CN109754057B - Reducer dead weight design method combined with speed disturbance mechanism chaotic locust algorithm - Google Patents
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Abstract
The invention relates to a reducer dead weight design method combining a speed disturbance mechanism chaotic locust algorithm, which comprises the steps of firstly, improving the traditional locust algorithm by adopting a chaotic strategy and a speed disturbance mechanism; and then adopting the locust algorithm improved in the step S1 to solve the dead weight design method of the speed reducer. The invention can better design the speed reducer with smaller self weight.
Description
Technical Field
The invention relates to the field of reducer design, in particular to a reducer dead weight design method combining a speed disturbance mechanism chaotic locust algorithm.
Background
Locust optimization (GOA) is a natural heuristic that mimics locust clustering behavior, and is a novel group intelligence algorithm proposed in 2017 by Shahrzad Saremi et al, an australian scholars. Some researchers have performed algorithm improvement and application.
Praven Tumuluru et al propose a chronologically ordered locust algorithm and use for gene selection and cancer classification. Ali Asghar Heidari et al propose a training method combining locust algorithm for multi-layer perceptive neural network. Devenda Potnuru et al, in conjunction with the locust algorithm, increase the drive speed of a brushless dc motor. In conclusion, the locust algorithm has some defects and development potential, and is worthy of improvement and application development.
For the design problem of the speed reducer, the problem is a nonlinear programming problem under multiple constraint conditions, and belongs to the NP difficult problem. Compared with a deterministic algorithm, the speed reducer with smaller dead weight is designed after parameter optimization is carried out through the locust algorithm. Teaching-learning-based optimization algorithm (TLBO) has been used for reducer design, but the design effect still needs to be improved.
Disclosure of Invention
In view of the above, the invention aims to provide a speed reducer dead weight design method combining a speed disturbance mechanism chaotic locust algorithm, which can better design a speed reducer with a smaller dead weight.
The invention is realized by adopting the following scheme: a speed reducer dead weight design method combined with a speed disturbance mechanism chaotic locust algorithm specifically comprises the following steps:
step S1: improving the traditional locust algorithm by adopting a chaos strategy and a speed disturbance mechanism;
step S2: and (5) adopting the locust algorithm improved in the step S1 to solve the dead weight design method of the speed reducer.
Further, in step S1, the improvement of the traditional locust algorithm by using the chaos strategy specifically comprises: chaotic initialization of the population by adopting Logistic mapping:
Cn＝μCn-1(I-Cn-1)
in the formula, CnIs a random number of 0-1, when the parameter mu is 4, a set of sequences in complete chaos can be obtained.
Further, the traditional locust algorithm is improved by adopting a speed disturbance mechanism, and the improvement is specifically as follows: introducing a group of velocity vectors and velocity updating formulas in the traditional locust algorithm, wherein the velocity of an individual is defined as a d-dimensional vector: vi d＝(Vi1,Vi2,…Vid) (ii) a To velocity Vi dRandom initialization is carried out, and the speed and position updating formula of the ith individual is as follows:
wherein w is the inertial weight; r is a value satisfying a Gaussian distribution between 0 and 1. Ranging between-0.5 and 0.5.
Further, the value of the inertial weight w is 0.9.
Further, the speed V of the individual locusti dIn the range of-0.5 to 0.5.
Further, step S2 specifically includes the following steps:
step S21: the dead weight design problem of the speed reducer is set to be composed of four linear constraints and seven nonlinear constraints. The mathematical model of the reducer design problem is as follows:
the defining variables are:
the objective function is:
the constraint conditions are as follows:
the domain is defined as:
in the formula, x1,x2,x3,x4,x5,x6,x7Respectively representing the width of a bull gear in an output shaft of a speed reducer, the width of a pinion gear of an intermediate shaft, the distance between a bearing and the pinion gear in the input shaft, the shaft spacing of the input shaft, the distance between the bull gear and the bearing in the output shaft, the diameter of the input shaft and the diameter of the output shaft;
step S22: and applying an improved locust algorithm to the solution of the mathematical model, wherein the aim is to minimize an objective function and obtain a reducer with the minimum dead weight.
