A method and apparatus for estimating automobile dismantling waste based on cone programming.

Abstract

This invention discloses a method and apparatus for estimating automobile dismantling waste based on cone programming, comprising: Step 1, establishing a coupling equation between vehicle model and waste based on pre-defined parameters related to automobile dismantling waste; Step 2, establishing a waste weight estimation model based on the coupling equation in Step 1; Step 3, optimizing the solution based on the estimation model in Step 2 to obtain the optimal solution for the weight of the j-th type of waste dismantled from the i-th vehicle model. This invention achieves high-precision estimation of waste output through mathematical optimization, solving the technical problem in existing technologies that make it difficult to accurately quantify the waste output and weight loss after dismantling different vehicle models, and providing a scientific basis for resource recycling and environmental management in the automobile dismantling industry.

Description

Technical Field

[0001] This invention relates to the field of industrial optimization and resource recycling technology, and in particular to a method and apparatus for estimating automobile dismantling waste based on cone programming. Background Technology

[0002] With the continuous growth of vehicle ownership, the dismantling and recycling of end-of-life vehicles has become a crucial link in resource recycling and environmental protection. However, traditional dismantling processes lack precise methods for predicting waste output, resulting in low resource utilization and difficulty in meeting the needs of refined management. Existing technologies mostly rely on empirical estimations or simple statistics, failing to accurately quantify the correspondence between different vehicle models and waste, thus hindering the efficient development of the industry. Summary of the Invention

[0003] The purpose of this invention is to provide a method and apparatus for estimating automobile dismantling waste based on cone programming, so as to overcome or at least mitigate at least one of the above-mentioned defects of the prior art.

[0004] To achieve the above objectives, this invention provides a method for estimating automobile dismantling waste based on cone programming, comprising:

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

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

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

[0008]

[0009] b. Non-negative constraint on the weight of waste material, which is expressed as Equation (7);

[0010]

[0011] In the formula, This represents the maximum disassembly weight of the i-th vehicle type in the m-th batch. Let represent the weight of the j-th type of waste material extracted from the i-th type of vehicle model in the m-th batch, where i∈[1,…,I];

[0012] Step 3: Based on the calculation model in Step 2, optimize the solution to obtain the weight x of the j-th type of waste material obtained from dismantling the i-th type of vehicle model. i,j The optimal solution.

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

[0014] The constraints of the derivation model are converted into cone constraints, as expressed in equation (14):

[0015]

[0016] Where G represents a 2I×I matrix, h is a vector of length 2I, and I I Let h1 be an I×I identity matrix, h2 represent variables, and the values ​​of (m-1)I+i elements in h2 are... j' indicates other types of waste.

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

[0018] Introducing primitive variables s represents the slack variable, Let R represent a vector space of 2I-dimensional nonnegative real numbers. + Represents the set of all non-negative real numbers;

[0019] The optimization problem of the extrapolation model can be expressed as the equivalent cone programming problem provided by equation (17):

[0020]

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

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

[0023] X j The optimization solution method 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 Let A represent a 2I×2I identity matrix. eq Let R represent a 2I×3I matrix. I Let u denote the I-dimensional real vector space, and let u denote the scaling dual variable. h is a vector of length 2I;

[0027] Step 3.2: Using the alternating direction multiplier method, update the three variables z, s, and u sequentially in each iteration:

[0028] a. Fixed s k and u k In the case of z, update z using equation (19). k+1 k represents the number of iterations. First, calculate z for L(z,s,u). k Taking the derivative of the equation and setting the gradient to 0, we obtain the linear equation (20). Then, we can numerically solve the linear equation (20) using the conjugate gradient method or direct inversion.

[0029]

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

[0031]

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

[0033]

[0034] in, Let represent the slack variable for the i-th car model in the (k+1)-th round;

[0035] c. Fixed z k+1 and s k+1 In this case, the dual variable u is updated by accumulating the constraint residuals. k+1 As shown in equation (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 criterion. If so, then as shown in equation (24), from z k+1 Obtaining the first I dimension from the middle

[0038]

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

[0040]

[0041] Where, ∈ pri and ∈ dual These are the preset tolerance parameters.

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

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

[0044] Based on the known or previous M-1 batches of historical scrap records of the i-th vehicle type, let x be the data. ij Construct a local waste dictionary, which is a mapping of "vehicle type → waste vector". If the j-th type of waste of the i-th vehicle type in the current batch is x ij There is already a history of x' in the local waste dictionary. ij Then directly use that historical record x' ij Value pair x ij Perform initialization; otherwise, initialize with small random positive numbers that follow a Gaussian distribution.

