https://orcid.org/0009-0006-4048-6190
Retraction
The PLOS One Editors retract this article [1] due to concerns about potential manipulation of the publication process. These concerns call into question the validity and provenance of the reported results. We regret that the issues were not identified prior to the article’s publication.
All authors did not agree with the retraction.
8 Apr 2026: The PLOS One Editors (2026) Retraction: Consumption quota compilation based on BP artificial neural network algorithm in mechanical and electrical installation engineering of prefabricated buildings. PLOS ONE 21(4): e0345984. https://doi.org/10.1371/journal.pone.0345984 View retraction
Figures
Abstract
The traditional quota compilation method has a large workload and requires a lot of manpower and material resources, making it difficult to apply to the consumption quota compilation in mechanical and electrical installation engineering of prefabricated buildings. Therefore, a consumption quota compilation model on the basis of artificial neural network is built. On the basis of the traditional quota formulation model based on statistical theory, artificial neural networks are introduced, and regularization techniques and particle swarm optimization algorithms are taken to optimize the model performance. The experiment was validated using project datasets covering different regions, scales, and types of prefabricated components. The results showed that the mean squared errors on the training and testing sets were 1.2% and 1.1%, and the average absolute errors were 8.3% and 8.1%, respectively. In addition, the determination coefficients on the training and testing sets were 95.1% and 92.8%, and the accuracy was 92.3% and 91.4%. Further case analysis also showed that the prediction error rates of the research model for material consumption, labor hours, and mechanical equipment usage were relatively low, not exceeding 2.48%, 1.25%, and 4.1%, respectively. In addition, in terms of quota compilation efficiency and economic benefits, the proposed model achieved a quota compilation efficiency value of 90.1%. The return on investment in material consumption, labor hours, and mechanical equipment use was 5.03, 6.09, and 5.92, respectively, and the cost savings rates were 6.21%, 4.85%, and 5.48%, respectively, all of which were better than traditional models. Overall, the designed model can optimize the accuracy of engineering budgeting and the ability to control costs.
Citation: Liu X, Tang W, Si L, Li Y (2025) RETRACTED: Consumption quota compilation based on BP artificial neural network algorithm in mechanical and electrical installation engineering of prefabricated buildings. PLoS One 20(6): e0324854. https://doi.org/10.1371/journal.pone.0324854
Editor: Dajiang Geng, China Construction Fourth Engineering Division Corp. Ltd, CHINA
Received: March 18, 2025; Accepted: April 30, 2025; Published: June 2, 2025
Copyright: © 2025 Liu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting Information files.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
With the continuous advancement of modern building technology and the deepening of the concept of sustainable development, prefabricated buildings, as a new type of construction method, have attracted much attention due to their high efficiency, environmental protection, and energy-saving characteristics. Prefabricated buildings use prefabricated components for standardized production in factories and rapid assembly on construction sites, greatly shortening the construction period, reducing construction difficulty, and improving building quality. In prefabricated buildings, Mechanical and Electrical Installation (MEI) engineering is an indispensable and important component, and the accurate consumption quota compilation has a crucial impact on cost control, construction efficiency, and overall project economic benefits. However, unlike traditional MEI, the construction process, on-site construction methods, and standardization of components in MEI engineering of prefabricated building are significantly different from traditional buildings, making it difficult for traditional quota compilation methods to adapt to new construction models. Therefore, how to scientifically and reasonably compile the consumption quota for MEI in prefabricated building has become a key issue.
