A construction waste total production prediction method and system

Abstract

The application is suitable for the technical field of construction waste prediction, and provides a construction waste total yield prediction method and system.The method comprises the following steps: obtaining historical data of construction waste in a target area, constructing a grey prediction model of the construction waste, obtaining a residual sequence, and finally obtaining a construction waste yield prediction result of the target area in a future year through a series of transformations.The application has the advantages that error adaptive learning can be realized through the structured use of residuals, directional judgment of the prediction result can be formed based on a state transition mechanism, the defects of traditional statistical models and neural network models, such as dependence on a large amount of data, difficult-to-explain error generation, and inability to identify the deviation direction in the future, are overcome, the prediction result is no longer a mechanical extrapolation of past trends, but a dynamic prediction containing directional correction capability, and the prediction output is closer to the actual urban construction rhythm change.

Description

Technical Field

[0001] This invention belongs to the field of construction waste prediction technology, and in particular relates to a method and system for predicting the total output of construction waste. Background Technology

[0002] With the rapid pace of urban development in my country, the amount of construction waste generated is increasing daily. According to statistics, my country generates more than 2 billion tons of construction waste annually, accounting for about 40% of urban waste. With the advancement of "zero-waste cities," the comprehensive management of construction waste has attracted great attention from the government, scholars, and enterprises.

[0003] Existing technologies have developed various model systems for calculating and predicting construction waste production, but all of them have obvious limitations and are difficult to support the real-world demand for high-precision prediction in urban waste management and resource planning.

[0004] For example, per capita coefficient methods and empirical coefficient methods heavily rely on human judgment, and the measurement results are greatly affected by subjective factors. Construction material consumption methods require calculating material consumption separately for different building structures and material usage methods, making calculations complex and difficult to standardize. Building area estimation methods have complex calculation processes, require repeated verification, and have high practical application costs. Dynamic material flow analysis models can describe the evolutionary relationship between construction activities and material demand at a macro scale, but the models have numerous parameters and high computational complexity, making it difficult to meet the rapid application needs in engineering practice. Multiple regression models, ARIMA, exponential smoothing, LSTM, and other time series or machine learning methods generally suffer from strong data dependence, large sample requirements, complex modeling processes, and sensitivity to external disturbances. In particular, construction waste data is significantly affected by statistical standards, changes in urban policies, and the cyclical nature of construction activities; it also has small sample sizes and strong nonlinear characteristics. Traditional prediction methods cannot effectively capture this complex dynamic relationship, resulting in large prediction errors and susceptibility to deviations when the external environment changes.

[0005] Therefore, it is necessary to further improve existing methods for predicting construction waste production. Summary of the Invention

[0006] The purpose of this application is to provide a method for predicting the total output of construction waste, which aims to solve the problems that construction waste data is significantly affected by statistical methods, changes in urban policies and the periodicity of construction activities, has a small sample size and strong nonlinear characteristics, and traditional prediction methods cannot effectively capture this complex dynamic relationship, resulting in large prediction errors and deviations when the external environment changes.

[0007] This application provides a method for predicting the total output of construction waste, the method comprising:

[0008] Obtain historical data on construction waste in the target area to obtain a time series of total construction waste production.

[0009] A grey prediction model for construction waste is constructed, and the time series is fitted based on the grey prediction model to predict the construction waste output in future years, thereby obtaining a baseline prediction value for construction waste.

[0010] The difference between the historical data sequence and the fitting result is calculated to obtain the residual sequence; based on the residual sequence and the gray prediction model, a gray residual prediction model is constructed, which is used to predict the residual magnitude for future years.

[0011] The residuals are divided into states based on the signs of the residual sequence, thereby obtaining the state transition matrix;

[0012] The residual state transition matrix is ​​applied to future years to obtain the residual sign prediction results for future years; based on the residual sign prediction results and the grey residual prediction model, the residual prediction values ​​for future years are obtained; the residual prediction values ​​for future years are superimposed with the baseline prediction values ​​to obtain the construction waste production prediction results for the target area in future years.

[0013] Preferably, the method for obtaining historical data on construction waste in the target area to obtain the time series of total construction waste production is as follows:

[0014] By obtaining the annual production of construction waste, demolition waste, and renovation waste, the total production of construction waste is obtained:

[0015] The annual output of construction waste is determined by the following formula:

[0016] ;

[0017] The annual output of construction demolition waste is determined by the following formula:

[0018] ;

[0019] The annual output of construction and renovation waste is determined by the following formula:

[0020] ;

[0021] The total annual output of construction waste is:

[0022] ;

[0023] in, The annual construction area, The annual building demolition area, The annual residential building completion area, The annual completed area of ​​public buildings, The coefficient for construction waste production per unit area. The waste production coefficient per unit area during demolition. This refers to the coefficient of decoration waste production per unit area in residential buildings. The coefficient for the amount of renovation waste per unit area in public buildings;

[0024] By arranging the total annual output of construction waste in different years in chronological order, a time series of total construction waste output is obtained.

