CN108438191B - A kind of fishing boat driving device and device selection method - Google Patents

Abstract

The invention discloses a fishing boat driving device and a device selection method. The fishing boat driving device mainly consists of an energy management system device, a diesel generator set, a battery pack, a bidirectional DC/DC converter, a frequency converter, a motor and a propeller. The design process includes two parts: structural design and equipment selection. The system structure design mainly adopts the power supply scheme mainly based on diesel generator sets and supplemented by battery packs. There are four power supply modes to ensure that diesel generator sets will not be under-loaded. or overload. The equipment selection adopts the multi-objective particle swarm algorithm based on chaotic motion to optimize the selection process, which can provide a variety of selection schemes for decision makers to choose. the most satisfactory solution.

Description

A kind of fishing boat driving device and device selection method

technical field

The invention belongs to the technical field of design of electric propulsion systems for fishing boats, and in particular relates to a driving device for fishing boats and a method for selecting device equipment.

Background technique

The power system of the fishing boat is one of its core systems. The quality of the design scheme is directly related to the safety, stability and economy of the fishing boat. The traditional design scheme of the power system of the fishing boat adopts the empirical design method, that is, the motor with the appropriate power is selected according to the sailing conditions of the fishing boat, the inverter with a slightly larger power is selected according to the power of the motor, and the inverter with a slightly higher power is selected according to the power of the inverter. For large diesel generator sets, this design method is simple and easy to learn, but the matching between the various equipment of the power system is poor, and due to the large load changes in each working mode of the fishing boat, it is difficult for the diesel engine to be in the best working condition, the efficiency is poor, and the fuel consumption is low. higher.

Intelligent optimization algorithms such as genetic algorithm, particle swarm algorithm, ant colony algorithm, etc., are more and more widely used in aircraft and automobiles. The selection and design of the system needs to consider many factors. Most of the popular intelligent optimization algorithms set weights to solve multi-objective problems into single-objective problems. Since the preference information is set in advance, better ones will inevitably be missed. Feasible solution.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a driving device for a fishing boat and a method for selecting the device equipment, so as to improve the safety, stability and economy of the fishing boat.

The technical scheme adopted by the present invention to solve the technical problem is to provide a driving device for fishing boat, which is mainly composed of an energy management system device, a diesel generator set, a battery pack, a bidirectional DC/DC converter, a frequency converter, a motor and a propeller , the energy management system device is respectively connected with the diesel generator set, the battery pack and the bidirectional DC/DC converter. The energy management system uses the CAN bus communication method to transmit the set target power value of the diesel generator set, the target power value of the battery pack and the command to switch the energy transmission mode of the bidirectional DC/DC converter to the PLC controller through RS485 communication. , and through the PLC controller to complete the diesel generator set start, stop, increase and decrease the throttle function, the charging and discharging function of the battery pack and the switching function between the boost and buck modes of the bidirectional DC/DC converter; at the same time, the CAN bus communication is used. By means of RS485 communication, the SoC value of the battery pack and the required power value of the motor are transmitted to the energy management system device; the three-phase electrical output port of the diesel generator set is connected to the three-phase electrical input port of the inverter through the power cable; the battery The DC output terminal interface of the group is connected to the low-voltage DC terminal interface of the bidirectional DC/DC converter through the power cable, and the high-voltage DC terminal interface of the bidirectional DC/DC converter is connected to the DC busbar wiring input terminal of the inverter through the power cable; The three-phase electrical output port of the inverter is connected to the three-phase electrical input port of the motor through a power cable; the output of the motor is connected to the propeller through a connecting shaft.

According to the above technical scheme, the input signal of the energy management system device is processed through the internal PLC program to process the input signal, and the diesel generator set, the battery pack and the bidirectional DC/DC converter are controlled by the PLC controller according to the processed signal, Realize the switching of four power supply modes. In mode one, the battery pack supplies power to the inverter and the motor through the bidirectional DC/DC converter. The diesel generator set does not work, the PLC controller controls the battery pack to discharge, and the bidirectional DC/DC is in boost mode. , the diesel generator set stops; mode 2 is for the diesel generator set to supply power to the inverter and the motor, and at the same time through the DC bus of the inverter, through the bidirectional DC/DC converter to charge the battery pack, the PLC controller controls the battery pack to charge, and the bidirectional DC/DC The DC is in the step-down mode, the diesel generator set works; the third mode is that the diesel generator set supplies power to the inverter and the motor alone, the battery pack does not work, the PLC controller controls the battery pack and the bidirectional DC/DC stops working, and the diesel generator set works; Mode The fourth is that the diesel generator set and the battery set are combined to supply power to the inverter and the motor. The PLC controller controls the discharge of the battery set. The two-way DC/DC is in the boost mode, and the diesel generator set works.