Zhang Y et al. took the Pareto optimal multi-objective Particle Swarm Optimization (PSO) to construct an initial carbon quota allocation optimization model and optimize the allocation results. This method not only reduced the relative exploitative significance of carbon quota allocation, but also helped achieve “30. 60”dual carbon target [1]. Chen Y et al. established a calculation method for energy consumption and carbon emissions on the basis of quota data, activity data, and carbon emission factors to explore the energy consumption and carbon emissions during the construction period of hot recycled asphalt pavement. This study combined a local geothermal regeneration project on a highway in Hunan Province. The experimental results showed that the energy consumption during the heating process of the old road surface was the highest, accounting for 47.4% of the total energy consumption. The energy consumption during the production and transportation of raw materials accounted for 24.6% of the total energy consumption. The energy consumption during the paving and rolling stages was relatively low, at 1.6% and 7.0% respectively [2]. Akpe A T et al. explored the development and implementation of cost control strategies for oil and gas engineering projects based on the lifecycle. It was found that using real-time cost tracking and predictive analysis software could optimize decision-making and financial supervision [3]. Matel E et al. took machine learning methods to estimate the cost of construction projects. The accuracy of the estimation model based on artificial neural networks was improved by 14.5% compared with traditional estimation methods [4]. Chao M H et al. built a domain information model for basic construction cost estimation. This method could enable manufacturers to obtain accurate product cost estimates [5]. Scholars Du M et al. proposed a source control method based on Energy Quota Trading (EQT), which combines the Difference in Differences (DiD) method and Spatial Durbin Model (SDM-DID) to study the impact of EQT on energy efficiency and its spatial effects. The experimental results show that EQT effectively improves energy efficiency in pilot areas compared to non pilot areas, and has positive energy efficiency spillover effects on neighboring areas, especially in southern regions, old industrial bases, resource-based cities, and large cities. In addition, mechanism testing has shown that EQT has achieved policy effects in improving energy efficiency through channels such as increasing marketization, energy allocation efficiency, and green taxation [6]. Scholars Wu F and others proposed a Convolutional Neural Network (MHA-CNN) model based on multi head attention mechanism for accurately predicting Carbon Dioxide Emission Performance Index (CEPIs) and providing suggestions for industrial structure optimization. This model introduces deep learning mechanisms and has efficient resolution strategies for model overfitting training, feature extraction, and self supervised learning to achieve adaptability to CEPIs. The multi head attention mechanism plays an important role in explaining the influence weights of variables on CEPIs, thereby improving the predictive performance of CNN for CEPIs. The experimental results show that the MHA-CNN model performs better than commonly used CNN models and Long Short Term Memory (LSTM) models in multi-objective prediction of CEPIs, especially in multi-dimensional feature extraction. The contribution of influencing variables to CEPIs based on MHA analysis is highly consistent with geographical distribution analysis, indicating that the MHA module has excellent ability in identifying variable weights and decomposing contributions. Based on the MHA-CNN model, more accurate prediction results show that the increase in the tertiary industry and the decrease in the primary and secondary industries can help improve the total factor carbon emission efficiency and further enhance the effective energy utilization in areas with low carbon emission efficiency[7].
Although previous research has achieved certain results, there is still room for improvement. Traditional quota compilation methods are mainly based on statistical theory and historical data, which are difficult to effectively address the complex nonlinear relationships and changing influencing factors in the MEI engineering of prefabricated buildings. In addition, existing research mostly focuses on single objective optimization (such as cost control or energy consumption analysis), lacking comprehensive consideration of multi-objective collaborative optimization, resulting in insufficient comprehensiveness and practicality of quota compilation. Although some studies have attempted to cite machine learning methods, their practical applications are still not mature enough, and the generalization ability and prediction accuracy of the models need further improvement. Therefore, a consumption quota compilation model based on an improved Back Propagation Neural Network (BP) is built. The innovation of this model mainly lies in introducing regularization techniques (dropout) and PSO on the basis of the traditional BP, to improve the generalization ability and stability. In addition, project datasets covering different regions, scales, and types of prefabricated components are taken to verify the applicability and reliability in practical engineering, providing a scientific basis for the quota compilation for MEI in prefabricated building.
2. Methods and materials
2.1. Consumption quota compilation for mechanical and electrical installation engineering based on statistical theory in prefabricated building
Prefabricated building refers to a building formed by connecting and assembling some or all components after being produced and processed in a factory and transported to the construction site through certain technical means. MEI in prefabricated buildings involves the layout, connection, debugging, and acceptance of electrical and mechanical equipment such as air conditioning, water supply and drainage, heating, strong and weak electricity, and fire protection within the prefabricated building. Unlike traditional MEI engineering, the MEI process of prefabricated buildings is usually more standardized, as shown in Fig 1.
Fig 1 shows the MEI process of prefabricated buildings. From the Fig, the process first uses 3D laser scanning to collect data on the completed civil engineering, and then uses this data to model using Building Information Modeling (BIM). During the BIM modeling process, it is necessary to inspect the pipelines to ensure that they do not collide with each other. After the model is established, the construction layout documents and processing lists are prepared, and then the layout machine is used to conduct layout on the construction site. Meanwhile, the factory will also prefabricate and process according to the processing list, prepare assembly and positioning drawings, and facilitate on-site installation [8–9]. After installation, another 3D scan is performed to compare the scan results with the BIM model and validate the installation accuracy. Finally, the final acceptance of the MEI engineering is conducted to ensure that the entire installation process meets the requirements. Based on this process, in MEI, the consumption of materials and equipment accounts for the majority of the project cost [10–11]. Therefore, in order to reasonably control the material consumption required during construction, reduce waste, and lower construction costs, a quota for its consumption is established. The specific steps for preparing the consumption quota are shown in Fig 2.