[0025] Preferably, the method for constructing a grey prediction model for construction waste includes:

[0026] The time series of total construction waste production is recorded as the original series:

[0027] ;

[0028] Perform a grade ratio test on the original sequence and calculate the grade ratio of adjacent terms:

[0029] ;

[0030] When all the level ratios fall within the preset acceptable range, the original sequence is considered to meet the grey modeling conditions; when the level ratios do not fall within the acceptable range, the original sequence is transformed so that the transformed sequence passes the level ratio test.

[0031] Perform an accumulation generation operation on the original sequence that passes the level ratio test to obtain the accumulated sequence:

[0032] ;

[0033] in:

[0034] ;

[0035] A first-order grey differential equation is established based on the accumulated sequence, and the whitened form of the grey differential equation is expressed as:

[0036] ;

[0037] in This represents the item with year number n. For the year sequence number, For the grade ratio test, Generate a sequence from the nearest neighbor mean of the cumulative sequence. For development coefficient, The amount of gray action, For cumulative sequences, This is the nth item in the cumulative sequence.

[0038] Preferably, the steps for obtaining the baseline predicted value of construction waste are as follows:

[0039] The parameters in the grey differential equation are calculated using the least squares method. and Construct parameter matrices based on the values ​​of each. , ,in, For coefficient parameters The least squares estimation result, B is the matrix generated by accumulation. It is a data vector:

[0040] ;

[0041] ;

[0042] ;

[0043] Establish a data sequence model:

[0044] ;

[0045] The baseline forecast for construction waste in future years is calculated as follows:

[0046] ;

[0047] ;

[0048] Among them, The fitted value of the original sequence. These are the predicted values ​​for the original sequence. and These are the values ​​of parameters a and b obtained based on the least squares method, respectively, and t represents the discrete time step. Indicates the first The cumulative generation of sequence prediction values ​​at each time point.

[0049] Preferably, the steps for calculating the residual sequence and constructing a residual grey prediction model based on the residual magnitude are as follows:

[0050] The time series of total construction waste production is recorded as the original series. The fitting result of the grey prediction model on the sequence is denoted as... The residual sequence is obtained using the following formula:

[0051] ;

[0052] ; ;

[0053] in, For the first The residual value for the year; n is the total number for the year; It is a residual sequence;

[0054] The residual sequence is predicted using a grey prediction model, resulting in a residual prediction model. :

[0055] ; ;

[0056] The grey prediction model and the residual prediction model are combined to obtain the grey residual model:

[0057] ;

[0058] Where 'a' is the development coefficient. Ash action amount, The second historical data point in the residual sequence, The coefficients are determined based on the signs of historical residuals. If the original residual for the (k+1)th historical year is positive, then... =1; if the original residual for the (k+1)th historical year is negative, then =-1;

[0059] Preferably, the method for dividing the residuals into states based on the signs of the residual sequence and obtaining the state transition matrix is ​​as follows:

[0060] Based on the residual sequence The state space is divided into state intervals to form the initial state interval. ,Depend on To determine the value that the state interval should take:

[0061] ;

[0062] Establish the state transition matrix:

[0063] ;

[0064] in, and Given two states, for the residual sequence Observe the data points from the state to state The number of times it occurred was For state The total sample; then For state to state Given the probability of occurrence, the state transition matrix is:

[0065] .

[0066] Preferably, the method for obtaining the residual sign prediction results for future years by applying the residual state transition matrix to future years is as follows:

[0067] Based on the original sequence The sign of the residuals between the fitted results and the actual results determines the residual state interval. ;

[0068] Based on the residual state interval The residual is calculated from the state. Transition to state From the transition probabilities, we obtain the state transition matrix:

[0069] ;

[0070] This leads to the initial state probability vector of the residual state. ;

[0071] Based on the Markov chain's no-aftereffect principle, the current residual state is used as the initial state of the system; the future state is calculated using the time state transition formula. Annual residual state probability vector:

[0072] ;

[0073] Based on the state corresponding to the highest probability in the probability vector, the residual sign prediction result for future years is obtained.

[0074] Another objective of this application is to provide a system for predicting the total amount of construction waste, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method for predicting the total amount of construction waste as described above.