The invention also provides a method for selecting a type of driving device for a fishing boat, the method includes the following steps, the first part: the process of finding the Pareto solution set by the multi-objective particle swarm algorithm.

Step 1, Chaos initializes the particle population:

Taking five factors of cost, fuel consumption, emission, weight and layout as the solution target of multi-objective particle swarm algorithm, a 5-dimensional vector z ₁ is randomly generated. Then, 100 components z ₁ , z ₂ , . . . , z ₁₀₀ are obtained according to the logistic equation of formula (1), where the value of μ is 4, forming a chaotic interval of 100 rows and 5 columns [z ₁ ; z ₂ ; .. .; z ₁₀₀ ], and then map the chaotic interval [z _l ; z ₂ ;...; z ₁₀₀ ] to the value range of the optimization variable (in the present invention, the optimization variable of the multi-objective particle swarm optimization is the system equipment, namely 6 types of diesel generator sets, 6 types of battery packs and 6 types of motors; where b _j and a _j are the upper and lower limits of the optimization variables, then b _j =6, a _j = 0; the value of x _ij is rounded) to form an initial particle population (100 particles) with 100 rows and 5 columns, that is, the equipment selection scheme, such as the first scheme (particles) [x ₁ , 1 , x _{1, 2} , x _1,3 , x _1,4 , x _1,5 ]=[123564], the second scheme (particles)[x _2,1 ,x _2,2 ,x _2,3 ,x _2,4 ,x _{2 , 5} ] = [654312], a total of 100 scenarios (particles).

Z _η+1 = μz _η (1−z _η )n=0, 1, 2, ...; 0<z _η <1; μ∈[0,4] (1)

X _ij =α _j +(b _j -α _j )z _ij i=1,2,...,N; j=1,2,...,D (2)

Step 2, define the initial individual extremum and global extremum of the population:

Define the current position of each particle i (that is, the initialized value of each particle) as the individual extreme value P _i , and randomly generate the initial particle swarm velocity vi ₍₁₎ (vi ₍₁₎ is a 5-dimensional vector), using non-dominated Evaluate the idea (delete the worst scheme among the schemes, such as one of the schemes has higher cost, higher fuel consumption, higher emission, larger weight, and difficulty in layout than the other scheme, then the scheme is deleted) to obtain the first generation solution set (except the deleted scheme) In addition, the other solutions constitute the first generation solution set), and one of the solutions is randomly selected, which is defined as the global extreme value P _g .

Step 3, population iteration:

Update the velocity and position of the particle swarm according to the velocity update formula (3) and position update formula (4) of the particle swarm (after the update, the velocity and position of each particle are 5-dimensional vectors), and compare the updated particle swarm with the previous generation. The solution set is combined to form a contemporary population, and the position of the contemporary particle is the contemporary individual extreme value P _i , and then the non-dominant evaluation idea is used to obtain the contemporary solution set, and a particle is randomly selected as the global extreme value P _g in the contemporary solution set, such as the first time The particle swarm updated after iteration is merged with the first-generation solution set to form the second-generation swarm. The position of the second-generation particle is the second-generation individual extreme value P _i , and then the non-dominated evaluation idea is adopted to obtain the second-generation solution set. A particle is randomly selected as the second-generation global extreme value P _g in the second-generation solution set,

v _i (t+1)=w×v _i (t)+C ₁ ×r ₁ ( _{pi -x i (} t))+C ₂ ×r ₂ (p _{g -xi} (t)) (3)

x _i (t+1)=x _i (t)+v _i (t+1) (4)

Among them, p _i and p _g are the individual extreme values and global extreme values, v _i (t) and v _i (t+1) are the particle velocities at the t-th iteration and the t+1-th iteration, _xi (t ) and x _i (t+1) are the particle positions at the t-th iteration and the t+1-th iteration, w is the inertia factor, C ₁ and C ₂ are the cognitive learning factor and social learning factor, r1, r2∈ [0,1] is a random variable that obeys a uniform distribution.