Fig 2 shows the steps for preparing the consumption quota. It mainly includes five core processes: data collection, classification analysis, calculation and preparation, review and revision, and release management. The compilation method based on the compilation steps usually adopts statistical analysis, which involves analyzing and calculating a large amount of statistical data on on-site materials and supplies to obtain data on material consumption. When statistical analysis is used for specific data processing, it usually combines physical discrimination and error limit adjustment to process the raw data. The physical discrimination method does not have a specific calculation formula, so it needs to rely on manual experience. Fig 3 displays the specific operation process.
Fig 3 shows the specific operation process of the physical discrimination method. From this process, the key stages of physical discrimination mainly include data collection, mean and standard deviation calculation, deviation degree calculation, threshold setting, and discrimination and exclusion [12–13]. Unlike physical discrimination methods, the error limit adjustment method can be calculated through specific mathematical formulas to process extreme values in the original data, as shown in formula (1).
In formula (1), represents the arithmetic mean.
is the maximum value.
is the adjustment coefficient.
is the maximum value after discrimination processing.
is the minimum value.
is the minimum value after discrimination processing [14–15]. After processing the collected raw data, the arithmetic mean method is used to calculate the consumption quota, as shown in formula (2).
In formula (2), signifies the arithmetic mean of the corresponding data group.
represents the number of data in the data group.
represents the i-th data value of the data group. Based on the above, the quota for consumption can be formulated. However, in MEI of prefabricated building, compared with other projects, the construction technology of MEI engineering is more complex, so the accuracy of quota data is required to be higher [16–17]. Traditional physical discrimination methods usually rely on manual experience and intuitive judgment, which has impacts on the data accuracy and objectivity. In addition, although the error limit adjustment method can eliminate some outliers, the limit values still relies on manual experience judgment and lacks a unified standard [18]. Therefore, introducing statistical theory can optimize the quality of quota data. The first one introduced is Grubbs criterion, as shown in formula (3).
In formula (3), represents the mean of
measured values.
represents the standard deviation.
represents the test statistic.
represents the critical value of Grubbs test.
and
are both coefficients in polynomials.
is the significance level [19]. The second is Dixon’s criterion, as shown in formula (4).
In formula (4), represents the maximum Dixon statistic.
represents the minimum Dixon statistic.
signifies the maximum value in the dataset.
signifies the second largest value.
signifies the minimum in the dataset, and
represents the second smallest value [20–21].
and
are the number of extreme values in the sample that are on the same side as the suspected outlier. The Dixon criterion identifies potential outliers by comparing the differences between the maximum or minimum in the dataset and other values. Based on this statistical theory, it is possible to improve the original consumption quota data. At this time, the consumption quota for MEI in prefabricated buildings is presented in formula (5).
In formula (5), represents the first average value.
is the average of
data points smaller than
.
represents the quadratic mean. Based on the above, a consumption quota for prefabricated building MEI engineering is established.
2.2. Consumption quota compilation based on improved artificial neural network
Although statistical theory can be used to establish consumption quotas for prefabricated building MEI projects, this method requires a high sample size and is susceptible to the influence of sample data distribution characteristics. When the sample data is small or the data distribution is uneven, the quota compilation based on statistical theory may weaken the ability to identify outliers in the data, which may lead to significant deviations in the processed data results. In addition, the Dixon criterion in statistical theory is also sensitive to the location of outliers. If the location of an outlier is in the middle of the data, the value may still be missed [22–23]. Therefore, to avoid the above situation, it is improved. Considering that BP has low requirements for the number and distribution characteristics of sample data, even in situations where the sample size is small or the data distribution is uneven, BP can still achieve good prediction results [24]. The study adopts BP for programming. The training process based on BP is displayed in Fig 4.
In Fig 4, the process involves first randomly initializing all weights and biases in the network, and then processing each input sample to calculate the output value through forward propagation of the network. Then, the error by is computed comparing the difference between the network output and the actual. Afterwards, the output error is back-propagated back into the network according to its weight, updating the weights and biases of each layer [25–26]. The iteration is repeated until the network output error drops to an acceptable range. Based on this training process, the network has non-linear mapping ability. In installation engineering, the complexity of consumption standards and construction environment, including terrain, climate, and spatial limitations, presents a non-linear correlation [27]. Therefore, the research model is constructed, as shown in Fig 5.