[0045] Furthermore, the j-th type of waste material x of the i-th type of vehicle model that has already been determined... ij Store it in the local waste dictionary for use in the initialization of subsequent batches.

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

[0047] The vehicle model and waste coupling equation construction unit is used to establish the coupling equation between the vehicle model and the waste based on pre-defined parameters related to vehicle dismantling waste: Y j =AX j , where Y j Let X be a vector of length M, representing the quantity of the j-th type of waste in all batches, where M represents the total number of batches of car dismantling; A is an M×I matrix representing the quantity distribution of each car model in each batch; X j It is a vector of length I, representing the quantity of the j-th type of waste material obtained from dismantling each type of car model, where I represents the total number of car models dismantled, j∈1,…,J].

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

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

[0050]

[0051] b. Non-negative constraint on the weight of waste material, which is expressed as Equation (7);

[0052]

[0053] In the formula, This represents the maximum disassembly weight of the i-th vehicle type in the m-th batch. Let represent the weight of the j-th type of waste material extracted from the i-th type of vehicle model in the m-th batch, where i∈[1,…,I];

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

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

[0056] The constraints of the derivation model are converted into cone constraints, as expressed in equation (14):

[0057]

[0058] Where G represents a 2I×I matrix, h is a vector of length 2I, and I ILet h1 be an I×I identity matrix, h2 represent variables, and the values ​​of (m-1)I+i elements in h2 are... j' indicates other types of waste;

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

[0060] Introducing primitive variables s represents the slack variable, Let R represent a vector space of 2I-dimensional nonnegative real numbers. + Represents the set of all non-negative real numbers;

[0061] The optimization problem of the extrapolation model can be expressed as the equivalent cone programming problem provided by equation (17):

[0062]

[0063] Where Q = A T A, q = -A T Y j The superscript T indicates transpose, st indicates constraint, and A eq =[GI 2I ], G represents a 2I×I matrix, I 2I Let A represent a 2I×2I identity matrix. eq Let R represent a 2I×3I matrix. I Let represent 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 method 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 Let A represent a 2I×2I identity matrix. eq Let R represent a 2I×3I matrix. I Let u denote the I-dimensional real vector space, and let u denote the scaling dual variable. h is a vector of length 2I;

[0069] Step 3.2: Using the alternating direction multiplier method, update the three variables z, s, and u sequentially in each iteration:

[0070] a. Fixed s k and u k In the case of z, update z using equation (19). k+1 k represents the number of iterations. First, calculate z for L(z,s,u). k Taking the derivative of the equation and setting the gradient to 0, we obtain the linear equation (20). Then, we can numerically solve the linear equation (20) using the conjugate gradient method or direct inversion.

[0071]

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

[0073]

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

[0075]

[0076] in, Let represent the slack variable for the i-th car model in the (k+1)-th round;

[0077] c. Fixed z k+1 and s k+1 In this case, the dual variable u is updated by accumulating the constraint residuals. k+1 As shown in equation (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 criterion. If so, then as shown in equation (24), from z k+1 Obtaining the first I dimension from the middle

[0080]

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

[0082] This invention achieves a scientific modeling of the relationship between vehicle model and waste weight by solving the coupled equations using cone programming. This method can be widely applied to automotive dismantling companies, recycling organizations, and environmental regulatory departments, providing reliable data support for waste classification, resource recovery rate improvement, and carbon emission accounting, thus promoting the industry's transformation towards intelligence and green practices. Automotive dismantling waste estimation refers to inferring the weight of different waste produced for each vehicle model and the resulting weight loss based on a list of vehicles (including model and weight) and the waste produced after dismantling (including waste name and weight) within a certain period.

[0083] This invention reduces the estimation of automotive dismantling waste to an optimization problem of solving a coupled equation relating vehicle model and waste. Given the quantity and weight of different vehicle models and waste materials in multiple batches of materials, a coupled equation relating vehicle model and waste materials is constructed from this known data. Through deduction, the estimation of automotive dismantling waste is transformed into a cone programming problem, which calculates the weight and loss of different waste materials from each vehicle model dismantling. Attached Figure Description

[0084] Figure 1 This is a flowchart illustrating the method for estimating automobile dismantling waste based on cone programming according to an embodiment of the present invention. Detailed Implementation

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

[0086] In the description of this invention, the terms "center," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

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

[0088] 1.1 Determine the known quantities in the equation

[0089] Suppose a car dismantling plant performs M batches of dismantling, involving I types of car models, and produces J types of waste. The known quantities in the equation include:

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

[0091] In the m-th batch of dismantling, the quantity of the j-th type of waste material dismantled is Where, j∈[1,…,J].