Step 4, local chaotic optimization of global extreme value P _g :

According to formula (5), P _g is mapped to the definition domain [0,1] of the logistic equation, where b _j and a _j are the upper and lower limits of the optimization variables, b _j =6, a _j =0. Then generate 50 chaotic variables z _{1 ,} z _{2 ,…} , z ₅₀ according to formula (1), as in step 1, map them to the value interval of the optimization variables, and obtain 50 particles, and obtain the global pole according to the non-dominated evaluation idea. value solution set, and then randomly select one of the particles as the global extreme value p' _g , and at the same time p' _g replaces the position of any particle in the population,

Step 5, return to step 3, until the number of iterations ends (the number of iterations is 100), and output the remaining solutions (a variety of different solutions), that is, the Pareto solution set.

Part II: The decision-making process.

Step 6, approximating the ideal solution sorting method to sort the Pareto solution set:

According to the multi-objective particle swarm optimization algorithm, there are many alternative schemes, all of which are feasible for the decision makers, but how should the decision makers choose the most suitable scheme from these schemes. The present invention uses the approximation ideal solution sorting method to sort these schemes according to the requirements of the decision maker, and provides the most suitable scheme to the decision maker. For the backup scheme, the optimal scheme is set as S ⁺ , and the worst scheme is set as S ^— . For any backup scheme S _i , according to formula (6) and formula (7), the best and worst schemes can be calculated according to the formula Then, according to formula (8), the relative closeness degree C _i of the scheme is obtained, that is, the degree of closeness of the scheme between the optimal scheme and the worst scheme to the optimal scheme, C _i =1, indicating that the most The best solution, C _i =0, represents the worst solution.

The approach to the ideal solution sorting method is to sort all Pareto solution sets from top to bottom according to the relative _closeness C _{i .} requirements of decision makers.

Equations (6) and (7) are the distances between the evaluation scheme Si and the positive and negative ideal solutions, denoted as d _i ⁺ and d _i ⁻ , and formula _{(8) is the calculation formula for the relative closeness C i of the} scheme Si .

Step 7, select the most preferred solution: according to the sorting result of step 1, select the solution with the largest value of relative closeness C _i .

The beneficial effects of the present invention are: the fishing boat in the present invention adopts an electric propulsion system structure, and its design process includes two parts: structural design and equipment selection. The power supply scheme, with four power supply modes, ensures that the diesel generator set will not be under-loaded or overloaded. The equipment selection adopts the multi-objective particle swarm algorithm based on chaotic motion to optimize the selection process, which can provide a variety of selection schemes for decision makers to choose. the most satisfactory solution.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

Fig. 1 is a schematic diagram of a fishing boat driving device;

Fig. 2 The selection and design process of the power system of the lure boat.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

In the embodiment of the present invention, a driving device for a fishing boat is provided, and the structure scheme of the fishing boat designed by the present invention is composed of three parts: a control system, a power supply system and a propulsion system. As shown in Figure 1, the main equipment of the control system is the energy management system device 7; the main equipment of the power supply system is a diesel generator set 1, a battery pack 6 and a bidirectional DC/DC converter 5; the main equipment of the propulsion system is a frequency converter 2, a motor 3 and propeller 4. Provided is a fishing boat driving device, which is mainly composed of an energy management system device, a diesel generator set, a battery pack, a bidirectional DC/DC converter, a frequency converter, a motor and a propeller. The energy management system device is respectively connected with the diesel generator set and the battery pack. Connect to a bidirectional DC/DC converter. The energy management system uses the CAN bus communication method to transmit the set target power value of the diesel generator set, the target power value of the battery pack and the command to switch the energy transmission mode of the bidirectional DC/DC converter to the PLC controller through RS485 communication. , and through the PLC controller to complete the diesel generator set start, stop, increase and decrease the throttle function, the charging and discharging function of the battery pack and the switching function between the boost and buck modes of the bidirectional DC/DC converter; at the same time, the CAN bus communication is used. By means of RS485 communication, the SOC value of the battery pack and the required power value of the motor are transmitted to the energy management system device; the three-phase electrical output port of the diesel generator set is connected to the three-phase electrical input port of the inverter through the power cable; the battery The DC output terminal interface of the group is connected to the low-voltage DC terminal interface of the bidirectional DC/DC converter through the power cable, and the high-voltage DC terminal interface of the bidirectional DC/DC converter is connected to the DC busbar wiring input terminal of the inverter through the power cable; The three-phase electrical output port of the inverter is connected to the three-phase electrical input port of the motor through a power cable; the output of the motor is connected to the propeller through a connecting shaft.