In Fig 5, the BP performs outlier removal on the original consumption quota data during the data processing stage, and then trains the network to determine the parameters. Based on trained neural networks, it is possible to process similar sample information and establish quotas [28–29]. Finally, the information that has undergone nonlinear transformation with the minimum output error is the consumption quota for MEI engineering. The neural network training in this model is the key to obtaining accurate quota values. Therefore, the layers, input layers, output layers, activation functions, etc. of the BP are designed. For the quantity of hidden layers, formula (6) is obtained.
In formula (6), represents the quantity of hidden layers.
represents the quantity of neurons in the input layer.
represents the quantity of neurons in the input layer.
signifies a constant. Table 1 displays the settings of other parameters.
Table 1 shows the parameter settings of the consumption quota compilation model based on BP. Due to the fact that the dimensionality of the input layer vector is mainly determined by the main factors affecting the consumption quota, the study summarizes the main factors affecting the consumption quota into eight categories, namely project scale, construction technology, material type, equipment configuration, construction environment, schedule requirements, quality standards, and market factors. In addition, the study sets the structure of the output layer as multiple output layers, with output types including material consumption, construction machinery consumption, and labor consumption. Based on the above, improvements can be made to the early consumption quota formulation model based on statistical theory. However, considering the shortcomings of BP, such as long training time, the possibility of falling into local minima, and over-fitting problems, this study further introduces regularization techniques on the basis of the consumption quota formulation model constructed based on BP, that is, to overcome the shortcomings of BP through random dropout. The calculation of Dropout can be seen in formula (7).
In formula (7), represents a random mask. When m is 0, it means discard, and when m is 1, it means keep.
represents the probability of neurons being discarded.
signifies the activation value input to the neuron.
signifies the output value after Dropout processing [30]. In addition, to further optimize the convergence speed and accuracy, the PSO is introduced to further enhance the weights and thresholds. The PSO optimization process is shown in Fig 6.
Fig 6 shows the optimization process of PSO. From the Fig, PSO has global search capability and can find better weights and thresholds. Therefore, combining Dropout with PSO can jointly optimize the consumption quota model of BP. Therefore, integrating Dropout regularization technology with PSO algorithm into the training process of neural networks can jointly optimize the consumption quota model of BP neural networks. Specifically, in the early stages of model training, the PSO algorithm first randomly initializes a set of particles, each representing a potential set of weights and threshold solutions in the neural network. In the forward propagation stage, for the network structure corresponding to each particle, the system will randomly generate a mask matrix according to the preset Dropout probability, temporarily blocking some neural nodes, thus simulating the random sparsity of the network structure. This dynamic shielding mechanism can effectively prevent excessive dependencies between neurons and improve the generalization ability of the model. At the same time, the PSO algorithm uses the predicted mean square error of the network as the fitness function to evaluate the performance quality of the solution represented by the current particles. In each iteration, each particle dynamically adjusts its weight and threshold parameters based on its historical optimal solution and the global optimal solution of the population using the velocity position update formula. It is worth noting that the random mask of Dropout will be regenerated every time it propagates forward, while the optimization process of PSO continues to search for the optimal solution space under this randomness constraint. Through this collaborative mechanism, the model not only maintains the regularization advantage of Dropout, but also efficiently converges by utilizing the global search capability of PSO. To provide a clearer explanation of this integrated optimization process, pseudocode for key steps is provided in Fig 7.
Fig 7 shows the pseudocode of the key steps. Based on the above process, through iterative collaborative optimization, the globally optimal weight and threshold parameters can ultimately be output. This design not only retains the suppression effect of Dropout on overfitting, but also optimizes the parameter search efficiency through PSO algorithm, thereby minimizing the training time of the model while ensuring prediction accuracy.
3. Results
3.1. Experimental setup
To validate the research method, actual construction records of multiple completed MEI projects are collected as pending data, covering projects of different regions, scales, and types of prefabricated components. The data is organized and a sample set containing labor, material, and mechanical consumption is created as the experimental dataset. After standardization, the sample data is separated into the training and the testing sets, in an 8:2 ratio for model training and validation. The experiment adopts a comparative method, incorporating the traditional Physical discrimination method-Error limit adjustment method and the Grubbs criterion Dixon criterion joint model based on statistical theory as the comparative model. For the convenience of subsequent explanation, they are named “FD-ELA” and “Grubbs-Dixon”, respectively. In traditional quota compilation methods, “FD-ELA” (Physical Discrimination Error Limit Adjustment Fusion Model) and “Grubbs Dixon” (Grubbs Dixon Joint Model) are two representative statistical analysis methods. The core of the FD-ELA model is to achieve data cleaning through the collaboration of Physical Discrimination Method and Error Limit Adjustment Method. Among them, the physical discrimination method relies on manual experience to qualitatively judge outliers, while the error limit adjustment method quantitatively corrects the extreme values of the data through formula (8).
