Automobile disassembly waste calculation method and device based on cone programming solution

Abstract

The invention discloses an automobile disassembly waste material calculation method and device based on cone programming solution, and the method comprises the steps: 1, building a coupling equation between an automobile model and waste materials according to the pre-set parameters related to the automobile disassembly waste materials; step 2, according to the coupling equation in the step 1, establishing a waste weight calculation model and a calculation model; and step 3, according to the calculation model in the step 2, carrying out optimization solution to obtain an optimal solution of the weight of the jth waste material disassembled from the ith vehicle model. According to the method, high-precision calculation of waste output can be achieved through a mathematical optimization method, the technical problem that in the prior art, waste output and weight loss are difficult to accurately quantify after different automobile types are disassembled is solved, and a scientific basis is provided for resource recovery and environmental protection management in the automobile disassembling industry.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial optimization and resource recovery technology, and in particular to a method and device for estimating automobile dismantling waste based on cone programming solution. Background Art

[0002] With the continued growth of vehicle ownership, the dismantling of end-of-life vehicles and the recycling of scrap have become crucial components of resource recycling and environmental protection. However, traditional dismantling processes lack accurate methods for predicting scrap output, resulting in low resource utilization and difficulty meeting the needs of refined management. Existing technologies, which often rely on empirical estimates or simple statistics, are unable to accurately quantify the correlation between different vehicle models and scrap, hindering the efficient development of the industry. Summary of the Invention

[0003] The object of the present invention is to provide a method and device for estimating automobile dismantling waste based on cone programming to overcome or at least alleviate at least one of the above-mentioned drawbacks of the prior art.

[0004] To achieve the above object, the present invention provides a method for estimating automobile dismantling waste based on cone programming, which comprises:

[0005] Step 1: Based on the expected parameters related to automobile dismantling waste, establish the coupling equation between the vehicle model and the waste: Y j =AX j , where Y j is a vector of length M, representing the number of the jth type of scrap in all batches, where M represents the total number of batches of car dismantling; A is an M×I matrix, representing the number distribution of models in each batch; X j is a vector of length I, representing the number of j-th scraps from each car model dismantled, where I represents the total number of car models dismantled, j∈[1,…,J];

[0006] Step 2: Based on the coupling equation in step 1, a waste weight estimation model is established. The objective function of the estimation model is expressed as: The constraints of the extrapolation model include:

[0007] a. The vehicle weight is greater than the total weight of the dismantled waste. This constraint is expressed as formula (6);

[0008]

[0009] b. The non-negative constraint of waste weight, which is expressed as formula (7);

[0010]

[0011] Where, represents the upper limit of the dismantling weight of the i-th vehicle type in the m-th batch, represents the weight of the jth type of scrap from the i-th car model dismantled in the m-th batch, i∈[1,…,I];

[0012] Step 3: Based on the estimated model in step 2, optimize and solve to obtain the weight x of the jth type of waste material dismantled from the i-th type of vehicle. i,j The optimal solution of .

[0013] Furthermore, the optimization solution in step 3 specifically includes:

[0014] The constraints of the inference model are converted into cone constraints, which can be expressed as formula (14):

[0015]

[0016] Where G represents a 2I×I matrix, h is a vector of length 2I, and I I It is an I×I identity matrix, h2 represents a variable, and the value of the (m-1)I+i elements in h2 is j' represents other waste types.

[0017] Furthermore, the optimization solution in step 3 specifically includes:

[0018] Introducing original variables s represents the slack variable, represents the 2I-dimensional vector space of non-negative real numbers, R + represents the set of all non-negative real numbers;

[0019] The optimization problem of the inference model is expressed as an equivalent cone programming problem provided by Equation (17):

[0020]

[0021] Where Q = A T A,q=-A T Y j , superscript T indicates transposition, st indicates constraint, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space.

