Minimum rolling thickness prediction method considering hot continuous rolling narrow strip steel reduction distribution ratio
By optimizing the reduction distribution ratio of hot continuous rolling narrow strip steel and using the random direction method to predict the minimum rollable thickness, the problem of the complexity of calculating the minimum rollable thickness of the multi-stand hot tandem rolling unit is solved, and more efficient production and more efficient production are achieved. Excellent product.
Patent Information
- Application Number
- CN202411350043.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-26
- Publication Date
- 2025-01-21
AI Technical Summary
In the process of hot continuous rolling narrow strip steel, it is difficult for the prior art to effectively calculate the minimum rollable thickness of a multi-frame hot continuous rolling mill, especially when the underpressure distribution ratio is complex.
By collecting key processes and equipment parameters of the hot -rolled unit, combined with the steel type and specifications of steel, the distribution ratio of each rack is optimized by random direction method, so as to predict the minimum rolling thickness.
This method can significantly reduce the calculation time and cost of minimum rolling thickness, improve production efficiency and product quality, and expand product outlines and specifications.
Smart Images
Figure CN119337027A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of hot rolling, in particular to a method for predicting the minimum rollable thickness by considering the reduction distribution ratio of hot continuous rolling narrow strip steel. Background Art
[0002] The export thickness of strip steel is one of the important assessment criteria for the quality of strip steel products. In recent years, with the development of society and the requirements of energy conservation and environmental protection, my country's home appliances, new energy vehicles and other fields have developed rapidly. Customers have an increasing demand for thin strip steel products and higher quality requirements for thin hot-rolled strip steel products. Under the background of increasingly fierce market competition, good product quality is conducive to enterprises to improve their market share and competitiveness. By evaluating the rolling capacity of the hot rolling production line, calculating the minimum rollable thickness of the production line, and then determining the production outline range of the production line, it is conducive to the company's accurate positioning of production goals, and it plays an important role in improving the production outline range of the company, improving production efficiency, and thus enhancing market competitiveness. For the calculation of the minimum rollable thickness of the rolling mill, the so-called calculation of the minimum rollable thickness of the rolling mill is the calculation of the reduction capacity. For strips of specific specifications and steel grades, the calculation process of its reduction capacity can be simply described as: according to the maximum rolling pressure allowed by the rolling mill, calculate the minimum thickness that the rolling mill can roll under specific lubrication conditions, specific rolling speed and maximum allowable tension. The reason for choosing the maximum tension is that during the rolling process, the greater the tension, the greater the pressure.
[0003] However, the actual hot rolling process is extremely complex. For a multi-stand hot rolling mill, the calculation of the reduction capacity is much more complicated than that of an ordinary single-stand rolling mill. It is not only a problem of calculating the reduction of the last stand, but also involves the reduction distribution problem between each stand. In particular, due to different reduction conditions, the degree of work hardening of the strip in each stand is different, so the deformation resistance of the strip in each stand is also different, and the corresponding reduction capacity of the strip in each stand is also different. Therefore, a minimum rollable thickness prediction method considering the reduction distribution ratio of hot rolling narrow strip is developed. Summary of the invention
[0004] The object of the present invention is to provide a method for predicting the minimum rollable thickness taking into account the reduction distribution ratio of hot rolled narrow strip steel, so as to solve the problems raised in the above background technology.