In formula (8), where is the arithmetic mean,
is the adjustment coefficient (usually taken as 0.5 ~ 0.8),
and
are the maximum and minimum values of the original data, respectively. The Grubbs Dixon model is based on statistical hypothesis testing and identifies outliers through the combination of Grubbs criterion and Dixon criterion, as shown in formula (9).
In formula (9), represents the statistical measure calculated by Grubbs criterion, which is used to compare whether it exceeds the critical value and to determine outliers in the data.
Indicate the
th observation value in the dataset.
represents the average value of the dataset.
represents the standard deviation of the dataset.
represents the statistic for the maximum value in the Dixon criterion, and
represents the statistic for the minimum value in the Dixon criterion. Conduct subsequent testing based on the above experimental setup.
3.2. Performance validation of consumption quota prediction
Before the formal experiment began, the study first verified the rationality of hyperparameter selection, using sensitivity analysis for testing. The results are shown in Table 2.
Table 2 shows the sensitivity analysis results of key hyperparameters. From the table, it can be seen that in the optimization of hidden layers, the model reaches the optimal MSE (1.15%) when h = 6, and the performance fluctuation caused by adjacent layers is less than 0.25%, indicating that the structural depth design is reasonable. Dropout rate p = 0.5 performs the best in suppressing overfitting, with a ± 10% fluctuation causing only about ±0.4% change in ACC, verifying the robustness of regularization strength. Particle swarm parameter testing shows that the algorithm has the highest convergence efficiency (127 iterations) when N = 50, and both large and small scales can reduce computational efficiency. The selection of learning factor c = 1.8 enables PSO to achieve a balance between exploration and development, with a fitness value 2.7% higher than the suboptimal combination. The linear decreasing strategy of inertia weight has been proven to be more effective than fixed values, accelerating convergence by about 18%. When all parameters fluctuate around the recommended values, the performance change of the model is controlled within 1.5%, confirming the stability of hyperparameter selection. After verifying the stability of hyperparameter selection, the experiment continued to test the mean squared error (MSE) of each model on the training and testing sets, as shown in Fig 8.
Fig 8 shows the MSE results of each model. In Fig 8(a), the FD-ELA had the highest MSE of 2.2%, while the Grubbs-Dixon model had a lower MSE value than FD-ELA, specifically 1.4%. In contrast, the MSE value of the I-BP model was the smallest, at 1.2%. In Fig 8(b), consistent with the results on the training set, the MSE of the FD-ELA was still the highest, at 2.3%, while the MSE of the Grubbs-Dixon was still lower than that of the FD-ELA, specifically at 1.6%. In contrast, the MSE of the I-BP was the smallest, at 1.1%. A small MSE value indicates a smaller difference between the predicted and actual values. The I-BP-based model can make accurate predictions based on this result. In addition, the study also calculates the Mean Absolute Error (MAE) of each model on the two sets, as presented in Fig 9.
Fig 9 shows the MAE of each model. In Fig 9(a), the MAE of the FD-ELA was the highest, at 13.4%, while the MAE value of the Grubbs-Dixon model was lower than that of the FD-ELA, specifically at 10.8%. In contrast, the MAE of the I-BP was the smallest, at 8.3%. In Fig 9(b), similar to the training set, the MAE of the FD-ELA was still the highest, at 13.7%, while the MAE value of the Grubbs-Dixon model was still lower than that of the FD-ELA, specifically 11.6%. In contrast, the MAE value of the I-BP model was the smallest, at 8.1%.
It should be noted that the mean square error (MSE) and mean absolute error (MAE) used in the study are both normalized percentage errors. The specific normalization process consists of two steps: first, perform Min Max normalization on the original absolute error value. The minimum and maximum values are determined based on the error distribution of the entire dataset, and the error is scaled to the [0,1] interval. Subsequently, multiply the normalized value by 100 and convert it into percentage form. This method ensures rationality through the following design: (1) scaling using the extreme values of the entire dataset (rather than a single sample) to ensure cross item comparability. (2) The error boundary value (min/max) is validated by the 5% and 95% quantiles of the data distribution to avoid outlier interference. (3) The final percentage error reflects the relative error level, which is consistent with the percentage evaluation system of engineering quotas.