The power supply system mainly supplies power to the frequency converter and the motor through a diesel generator set and a battery pack. Diesel generator sets can only provide electrical energy as an energy source, while battery packs can not only provide electrical energy as an energy source, but also serve as an energy storage device to recover electrical energy.

The propulsion system mainly controls the start, stop, acceleration and deceleration of the motor through the frequency converter, and then the motor drives the propeller to rotate through the connecting shaft, thereby propelling the ship forward.

Further, the input signal of the energy management system device is processed through the internal PLC program to process the input signal, and the diesel generator set, the battery pack and the two-way DC/DC converter are controlled by the PLC controller according to the processed signal, so as to realize the Switching between four power supply modes, mode 1 is that the battery pack supplies power to the inverter and the motor through the bidirectional DC/DC converter, the diesel generator set does not work, the PLC controller controls the discharge of the battery pack, the bidirectional DC/DC is in boost mode, and the diesel generator set is in boost mode. The generator set is stopped; in mode 2, the diesel generator set supplies power to the inverter and the motor, and at the same time, the DC bus of the inverter is used to charge the battery pack through the bidirectional DC/DC converter. The PLC controller controls the battery pack to charge, and the bidirectional DC/DC is in Step-down mode, the diesel generator set works; mode three is that the diesel generator set supplies power to the inverter and the motor alone, the battery pack does not work, the PLC controller controls the battery pack and bidirectional DC/DC to stop working, and the diesel generator set works; mode four: The diesel generator set and the battery set are combined to supply power to the inverter and the motor, the PLC controller controls the discharge of the battery set, the bidirectional DC/DC is in the boost mode, and the diesel generator set works.

The main equipment selection and design process of the power system of the fishing boat designed by the invention consists of two parts. The first part is responsible for selecting parts from a large number of schemes according to the factors (such as cost, fuel consumption, emissions, weight, layout, etc.) that decision makers (such as designers, shipyards, ship owners, etc.) need to consider during construction and operation. Appropriate solutions (there is no absolute best or worst solution for these solutions). The second part is to screen out the optimal solution according to the specific opinion of a decision maker.

The present invention provides a type selection method for a fishing boat driving device, as shown in FIG. 2 , the method includes the following steps:

The first part: the multi-objective particle swarm algorithm to find the Pareto solution set process.

Step 1, Chaos initializes the particle population:

Taking five factors of cost, fuel consumption, emission, weight and layout (decision-makers decide which factors to consider) as the solution target of multi-objective particle swarm algorithm, a 5-dimensional vector z ₁ is randomly generated. Then, ₁₀₀ components z ₁ , _{z 2} , _. .; z _l00 ], and then according to formula (2), the chaotic interval [z ₁ ; z ₂ ; ... _; is the system equipment, namely 6 types of diesel generator sets, 6 types of battery packs and 6 types of motors; where b _j and a _j are the upper and lower limits of the optimization variables, then b _j =6, a _j = 0; the value of x _ij is rounded) to form an initial particle population (100 particles) with 100 rows and 5 columns, that is, the equipment selection scheme, such as the first scheme (particles) [x ₁ , 1 , x _{1, 2} , x _1,3 , x _1,4 , x 1,5 ]=[ ₁₂₃₅₆₄ ], the second scheme (particles)[x _2,1 ,x _2,2 ,x _2,3 ,x _2,4 ,x _{2 , 5} ] = [654312], a total of 100 scenarios (particles).

Z _η+1 = μz _η (1−z _η )a=0,1,2,...; 0<Z _η <1; μ∈[0,4] (1)

X _ij =α _j +(b _j -α _j )z _ij i=1,2,...,N; j=1,2,...,D (2)

Step 2, define the initial individual extremum and global extremum of the population:

Define the current position of each particle i (that is, the initialized value of each particle) as the individual extreme value P _i , and randomly generate the initial particle swarm velocity vi ₍₁₎ (vi ₍₁₎ is a 5-dimensional vector), using non-dominated Evaluate the idea (delete the worst scheme among the schemes, such as one of the schemes has higher cost, higher fuel consumption, higher emission, larger weight, and difficulty in layout than the other scheme, then the scheme is deleted) to obtain the first generation solution set (except the deleted scheme) In addition, the other solutions constitute the first generation solution set), and one of the solutions is randomly selected, which is defined as the global extreme value P _g .

