Special steel steelmaking alloy reduction method based on nonlinear programming
Through the nonlinear planning method, the alloy database is established and the nonlinear constraints are considered, the problem of limited reduction effect of special steel steelmaking alloys is solved, and the optimization of alloy ingredients and the satisfaction of high performance requirements are achieved.
Patent Information
- Application Number
- CN202411916944.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-24
- Publication Date
- 2025-04-08
AI Technical Summary
The prior art is difficult to effectively realize the reduction of special steel steel-making alloys, especially when the nonlinear performance constraints are met, resulting in limited reduction effect of alloys.
An alloy database is established based on nonlinear planning, combined with the requirements of steelmaking production process, and the selection of each alloy is constrained. Taking into account the nonlinear constraints, an optimization model including alloy cost, steel seed chemical composition and production process constraints is constructed, and the optimization model is solved to obtain the optimal alloy batching scheme.
The optimization of alloy batching is achieved, which not only reduces the total cost of the alloy, but also ensures that special steel products meet high-standard performance requirements.
Smart Images
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Abstract
Description
Technical Field
[0001] The invention relates to the technical field of iron and steel metallurgy, and in particular to a special steelmaking alloy reduction method based on nonlinear programming. Background Art
[0002] The process of steel production mainly consists of five links: blast furnace ironmaking, converter steelmaking, steel alloying, refining outside the furnace, and continuous casting. Among them, the cost of blast furnace ironmaking and converter steelmaking mainly depends on raw materials such as iron ore, lime, coke, scrap steel, etc., and the cost reduction space is low and uncontrollable. In the process of refining outside the furnace and continuous casting, energy costs account for the largest proportion, and the cost reduction space is limited. The reduction of steel alloying process is widely used in cost reduction projects of production enterprises due to its efficient and economical way. The steel alloying process is a complex physical and chemical process with many influencing factors, and there are mutual influences between the factors. It is difficult to obtain the key technical methods that affect the alloying reduction, resulting in limited alloy reduction effect. At present, the lowest cost alloy batch optimization technology mainly adopts the linear optimization method, but for the production of special steel, in addition to meeting the basic composition requirements, the elements must also meet the constraints of various nonlinear formulas to meet the requirements of mechanical properties, welding properties, etc. The existing methods cannot meet the production needs of special steel. Summary of the invention
[0003] In order to solve the problems existing in the prior art, the main purpose of the present invention is to propose a special steelmaking alloy reduction method and system based on nonlinear programming.
[0004] To solve the above technical problems, according to one aspect of the present invention, the present invention provides the following technical solutions:
[0005] A method for reducing alloy content in special steelmaking based on nonlinear programming, comprising:
[0006] An alloy database is established based on alloy grade and the corresponding unit price of alloys of different grades; in combination with the steelmaking production process requirements, constraints are imposed on the selection of each alloy to ensure that the selected alloy can meet the technical requirements of the production process, and nonlinear constraints are considered in the constraints to ensure that the optimized alloy ingredients can not only meet the production process requirements, but also meet the performance indicators of the final product; an optimization model that includes alloy cost, steel chemical composition and production process constraints is constructed; the optimization model is solved to obtain the optimal alloy ingredient solution. The objective function of the optimization model is to minimize the total alloy cost, thereby minimizing the cost while ensuring that special steel products meet high-standard performance requirements.
[0007] As a preferred scheme of the special steelmaking alloy reduction method based on nonlinear programming described in the present invention, the nonlinear constraints include the mechanical properties of the steel (such as strength, ductility, etc.), welding properties (such as weldability, joint strength, etc.), and other performance indicators that need to be met.
[0008] As a preferred solution of the special steelmaking alloy reduction method based on nonlinear programming described in the present invention, the IPOPT (Interior Point Optimizer) solver is used to solve the optimization model.
[0009] As a preferred solution of the special steelmaking alloy reduction method based on nonlinear programming described in the present invention, the product of the alloy unit price and the alloy addition amount is used as the objective function of the mathematical model.
[0010] The objective function f(x) is:
[0011]
[0012] Among them, c i is the unit price of the ith alloy; x i is the amount of alloy added, x i ≥0.