Furthermore, the Determination Coefficients (R2) of each model is calculated in the experiment, and the results are shown in Fig 10.
Fig 10 displays the R2 of each model. In Fig 10(a), the FD-ELA had the smallest R2 value, which was 79.9%, while the Grubbs-Dixon had a larger R2 value than FD-ELA, which was 88.7%. In contrast, the I-BP had the highest R2, at 95.1%. In Fig 10(b), similar to the training set, the R2 value of the FD-ELA model was still the smallest, at 79.4%, while the R2 value of the Grubbs-Dixon model was still greater than that of the FD-ELA, specifically at 88.3%. In contrast, the I-BP had the highest R2, at 92.8%. Furthermore, the experiment also verifies the accuracy of quota prediction for each model, as shown in Fig 11.
Fig 11 displays the prediction accuracy results. In Fig 11(a), the accuracy of the FD-ELA was the smallest, at 73.6%, while the accuracy of the Grubbs-Dixon model was greater than that of the FD-ELA, specifically at 80.1%. In contrast, the accuracy of the I-BP model was the highest, at 92.3%. In Fig 11(b), similar to the training set, the accuracy of the FD-ELA was still the smallest, at 71.6%, while the accuracy of the Grubbs-Dixon model was greater than that of the FD-ELA, specifically at 77.8%. In contrast, the accuracy of the I-BP model was the highest, at 91.4%. Overall, it can be seen that the quota compilation model based on I-BP has the best performance and prediction effect.
3.3. Example analysis of consumption quota compilation
Due to the fact that the above results only test the specific performance of each model in the consumption quota compilation for MEI engineering, and do not examine the performance of the model in practical applications. Therefore, the study continues with case analysis. Taking the comprehensive MEI project in a second tier city of a certain city as an example, the project is located in the center of the second tier city with a building area of 140,000m2. The MEI project includes electrical systems, water supply and drainage systems, HVAC systems, etc. The project duration is 13 months and the project budget is 130 million RMB. The experiment collects data on the MEI of the project over the past 6 months, including material consumption, labor hours, and mechanical equipment usage. The data is cleaned and normalized to ensure accuracy and consistency. Table 3 displays the specific sample data. In terms of model input design, the study fully considers the impact of on-site construction conditions and weather environment, and systematically integrates them into the prediction system. The complexity of the construction environment is quantified through the spatial conflict index extracted from the BIM model, which comprehensively evaluates the three-dimensional spatial features such as pipeline layout density and equipment installation clearance height, and directly participates in network calculations as explicit variables in the input layer. At the same time, in response to the dynamic impact of weather conditions, the model adopts a two-stage processing mechanism, which includes the proportion of inoperable days obtained from historical meteorological data statistics in the early input layer for basic prediction. Introduce a meteorological correction coefficient α = 1+(rainy season days/total construction period) in the later output layer to dynamically calibrate sensitive indicators such as mechanical equipment usage and anti-corrosion material consumption.
Table 3 shows the sample data of the MEI project in prefabricated buildings over the past six months. The sample data not only includes the data of MEI projects in the past six months, but also includes the corresponding months and their building area and construction period. Considering that the BP model performs better than other comparison models in performance testing, this experiment only uses the I-BP to predict the consumption of MEI engineering. In addition, considering that the sample collected data from the past six months, for ease of calculation, the experiment randomly selects three months for testing. The input variables of the model include building area, construction period, material prices, etc., and the output variables are material consumption, labor hours, etc. The prediction results are shown in Fig 12.
Fig 12 shows the predicted results of quota compilation based on the I-BP model. Fig 12 (a) shows the predicted material consumption for January, February, and June. The actual material consumption in January was 200 tons, the predicted material consumption was 204.7 tons, and the material error rate was 2.48%. The actual material consumption in February was 220 tons, with a predicted material consumption of 214.8 tons and a material error rate of 2.27%. The actual material consumption in June was 300 tons, with a predicted material consumption of 295.1 tons and a material error rate of 1.66%. Fig 12 (b) shows the predicted labor hours for January, February, and June. The actual labor hours in January were 800 hours, the predicted labor hours were 809.6 hours, and the labor hour error rate was 1.25%. The actual labor hours in February were 850 hours, and the predicted labor hours were 841.2 hours, with a labor hour error rate of 1.17%. The actual labor hours in June were 1,050 hours, and the predicted labor hours were 1,045.2 hours, with a labor hour error rate of 0.47%. Fig 12 (c) shows the predicted mechanical equipment usage in January, February, and June. The actual mechanical equipment usage in January was 50shift, the predicted usage was 52.2t, and the error rate of mechanical equipment usage was 4.1%. The actual mechanical equipment usage in February was 55shift, with a predicted mechanical equipment usage of 53.9t and a mechanical equipment usage error rate of 1.81%. The actual mechanical equipment usage in June was 75 shifts, with a predicted mechanical equipment usage of 73.8t and a mechanical equipment usage error rate of 1.34%. Based on the above random test results, the model has a prediction error of less than 5% in terms of material consumption, labor hours, and mechanical equipment usage, indicating that the model has high prediction accuracy and can effectively achieve consumption quota compilation of MEI engineering. In addition, based on the above operations and results, a consumption quota for MEI engineering can be formulated, as shown in Table 4.