[0075] The method for predicting the total output of construction waste provided in this application has the following advantages: it can achieve adaptive error learning through the structured utilization of residuals, and can also form a directional judgment of the prediction result based on state transition. It overcomes the shortcomings of traditional statistical models and neural network models, such as reliance on large amounts of data, difficult-to-explain error generation, and inability to identify the direction of future deviations. The prediction result is no longer a mechanical extrapolation of past trends, but a dynamic prediction that includes the ability to correct directions, making the prediction output closer to the actual changes in the pace of urban construction. Attached Figure Description

[0076] Figure 1 A flowchart illustrating a method for predicting total construction waste production, provided as an embodiment of this application;

[0077] Figure 2A schematic diagram illustrating the comparison results between the traditional prediction model and the model used in this application;

[0078] Figure 3 This is a block diagram of the internal structure of a computer device in one embodiment. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0080] It is understood that the terms "first," "second," etc., used in this application may be used herein to describe various elements, but unless otherwise stated, these elements are not limited by these terms. These terms are used only to distinguish the first unit or module from another unit or module. For example, without departing from the scope of this application, the first script may be referred to as the second script, and similarly, the second script may be referred to as the first script.

[0081] like Figure 1 As shown, in one embodiment, a method for predicting the total output of construction waste is proposed, which may specifically include the following steps:

[0082] Step S10: Obtain historical data on construction waste in the target area to obtain the time series of total construction waste production.

[0083] In this embodiment, historical data on construction waste generation in the target area over the years is collected. The total construction waste output for each year is then organized chronologically, using the year as the time granularity, to form a time series reflecting the changing pattern of total construction waste output over time. This time series serves as the foundational input for subsequent predictive modeling, accurately reflecting the historical evolution of the scale of construction activities, the pace of urban development, and the intensity of construction waste generation.

[0084] Step S20: Construct a grey prediction model for construction waste, fit the time series based on the grey prediction model, and predict the output of construction waste in future years to obtain a baseline prediction value for construction waste.

[0085] In this embodiment, a grey prediction model is constructed based on the time series of total construction waste production. This model is fitted to historical data and further used to predict the future annual trends in construction waste production. The grey prediction model generates its output by accumulating the original data, thus mitigating the impact of random disturbances on the sequence. This allows the model to focus more on the overall development trend. The grey prediction model does not rely on large-sample training and can stably model even with insufficient data or a limited time span. Therefore, it is suitable for non-stationary sequences like construction waste, which are significantly affected by policies, economic cycles, and the pace of construction projects.

[0086] Step S30: Calculate the difference between the historical data sequence and the fitting result to obtain the residual sequence; based on the residual sequence and the gray prediction model, construct a gray residual prediction model, which is used to predict the residual magnitude for future years.

[0087] In this embodiment, the actual value of the total historical construction waste production is compared with the fitting result of the grey prediction model, and the difference between the two is calculated to form a residual sequence reflecting the prediction deviation. Subsequently, based on this residual sequence and combined with the grey prediction concept, a grey residual prediction model is constructed to characterize the law of residual amplitude change over time. By modeling the prediction error itself separately, the model can describe the main trend of the total amount of construction waste, capture deviations caused by factors such as policy adjustments, economic fluctuations, or changes in the construction cycle, significantly enhance the model's ability to characterize nonlinear fluctuations, and improve prediction accuracy.

[0088] Step S40: Divide the residuals into states according to the signs of the residual sequence to obtain the state transition matrix.

[0089] In this embodiment, the residuals are divided into different state intervals based on the sign of the residuals for each year in the residual sequence. The transition of residual states between adjacent years is then statistically analyzed, thereby constructing a residual state transition matrix. This matrix reflects the evolution of the residual sign over time and characterizes the probabilistic characteristics of the prediction bias transitioning between positive and negative states.

[0090] Step S50: Apply the residual state transition matrix to future years to obtain the residual sign prediction results for future years; based on the residual sign prediction results and the grey residual prediction model, obtain the residual prediction values ​​for future years; superimpose the residual prediction values ​​for future years with the baseline prediction values ​​to obtain the construction waste production prediction results for the target area in future years.

[0091] In this embodiment, the residual prediction value is a signed correction obtained by multiplying the future year residual amplitude output by the grey residual prediction model by the residual sign prediction result (i.e., a value of + or -1). The constructed residual state transition matrix is ​​applied to future years, and the possible values ​​of the residual sign for future years are predicted using the state transition principle of a Markov chain. Simultaneously, combined with the grey residual prediction model's prediction result of the residual amplitude, the complete residual prediction value for future years is obtained. This residual prediction value is then superimposed with the aforementioned baseline prediction value to finally obtain the predicted total construction waste production of the target area for future years.