[0013] As a preferred solution of a special steel alloy reduction method based on nonlinear programming described in the present invention, the constraint conditions include linear constraint conditions (1) and nonlinear constraint conditions (2), which are respectively:
[0014]
[0015] (1) is a linear constraint, which means that the content of each alloy element j is determined by the addition amount x of different alloys. i Contributions, the sum of which must be located at d j within the scope of
[0016] Among them, g j (x) is a i The weighted sum of represents the content of the jth element in the steel grade;
[0017] k ij is the grade of the ith alloy, j is the element j contained in the alloy;
[0018] x i is the amount of alloy added, x i ≥0;
[0019] d j It is the content range of element j for smelting steel.
[0020]
[0021] (2) is a nonlinear constraint condition, which is determined by the content of each alloy element g j (x) and constant coefficients a0, a1, a2, b j To describe the comprehensive performance of the steel grade, and finally meet a standard threshold D of the steel grade performance;
[0022] Among them, z(x) is the empirical model of the influence of the content of each component of steel on the performance of steel, which is obtained through regression analysis and fitting of field experimental data; g1(x) in the formula is the carbon content required to be added to the alloy. Carbon content is usually a key factor affecting the strength and hardness of steel. A lower carbon content can improve the plasticity and toughness of steel, while a higher carbon content helps to increase strength, but at the same time it will also reduce plasticity and toughness. Therefore, the influence on carbon content is expressed by a quadratic equation to capture this effect;
[0023] a0, a1, and a2 are used to adjust the carbon content to balance the mechanical properties of the steel;
[0024] g j (x)(j=2,3…,n) the content of other alloying elements in the steel grade;
[0025] b j The constant that regulates the effect of the jth element on the properties of the steel grade;
[0026] D is an empirical value derived from the summary of on-site production data, representing a standard threshold value of steel grade performance. As mentioned above, z(x) represents the performance of a certain steel grade, and its calculation result must satisfy z(x)∈D, that is, the performance value of the steel grade should be within the standard range D, indicating that the performance of the steel grade meets the requirements. Specifically, the calculation result of the formula is weighted based on the various components of the steel grade. Only when the performance value z(x) of the steel grade falls within the standard range D, the steel grade meets the predetermined performance standard.
[0027] As a preferred solution of the special steel alloy reduction method based on nonlinear programming described in the present invention, the constraint condition function Φ(x) is: Φ(x) = (g1(x), ..., g m (x),z(x)), then Φ(x)∈(d1,…,d m ,D).
[0028] The beneficial effects of the present invention are as follows:
[0029] The present invention proposes a special steel alloy reduction method based on nonlinear programming, establishes a database based on alloy grade and unit prices corresponding to alloys of different grades, constrains the selection of each alloy in combination with steelmaking production process requirements, ensures that the selected alloy can meet the technical requirements in the production process, and considers nonlinear constraints in the constraints to ensure that the optimized alloy ingredients can not only meet the production process requirements but also meet the performance indicators of the final product; constructs an optimization model including alloy cost, steel chemical composition and production process constraints; solves the optimization model to obtain the optimal alloy ingredient plan, and the objective function of the optimization model is to minimize the total alloy cost, thereby minimizing the cost while ensuring that the special steel product meets high-standard performance requirements. DETAILED DESCRIPTION
[0030] The following will be described clearly and completely in conjunction with the technical solutions in the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0031] A method for reducing alloy content in special steelmaking based on nonlinear programming, comprising:
[0032] An alloy database is established based on alloy grade and the corresponding unit price of alloys of different grades; in combination with the steelmaking production process requirements, constraints are imposed on the selection of each alloy to ensure that the selected alloy can meet the technical requirements of the production process, and nonlinear constraints are considered in the constraints to ensure that the optimized alloy ingredients can not only meet the production process requirements, but also meet the performance indicators of the final product; an optimization model that includes alloy cost, steel chemical composition and production process constraints is constructed; the optimization model is solved to obtain the optimal alloy ingredient solution. The objective function of the optimization model is to minimize the total alloy cost, thereby minimizing the cost while ensuring that special steel products meet high-standard performance requirements.
[0033] Preferably, the nonlinear constraint conditions include mechanical properties (such as strength, ductility, etc.) of the steel grade, welding properties (such as weldability, joint strength, etc.), and other performance indicators that need to be met.
[0034] Preferably, an IPOPT (Interior Point Optimizer) solver is used to solve the optimization model.