[0022] Furthermore, the optimization solution in step 3 specifically includes:

[0023] X j The optimization solution is as follows:

[0024] Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u):

[0025]

[0026] in: Q=A T A,q=-A T Y j , A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space, u represents the scaling dual variable, h is a vector of length 2I;

[0027] In step 3.2, use the alternating direction multiplication method to update the three variables z, s, and u in sequence in each iteration:

[0028] a. Fixed s k and u k In the case of , update z using formula (19) k+1 , k represents the number of iterations, first calculate z for L(z,s,u) k The derivative of and setting the gradient to 0 can obtain the linear equation (20), and then the linear equation (20) can be numerically solved using the conjugate gradient method or direct inversion method:

[0029]

[0030] b. Fixed z k+1 and u k In the case of minimizing L(z k+1 ,s,u k ), while satisfying Update s using formula (21) k +1 :

[0031]

[0032] Pass-A eq z k+1 +hu k Projecting onto the non-negative orthogonal cone space, we get s k+1 , that is, taking the maximum value element by element:

[0033]

[0034] in, represents the slack variable of the i-th model in the k+1th round;

[0035] c. Fixed z k+1 and s k+1 In the case of , the dual variable u is updated by accumulating the constraint residuals k+1 , as shown in formula (23):

[0036] u k+1 =u k +A eq z k+1 +s k+1 -h(23)

[0037] Step 3.3, determine whether the update process in step 3.2 meets the preset termination criteria. If yes, then as shown in formula (24), k+1 Take the first I dimensions to get

[0038]

[0039] Furthermore, the termination criterion of step 3.3 is set as formula (25):

[0040]

[0041] Among them, ∈ pri and ∈ dual is the preset tolerance parameter.

[0042] Furthermore, the optimization solution in step 3 specifically includes:

[0043] Before iterative solution, for each type of waste X j Perform the following initialization:

[0044] Based on the historical scrap record of the i-th vehicle model in the known or previous M-1 batch as x ij , build a local waste dictionary, the local waste dictionary is a mapping of "car model → waste vector", if the jth waste x of the i-th car model in the current batch ij There is already a history record x' in the local scrap dictionary ij , then directly use the historical record x' ij Value pair x ij Otherwise, use a small random positive number that follows a Gaussian distribution for initialization.

[0045] Furthermore, the j-th type of waste x of the i-th type of vehicle has been obtained. ij Stores the local waste dictionary for use in initializing subsequent batches.

[0046] The present invention also provides a device for estimating automobile dismantling waste based on cone programming, which comprises:

[0047] The vehicle model and waste coupling equation construction unit is used to establish the coupling equation between the vehicle model and waste according to the expected parameters related to the automobile dismantling waste: Y j =AX j , where Y j is a vector of length M, representing the number of the jth type of scrap in all batches, where M represents the total number of batches of car dismantling; A is an M×I matrix, representing the number distribution of models in each batch; X j is a vector of length I, representing the number of j-th scraps from each car model dismantled, where I represents the total number of car models dismantled, j∈1,…,J];

[0048] The scrap weight estimation model establishment unit is used to establish the coupling equation of the unit based on the vehicle model and the scrap weight coupling equation, and establish the scrap weight estimation model. The objective function of the estimation model is expressed as: The constraints of the extrapolation model include:

[0049] a. The vehicle weight is greater than the total weight of the dismantled waste. This constraint is expressed as formula (6);

[0050]

[0051] b. The non-negative constraint of waste weight, which is expressed as formula (7);

[0052]

[0053] Where, represents the upper limit of the dismantling weight of the i-th vehicle type in the m-th batch, represents the weight of the jth type of scrap from the i-th car model dismantled in the m-th batch, i∈[1,…,I];

[0054] The waste weight calculation optimization unit is used to establish a unit calculation model based on the waste weight calculation model, and optimize the solution to obtain the weight x of the jth type of waste dismantled from the i-th type of vehicle. i,j The optimal solution of .

[0055] Furthermore, the optimization solution in the waste weight calculation optimization unit specifically includes:

[0056] The constraints of the inference model are converted into cone constraints, which can be expressed as formula (14):

[0057]

[0058] Where G represents a 2I×I matrix, h is a vector of length 2I, and I IIt is an I×I identity matrix, h2 represents a variable, and the value of the (m-1)I+i elements in h2 is j' represents other waste types;

[0059] The optimization solution in the waste weight calculation optimization unit specifically includes:

[0060] Introducing original variables s represents the slack variable, represents the 2I-dimensional vector space of non-negative real numbers, R + represents the set of all non-negative real numbers;

[0061] The optimization problem of the inference model is expressed as an equivalent cone programming problem provided by Equation (17):

[0062]

[0063] Where Q = A T A,q=-A T Y j , superscript T indicates transposition, st indicates constraint, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space.