[0092] 1.2 Determining the unknowns of the equation

[0093] By obtaining the weight of different scrap materials and the weight loss for each vehicle model, auto dismantling plants can assess the value of used vehicles and guide their operations based on the scrap material. The unknowns in the equation are...

[0094] (1) The weight of different types of waste produced and the weight of loss for each type of vehicle model. The weight of type j waste produced from dismantling type i is x. i,j Where i∈[1,…,I],j∈[1,…,J].

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

[0096] In the m-th batch of dismantling, the j-th type of waste material is the sum of all the waste materials from all vehicle models. The weight of the j-th type of waste material from the i-th vehicle model is equal to the quantity of the i-th vehicle model. Multiplied by the weight of the j-th type of waste material obtained from dismantling the i-th type of vehicle model x I,j ,Right now Therefore, the total amount of the j-th type of waste dismantled in the m-th batch is:

[0097]

[0098] For the sake of formal expression, let

[0099]

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

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

[0102] Y j =AX j (4)

[0103] Among them, Y jX is a vector of length M, representing the quantity of waste material j in all batches; A is an M×I matrix representing the quantity distribution of each vehicle model in each batch; X j It is a vector of length I, representing the amount of waste j produced from the dismantling of each vehicle model.

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

[0105]

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

[0107] (1) Constraint that the weight of the vehicle model is greater than the total weight of the dismantled scrap.

[0108] For each batch, the weight constraint for vehicle type I is:

[0109]

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

[0111] The weight of the scrap material from each vehicle model dismantling is non-negative:

[0112]

[0113] All that involves or is not limited to All the constraints are alternative solutions.

[0114] Step 2: Based on the coupling equations from Step 1, the problem of solving the coupling equations between vehicle model and waste 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 of solving this constrained objective function is an alternative solution.

[0115]

[0116] The constraints of the extrapolation model include two constraints represented by equations (6) and (7).

[0117] Among them, X j ∈R I Represents the weight distribution vector of type j waste across all vehicle models and batches; A∈R M×I Y is the projection matrix; j ∈R M The observed waste projection vector; This represents the maximum disassembly 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, the constraint condition (7) of the calculation model is... Write it in vector form X j Then it includes:

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

[0124]

[0125] Where h1 and G1 both represent variables, I I It is an I×I identity matrix, that is, a matrix in which all diagonal elements are 1 and the rest are 0. The bold O is a vector of length I.

[0126] (2) Upper limit constraint on dismantling weight: For each vehicle type i and each batch m, the weight of the j-th type of waste material dismantled from the i-th vehicle type. The total dismantling weight of this model in this batch must not exceed the upper limit. Weight already allocated to other waste types The difference is that

[0127]

[0128] Where j' represents other types of waste.

[0129] Record X j The [(m-1)I+i]th element is Equation (6) is expressed as equation (13) in cone constraints:

[0130]

[0131] Here, h2 and G2 both represent 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 equation (15), which ultimately takes the form of a quadratic programming problem:

[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, to solve the above optimization problem, slack variables need to be introduced to transform the constraint into an equality constraint plus a non-negative cone constraint. To transform the inequality constraint provided by equation (15) into an equality constraint, slack variables are introduced. 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 derived model can also be expressed as the equivalent cone programming problem provided by equation (17):

[0141]

[0142] Among them, A eq =[GI 2I ], G represents a 2I×I matrix, I 2I Let A represent a 2I×2I identity matrix. eq It is a 2I×3I matrix, R I Let R represent an I-dimensional real vector space. 2I Represents a 2I-dimensional real vector space. Let R represent a vector space of 2I-dimensional nonnegative real numbers. + R represents the set of all non-negative real numbers. + ={x∈R|x≥0}, The variable z has the following dimensions: the first I components are any 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 of formula (17). Using the cone augmented Lagrange method, the weight distribution vector X of the j-th type of waste in all vehicle models and batches can be obtained. j .