[0092] In this embodiment, to avoid the residuals being ignored simply as error terms, the absolute value of the residuals or the data after non-negative transformation are incorporated back into the grey prediction system. The grey prediction model for the residuals is used to fit and predict the trend of residual amplitude changes over the years. The essence of this method is to enable the system to learn from the error itself, allowing it to identify trends such as periodic disturbances in construction activities, changes in construction intensity, or policy adjustments, thereby achieving trend prediction of future error amplitude. Since the magnitude of the residuals does not reflect whether the predicted value should be revised upwards or downwards in future years, the system determines the sign of the residuals, i.e., whether the residuals are positively or negatively biased in future years. This application utilizes the idea of ​​a Markov chain model, dividing historical residuals into different states according to their positive and negative relationships and calculating the probability of the residuals transitioning from one state to another between adjacent years. By constructing a residual state transition probability matrix, the evolution law of the residuals across different years can be expressed mathematically. Because Markov chains have the property of no aftereffect—meaning future states are only related to the current state and not to earlier states—the system can determine the initial state vector by using the state corresponding to the current year's residuals. It then uses the time state transition formula to predict whether the residuals will show a positive or negative bias in future years. The grey prediction model provides the basic trend of future construction waste production, the residual grey prediction model provides the magnitude of the possible deviation from this trend, and the Markov chain determines the direction of the deviation. These three elements work together to form the prediction result. The predicted sign of the residuals for future years is combined with the predicted magnitude of the residuals to generate the predicted residual amount for that year. This is then superimposed with the baseline prediction value to obtain the final predicted value of construction waste. Therefore, the prediction result is no longer a mechanical extrapolation of past trends but a dynamic prediction that includes directional correction capabilities, making the prediction output closer to the actual pace of urban construction changes. The historical data series used in this application can refer to the time series of total construction waste production.

[0093] This application, based on the grey prediction model, employs the Markov method to reasonably adjust positive and negative residuals. Leveraging the Markov model's ability to handle data volatility, and combined with the grey model, a grey residual Markov prediction model is formed. This approach not only maintains predictive capability even with insufficient data samples but also achieves adaptive error learning through the structured utilization of residuals. Furthermore, it can form directional judgments of prediction results based on state transition mechanisms. This overcomes the shortcomings of traditional statistical and neural network models, such as reliance on large amounts of data, difficulty in explaining error generation mechanisms, and inability to identify future deviation directions. It transforms construction waste production prediction from traditional static extrapolation into a dynamic, interpretable, and corrective prediction process. Therefore, this method is applicable to fields such as construction waste management, urban solid waste planning, and regional construction intensity control, providing forward-looking decision-making references for government regulatory departments and solid waste resource utilization enterprises.

[0094] In a preferred embodiment, the method for obtaining historical data on construction waste in the target area and obtaining the time series of total construction waste production is as follows:

[0095] By obtaining the annual production of construction waste, demolition waste, and renovation waste, the total production of construction waste is obtained:

[0096] The annual output of construction waste is determined by the following formula:

[0097] ;

[0098] The annual output of construction demolition waste is determined by the following formula:

[0099] ;

[0100] The annual output of construction and renovation waste is determined by the following formula:

[0101] ;

[0102] The total annual output of construction waste is:

[0103] ;

[0104] in, The annual construction area, The annual building demolition area, The annual residential building completion area, The annual completed area of ​​public buildings, The coefficient for construction waste production per unit area. The waste production coefficient per unit area during demolition. This refers to the coefficient of decoration waste production per unit area in residential buildings. The coefficient for the amount of renovation waste per unit area in public buildings;

[0105] By arranging the total annual output of construction waste in different years in chronological order, a time series of total construction waste output is obtained.

[0106] In this embodiment, the first step is to estimate the amount of construction waste. Construction waste is defined as engineering spoil, engineering mud, engineering waste, demolition waste, and decoration waste. Construction waste is mainly generated in three stages: construction, demolition, and decoration. Taking Jiangxi Province as an example, historical data on construction waste production in Jiangxi Province from 2011 to 2022 were collected based on the *Jiangxi Statistical Yearbook*. The building area estimation method was used to estimate the annual construction waste production (…). The annual construction waste production is estimated based on the annual construction area ( ). Annual building demolition area ( ), annual residential building completion area ( ) and annual completed area of ​​public buildings ( ).

[0107] Estimated Annual Production of Construction Waste: Construction waste mainly refers to broken bricks, concrete, mortar, pile heads, packaging materials, and roofing materials generated during the construction process. Based on extensive literature and statistical data, my country generates approximately 0.05-0.06 tons of construction waste per year during construction. For construction waste, this study proposes a yield of 0.055 t / unit area. Annual production of construction waste ( The formula for calculating ) is: =0.055× .