[0064] Furthermore, the optimization solution in the waste weight calculation optimization unit specifically includes:

[0065] X j The optimization solution is as follows:

[0066] Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u):

[0067]

[0068] in: Q=A T A,q=-A T Y j , A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space, u represents the scaling dual variable, h is a vector of length 2I;

[0069] In step 3.2, use the alternating direction multiplication method to update the three variables z, s, and u in sequence in each iteration:

[0070] a. Fixed s k and u k In the case of , update z using formula (19) k+1 , k represents the number of iterations, first calculate z for L(z,s,u) k The derivative of and setting the gradient to 0 can obtain the linear equation (20), and then the linear equation (20) can be numerically solved using the conjugate gradient method or direct inversion method:

[0071]

[0072] b. Fixed z k+1 and u k In the case of minimizing L(z k+1 ,s,u k ), while satisfying Update s using formula (21) k +1 :

[0073]

[0074] Pass-A eq z k+1 +hu k Projecting onto the non-negative orthogonal cone space, we get s k+1 , that is, taking the maximum value element by element:

[0075]

[0076] in, represents the slack variable of the i-th model in the k+1th round;

[0077] c. Fixed z k+1 and s k+1 In the case of , the dual variable u is updated by accumulating the constraint residuals k+1 , as shown in formula (23):

[0078] u k+1 =u k +A eq z k+1 +s k+1 -h(23)

[0079] Step 3.3, determine whether the update process in step 3.2 meets the preset termination criteria. If yes, then as shown in formula (24), k+1 Take the first I dimensions to get

[0080]

[0081] The present invention has the following advantages due to the adoption of the above technical solution:

[0082] This invention uses cone programming to solve coupled equations, achieving scientific modeling of the relationship between vehicle model and waste weight. This method can be widely used by automobile dismantling companies, resource recycling agencies, and environmental regulatory authorities, providing reliable data support for waste classification, improving resource recovery rates, and carbon emissions accounting, driving the industry's transformation towards intelligent and green processes. Vehicle dismantling waste estimation involves inferring the weight of different waste generated by each vehicle model, as well as the weight loss, based on a list of vehicles (including models and weights) over a certain period of time and information on the waste generated after dismantling (including waste name and weight).

[0083] This invention reduces the calculation of scrap from automobile dismantling to an optimization problem involving the coupling equation between vehicle type and scrap. Given the number and weight of different vehicle types and scrap materials in multiple batches of materials, the coupling equation between vehicle type and scrap is constructed from this known data. Through deduction, the calculation of scrap from automobile dismantling is transformed into a cone programming problem, solving for the weight and loss of scrap materials from each vehicle type. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 The figure is a flow chart of a method for estimating automobile dismantling waste based on cone programming according to an embodiment of the present invention. DETAILED DESCRIPTION

[0085] In the accompanying drawings, the same or similar reference numerals are used to represent the same or similar elements or elements with the same or similar functions. The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0086] In the description of the present invention, the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like to indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they should not be understood as limiting the scope of protection of the present invention.

[0087] like Figure 1 As shown, step 1 is to establish the coupling equation between the vehicle model and the waste.

[0088] 1.1 Determine the known quantities of the equation

[0089] Assume that a car dismantling plant has dismantled M batches of vehicles, has I types of vehicles, and produces J types of scrap. The known quantities in the equation include:

[0090] In the mth batch of disassembly, the number of the i-th model is The weight of the i-th vehicle type Among them, m∈[1,…,M],i∈[1,…,I].

[0091] In the mth batch of dismantling, the amount of jth type of waste dismantled is where j∈[1,…,J].