[0005] To achieve the above object, the present invention provides the following technical solutions:
[0006] A method for predicting the minimum rollable thickness considering the reduction distribution ratio of hot-rolled narrow strip steel comprises the following steps:
[0007] a) Collect key process and equipment parameters of the hot rolling mill, mainly including: working roll diameter Dw , Support roller diameter D b , the maximum rolling pressure setting value P of the rolling mill max , mill entrance and exit tension τ b , τ f , maximum rolling power setting value F max , safety factor η, rolling speed V i , rolling temperature t, number of passes n;
[0008] b) Given the steel grade and specification characteristics of the product, the main parameters include the incoming thickness of the strip h0, the initial strength σ s0 , the width of the strip B;
[0009] c) define the process parameters involved in the calculation of the pressing capacity, mainly including the optimization search step length Δ=0.01;
[0010] d) Establishing an objective function; Establishing an objective function according to the pressure distribution ratio:
[0011] Where: i Determine the ratio of pressure distribution for each rack;
[0012] e) Assign the total pressure reduction Δh z ;
[0013] f) Randomly assign the initial pressure distribution ratio λ of each rack i ;
[0014] g) Condition judgment: Make safety judgment on the rolling pressure and rolling power corresponding to the randomly given initial pressure distribution ratio of each stand: P i ≤ηP imax and F i ≤ηF imax Is it true, where P i is the rolling force of the i-th stand, F i is the rolling power of the i-th pass; if the condition is met, proceed to step h); if the condition is not met, proceed to step f) and randomly set the initial reduction distribution ratio again until success;
[0015] h) Establish a random direction method to optimize the pressure distribution ratio of each rack;
[0016] i) Determine whether the optimized press-down amount of each rack is established; the discriminant is as follows:
[0017]
[0018] If the condition is satisfied, step j) is executed; if not, step h) is executed to recalculate the pressing distribution ratio of each rack until the condition is satisfied;
[0019] j) Objective function judgment: judge whether the objective function G(λ) = 1 holds; if so, output the minimum rollable thickness; if not, set Δh z =Δh z -Δ, and go to step f) to recalculate until the objective function is established;
[0020] k) Output the minimum rollable thickness h min =h0-Δh z .
[0021] As a preferred technical solution, the method for calculating the rolling pressure and rolling power in step g) is as follows:
[0022] g1) Calculate the pressure reduction of each rack according to the pressure reduction distribution ratio. The formula is as follows:
[0023]
[0024] g2)P i =Bl c 'Q P K T K; where: B is the average width of the rolled piece, in millimeters; l c is the contact arc length of the deformation zone; Q P is the external friction coefficient; K T is the influence coefficient of front and rear tension; K is the deformation resistance;
[0025] g3) Rolling power F for the i-th pass i The calculation is done using the following formula:
[0026]
[0027] Where: ψ is the force arm coefficient, which is 0.04; Δh is the reduction of the i-th pass; V is the rolling speed of the i-th pass.
[0028] As a preferred technical solution, in step h), a random direction method is established to optimize the pressure distribution ratio of each rack, and the specific process is as follows:
[0029] h1) Obtain a feasible initial point λ according to the initial pressure distribution ratio i =[λ1,λ2,λ3…,λ n ] T ;
[0030] h2) Create k n-dimensional random unit vectors e according to the number of racks j , (j=1,2,…,k):
[0031]
[0032] h3) According to the optimized search step size Δ = 0.01, k random points are calculated as follows:
[0033] λ′ i =λ i +Δe j (j=1,2,…,k).
[0034] Compared with the prior art, the present invention has the following beneficial effects:
[0035] Through the prediction method of this patent, the minimum rollable thickness of the hot rolling mill can be predicted according to the strip specifications, strip rolling temperature, unit running speed, roll system equipment parameters, roll reduction distribution ratio, etc., and the prediction of the minimum strip thickness can be guided by optimizing the reduction distribution ratio through the random vector method, which can greatly reduce the calculation time and cost of the minimum rollable thickness. It can also expand the product outline and product specifications, and improve production efficiency and product quality by optimizing the reduction distribution ratio of each stand. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] Figure 1 It is a flow chart of a method for predicting the minimum rollable thickness taking into account the rolling mill reduction distribution value described in the present invention. DETAILED DESCRIPTION
[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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.
[0038] Embodiment 1:
[0039] See also Figure 1 The present invention provides a method for predicting the minimum rollable thickness considering the reduction distribution ratio of hot-rolled narrow strip steel, comprising the following steps:
[0040] a) Collect the main equipment and process parameters of the rolling mill, including: working roll diameter D wi ={650,650,400,400,400,400,400,400,400}, support roller diameter D b =600mm, maximum rolling pressure setting value P i ={7000,7000,6000,6000,6000,6000,6000,6000,6000}KN, maximum mill entrance tension τ b =5MPa, outlet tension τ f =5MPa, maximum rolling power setting value Fi ={1800,1800,1800,1800,1600,1600,1600,1600,1600}KW, safety factor η=0.9, rolling speed V i ={1.5, 2.1, 3.1, 4.0, 5.2, 6.7, 8.6, 10.3, 11.9} m / s, rolling temperature t = 1100 ° C, number of passes n = 9;
[0041] b) Given the steel grade Q195 to be expanded, its specification parameters mainly include the incoming strip thickness h0 = 18mm, initial strength σ s0 =195MPa, strip width B = 310mm;
[0042] c) define the process parameters involved in the calculation of the pressing capacity, mainly including the optimization search step length Δ=0.01;
[0043] d) Establishing the objective function: Establishing the objective function according to the pressure distribution ratio of each rack:
[0044] e) Assign the total pressure reduction Δh z =16.84mm.