Step 3, population iteration:

Update the velocity and position of the particle swarm according to the velocity update formula (3) and position update formula (4) of the particle swarm (after the update, the velocity and position of each particle are 5-dimensional vectors), and compare the updated particle swarm with the previous generation. The solution set is combined to form a contemporary population, and the position of the contemporary particle is the contemporary individual extreme value P _i , and then the non-dominant evaluation idea is used to obtain the contemporary solution set, and a particle is randomly selected as the global extreme value P _g in the contemporary solution set, such as the first time The particle swarm updated after iteration is merged with the first-generation solution set to form the second-generation swarm. The position of the second-generation particle is the second-generation individual extreme value P _i , and then the non-dominated evaluation idea is adopted to obtain the second-generation solution set. A particle is randomly selected as the second-generation global extreme value P _g in the second-generation solution set,

v _i (t+1)=w×v _i (t)+C ₁ ×r ₁ ( _{pi -x i (} t))+C ₂ ×r ₂ (p _{g -xi} (t)) (3)

x _i (t+1)=x _i (t)+v _i (t+1) (4)

Among them, p _i and p _g are the individual extreme values and global extreme values, v _i (t) and v _i (t+1) are the particle velocities at the t-th iteration and the t+1-th iteration, _xi (t ) and x _i (t+1) are the particle positions at the t-th iteration and the t+1-th iteration, w is the inertia factor, C ₁ and C ₂ are the cognitive learning factor and social learning factor, r1, r2∈ [0,1] is a random variable that obeys a uniform distribution.

Step 4, local chaotic optimization of global extreme value P _g :

According to formula (5), P _g is mapped to the definition domain [0,1] of the logistic equation, where b _j and a _j are the upper and lower limits of the optimization variables, b _j =6, a _j =0. Then generate 50 chaotic variables z ₁ , z _{2 ,…} , z ₅₀ according to formula (1), as in step 1, map them to the value range of the optimized variables to obtain 50 particles, and obtain the global pole according to the non-dominated evaluation idea. value solution set, and then randomly select one of the particles as the global extreme value p' _g , and at the same time p' _g replaces the position of any particle in the population,

Step 5, return to step 3, until the number of iterations ends (the number of iterations is 100), and output the remaining solutions (a variety of different solutions), that is, the Pareto solution set.

Part II: The decision-making process.

Step 6, approximating the ideal solution sorting method to sort the Pareto solution set.

According to the multi-objective particle swarm optimization algorithm, there are many alternative schemes, all of which are feasible for the decision makers, but how should the decision makers choose the most suitable scheme from these schemes. The present invention uses the approximation ideal solution sorting method to sort these schemes according to the requirements of the decision maker, and provides the most suitable scheme to the decision maker. For the backup plan, set the optimal plan as S ⁺ (the most ideal result for decision makers to consider the factors that need to be considered in the model selection, such as the cost of a million, the fuel consumption of b liters, the emission of c grams, the weight of d tons, and the layout of e cubic meters), the worst solution is S ^— (the most unsatisfactory result of the factors that decision makers need to consider in the selection, such as the cost of A million, the fuel consumption of B liters, the emission of C grams, the weight of D tons, and the layout of E cubic meters), for any alternative S _i , the distance between the scheme and the optimal and worst schemes can be obtained according to formula (6) and formula (7), and then the scheme can be obtained according to formula (8) The relative closeness C _i of , that is, the degree of closeness of the solution to the optimal solution between the optimal solution and the worst solution, C _i =1, represents the optimal solution, and C _i =0, represents the worst solution.

The approach to the ideal solution sorting method is to sort all Pareto solution sets from top to bottom according to the relative _closeness C _{i .} requirements of decision makers.

Equations (6) and (7) are the distances between the evaluation scheme Si and the positive and negative ideal solutions, denoted as d _i ⁺ and d _i ⁻ , and formula _{(8) is the calculation formula for the relative closeness C i of the} scheme Si .