[0092] 1.2 Determine the unknown quantity of the equation

[0093] By obtaining the weight of different scraps produced by each car model and the weight of loss, the car dismantling factory can evaluate the value of scrap cars and guide business management based on the scrap situation. The unknown quantity in the equation is

[0094] (1) The weight of different waste materials produced by each car model and the weight of loss. The weight of the jth type of waste material dismantled from the i-th car model is x i,j . Where, i∈[1,…,I],j∈[1,…,J].

[0095] 1.3 Establish the coupling equation between vehicle type and waste

[0096] In the mth batch of dismantling, the jth type of scrap dismantled is the cumulative weight of all models dismantled. The weight of the jth type of scrap dismantled from the i-th model is equal to the number of i-th models. Multiply by the weight x of the jth type of scrap from the dismantling of the i-th car model I,j ,Right now Therefore, the total amount of the jth type of waste dismantled from the mth batch is

[0097]

[0098] For the purpose of formal expression,

[0099]

[0100] X j =(x 1,j ,…,x i,j ,…,x I,j ) T (3)

[0101] Considering a total of M batches of dismantling, the coupling equation between vehicle type and scrap is described by the following matrix equation (4):

[0102] Y j =AX j (4)

[0103] Among them, Y jis a vector of length M, representing the number of scrap j in all batches; A is an M×I matrix, representing the number distribution of models in each batch; X j is a vector of length I, representing the amount of scrap j dismantled from each vehicle type.

[0104] In another embodiment, the coupling equation between vehicle type and waste material can also be described by the following matrix equation (5), expressed in component form:

[0105]

[0106] The weight of different waste materials and loss weight produced by each vehicle model should meet the following constraints:

[0107] (1) The vehicle weight is greater than the total weight of the dismantled waste

[0108] In each batch, the weight constraint for the first vehicle type is:

[0109]

[0110] (2) Non-negative constraints on waste weight

[0111] The weight of scrap dismantled from each car model is non-negative:

[0112]

[0113] Anything involving or not limited to The constraints belong to the alternative scheme.

[0114] Step 2: Based on the coupling equations from step 1, the problem of solving the coupling equations between the vehicle model and the waste material is reduced to a least squares problem with a constrained objective function. A waste weight estimation model is established, and the objective function of the estimation model is expressed as Equation (8). Of course, any method involving the least squares problem solution for this constrained objective function is an alternative solution.

[0115]

[0116] The constraints of the inference model include two constraints expressed in equations (6) and (7).

[0117] Among them, X j ∈R I represents the weight distribution vector of the jth type of waste in all models and batches; A∈R M×I is the projection matrix; Y j ∈R M is the observed waste projection vector; It represents the upper limit of dismantling weight of the i-th vehicle type in the m-th batch.

[0118] In another embodiment, the objective function of the inference model can also be expressed as Equation (9), in standard quadratic form:

[0119]

[0120] in,

[0121] Q=A T A,q=-A T Y j (10)

[0122] In one embodiment, in the constraint condition (7) of the inference model, Written in vector form X j , then it contains:

[0123] (1) Non-negativity constraint: X j ≥0 is equivalent to -X j ≤0, which is expressed in cone constraint as formula (11):

[0124]

[0125] Among them, h1 and G1 are variables, I I It is an I×I identity matrix, that is, a matrix with all diagonal elements set to 1 and all other elements set to 0. The bold O is a vector of length I.

[0126] (2) Disassembly weight upper limit constraint: For each vehicle model i and each batch m, the weight of the jth type of scrap disassembled from the i-th vehicle model is The total dismantling weight limit of this model in this batch cannot be exceeded Compared to the weight already assigned to other waste categories The difference is

[0127]

[0128] Wherein, j' represents other waste types.

[0129] Note X j The [(m-1)I+i]th element of Then Equation (6) is expressed as Equation (13) in cone constraint:

[0130]

[0131] Among them, h2 and G2 are variables, and the values of (m-1)I+i elements in h2 are

[0132] The cone constraints provided by equations (11) and (13) are combined into a unified form, expressed as equation (14):

[0133]

[0134] Where G represents a 2I×I matrix and h is a vector of length 2I.