[0108] Annual Demolition Waste Estimation: Demolition waste mainly refers to waste bricks, tiles, concrete fragments, metal, glass, ceramics, and wood blocks generated during the demolition of building projects. In my country, the output rate coefficient for each type of demolition waste needs to be selected based on the structural characteristics of the building. Building structure types are categorized as steel structure, reinforced concrete structure, brick-wood structure, and mixed structure. This example selects the output rate coefficient for each type of demolition waste based on the structural characteristics of the demolished building:

[0109] structure Scrap steel waste bricks Waste glass Combustible waste Waste concrete and gravel total steel structure 29.2 217.1 2.6 7.9 651.3 reinforced concrete structure 18 233.8 1.7 25.0 1484.7 brick and wood structure 1.4 384.1 1.8 37.2 482.2 Hybrid structure 13.8 400.8 1.7 25.0 894.3

[0110] Taking Jiangxi Province as an example, since the structure of construction waste in Jiangxi Province is mainly a mixed result, the demolition waste production rate coefficient selected in this embodiment is: Annual production of construction demolition waste The calculation formula is as follows:

[0111] ;

[0112] = × ;

[0113] Estimated Annual Production of Construction and Renovation Waste: Construction and renovation waste mainly refers to waste bricks, cement mortar, waste boards, and other waste materials generated during the renovation process of construction projects. Construction and renovation waste is divided into residential construction waste and public building construction waste. According to the classification, the annual production of residential construction and renovation waste per unit area in this embodiment is (…). ) is 0.1t / Public category building and renovation waste output per unit area ( The value is 0.15t / [2] Annual production of construction and renovation waste The specific formula is as follows: = ×0.1+ ×0.15.

[0114] Estimation of Total Annual Construction Waste Production: Total construction waste production is the sum of total construction waste production, total demolition waste production, and total renovation waste production. The specific formula is as follows: .

[0115] The annual output of construction waste in Jiangxi Province from 2011 to 2022 was calculated, as shown in the table below:

[0116] years Total construction waste production (10,000 tons) 2011 3851.60 2012 4776.21 2013 5759.88 2014 6712.43 2015 7131.98 2016 7102.48 2017 7559.12 2018 8149.40 2019 8148.72 2020 8121.09 2021 8429.96 2022 8772.02

[0117] In a preferred embodiment, due to the characteristics of raw construction waste data such as difficulty in collection, incompleteness, volatility, and weak orderliness in the cumulative data series, and considering the dynamic characteristics of time series data, this application aims to better capture the changing trends and patterns of the data and achieve better predictive capabilities. Based on the grey prediction model, this application uses the Markov method to reasonably adjust the positive and negative residuals, leveraging the Markov model's ability to handle data volatility, and combines it with the grey model to form a grey residual Markov prediction model. The grey prediction method used in this application is based on grey system theory and is an effective prediction method in actual production. It is denoted as GM(r, h), where r refers to the order of the differential equation in the model, and h refers to the number of variables in the model.

[0118] In practical applications, the first-order differential equation GM(r,h) containing a single variable is often used to predict the system. This model is actually a special case of GM(r,h) when r=1 and h=1, that is, the common GM(1,1) model.

[0119] In this application, the model is established using the following method:

[0120] First, the original data is subjected to a grade ratio test.

[0121] Let the original sequence be:

[0122] ;

[0123] Perform a grade ratio test:

[0124] ;

[0125] Inspection grade ratio Does it fall within the acceptable range? ,like If the data falls within the acceptable interval, it means the original sequence passed the level ratio test and can be modeled using a traditional grey prediction model. If the level ratio test fails, the original data must be transformed to ensure the transformed data falls within the acceptable interval. Common transformation methods include logarithmic transformation, translation transformation, and square root transformation.

[0126] For the original sequence Perform an accumulation of AGO to generate a new sequence:

[0127] ;

[0128] in:

[0129] ;

[0130] For the newly generated sequence Establish a differential equation in whitening form, called a first-order graying differential equation, where... For development coefficient, This represents the gray action quantity.

[0131] ;

[0132] Construct parameter matrix , , :

[0133] Calculated using the least squares method , The value of the parameter matrix is ​​used to construct the parameter matrix. , ,in For coefficient parameters The least squares estimation result, B is the matrix generated by accumulation. It is a data vector.

[0134] ;

[0135] ;

[0136] Establish a model for generating data sequences:

[0137] ;

[0138] Establish the original data sequence model:

[0139] ;

[0140] ;

[0141] in, Original sequence The fitted value, These are the predicted values ​​for the original sequence.

[0142] In a preferred embodiment, the method for constructing the residual grey model is as follows:

[0143] First, let the residual sequence be:

[0144] ;

[0145] The residual value is the difference between the original data and the simulated value calculated by the traditional grey prediction model.

[0146] ;

[0147] By performing mean GM(1,1) model prediction on the residual series, the residual prediction model can be obtained:

[0148] ;

[0149] By merging the mean GM(1,1) prediction model with the mean GM(1,1) residual prediction model, a residual grey model is obtained:

[0150] ;

[0151] ;

[0152] Where m(k+1) is a coefficient determined based on the sign of the historical residuals. If the original residual of the (k+1)th historical year is positive, then m(k+1) = 1; if the original residual of the (k+1)th historical year is negative, then m(k+1) = -1. At this point, it can be seen that... There are only two states:

[0153] ;

[0154] status Determined by the residual series, the residual grey prediction model aims not only to improve accuracy but also to predict future data while maintaining that accuracy. (Current state) The value of can only be derived from the known residual sequence, but it cannot be determined for future data. In this state, a Markov prediction model is introduced, ultimately forming a complete grey residual Markov prediction model.