[0035] Preferably, the product of the alloy unit price and the alloy addition amount is used as the objective function of the mathematical model. The objective function f(x) is:
[0036]
[0037] Among them, ci is the unit price of the ith alloy; x i is the amount of alloy added, x i ≥0.
[0038] Preferably, the constraints include linear constraints (1) and nonlinear constraints (2), which are respectively:
[0039]
[0040] (1) is a linear constraint, which means that the content of each alloy element j is determined by the addition amount x of different alloys. i Contributions, the sum of which must be located at d j within the scope of
[0041] Among them, g j (x) is a i The weighted sum of represents the content of the jth element in the steel grade;
[0042] k ij is the grade of the ith alloy, j is the element j contained in the alloy;
[0043] x i is the amount of alloy added, x i ≥0;
[0044] d j It is the content range of element j for smelting steel.
[0045]
[0046] (2) is a nonlinear constraint condition, which is determined by the content of each alloy element g j (x) and constant coefficients a0, a1, a2, b j To describe the comprehensive performance of the steel grade, and finally meet a standard threshold D of the steel grade performance;
[0047] Among them, z(x) is the empirical model of the influence of the content of each component of steel on the performance of steel, which is obtained through regression analysis and fitting of field experimental data; g1(x) in the formula is the carbon content required to be added to the alloy. Carbon content is usually a key factor affecting the strength and hardness of steel. A lower carbon content can improve the plasticity and toughness of steel, while a higher carbon content helps to increase strength, but at the same time it will also reduce plasticity and toughness. Therefore, the influence on carbon content is expressed by a quadratic equation to capture this effect;
[0048] a0, a1, and a2 are used to adjust the carbon content to balance the mechanical properties of the steel;
[0049] g j (x)(j=2,3…,n) the content of other alloying elements in the steel grade;
[0050] b j The constant that regulates the effect of the jth element on the properties of the steel grade;
[0051] D is an empirical value derived from the summary of on-site production data, representing a standard threshold value of steel grade performance. As mentioned above, z(x) represents the performance of a certain steel grade, and its calculation result must satisfy z(x)∈D, that is, the performance value of the steel grade should be within the standard range D, indicating that the performance of the steel grade meets the requirements. Specifically, the calculation result of the formula is weighted based on the various components of the steel grade. Only when the performance value z(x) of the steel grade falls within the standard range D, the steel grade meets the predetermined performance standard.
[0052] Preferably, the constraint condition function Φ(x) is: Φ(x)=(g1(x),…,g m (x),z(x)), then Φ(x)∈(d1,…,d m ,D).
[0053] The special steel alloy reduction method based on nonlinear programming of the present invention is applied to the steelmaking process of a certain plant. The steel type to be smelted is B350AM billet. The target requirements are shown in Table 1.
[0054] Table 1 B350AM billet target requirements (wt%)
[0055]
[0056] The alloy unit price (yuan / kg) multiplied by the alloy addition amount (kg) is used as the objective function, then,
[0057] minf(x)
[0058] =7.55*x1+12.7*x2+8.38*x3+9.3*x4+13*x5+15.9*x6
[0059] +9.1*x7+13.2*x8+9.008*x9+9.009*x 10 +9.011*x 11
[0060] +9.012*x 12 +9.013*x 13 +4.3*x 14 +9.01*x 15 +11.1*x 16
[0061] +4.5*x 17 +5.5*x 18
[0062] The unit price and alloy composition of the alloy are shown in Table 2.
[0063] Table 2 Alloy unit price (yuan / kg) and alloy composition (wt%)
[0064]
[0065]
[0066] Linear constraint g j The number of (x) is equal to the number of elements contained in the alloy (as shown in Table 2, m = 11), then
[0067] z(x)=[0.062+0.409*(%C)-0.135*(%C)*(%C)]*[1+3.333*(%Mn)]*[1+0.7*( %Si)]*[1+2.16*(%Cr)]*[1+3*(%Mo)]*[1+0.363*(%Ni)]*[1+0.365*(%Cu)]
[0068] Finally, the constrained optimization model is solved by the interior point method to obtain the alloy ratio that meets all process requirements and performance standards. The results are shown in Table 3-4.