[0135] In another embodiment, the optimization problem of the inference model can also be expressed as formula (15), and the final quadratic programming form is:

[0136]

[0137] Among them, X j is an I×1 vector, h is a vector of length 2I×1, the superscript T indicates transpose, and st indicates constraint.

[0138] In another embodiment, in order to solve the above optimization problem, it is necessary to introduce slack variables to convert it into an equality constraint plus a non-negative cone constraint. In order to convert the inequality constraint provided by equation (15) into an equality constraint, it is necessary to introduce slack variables Make

[0139] GX j +s=h(16)

[0140] Let the new variable be The inequality constraints can be replaced by cone constraints, and the optimization problem of the inference model can also be expressed as an equivalent cone programming problem provided by formula (17):

[0141]

[0142] Among them, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq is a 2I×3I matrix, R I represents an I-dimensional real vector space, R 2I represents a 2I-dimensional real vector space, represents the 2I-dimensional vector space of non-negative real numbers, R + represents the set of all non-negative real numbers, that is, R + ={x∈R|x≥0}, The first I components of the variable z are arbitrary real numbers (unrestricted), and the last 2I components must be non-negative. The dimension of z is 3I×1, and the dimension of q is I×1.

[0143] Step 3: Solve the cone programming problem in formula (17) by using the cone augmented Lagrangian solution to obtain the weight distribution vector X of the j-th type of waste in all models and batches. j .

[0144] In one embodiment, the optimization solution in step 3 specifically includes:

[0145] X j The optimization solution is as follows:

[0146] Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u):

[0147]

[0148] in: u represents the scaled dual variable, ρ represents the regularization parameter used to adjust the intensity of the scaling dual variable u and control the balance between the original constraint and the dual variable u, also known as the penalty coefficient. It is a hyperparameter. The augmented Lagrangian term contains a square term. measures the residual of the original constraint, and is the regularization term for the dual variable u, and ρ acts as a weight for the contribution of these two terms. If not dynamically adjusted, ρ can be set to a fixed value during the optimization process, usually around 10 -3 to 10 3 The specific value can be adjusted through experimentation. If dynamic adjustment is required, the value of ρ can be adjusted based on the changes in the primal and dual residuals. Usually, ρ is increased or decreased by some heuristic or residual-based criteria. The default value is ρ = 1.

[0149] Step 3.2: To minimize the cone augmented Lagrangian function, the alternating direction multiplier method is used to update the three variables z, s, and u in each iteration:

[0150] a. Fixed s k and u k In the case of , update z using formula (19) k+1 , k represents the number of iterations, first calculate z for L(z,s,u) k The derivative of and setting the gradient to 0 can obtain the linear equation (20), and then the linear equation (20) can be numerically solved using the conjugate gradient method or direct inversion method:

[0151]

[0152] b. Fixed z k+1 and u k In the case of minimizing L(z k+1 ,s,u k ), while satisfying Update s using formula (21) k +1 :

[0153]

[0154] Pass-A eq z k+1 +hu k Projecting onto the non-negative orthogonal cone space, we get s k+1 , that is, taking the maximum value element by element:

[0155]

[0156] in, represents the slack variable of the i-th model in the k+1th round;

[0157] c. Fixed z k+1 and s k+1 In the case of , the dual variable u is updated by accumulating the constraint residuals k+1 , as shown in formula (23):

[0158] u k+1 =u k +A eq z k+1 +s k+1 -h(23)

[0159] Step 3.3, determine whether the update process in step 3.2 meets the preset termination criteria. If yes, then as shown in formula (24), k+1 Take the first I dimensions to get

[0160]

[0161] In one embodiment, the termination criterion of step 3.3 may be, but is not limited to, set as follows:

[0162]

[0163] Among them, ∈ pri and ∈ dual The tolerance parameter set by the user. The smaller the tolerance parameter, the more accurate the solution. This means that the user can improve the accuracy of the algorithm by reducing the tolerance parameter, but it may also increase the complexity and time of the calculation. Of course, it can also be dynamically adjusted according to the convergence behavior of the iteration. The default parameter ∈ pri =10 -4 ,∈ dual =10 -3 .