[0155] In a preferred embodiment, to verify the effectiveness of the improved model, a feasibility verification of the selected model can be performed. Accuracy verification methods that can be used include: mean relative residual test, posterior error test, and small probability error test. The relative error of each residual value in the residual sequence is calculated using the following formula:

[0156] ;

[0157] Mean relative residual test: where For the average relative residual, For sample size.

[0158] ;

[0159] Posterior difference test: where Standard deviation, The variance ratio, .

[0160] ;

[0161] ;

[0162] Small probability error test:

[0163] ;

[0164] The conclusion is and The accuracy of the model is then evaluated according to the table below after determining the value.

[0165] Model accuracy level P C First level, Excellent ≤0.01 P≥0.95 C≤0.35 Second level, good ≤0.05 0.80≤P<0.95 0.35<C≤0.5 Level 3, Qualified ≤0.10 0.70≤P<0.80 0.50<C≤0.65 Fourth level, unqualified ≤0.20 P<0.70 C>0.65

[0166] In a preferred embodiment, the Markov prediction model used in this application refers to a method model that predicts future changes based on the current state of an event. The process of transitioning from one state to another in a specified state space is called a Markov chain, and the values ​​of the Markov chain in the state space are called states. middle It is called a Markov chain, and the multiple countable sets are called the state space.

[0167] State partitioning: based on the residual sequence The state space is divided into state intervals to form the initial state interval. ,Depend on To determine the value that the state interval should take:

[0168] ;

[0169] Establish the state transition matrix:

[0170] ;

[0171] By analyzing the residual sequence Observing these data points, we found that from the state... to state The number of times it occurred was For state The total sample; then For state to state The probability of occurrence. Then the state transition matrix is:

[0172] ;

[0173] Since this application only uses 1 and -1 to represent the positive and negative states of the residual sequence for state interval division, the method for establishing the state transition matrix is ​​simplified. A Markov prediction model is introduced to calculate the positive and negative state transition probabilities of the residuals, thereby determining the sign of the residuals. Specifically, this may include the following four steps:

[0174] Step 1, confirm the status and residuals. It belongs to the positive state residual A negative value belongs to the state. .

[0175] Step 2, based on the state interval Calculate the state transition matrix Find the state transition probability matrix. .

[0176] Step 3, based on the state interval The initial state is the residual state of the prediction starting year (the most recent year). If the state of that year is... ,Other If the state of that year is ,make .

[0177] Step 4, Calculate the time state transition formula Predicting future time The state transition result.

[0178] As an embodiment of this application, the construction waste data of Jiangxi Province given in the above embodiments is used as the raw data. An empirical analysis was conducted on Jiangxi Province, and the detailed process is as follows:

[0179] It can be calculated from the GM(1,1) model that , According to the formula, we can obtain The prediction formula:

[0180] ;

[0181] Based on the raw data and forecast data The difference between them generates a residual sequence:

[0182] ;

[0183] The absolute value of the residual sequence The results were obtained by performing calculations using the GM(1,1) model. , According to formula (2), we can obtain The prediction formula:

[0184] ;

[0185] Using formula (3) and By merging the results, we can obtain the grey residual prediction model. The final prediction results are as follows:

[0186] ;

[0187] in, .

[0188] Based on the above GM(1,1) and residual prediction formulas, the predicted values ​​of construction waste production in Jiangxi Province from 2011 to 2022 were calculated, and the relative residual values ​​were calculated according to the formulas. The results are shown in the table below, which lists the fitting values ​​and state classifications of the traditional GM(1,1) and the grey residual Markov combination model provided in this application from 2011 to 2022:

[0189] years GM(1,1) fitted value relative error rate Grey residual Markov fitting value relative error rate residual state 2011 3851.60 0.00% 3851.60 0.00% 0 2012 5797.87 21.39% 4776.21 0.00% -1 2013 6065.63 5.31% 5707.07 0.92% -1 2014 6345.75 5.46% 6694.30 0.27% 1 2015 6638.81 6.91% 6977.62 2.16% 1 2016 6945.41 2.21% 7274.75 2.43% 1 2017 7266.16 3.88% 7586.30 0.36% 1 2018 7601.73 6.72% 7912.92 2.90% 1 2019 7952.79 2.40% 8255.29 1.31% 1 2020 8320.07 2.45% 8026.03 1.17% -1 2021 8704.31 3.25% 8418.49 0.14% -1 2022 9106.30 3.81% 8828.46 0.64% -1

[0190] To more intuitively reflect the fit between the two prediction models and the actual values, a line graph of the prediction model fit is plotted, such as... Figure 2 The diagram shows a comparison of prediction results between the traditional prediction model and the gray residual fitting values ​​obtained by the residual gray prediction model combined with the Markov method constructed in this application.