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

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

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

[0147]

[0148] in: u represents the scaling dual variable. ρ represents the regularization parameter, also known as the penalty coefficient, used to adjust the strength of the scaling effect on the dual variable u and to control the balance between the primal constraint and the dual variable u. It is a hyperparameter, and the augmented Lagrange term contains a squared term. The residuals of the original constraints were measured, while The term ρ is the regularization term for the dual variable u, and its contribution to both terms acts as a weight. If not dynamically adjusted, ρ can be set to a fixed value during optimization, typically around 10. -3 Up to 10 3 The specific value of ρ can be adjusted experimentally. If dynamic adjustment is required, the value of ρ can be adjusted based on the changes in the original residual and the dual residual. 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 sequentially in each iteration:

[0150] a. Fixed s k and u k In the case of z, update z using equation (19). k+1 k represents the number of iterations. First, calculate z for L(z,s,u). k Taking the derivative of the equation and setting the gradient to 0, we obtain the linear equation (20). Then, we can numerically solve the linear equation (20) using the conjugate gradient method or direct inversion.

[0151]

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

[0153]

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

[0155]

[0156] in, Let represent the slack variable for the i-th car model in the (k+1)-th round;

[0157] c. Fixed z k+1 and s k+1 In this case, the dual variable u is updated by accumulating the constraint residuals. k+1 As shown in equation (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 criterion. If so, then as shown in equation (24), from z k+1 Obtaining the first I dimension from the middle

[0160]

[0161] In one embodiment, the termination criterion for step 3.3 may be set as follows (25):

[0162]

[0163] Where, ∈ pri and ∈ dual The tolerance parameter is set by the user. A smaller tolerance parameter results in a more accurate solution. This means that users can improve the algorithm's accuracy by decreasing the tolerance parameter, but this may also increase computational complexity and time. It can also be dynamically adjusted based on the convergence behavior of the iteration. Default parameter ∈ pri =10 -4 ,∈ dual =10 -3 .

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

[0165] To improve the stability and convergence speed of the algorithm, before iterative solution, each type of waste X is...j Perform the following initialization:

[0166] Based on the known or previous M-1 batches of historical scrap records of the i-th vehicle type, let x be the data. ij Construct a local waste dictionary, which is a mapping of "vehicle type → waste vector". If the j-th type of waste of the i-th vehicle type in the current batch is x ij There is already a history of x' in the local waste dictionary. ij Then directly use that historical record x' ij Value pair x ij Initialize; otherwise, use a Gaussian distribution (mean 0, standard deviation 1×10⁻⁶). -2 Initialize with small random positive numbers.

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

[0168] Use an Excel spreadsheet to organize and store the data, such as the simulated data in the waste dictionary storage structure shown in Table 1. Each row represents a vehicle model, and columns 2 through J+1 are used to store waste materials associated with that vehicle model.

[0169] Table 1

[0170] Model Zinc alloy scrap aluminum scrap copper Heavy steel Waste engine 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 iterate through all vehicle models and check if the corresponding vehicle model's waste data has been stored in the local waste dictionary.

[0172] If the dictionary already contains the following:

[0173] The error is calculated by comparing the data already stored in the Excel spreadsheet with the data to be stored. If the error is large, a weighted average is calculated based on the magnitude of the error difference.

[0174] If the error is small, then the average of the data already stored in the Excel sheet and the data to be stored is used for updating.

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

[0176] If the dictionary does not store:

[0177] Then create a new model in the Excel spreadsheet, 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 model has been determined. ij Store it in the local waste dictionary for use in the initialization of subsequent batches.

[0179] This invention also provides a vehicle dismantling waste estimation device 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 the waste based on pre-defined parameters related to vehicle dismantling waste: Y j =AX j .

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

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

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

[0184] The constraints of the extrapolation model are converted into cone constraints, as shown in equation (14).

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

[0186] Introducing primitive variables The optimization problem of the extrapolation 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 The optimized solution method.

[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Those skilled in the art should understand that modifications can be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting automobile disassembly scrap based on cone programming solution, characterized in that, Comprise: Step 1, according to the pre-set parameters related to automobile dismantling waste, the coupling equation between vehicle type and waste is established: Y j = AX j , where Y j is a vector of length M, representing the quantity of the jth waste in all batches, M represents the total number of batches of automobile dismantling; A is an M×I matrix, representing the quantity distribution of each batch of vehicle type; X j is a vector of length I, representing the quantity of the jth waste dismantled from each vehicle type, I represents the total number of vehicle types of automobile dismantling, j∈[1,…,J]; Step 2, according to the coupling equation of step 1, the waste weight estimation model is established, and the objective function of the estimation model is expressed as: The constraint conditions of the estimation model include: a. a constraint that the weight of the vehicle model is greater than the total weight of the disassembled scrap, which is represented as formula (6); b. a non-negative constraint of the weight of the scrap, which is represented as formula (7); In the formula, represents the upper limit of the disassembly weight of the ith vehicle model in the mth batch, represents the weight of the jth waste material disassembled from the ith vehicle model in the mth batch, i∈[1,…,I]; Step 3, according to the prediction model of step 2, the weight x of the jth waste material disassembled from the ith vehicle model is obtained by optimization solution i,j the optimal solution.