[0164] In one embodiment, the optimization solution in step 3 specifically includes:

[0165] In order to improve the stability and convergence speed of the algorithm, before iterative solution, each type of waste Xj Perform the following initialization:

[0166] Based on the historical scrap record of the i-th vehicle model in the known or previous M-1 batch as x ij , build a local waste dictionary, the local waste dictionary is a mapping of "car model → waste vector", if the jth waste x of the i-th car model in the current batch ij There is already a history record x' in the local scrap dictionary ij , then directly use the historical record x' ij Value pair x ij Initialize; otherwise, adopt a Gaussian distribution (mean 0, standard deviation 1×10 -2 ) is initialized with a small random positive number.

[0167] In one embodiment, a method for obtaining a local waste dictionary may include:

[0168] Excel spreadsheets are used to organize and store data, such as the simulated data in the scrap dictionary storage structure shown in Table 1. Each row represents a car model, and columns 2 to J+1 are used to store scrap related to the car model.

[0169] Table 1

[0170] Model zinc alloy scrap aluminum scrap copper Heavy steel Waste oil Waste gasoline … liberation 1163.25 3688.44 2240.71 1024.8 766.58 877.45 Wind God 88.45 206.32 142.64 77.34 57.49 64.35 Fox 99.79 217.66 153.98 88.68 68.83 75.69 Beijing Hyundai 112.37 230.24 166.57 101.26 81.41 88.27 Dongfeng Peugeot 68.27 169.26 114.97 61.9 49.35 55.36 …

[0171] When storing data, first traverse all car models and check whether the scrap data of the corresponding car model has been stored in the local scrap dictionary.

[0172] If the dictionary already has storage:

[0173] Take the data stored in the Excel table and the data to be stored to calculate the error. If the error is large, perform weighted average according to the size of the error difference.

[0174] If the error is small, the average value of the data stored in the Excel table and the data to be stored is taken for update.

[0175] In this way, this embodiment can enhance the robustness of the data stored in the dictionary and ensure the accuracy and reliability of the data.

[0176] If the dictionary does not contain:

[0177] Then create a new model in the Excel table, store the data to be stored, and then update the dictionary.

[0178] In one embodiment, the j-th type of waste material x of the i-th type of vehicle has been obtained. ij Stores the local waste dictionary for use in initializing subsequent batches.

[0179] An embodiment of the present invention further provides a device for estimating automobile dismantling waste based on cone programming, which includes a vehicle model and waste coupling equation construction unit, a waste weight estimation model establishment unit, and a waste weight calculation optimization unit, wherein:

[0180] The vehicle model and waste coupling equation construction unit is used to establish the coupling equation between the vehicle model and waste according to the expected parameters related to the automobile dismantling waste: Y j =AX j .

[0181] The waste weight estimation model building unit is used to build a waste weight estimation model based on the coupling equations of the vehicle model and waste coupling equation building unit.

[0182] The waste weight calculation optimization unit is used to establish a unit estimation model based on the waste weight estimation model, and optimize the solution to obtain the weight x of the jth type of waste dismantled from the i-th type of vehicle. i,j The optimal solution of .

[0183] In one embodiment, the optimization solution in the waste weight calculation optimization unit specifically includes:

[0184] The constraints of the inference model are converted into cone constraints, which are expressed as Equation (14).

[0185] The optimization solution in the waste weight calculation optimization unit specifically includes:

[0186] Introducing original variables The optimization problem of the inference model is expressed as an equivalent cone programming problem provided by Equation (17).

[0187] In one embodiment, the optimization solution in the waste weight calculation optimization unit specifically includes the X provided in the above embodiment. j Optimization solution method.