[0045] f) The preset pressure distribution ratio of each rack is as follows: i ={0.14,0.10,0.08,0.06,0.06,0.04,0.04,0.02,0.01}.
[0046] g) Conditional judgment; after calculation:
[0047] The first pass rolling pressure is Δh1 = 2.3576 mm; the pass rolling pressure P1 = Bl c Q P K T K = 604.2KN; rolling power per pass
[0048] The second pass rolling pressure is Δh2 = 1.684 mm; the rolling pressure P2 = Bl c Q P K T K = 544KN; rolling power per pass
[0049] The third pass rolling pressure is Δh3 = 1.3472 mm; the rolling pressure is P3 = Bl c Q P K T K = 659.4KN; rolling power per pass
[0050] The 4th pass rolling pressure is Δh4 = 1.0104 mm; the pass rolling pressure P4 = Bl c Q P K T K = 793.4KN; rolling power per pass
[0051] The 5th pass rolling pressure is Δh5 = 1.0104 mm; the pass rolling pressure P5 = Bl c Q P K T K = 735KN; rolling power per pass
[0052] The 6th pass rolling pressure is Δh6 = 0.6736 mm; the pass rolling pressure P6 = Bl c Q P K T K = 1048.1KN; rolling power per pass
[0053] The 7th pass rolling pressure is Δh7 = 0.6736 mm; the pass rolling pressure P7 = Bl c Q P K T K = 1070KN; rolling power per pass
[0054] The 8th pass rolling pressure is Δh8 = 0.3368 mm; the pass rolling pressure P8 = Bl c Q P K T K = 1590.5KN; rolling power per pass
[0055] The 9th pass rolling pressure is Δh9 = 0.1684 mm; the pass rolling pressure P9 = Bl c Q P K T K = 2273.2KN; rolling power per pass
[0056] P i ={604.2,544,659.4,793.4,735,1048.1,1070,1590.5,2273.2}
[0057] F i ={284,216.2,332.4,378.4,244.9,482.5,531.2,581.2,599.6}
[0058] ηP maxi={6300,6300,5400,5400,5400,5400,5400,5400,5400,5400}
[0059] ηF maxi ={1620,1620,1620,1620,1440,1440,1440,1440,1440}
[0060] It is judged that the rolling force and rolling power of each stand meet the conditions, that is, P i ≤ηP imax and F i ≤ηF imax Established;
[0061] h) Establish a random direction method to optimize the pressure distribution ratio of each rack, and the calculation process is as follows:
[0062] h1) Obtain a feasible initial point λ according to the initial pressure distribution ratio i =[0.14,0.10,0.08,0.06,0.06,0.04,0.04,0.02,0.01] T ;
[0063] h2) Create k n-dimensional random unit vectors e according to the number of racks j , (j=1,2,…,k):
[0064]
[0065] h3) According to the optimized search step size Δ = 0.01, k random points are calculated as follows:
[0066] λ′ i =λ i +Δe j (j=1,2,…,k)
[0067] i) After calculation in step h), the cumulative reduction of each pass λ is obtained i =[0.3,0.22,0.15,0.13,0.08,0.05,,0.04,0.02,0.01] T , make conditional judgment on the optimized pressure distribution ratio;
[0068] i1) After judging condition λ i =[0.3,0.22,0.15,0.13,0.08,0.05,,0.04,0.02,0.01] T , 1 ≥ λ i ≥λ i+1 ≥0 and G(λ i ')=max{G(λ i ')j＝1,2,…,k}Established;
[0069] i2) Calculate the corresponding rolling pressure and rolling power:
[0070] The first pass rolling pressure is Δh1 = 2.38 mm; the rolling pressure P1 = Bl c Q P K T K = 1043KN; rolling power per pass
[0071] The second pass rolling pressure is Δh2 = 1.7 mm; the rolling pressure P2 = Bl c Q P K T K = 1122KN; rolling power per pass
[0072] The third pass rolling pressure is Δh3 = 1.36 mm; the rolling pressure is P3 = Bl c Q P K T K = 1260KN; rolling power per pass
[0073] The 4th pass rolling pressure is Δh4 = 1.02 mm; the pass rolling pressure P4 = Bl c Q P K T K = 1132KN; rolling power per pass
[0074] The 5th pass rolling pressure is Δh5 = 1.02 mm; the pass rolling pressure P5 = Bl c Q P K T K = 1531KN; rolling power per pass
[0075] The 6th pass rolling pressure is Δh6 = 0.68 mm; the pass rolling pressure P6 = Bl c Q P K T K = 1517KN; rolling power per pass
[0076] The 7th pass rolling pressure is Δh7 = 0.68 mm; the pass rolling pressure P7 = Bl c Q P K T K = 1518KN; rolling power per pass
[0077] The 8th pass rolling pressure is Δh8 = 0.34 mm; the pass rolling pressure P8 = Bl c Q P K T K = 2169KN; rolling power per pass
[0078] The 9th pass rolling pressure is Δh9 = 0.17 mm; the pass rolling pressure P9 = Bl c Q P K T K = 3403KN; rolling power per pass
[0079] P i ={1043,1122,1260,1132,1531,1517,1518,2169,3403}
[0080] F i ={120,155,198,263,378,403,506,651,1289}
[0081] ηP maxi ={6300,6300,5400,5400,5400,5400,5400,5400,5400,5400}
[0082] ηF maxi ={1620,1620,1620,1620,1440,1440,1440,1440,1440}
[0083] It is judged that the rolling force and rolling power of each stand meet the conditions, that is, P i ≤ηP imax and F i ≤ηF imax Established;
[0084] i3) Obviously G(λ i ) <G(λ i ') condition is established;
[0085] j) Objective function judgment If the condition is met, continue to step k);
[0086] k) Output the minimum rollable thickness h min =h0-Δh z =1.16mm.
[0087] Embodiment 2:
[0088] a) Collect the main equipment and process parameters of the rolling mill, including: working roll diameter D wi={650,650,400,400,400,400,400,400,400}, support roller diameter D b =700mm, maximum rolling pressure setting value P i ={7000,7000,6000,6000,6000,6000,6000,6000,6000}KN, maximum mill entrance tension τ b =5MPa, outlet tension τ f =5MPa, maximum rolling power setting value F i ={1800,1800,1800,1800,1600,1600,1600,1600,1600}KW, safety factor η=0.9, rolling speed V i ={1.5, 2.1, 3.1, 4.0, 5.2, 6.7, 8.6, 10.3, 11.9} m / s, rolling temperature t = 1100 ° C, number of passes n = 9;
[0089] b) Given the steel grade Q235 to be expanded, its specification parameters mainly include the incoming strip thickness h0 = 22mm, initial strength σ s0 =235MPa, strip width B = 330mm;
[0090] c) Define the process parameters involved in the calculation of the pressing capacity, mainly including the optimization search step Δ=0.01.