Table 4 shows the specific consumption quota for MEI engineering. The quota value for material consumption was 1200t, while the actual value was 1180t, with an error of 1.67%. The quota value for manual labor hours was 5,000 hours, while the actual value was 5,100 hours, with an error of 1.96%. The rated value used for mechanical equipment was 300shift, while the actual value was 310shift, with an error of 3.23%. The results of the quota compilation are applied to actual engineering projects. To more intuitively exhibit the specific application, “FD-ELA” is compared with the “Grubbs-Dixon” model. The efficiency and economic benefits of quota compilation are displayed in Fig 13.
Fig 13 shows the efficiency and economic benefits of quota compilation. Fig 13 (a) shows the quota compilation efficiency. The FD-ELA model had the lowest quota compilation efficiency value, which was 71.2%, while the Grubbs-Dixon model had a higher efficiency value, specifically 80.7%, than FD-ELA. In contrast, the I-BP model had the highest efficiency value for quota compilation, at 90.1%. Fig 13 (b) shows the economic results of the MEI project. It should be pointed out that return on investment (ROI) and cost savings rate are dimensionless ratios. The return on investment is calculated by dividing the cost savings by the total implementation cost. Among them, the cost saving rate is calculated by the difference between the actual cost without the model and the actual cost when using the I-BP model. The total implementation cost includes model development and data collection expenses. The cost saving rate only represents the percentage of cost reduction achieved through optimization. In terms of material consumption, the Return on Investment (ROI) of the FD-ELA model was 1.87, the ROI value of the Grubbs-Dixon model was 2.13, and the ROI value of the I-BP model was 5.03. In terms of labor hours, the ROI value of the FD-ELA model was 2.88, the ROI value of the Grubbs-Dixon model was 3.12, and the ROI value of the I-BP model was 6.09. In the mechanical equipment usage, the ROI value of the FD-ELA model was 2.91, the ROI value of the Grubbs-Dixon model was 3.68, and the ROI value of the BP model was 5.92. In addition, regarding the cost savings rate, the FD-ELA model had a cost savings rate of 1.87% in material consumption, the Grubbs-Dixon model had a cost savings rate of 3.24%, and the I-BP model had a cost savings rate of 6.21%. In terms of manual labor hours, the cost savings rate of FD-ELA model was 1.88%, Grubbs-Dixon model was 2.69%, and I-BP model was 4.85%. In the mechanical equipment usage, the cost savings rate of FD-ELA model was 1.67%, Grubbs-Dixon model was 2.63%, and I-BP model was 5.48%. Overall, the quota compilation model for MEI engineering of prefabricated building based on I-BP has higher efficiency, better ROI, and the highest cost solution rate. Therefore, it has better overall performance. In addition, since the above results are all based on a second tier city complex project, in order to further verify the generalization ability of the model in different geographical and economic environments, the study adopted cross project cross validation method based on the original case and added three independent engineering tests. The specific verification process is as follows: select one item as the test set each time, use the remaining items as the training set, and cycle through all combinations for verification. The three newly added projects cover the following types: (1) super high-rise projects in first tier cities with a building area of 280000 square meters, high complexity of mechanical and electrical systems (including intelligent building control systems), and a construction period of 18 months. (2) The residential project in a third tier city is characterized by a standardized prefabrication rate of 85%, a construction period of 8 months, and low labor costs. (3) Projects in special climate zones are characterized by a 20% increase in the amount of anti-corrosion materials used and frequent construction intervals. The test results are shown in Table 5.