[0188] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit them. Those skilled in the art will appreciate that the technical solutions described in the aforementioned embodiments may be modified, or some of the technical features thereof may be replaced with equivalents; such modifications or replacements do not deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for estimating automobile dismantling waste based on cone programming, characterized in that: include: Step 1: Based on the expected parameters related to automobile dismantling waste, establish the coupling equation between the vehicle model and the waste: Y j =AX j , where Y j is a vector of length M, representing the number of the jth type of scrap in all batches, where M represents the total number of batches of car dismantling; A is an M×I matrix, representing the number distribution of models in each batch; X j is a vector of length I, representing the number of j-th scraps from each car model dismantled, where I represents the total number of car models dismantled, j∈[1,…,J]; Step 2: Based on the coupling equation in step 1, a waste weight estimation model is established. The objective function of the estimation model is expressed as: The constraints of the extrapolation model include: a. The vehicle weight is greater than the total weight of the dismantled waste. This constraint is expressed as formula (6); b. The non-negative constraint of waste weight, which is expressed as formula (7); Where, represents the upper limit of the dismantling weight of the i-th vehicle type in the m-th batch, represents the weight of the jth type of scrap from the i-th car model dismantled in the m-th batch, i∈[1,…,I]; Step 3: Based on the estimated model in step 2, optimize and solve to obtain the weight x of the jth type of waste material dismantled from the i-th type of vehicle. i,j The optimal solution of .

2. The method for estimating automobile dismantling waste based on cone programming as claimed in claim 1, characterized in that: The optimization solution in step 3 specifically includes: The constraints of the inference model are converted into cone constraints, which can be expressed as formula (14): Where G represents a 2I×I matrix, h is a vector of length 2I, and I I It is an I×I identity matrix, h2 represents a variable, and the value of the (m-1)I+i elements in h2 is j' represents other waste types.

3. The method for estimating automobile dismantling waste based on cone programming as claimed in claim 2, characterized in that: The optimization solution in step 3 specifically includes: Introducing original variables s represents the slack variable, represents the 2I-dimensional vector space of non-negative real numbers, R + represents the set of all non-negative real numbers; The optimization problem of the inference model is expressed as an equivalent cone programming problem provided by Equation (17): Where Q = A T A,q=-A T Y j , superscript T indicates transposition, st indicates constraint, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space.

4. The method for estimating automobile dismantling waste based on cone programming as claimed in claim 3, characterized in that: The optimization solution in step 3 specifically includes: X j The optimization solution is as follows: Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u): in: Q=A T A,q=-A T Y j , A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space, u represents the scaling dual variable, h is a vector of length 2I; In step 3.2, use the alternating direction multiplication method to update the three variables z, s, and u in sequence in each iteration: a. Fixed s k and u k In the case of , update z using formula (19) k+1 , k represents the number of iterations, first calculate z for L(z,s,u) k The derivative of and setting the gradient to 0 can obtain the linear equation (20), and then the linear equation (20) can be numerically solved using the conjugate gradient method or direct inversion method: b. Fixed z k+1 and u k In the case of minimizing L(z k+1 ,s,u k ), while satisfying Update s using formula (21) k+1 : Pass-A eq z k+1 +hu k Projecting onto the non-negative orthogonal cone space, we get s k+1 , that is, taking the maximum value element by element: in, represents the slack variable of the i-th model in the k+1th round; c. Fixed z k+1 and s k+1 In the case of , the dual variable u is updated by accumulating the constraint residuals k+1 , as shown in formula (23): u k+1 =u k +A eq z k+1 +s k+1 -h (23) Step 3.3, determine whether the update process in step 3.2 meets the preset termination criteria. If yes, then as shown in formula (24), k+1 Take the first I dimensions to get 5. The method for estimating automobile dismantling waste based on cone programming as claimed in claim 4, characterized in that: The termination criterion of step 3.3 is set as formula (25): Among them, ∈ pri and ∈ dual is the preset tolerance parameter.

6. The method for estimating automobile dismantling waste based on cone programming according to any one of claims 1 to 5, characterized in that: The optimization solution in step 3 specifically includes: Before iterative solution, for each type of waste X j Perform the following initialization: Based on the historical scrap record of the i-th vehicle model in the known or previous M-1 batch as x ij , build a local waste dictionary, the local waste dictionary is a mapping of "car model → waste vector", if the jth waste x of the i-th car model in the current batch ij There is already a history record x' in the local scrap dictionary ij , then directly use the historical record x' ij Value pair x ij Otherwise, use a small random positive number that follows a Gaussian distribution for initialization.