[0091] d) Establishing the objective function: Establishing the objective function according to the pressure distribution ratio of each rack:
[0092] e) Assign the total pressure reduction Δh z =20.66mm
[0093] f) The preset pressure distribution ratio of each rack is as follows: i ={0.14,0.10,0.08,0.06,0.06,0.04,0.04,0.02,0.01};
[0094] g) Conditional judgment; after calculation:
[0095] The first pass rolling pressure is Δh1 = 2.8924 mm; the pass rolling pressure P1 = Bl c Q P K T K = 598KN; rolling power per pass
[0096] The second pass rolling pressure is Δh2 = 2.066 mm; the rolling pressure is P2 = Bl c QP K T K = 539KN; rolling power per pass
[0097] The third pass rolling pressure is Δh3 = 1.6528 mm; the rolling pressure is P3 = Bl c Q P K T K = 653.8KN; rolling power per pass
[0098] The 4th pass rolling pressure is Δh4 = 1.2396 mm; the pass rolling pressure P4 = Bl c Q P K T K = 778.2KN; rolling power per pass
[0099] The 5th pass rolling pressure is Δh5 = 1.2396 mm; the pass rolling pressure P5 = Bl c Q P K T K = 728.2KN; rolling power per pass
[0100] The 6th pass rolling pressure is Δh6 = 0.8264 mm; the pass rolling pressure P6 = Bl c Q P K T K = 1040.2KN; rolling power per pass
[0101] The 7th pass rolling pressure is Δh7 = 0.8264 mm; the pass rolling pressure P7 = Bl c Q P K T K = 1061.3KN; rolling power per pass
[0102] The 8th pass rolling pressure is Δh8 = 0.4132 mm; the pass rolling pressure P8 = Bl c Q P K T K = 1580.1KN; rolling power per pass
[0103] The 9th pass rolling pressure is Δh9 = 0.2066 mm; the pass rolling pressure P9 = Bl c Q P K T K = 2260.4KN; rolling power per pass
[0104] It is judged that the rolling force and rolling power of each stand meet the conditions, that is, P i ≤ηP imax and F i ≤ηF imax Established.
[0105] h) Establish a random direction method to optimize the pressure distribution ratio of each rack, and the calculation process is as follows:
[0106] h1) Obtain a feasible initial point λ according to the initial pressure distribution ratio i =[0.14,0.10,0.08,0.06,0.06,0.04,0.04,0.02,0.01] T ;
[0107] h2) Create k n-dimensional random unit vectors e according to the number of racks j , (j=1,2,…,k):
[0108]
[0109] h3) According to the optimized search step size Δ = 0.01, k random points are calculated as follows:
[0110] λ′ i =λ i +Δe j (j=1,2,…,k)
[0111] i) After calculation in step h), the cumulative reduction of each pass λ is obtained i =[0.3,0.22,0.14,0.13,0.08,0.05,,0.04,0.02,0.01] T , make conditional judgment on the optimized pressure distribution ratio;
[0112] i1) After judging condition λ i =[0.3,0.22,0.14,0.13,0.08,0.05,,0.04,0.02,0.01] T , 1 ≥ λ i ≥λ i+1 ≥0 and G(λ i ')=max{G(λ i ') j＝1,2,…,k}Established;
[0113] i2) Calculate the corresponding rolling pressure and rolling power:
[0114] The first pass rolling pressure is Δh1 = 6.2 mm; the pass rolling pressure P1 = Bl c Q P K TK = 1192.44KN; rolling power per pass
[0115] The second pass rolling pressure is Δh2 = 4.54 mm; the rolling pressure P2 = Bl c Q P K T K = 1278.89KN; rolling power per pass
[0116] The third pass rolling pressure is Δh3 = 3.1 mm; the rolling pressure is P3 = Bl c Q P K T K = 1432.98KN; rolling power per pass
[0117] The 4th pass rolling pressure is Δh4 = 3.1 mm; the pass rolling pressure P4 = Bl c Q P K T K = 1026.53KN; rolling power per pass
[0118] The 5th pass rolling pressure is Δh5 = 1.76 mm; the pass rolling pressure P5 = Bl c Q P K T K = 2160.65KN; rolling power per pass
[0119] The 6th pass rolling pressure is Δh6 = 1.03 mm; the pass rolling pressure P6 = Bl c Q P K T K = 1685.26KN; rolling power per pass
[0120] The 7th pass rolling pressure is Δh7 = 0.83 mm; the pass rolling pressure P7 = Bl c Q P K T K = 1661.67KN; rolling power per pass
[0121] The 8th pass rolling pressure is Δh8 = 0.41 mm; the pass rolling pressure P8 = Bl c Q P K T K = 2358.37KN; rolling power per pass
[0122] The 9th pass rolling pressure is Δh9 = 0.21 mm; the pass rolling pressure P9 = Blc Q P K T K = 3681.35KN; rolling power per pass
[0123] P i ={1192,1279,1433,1027,2161,1685,1662,2358,3681}
[0124] F i ={117,151,193,255,365,391,490,632,1255}
[0125] ηP maxi ={6300,6300,5400,5400,5400,5400,5400,5400,5400,5400}
[0126] ηF maxi ={1620,1620,1620,1620,1440,1440,1440,1440,1440};
[0127] It is judged that the rolling force and rolling power of each stand meet the conditions, that is, P i ≤ηP imax and F i ≤ηF imax Established;
[0128] i3) Obviously G(λ i ) <G(λ i ') condition is established;
[0129] j) Objective function judgment If the condition is met, continue to step k);
[0130] k) Output the minimum rollable thickness h min =h0-Δh z =1.34mm.