[0069] Table 3 Results of alloy addition
[0070] Alloy Name Addition amount (kg) Alloy Name Addition amount (kg) High manganese 1140.7376 Ferromolybdenum 0 Medium Manganese 0 Low vanadium iron 0 Silicon Manganese 215.2524 Nickel Plate 0 High Silicon 0 High purity ferrosilicon 0 Industrial Silicon 0 Carbon Raiser 722.7436 Low chromium 0 nickel 0 High chromium 1083.3022 molybdenum 0 Low titanium and high chromium 0 copper 0 Ferrotitanium 10.6966 vanadium 0
[0071] Table 4 Steel composition results
[0072] Element Name wt% Element Name wt% C 0.98 Cr 0.68 Si 0.2 Ni 0 Mn 1.07 Mo 0 P 0.011 Cu 0 S 0.0006 V 0 Ti 0.012
[0073] Then z(x)=[0.062+0.409*(%C)-0.135*(%C)*(%C)]*[1+3.333*(%Mn)]*[1+0.7*(%Si)]*[1+2.16*(%Cr)]*[1+3*(%Mo)]*[1+0.363*(%Ni)]*[1+0.365*(%Cu)]=4.28∈D, and the steel grade meets the predetermined performance standards.
[0074] The optimal value of the objective function (alloy cost required for 100t of molten steel) is 23478.58783 yuan.
[0075] The present invention establishes a database based on alloy grade and unit prices corresponding to alloys of different grades, and constrains the selection of each alloy in combination with steelmaking production process requirements to ensure that the selected alloy can meet the technical requirements in the production process, and considers nonlinear constraints in the constraints to ensure that the optimized alloy ingredients can not only meet the production process requirements but also meet the performance indicators of the final product; constructs an optimization model including alloy cost, steel chemical composition and production process constraints; solves the optimization model to obtain the optimal alloy ingredient plan, and the objective function of the optimization model is to minimize the total alloy cost, thereby minimizing the cost while ensuring that special steel products meet high-standard performance requirements.
[0076] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.
Claims
1. A special steel alloy reduction method based on nonlinear programming, characterized in that: include: Establish an alloy database based on alloy grades and corresponding unit prices of alloys of different grades; In combination with the steelmaking production process requirements, constraints are imposed on the selection of each alloy to ensure that the selected alloy can meet the technical requirements of the production process, and nonlinear constraints are considered in the constraints to ensure that the optimized alloy ingredients can not only meet the production process requirements, but also meet the performance indicators of the final product; an optimization model that includes alloy cost, steel chemical composition and production process constraints is constructed; the optimization model is solved to obtain the optimal alloy ingredient scheme. The objective function of the optimization model is to minimize the total alloy cost, thereby minimizing the cost while ensuring that special steel products meet high-standard performance requirements.
2. The special steel alloy reduction method based on nonlinear programming according to claim 1, characterized in that: The nonlinear constraints include the mechanical properties of the steel, welding properties and other performance indicators that need to be met.
3. The special steel alloy reduction method based on nonlinear programming according to claim 1, characterized in that: The IPOPT solver is used to solve the optimization model.
4. The special steel alloy reduction method based on nonlinear programming according to claim 1, characterized in that: The objective function f(x) is: Among them, c i is the unit price of the ith alloy; x i is the amount of alloy added, x i ≥0.
5. The special steel alloy reduction method based on nonlinear programming according to claim 1, characterized in that: The constraints include linear constraints (1) and nonlinear constraints (2), which are: Among them, g j (x) is the content of the jth element in the steel grade; k ij is the grade of the ith alloy, j is the element j contained in the alloy; x i is the amount of alloy added, x i ≥0; d j is the content range of element j in smelting steel; Among them, z(x) is the empirical model of the influence of the content of each component of steel on the performance of steel; g1(x) is the carbon content required to be added to the alloy; a0, a1, and a2 are constants used to adjust the carbon content to balance the mechanical properties of the steel; g j (x)(j=2,3…,n) the content of other alloying elements in the steel grade; b j The constant that regulates the effect of the jth element on the properties of the steel grade; D is an empirical value derived from the summary of field production data, representing a standard threshold value of steel grade performance.
6. The special steel alloy reduction method based on nonlinear programming according to claim 5, characterized in that: The constraint function Φ(x) is: Φ(x)=(g1(x),…,g m (x),z(x)), then Φ(x)∈(d1,…,d m ,D).