[0191] The accuracy of the two models was verified, and the results are shown in the table below:

[0192] Error Comparison Traditional model The model constructed in this application 0.053 0.01 0.29 0.07 1 1

[0193] As shown in the table above, in the grey GM(1,1) prediction model, the average relative error is... The value is 0.053, and the posterior difference ratio The value is 0.29, indicating a small error probability. The accuracy is 1, indicating a good, second-level accuracy. The model constructed in this application has a relative error... The value is 0.01, and the posterior difference ratio The probability of a small error is 0.07. The accuracy is 1, indicating an excellent, first-class accuracy. In summary, by comparing the fitting accuracy of the GM(1,1) model and the grey residual Markov prediction model constructed in this application using the three accuracy verification methods described above, and observing the calculated data and graphs, it can be seen that the fitting accuracy of the grey residual Markov model in this application has been significantly improved. Furthermore, the fitting value of the grey residual Markov model is closer to the actual data of recent years, making this method more suitable for predicting the production of construction waste in Jiangxi Province over the next five years.

[0194] As an embodiment of this application, in order to predict the amount of construction waste produced in Jiangxi Province over the next five years, it is necessary to reasonably determine the future residual value using Markov. Due to the Markov principle of no aftereffect, ω can be derived from the current state value. =[1,0].

[0195] Determining using Markov processes hour The value of . From the Jiangxi Province example above, we can see that the state transition probability matrix is ​​obtained based on the state (+1, -1) of the residual data. :

[0196] ;

[0197] Last value Therefore, the initial state vector is determined. .

[0198] According to the time state transition formula We can obtain the state transition result for year t:

[0199] ;

[0200] The t-value represents the residual correction sign in the t-th year after 2022. By substituting t=1, 2, 3, 4, 5 into the above formula, the residual state transition vector from 2023 to 2027 can be calculated.

[0201] The predicted data on construction waste production in Jiangxi Province from 2023 to 2027 and the state transition probabilities were obtained using a grey residual Markov model, as shown in the table below:

[0202]

[0203] The table above shows the residual state probabilities for the next five years, and the residual states. The highest probabilities are found in the following five years: 75%, 64.6%, 60.4%, 58.4%, and 57.7%, respectively. Therefore, the predicted values ​​for the next five years are used to determine the state. After error adjustment, the predicted output of construction waste in Jiangxi Province for 2023-2027 is 92.59591 million tons, 97.08475 million tons, 101.77661 million tons, 106.68089 million tons, and 111.80729 million tons, respectively.

[0204] Figure 3 An internal structural diagram of a computer device in one embodiment is shown. The computer device includes a processor, memory, network interface, input device, and display screen connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to implement a method for predicting the total amount of construction waste. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to execute the method for predicting the total amount of construction waste. The display screen of the computer device may be an LCD screen, etc. The input device may be a touch layer covering the display screen, or buttons, a trackball, or a touchpad mounted on the casing of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0205] In one embodiment, the construction waste total production prediction device provided in this application can be implemented as a computer program, which can be implemented as follows: Figure 3 It runs on the device shown.

[0206] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0207] In one embodiment, a total construction waste production prediction system is provided, the system including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the total construction waste production prediction method as described above.

[0208] In this embodiment of the application, the system can be a computer hardware system that executes its corresponding method when the system is running. For a description of the above-mentioned method for predicting the total amount of construction waste, please refer to the preceding text; it will not be repeated here.

[0209] It should be understood that although the steps in the flowcharts of the various embodiments of this application are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in each embodiment may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0210] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for predicting the total output of construction waste, characterized in that, The method includes: Obtain historical data on construction waste in the target area to obtain a time series of total construction waste production. A grey prediction model for construction waste is constructed, and the time series is fitted based on the grey prediction model to predict the construction waste output in future years, thereby obtaining a baseline prediction value for construction waste. The difference between the historical data sequence and the fitting result is calculated to obtain the residual sequence; based on the residual sequence and the gray prediction model, a gray residual prediction model is constructed, which is used to predict the residual magnitude for future years. The residuals are divided into states based on the signs of the residual sequence, thereby obtaining the state transition matrix; The residual state transition matrix is ​​applied to future years to obtain the residual sign prediction results for future years; based on the residual sign prediction results and the grey residual prediction model, the residual prediction values ​​for future years are obtained; the residual prediction values ​​for future years are superimposed with the baseline prediction values ​​to obtain the construction waste production prediction results for the target area in future years.