[0131] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A method for predicting the minimum rollable thickness considering the reduction distribution ratio of hot-rolled narrow strip steel, characterized in that: The steps include: a) Collect key process and equipment parameters of the hot rolling mill, mainly including: working roll diameter D w , Support roller diameter D b , the maximum rolling pressure setting value P of the rolling mill max , mill entrance and exit tension τ b , τ f , maximum rolling power setting value F max , safety factor η, rolling speed V i , rolling temperature t, number of passes n; b) Given the steel grade and specification characteristics of the product, the main parameters include the incoming thickness of the strip h0, the initial strength σ s0 , the width of the strip B; c) define the process parameters involved in the calculation of the pressing capacity, mainly including the optimization search step length Δ=0.01; d) Establishing an objective function; Establishing an objective function according to the pressure distribution ratio: Where: i Determine the ratio of pressure distribution for each rack; e) Assign the total pressure reduction Δh z ; f) Randomly assign the initial pressure distribution ratio λ of each rack i ; g) Condition judgment: Make safety judgment on the rolling pressure and rolling power corresponding to the randomly given initial pressure distribution ratio of each stand: P i ≤ηP imax and F i ≤ηF imax Is it true, where P i is the rolling force of the stand at the i-th pass, F i is the rolling power of the i-th pass; if the condition is met, proceed to step h); if the condition is not met, proceed to step f) and randomly set the initial reduction distribution ratio again until success; h) Establish a random direction method to optimize the pressure distribution ratio of each rack; i) Determine whether the optimized press-down amount of each rack is established; the discriminant is as follows: If the condition is satisfied, step j) is executed; if not, step h) is executed to recalculate the pressing distribution ratio of each rack until the condition is satisfied; j) Objective function judgment: judge whether the objective function G(λ) = 1 holds; if so, output the minimum rollable thickness; if not, set Δh z =Δh z -Δ, and go to step f) to recalculate until the objective function is established; k) Output the minimum rollable thickness h min =h0-Δh z .
2. The method for predicting the minimum rollable thickness considering the reduction distribution ratio of hot-rolled narrow strip steel according to claim 1, characterized in that: The calculation method of rolling pressure and rolling power in step g) is as follows: g1) Calculate the pressure reduction of each rack according to the pressure reduction distribution ratio. The formula is as follows: g2)P i =Bl c 'Q P K T K; where: B is the average width of the rolled piece, in millimeters; l c is the contact arc length of the deformation zone; Q P is the external friction coefficient; K T is the influence coefficient of front and rear tension; K is the deformation resistance; g3) Rolling power F for the i-th pass i The calculation is done using the following formula: Where: ψ is the force arm coefficient, which is 0.04; Δh is the reduction of the i-th pass; V is the rolling speed of the i-th pass.
3. The method for predicting the minimum rollable thickness considering the reduction distribution ratio of hot-rolled narrow strip steel according to claim 1, characterized in that: In step h), a random direction method is established to optimize the pressing distribution ratio of each rack, and the specific process is as follows: h1) Obtain a feasible initial point λ according to the initial pressure distribution ratio i =[λ1,λ2,λ3…,λ n ] T ; h2) Create k n-dimensional random unit vectors e according to the number of racks j , (j=1,2,…,k): h3) According to the optimized search step size Δ = 0.01, k random points are calculated as follows: λ′ i =λ i +Δe j (j=1,2,…,k)。