2. The method of claim 1, wherein, The optimization solving in step 3 specifically comprises: The constraint conditions of the estimation model are respectively converted into cone constraints, represented as formula (14): where G represents a 2I x I matrix, h is a vector of length 2I, I I is an I x I identity matrix, h2represents a variable, the values of the (m-1)I+i elements in h2are j' represents other waste categories.

3. The method of claim 2, wherein the method is based on a cone programming solution for vehicle disassembly scrap estimation. The optimization solving in step 3 specifically comprises: Introduce the original variable The first I components of the variable z are arbitrary real numbers, while the last 2I components must be non-negative, the dimension of z is 3I x 1, s represents the slack variable, denotes the vector space of 2I-dimensional non-negative real numbers, R + denotes the set of all non-negative real numbers; The optimization problem of the estimation model is represented as the equivalent cone programming problem provided by formula (17): where Q = A T A, q = -A T Y j , the superscript T denotes the transpose, s.t. denotes a constraint, A eq = [G I 2I ], G denotes a 2I x I matrix, I 2I denotes a 2I x 2I identity matrix, A eq denotes a 2I x 3I matrix, R I denotes an I-dimensional real vector space.

4. The method of claim 3, wherein the method is based on a cone programming solution. The optimization solving in step 3 specifically comprises: X j The optimization solution method of the above is as follows: Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u): wherein: Q = A T A, q = -A T Y j , A eq = [G I 2I ], G denotes a 2I x I matrix, I 2I denotes a 2I x 2I identity matrix, A eq denotes a 2I x 3I matrix, R I denotes an I-dimensional real vector space, u denotes a scaled dual variable, h is a 2I-dimensional vector, p denotes a regularization parameter for adjusting the strength of the action of the scaled dual variable u and controlling the balance between the original constraints and the dual variable u; Step 3.2, adopt the alternating direction multiplier method, and update the three variables z, s, and u in each round of iteration in turn: 3.2.

1. Fix s k and u k In this case, update z k+1 , k represents the iteration number, first take the derivative of L(z, s, u) with respect to z k and let the gradient be 0, the linear equation (20) can be obtained, and then use the conjugate gradient method or direct inversion method to solve the linear equation (20) numerically: 3.2.

2. Fixing z k+1 and u k In this case, minimize L(z k+1 , s, u k ) subject to Update s k +1 : By -A eq z k+1 +h-u k Project onto the non-negative orthogonal cone space, to get s k+1 i.e. element-wise max wherein, denotes the slack variable of the i-th vehicle type in the k+1 round. 3.2.

3. Fixing z k+1 and s k+1 In the case of the constraint residual being updated cumulatively, the dual variable u k+1 as shown in equation (23): u k+1 = u k + A eq z k+1 + s k+1 - h (23) Step 3.3, determine whether the update procedure in step 3.2 meets the preset termination criterion, if yes, obtain the first I dimensions from z k+1 ​ 5. The method of claim 4, wherein the method is based on a cone programming solution. The termination criterion of step 3.3 is set as formula (25): where ∈ pri and ∈ dual is a preset tolerance parameter.

6. The vehicle teardown scrap estimation method based on cone programming solution according to any one of claims 1-5, characterized in that, The optimization solving in step 3 specifically comprises: Before the iterative solution, for each type of waste X j the following initializations are made: Based on the historical scrap record x of the i-th vehicle model in the known or previous M-1 batches ij , a local scrap dictionary is constructed, which is a mapping of "vehicle model→scrap vector". If the j-th scrap x of the i-th vehicle model in the current batch has a historical record x′ in the local scrap dictionary ij , the value of the historical record x′ is directly used to initialize x ij ; otherwise, a small random positive number subject to Gaussian distribution is used for initialization. ij ij ​​ 7. The method of claim 1-5, wherein, The jth scrap material x of the ith vehicle model that has been found ij is stored in the local scrap material dictionary for initialization of subsequent batches.