Step 7, select the most preferred solution: according to the sorting result of step 1, select the solution with the largest value of relative closeness C _i .

It should be understood that, for those skilled in the art, improvements or changes can be made according to the above description, and all these improvements and changes should fall within the protection scope of the appended claims of the present invention.

Claims (1)

1. a method for selecting type of fishing boat driving device equipment, is characterized in that, the method comprises the following steps, Step 1, Chaos initializes the particle population: Taking the five factors of cost, fuel consumption, emission, weight and layout as the solution target of the multi-objective particle swarm algorithm, a 5-dimensional vector z ₁ is randomly generated, and then 100 components z ₁ , z ₂ are obtained according to the logistic equation of formula (1). ,...,z ₁₀₀ , where the value of μ is 4 to form _a chaotic interval [z ₁ ; z _{2 ;} ... _; ...; z ₁₀₀ ] is mapped to the value range of the optimization variable, that is, the equipment selection scheme, z _n+1 = μz _n (1−z _n ) n=0, 1, 2, . . . ; 0<z _n <1; μ∈[0,4] (1) x _ij =a _j +(b _j -a _j )z _ij i=1,2,...,N; j=1,2,...,D (2) Step 2, define the initial individual extremum and global extremum of the population: Define the current position of each particle i as the individual extreme value P _i , randomly generate the initial particle swarm velocity v _i(1) , use the non-dominated evaluation idea to obtain the first generation solution set, randomly select one of the solutions, and define it as the global extreme value P _g ; Step 3, population iteration: Update the speed and position of the particle swarm according to the velocity update formula (3) and the position update formula (4) of the particle swarm, and combine the updated particle swarm with the previous generation solution set to form a contemporary population, and the contemporary particle position is the contemporary individual extreme value P _i , and then adopt the non-dominated evaluation idea to obtain the contemporary solution set, randomly select a particle in the contemporary solution set as the global extreme value P _g , and then adopt the non-dominated evaluation idea to obtain the second generation solution set, in the second generation solution set Randomly select a particle as the second generation global extreme value P _g , v _i (t+1)=w×v _i (t)+C ₁ ×r ₁ ( _{pi -x i (} t))+C ₂ ×r ₂ (p _{g -xi} (t)) (3) x _i (t+1)=x _i (t)+v _i (t+1) (4) Among them, p _i and pg are the individual extreme values and global extreme values, v _i (t) and v _i (t+1) are the particle velocities at the t-th iteration and the t+1-th iteration, and x _i (t) and x _i (t+1) are the particle positions at the t-th iteration and the t+1-th iteration, w is the inertia factor, C ₁ and C ₂ are the cognitive learning factor and social learning factor, r1,r2∈[ 0,1], is a random variable obeying a uniform distribution; Step 4, local chaotic optimization of global extreme value P _g : According to the formula (5), P _g is mapped to the definition domain [0,1] of the Logistic equation, where b _j and a _j are the upper and lower limits of the optimization variables, respectively, b _j =6, a _j =0, and then according to the formula ( 1) Generate 50 chaotic variables z ₁ , z ₂ ,..., z ₅₀ , as in step 1, map them to the value interval of the optimization variables, get 50 particles, and obtain the solution set of the global extremum according to the non-dominated evaluation idea , and then randomly select one of the particles as the global extreme value p' _g , and at the same time p' _g replaces the position of any particle in the population,

Step 5, return to step 3, until the number of iterations ends, output the remaining solutions, that is, the Pareto solution set; Step 6, approximating the ideal solution sorting method to sort the Pareto solution set: For the backup scheme, the optimal scheme is set as S ⁺ , and the worst scheme is set as S ^— . For any backup scheme S _i , according to formula (6) and formula (7), the best and worst schemes can be calculated according to the formula Then, according to formula (8), the relative closeness degree C _i of the scheme is obtained, that is, the degree of closeness of the scheme between the optimal scheme and the worst scheme to the optimal scheme, C _i =1, indicating that the most The optimal solution, C _i =0, represents the worst solution;

Equations (6) and (7) are the distances between the evaluation scheme Si and the positive and negative ideal solutions, denoted as d _i ⁺ and d _i ⁻ , and formula _{(8) is the calculation formula for the relative closeness C i of the} scheme Si ; Step 7, select the most preferred solution: according to the sorting result of step 1, select the solution with the largest value of relative closeness C _i .

Images