2. The method for predicting the total output of construction waste according to claim 1, characterized in that, The method for obtaining historical data on construction waste in a target area and compiling a time series of total construction waste production is as follows: By obtaining the annual production of construction waste, demolition waste, and renovation waste, the total production of construction waste is obtained: The annual output of construction waste is determined by the following formula: ； The annual output of construction demolition waste is determined by the following formula: ； The annual output of construction and renovation waste is determined by the following formula: ； The total annual output of construction waste is: ； in, The annual construction area, The annual building demolition area, The annual residential building completion area, The annual completed area of ​​public buildings, The coefficient for construction waste production per unit area. The waste production coefficient per unit area during demolition. This refers to the coefficient of decoration waste production per unit area in residential buildings. The coefficient for the amount of renovation waste per unit area in public buildings; By arranging the total annual output of construction waste in different years in chronological order, a time series of total construction waste output is obtained.

3. The method for predicting the total output of construction waste according to claim 1, characterized in that, The methods for constructing grey prediction models for construction waste include: The time series of total construction waste production is recorded as the original series: ； Perform a grade ratio test on the original sequence and calculate the grade ratio of adjacent terms: ； When all the level ratios fall within the preset acceptable range, the original sequence is considered to meet the grey modeling conditions; when the level ratios do not fall within the acceptable range, the original sequence is transformed so that the transformed sequence passes the level ratio test. Perform an accumulation generation operation on the original sequence that passes the level ratio test to obtain the accumulated sequence: ； in: ； A first-order grey differential equation is established based on the accumulated sequence, and the whitened form of the grey differential equation is expressed as: ； in This represents the item with year number n. For the year sequence number, For the grade ratio test, Generate a sequence from the nearest neighbor mean of the cumulative sequence. For development coefficient, The amount of gray action, For cumulative sequences, This is the nth item in the cumulative sequence.

4. The method for predicting the total output of construction waste according to claim 3, characterized in that, The steps for obtaining the baseline prediction value of construction waste are as follows: The parameters in the grey differential equation are calculated using the least squares method. and Construct parameter matrices based on the values ​​of each. , ,in, For coefficient parameters The least squares estimation result, B is the matrix generated by accumulation. It is a data vector: ； ； ； Establish a data sequence model: ； The baseline forecast for construction waste in future years is calculated as follows: ； ； Among them, The fitted value of the original sequence. These are the predicted values ​​for the original sequence. and These are the values ​​of parameters a and b obtained based on the least squares method, respectively, and t represents the discrete time step. Indicates the first The cumulative generation of sequence prediction values ​​at each time point.

5. The method for predicting the total output of construction waste according to claim 1, characterized in that, The steps for calculating the residual sequence and constructing a residual grey prediction model based on the residual magnitude are as follows: The time series of total construction waste production is recorded as the original series. The fitting result of the grey prediction model on the sequence is denoted as... The residual sequence is obtained using the following formula: ； ； ； in, For the first The residual value for the year; n is the total number for the year; It is a residual sequence; The residual sequence is predicted using a grey prediction model, resulting in a residual prediction model. : ； ； The grey prediction model and the residual prediction model are combined to obtain the grey residual model: ； Where 'a' is the development coefficient. Ash action amount, The second historical data point in the residual sequence, The coefficients are determined based on the signs of historical residuals. If the original residual for the (k+1)th historical year is positive, then... =1; if the original residual for the (k+1)th historical year is negative, then =-1.

6. The method for predicting the total output of construction waste according to claim 1, characterized in that, The method for dividing the residuals into states based on the signs of the residual sequence and obtaining the state transition matrix is ​​as follows: Based on the residual sequence The state space is divided into state intervals to form the initial state interval. ,Depend on To determine the value that the state interval should take: ； Establish the state transition matrix: ； in, and Given two states, for the residual sequence Observe the data points from the state to state The number of times it occurred was For state The total sample; then For state to state Given the probability of occurrence, the state transition matrix is: 。 7. The method for predicting the total output of construction waste according to claim 6, characterized in that, The method for obtaining the residual sign prediction results for future years by applying the residual state transition matrix is ​​as follows: Based on the original sequence The sign of the residuals between the fitted results and the actual results determines the residual state interval. ; Based on the residual state interval The residual is calculated from the state. Transition to state From the transition probabilities, we obtain the state transition matrix: ； This leads to the initial state probability vector of the residual state. ; Based on the Markov chain no aftereffect principle, the current residual state is used as the initial state of the system. Calculate the future state transition formula using the time state transition formula. Annual residual state probability vector: ； Based on the state corresponding to the highest probability in the probability vector, the residual sign prediction result for future years is obtained.

8. A system for predicting the total output of construction waste, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method for predicting total construction waste production as described in any one of claims 1 to 7.

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