8. A vehicle disassembly scrap estimation device based on conic programming solution, characterized by, Comprise: A vehicle type and waste coupling equation construction unit is configured to construct a coupling equation between vehicle types and waste according to pre-set parameters related to automobile disassembly waste: Y j = AX j , where Y j is a vector of length M, representing the quantity of the jth waste in all batches, M representing the total number of batches of automobile disassembly; A is an M×I matrix, representing the quantity distribution of each batch of vehicle types; X j is a vector of length I, representing the quantity of the jth waste disassembled from each vehicle type, I representing the total number of vehicle types of automobile disassembly, j∈1,…,J]. The waste weight estimation model establishing unit is configured to establish a waste weight estimation model according to the coupling equation of the vehicle type and the coupling equation constructing unit, and a target function of the estimation model is represented as: The constraint conditions of the estimation model include: a. a constraint that the weight of the vehicle model is greater than the total weight of the disassembled scrap, which is represented as formula (6); b. a non-negative constraint of the weight of the scrap, which is represented as formula (7); In the formula, represents the upper limit of the disassembly weight of the ith vehicle model in the mth batch, represents the weight of the jth waste material disassembled from the ith vehicle model in the mth batch, i ∈ [1, …, I]; The waste weight calculation optimization unit is used to establish the estimation model according to the waste weight estimation model establishment unit, and the optimal solution of the weight x of the jth waste material disassembled from the ith vehicle type is obtained by optimization solution. i,j the optimal solution.

9. The vehicle dismantling scrap estimation device based on cone programming solution according to claim 8, characterized in that, The optimization solving in the scrap weight calculation optimization unit specifically comprises: The constraint conditions of the estimation model are respectively converted into cone constraints, represented as formula (14): where G represents a 2I x I matrix, h is a vector of length 2I, I I is an I x I identity matrix, h2represents a variable, the values of the (m-1)I+i elements in h2are j' represents other scrap species; The optimization solving in the scrap weight calculation optimization unit specifically comprises: Introducing the original variables The first I components of the vector z are arbitrary real numbers, while the last 2I components must be non-negative. The dimension of z is 3I x 1, s represents the slack variables, denotes the vector space of 2I-dimensional non-negative real numbers, R + denotes the set of all non-negative real numbers; The optimization problem of the estimation model is represented as the equivalent cone programming problem provided by formula (17): where Q = A T A, q = -A T Y j , the superscript T denotes the transpose, s.t. denotes a constraint, A eq = [G I 2I ], G denotes a 2I x I matrix, I 2I denotes a 2I x 2I identity matrix, A eq denotes a 2I x 3I matrix, R I denotes an I-dimensional real vector space.

10. The vehicle dismantling scrap estimation device based on cone programming solution according to claim 9, characterized in that, The optimization solving in the scrap weight calculation optimization unit specifically comprises: X j The optimization solution method of the above is as follows: Step 3.1, construct the following cone augmented Lagrangian function L(z,s,u): wherein: Q = A T A, q = -A T Y j , A eq = [G I 2I ], G denotes a 2I x I matrix, I 2I denotes a 2I x 2I identity matrix, A eq denotes a 2I x 3I matrix, R I denotes an I-dimensional real vector space, u denotes a scaled dual variable, h is a 2I-dimensional vector, p denotes a regularization parameter for adjusting the strength of the action of the scaled dual variable u and controlling the balance between the original constraints and the dual variable u; Step 3.2, adopt the alternating direction multiplier method, and update the three variables z, s, and u in each round of iteration in turn: 3.2.

1. Fixed s k and u k In this case, z k+1 is updated by formula (19). k denotes the iteration number. First, the derivative of L(z, s, u) with respect to z k is calculated and set to zero to obtain the linear equation (20). Then, the conjugate gradient method or direct inversion method is used to solve the linear equation (20) numerically. 3.2.

2. Fixing z k+1 and u k In this case, minimize L(z k+1 , s, u k ) subject to Update s k +1 : By -A eq z k+1 +h-u k Project onto the non-negative orthogonal cone space, to get s k+1 i.e. element-wise max wherein denotes the slack variable of the i-th vehicle type in the k+1 round; 3.2.

3. Fixing z k+1 and s k+1 In the case of the constraint residual being updated cumulatively, the dual variable u k+1 as shown in equation (23): u k+1 = u k + A eq z k+1 + s k+1 - h (23) Step 3.3, determine whether the update procedure in step 3.2 meets the preset termination criterion, if yes, obtain the first I dimensions from z k+1 ​

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