7. The method for estimating automobile dismantling waste based on cone programming according to any one of claims 1 to 5, characterized in that: The j-th type of waste x of the i-th type of vehicle has been obtained ij Stores the local waste dictionary for use in initializing subsequent batches.

8. A device for estimating automobile dismantling waste based on cone programming, characterized in that: include: The vehicle model and waste coupling equation construction unit is used to establish the coupling equation between the vehicle model and waste according to the expected parameters related to the automobile dismantling waste: Y j =AX j , where Y j is a vector of length M, representing the number of the jth type of scrap in all batches, where M represents the total number of batches of car dismantling; A is an M×I matrix, representing the number distribution of models in each batch; X j is a vector of length I, representing the number of j-th scraps from each car model dismantled, where I represents the total number of car models dismantled, j∈1,…,J]; The scrap weight estimation model establishment unit is used to establish the coupling equation of the unit based on the vehicle model and the scrap weight coupling equation, and establish the scrap weight estimation model. The objective function of the estimation model is expressed as: The constraints of the extrapolation model include: a. The vehicle weight is greater than the total weight of the dismantled waste. This constraint is expressed as formula (6); b. The non-negative constraint of waste weight, which is expressed as formula (7); Where, represents the upper limit of the dismantling weight of the i-th vehicle type in the m-th batch, represents the weight of the jth type of scrap from the i-th car model dismantled in the m-th batch, i∈[1,…,I]; The waste weight calculation optimization unit is used to establish a unit calculation model based on the waste weight calculation model, and optimize the solution to obtain the weight x of the jth type of waste dismantled from the i-th type of vehicle. i,j The optimal solution of .

9. The automobile dismantling waste estimation device based on cone programming as claimed in claim 8, characterized in that: The optimization solution in the waste weight calculation optimization unit specifically includes: The constraints of the inference model are converted into cone constraints, which can be expressed as formula (14): Where G represents a 2I×I matrix, h is a vector of length 2I, and I I It is an I×I identity matrix, h2 represents a variable, and the value of the (m-1)I+i elements in h2 is j' represents other waste types; The optimization solution in the waste weight calculation optimization unit specifically includes: Introducing original variables s represents the slack variable, represents the 2I-dimensional vector space of non-negative real numbers, R + represents the set of all non-negative real numbers; The optimization problem of the inference model is expressed as an equivalent cone programming problem provided by Equation (17): Where Q = A T A,q=-A T Y j , superscript T indicates transposition, st indicates constraint, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space.

10. The automobile dismantling waste estimation device based on cone programming as claimed in claim 9, characterized in that: The optimization solution in the waste weight calculation optimization unit specifically includes: X j The optimization solution is as follows: Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u): in: Q=A T A,q=-A T Y j , A eq =[GI 2I ], G represents a 2I×I matrix, I 2I represents the 2I×2I identity matrix, A eq represents a 2I×3I matrix, R I represents an I-dimensional real vector space, u represents the scaling dual variable, h is a vector of length 2I; In step 3.2, use the alternating direction multiplication method to update the three variables z, s, and u in sequence in each iteration: a. Fixed s k and u k In the case of , update z using formula (19) k+1 , k represents the number of iterations, first calculate z for L(z,s,u) k The derivative of and setting the gradient to 0 can obtain the linear equation (20), and then the linear equation (20) can be numerically solved using the conjugate gradient method or direct inversion method: b. Fixed z k+1 and u k In the case of minimizing L(z k+1 ,s,u k ), while satisfying Update s using formula (21) k+1 : Pass-A eq z k+1 +hu k Projecting onto the non-negative orthogonal cone space, we get s k+1 , that is, taking the maximum value element by element: in, represents the slack variable of the i-th model in the k+1th round; c. Fixed z k+1 and s k+1 In the case of , the dual variable u is updated by accumulating the constraint residuals k+1 , as shown in formula (23): u k+1 =u k +A eq z k+1 +s k+1 -h (23) Step 3.3, determine whether the update process in step 3.2 meets the preset termination criteria. If yes, then as shown in formula (24), k+1 Take the first I dimensions to get

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