameters for accelerated aging test. S2: Collect crack parameters of each sample after the test to quantify its aging degree. Based on the crack parameters, generate the first fit degree of each sample to each test environment parameter, and use it as the fitting point. Use neural network interpolation method to construct the fit degree function of each sample. S3: Collect historical environmental parameters at the target area where the paving bricks are to be installed, estimate their probability distribution to generate a joint probability distribution of historical environmental parameters, and use the Monte Carlo method to combine the joint probability distribution and the fitness function to obtain the second fitness of each sample to the target area. S4: Based on the second fit degree, select several sets of paving brick samples suitable for the target area, calculate the production cost according to the real-time unit price and the component mix ratio of each sample, combine them with the second fit degree to generate a comprehensive optimization coefficient, and take the component mix ratio corresponding to the paving brick sample with the highest comprehensive optimization coefficient as the optimal mix ratio.

2. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 1, characterized in that: The components of the paving bricks include fine aggregate, coarse aggregate, cementitious material, water-reducing agent, and water; the test environment parameters and historical environment parameters both include ambient temperature and ambient humidity; the crack parameters include the number of cracks and the average crack length.

3. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 2, characterized in that: For each paving brick sample, an aging index is generated by weighting the number of cracks and the average crack length. The degree of aging is quantified based on the aging index, and the degree of aging is positively correlated with the aging index, while the first fit is negatively correlated with the aging index.

4. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 3, characterized in that: The neural network interpolation method is a radial basis function network, the environmental parameters are represented in vector form, and the fitness function is used to reflect the mapping relationship between the environmental parameters and the first fitness.

5. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 4, characterized in that: The radial basis function network includes: The input layer receives an environment parameter vector and sends it to the hidden layer. The hidden layer comprises several groups of neurons, each group of neurons corresponding to a radial basis function. The hidden layer is used to calculate the distance between the environmental parameter vector and the center of each radial basis function, and then sends it to the output layer after mapping through the radial basis functions. The output layer is used to linearly combine the mapping results of the hidden layer to generate the corresponding first fitness.

6. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 5, characterized in that: The number of neurons is the same as the number of experimental environment parameters and corresponds one-to-one. Gaussian functions are used as radial basis functions, and the experimental environment parameters are determined with the center of each radial basis function as the corresponding fitting point.

7. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 4, characterized in that: The logic for obtaining the second degree of fit is as follows: Based on the Monte Carlo method, several sets of sampling points are randomly collected from the joint probability distribution of the target region; Substitute the environmental parameter vectors of each sampling point into the fitness function to calculate the corresponding first fitness prediction value; The average of the first fitness prediction values ​​for each sampling point is taken and calibrated as the second fitness.

8. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 7, characterized in that: Step S4 includes: S401: Sort the second fit of each paving brick sample to the target area in descending order, and consider the top 20% of the paving brick samples to be suitable for the target area. S402: For paving brick samples applicable to this target area, calculate the corresponding production cost according to their component mix ratio and the real-time unit price of each component. S403: The production cost and the second fit are weighted and summed to generate a comprehensive optimization coefficient. The paving brick sample with the largest comprehensive optimization coefficient is considered to be the most suitable for the target area, and the component mix ratio corresponding to the paving brick sample is taken as the optimal mix ratio.

9. The method for optimizing the mix proportion of paving bricks based on multi-objective collaborative decision-making according to claim 8, characterized in that: The calculation logic for the production cost is as follows: Calculate the weight of each component based on the composition ratio and weight of the paving brick sample. Calculate the real-time total price of each component based on its weight and real-time unit price. The total cost of the paving brick sample is obtained by summing the real-time total prices of each component.

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