Table 5 shows the results of cross project cross validation. It can be seen from the table that under the traditional single project validation mode, namely the second tier city complex project, the model performs the best with an MSE of 1.1%. In cross project validation, when the model is faced with completely unfamiliar project types, such as super high-rise buildings in first tier cities, the MSE remains at 1.4% after training only with data from other regions, with an error increase of no more than 0.3%. In the most challenging special climate zone project, although the training set does not contain any climate zone data, the MSE of the model is 2.0%, which is still significantly better than traditional methods and demonstrates strong environmental adaptability. In all cross project validation scenarios, the ROI remains above 4.0, demonstrating the universality of the model for economic forecasting.
4. Discussion
To optimize the accuracy and efficiency of consumption quota compilation in MEI engineering of prefabricated building, a BP was introduced based on traditional statistical theory models. The model was further optimized through regularization technology and PSO algorithm. A consumption quota compilation model on the basis of I-BP was built. The study first compared the predictive performance of the I-BP with the traditional FD-ELA model and Grubbs-Dixon model. The results showed that the MSE values of the BP model on the training and testing sets were 1.2% and 1.1%, respectively, and the MAE values were 8.3% and 8.1%, respectively, which were significantly lower than those of traditional models. In addition, the BP model achieved an R2 value of 95.1% and an accuracy of 92.3% on the training set, and an R2 value of 92.8% and an accuracy of 91.4% on the testing set, both of which were superior to traditional models. This result was partially consistent with the research findings of Arabiat A et al., which suggested that neural network models had significant advantages in predicting complex engineering data [31]. The reason for this result may be that BP has strong nonlinear fitting ability, which can better capture the complex variable relationships in MEI engineering of prefabricated building. The regularization technology further enhances the generalization ability and avoids over-fitting problems.
To further verify the practical application effect of the I-BP model, a case study was conducted on the MEI engineering of a comprehensive prefabricated building in a second tier city in a certain city. The I-BP exhibited high accuracy in predicting material consumption, labor hours, and mechanical equipment usage. For example, the prediction error rates for material consumption in January, February, and June were 2.48%, 2.27%, and 1.66%, respectively. The prediction error rates for manual labor hours were 1.25%, 1.17%, and 0.47%, respectively. The prediction error rates for mechanical equipment usage were 4.1%, 1.81%, and 1.34%, respectively. These results indicated that the BP model had high applicability and reliability in practical engineering. In addition, the quota compilation efficiency of the I-BP model reached 90.1%, significantly higher than traditional models. In terms of economic benefits, the I-BP model had ROI values of 5.03, 6.09, and 5.92 for material consumption, labor hours, and mechanical equipment usage, respectively, with cost savings rates of 6.21%, 4.85%, and 5.48%, all of which were superior to traditional models. This result was partially consistent with the research findings drawn by Zou Y F et al., but in terms of specific effects, it was superior to Zou Y F et al. That is, the quota compilation method based on advanced algorithms could significantly reduce engineering costs and improve economic benefits [32]. The reason for this result may be that the I-BP model can more accurately predict resource consumption, providing a more scientific basis for engineering budgeting and cost control. The designed I-BP has demonstrated significant advantages in installation engineering. Compared with traditional methods, the research model not only has higher prediction accuracy and stability, but also significantly improves compilation efficiency and economic benefits.
Conclusion
In order to improve the accuracy of consumption quota preparation for prefabricated building electromechanical installation engineering, optimize budget control and cost management, this study introduces BP artificial neural network on the basis of traditional quota preparation model based on statistical theory, and further improves the model performance through regularization technology and PSO algorithm. The experimental results show that the consumption quota formulation model based on I-BP artificial neural network has MSE, MAE, R ², and ACC values of 1.2%, 8.3%, 95.1%, and 92.3% on the training set, and 1.1%, 8.1%, 92.8%, and 91.4% on the test set, respectively. In practical engineering applications, the model has a prediction error rate of less than 2.5% for material consumption, labor hours, and mechanical equipment usage, and performs excellently in terms of quota preparation efficiency and economic benefits. However, the inherent “black box” nature of BP neural networks makes it difficult for the model to clearly reveal the causal relationship between input features and output results, which to some extent limits its applicability in engineering practice. Future research will focus on exploring interpretable artificial intelligence technology paths, such as: (1) using Kolmogorov Arnold networks (KAN) instead of traditional MLP structures to explicitly express nonlinear relationships between variables through interpretable spline basis functions; (2) Introducing attention based quota attribution analysis to quantify the contribution of input features such as engineering scale and environmental complexity to prediction results; (3) Using symbolic regression techniques, extract human readable quota calculation rules from the prediction model. These improvements can not only maintain the prediction accuracy of existing models, but also provide transparent calculation basis for engineering decisions, which helps to establish a knowledge system for quota preparation that complies with industry standards.
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