Further, step S22 specifically includes the following steps:
step S221: initializing all parameters including a population size N and iteration times t;
step S222: chaotic initialization of the population by adopting Logistic mapping;
step S223: setting T as an optimal solution;
step S224: judging whether the current iteration number is smaller than the maximum iteration number, if so, entering a step S225, otherwise, entering a step S228;
step S225: checking the upper bound and the lower bound of the solution, and updating the adaptive coefficient c in the traditional locust individual position updating formula;
step S226: calculating according to the objective function to obtain a fitness value, and judging whether the current individual i is smaller than the population size N, if so, entering step S227, otherwise, entering step S228;
step S227: defining a speed vector by adopting a speed disturbance mechanism, and updating the speed; simultaneously, updating the position;
step S228: and substituting the optimal position into the solution calculated by the objective function, namely outputting the optimal solution T by the optimal solution.
Compared with the prior art, the invention has the following beneficial effects: the invention abstracts the design problem of the reducer into 7 structural parameters, 11 constraint conditions and 1 mathematical model of an objective function for the optimization design of the algorithm. Aiming at the defects that the locust algorithm is easy to generate premature phenomena, the search performance is poor and the like, the chaotic strategy and the speed disturbance mechanism are adopted to improve the locust algorithm, and aiming at the common reducer design effect of the current method, the design problem of the reducer is optimized by utilizing the improved locust algorithm, so that the reducer with smaller self weight can be well designed.
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FIG. 1 is a schematic flow chart of the optimization of reducer design problem by using improved locust algorithm according to the embodiment of the present invention.
Fig. 2 is a schematic diagram of an output result according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a model of a retarder according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the embodiment provides a reducer dead weight design method combining a speed disturbance mechanism chaotic locust algorithm, which specifically includes the following steps:
step S1: improving the traditional locust algorithm by adopting a chaos strategy and a speed disturbance mechanism;
step S2: and (5) adopting the locust algorithm improved in the step S1 to solve the dead weight design method of the speed reducer.
In particular, the traditional locust algorithm is specifically as follows:
the locust individual position updating formula is as follows:
in the formula (I), the compound is shown in the specification,
is the position of the ith individual locust in the d dimension; the parameter c is an adaptive coefficient and is updated according to the formula (2); ubdAnd lbdUpper and lower bounds of the D-dimensional search space, respectively; s represents the action intensity among the locust individuals and is updated according to the formula (3); dijIs the distance between the i-th and j-th locusts, i.e. dij＝|xj-xi|；TdThe optimal position in D dimension.
Wherein, the updating formula of the parameter c is as follows:
c ranges from 0.00001 to 1, cmaxAnd cminRespectively the maximum value and the minimum value of the adaptive coefficient; t is the current number of iterations, tmaxIs the maximum number of iterations;
wherein, the action strength s is updated according to the following formula:
wherein f is the strength of the attraction force; l is an attractive length ratio.
In this embodiment, in step S1, the improvement of the traditional locust algorithm by using the chaos strategy specifically includes: chaotic initialization of the population by adopting Logistic mapping:
Cn＝μCn-1(1-Cn-1) (4)
in the formula, CnIs a random number of 0-1, when the parameter mu is 4, a set of sequences in complete chaos can be obtained.
In this embodiment, the improvement of the traditional locust algorithm by using a speed disturbance mechanism specifically includes: introducing a group of velocity vectors and velocity updating formulas in the traditional locust algorithm, wherein the velocity of an individual is defined as a d-dimensional vector: vi d＝(Vi1,Vi2,…Vid) (ii) a To velocity Vi dRandom initialization is carried out, and the speed and position updating formula of the ith individual is as follows:
wherein w is the inertial weight; r is a value satisfying a Gaussian distribution between 0 and 1. Ranging between-0.5 and 0.5.
In this embodiment, the inertial weight w takes a value of 0.9.
In this example, the speed V of an individual locusti dIn the range of-0.5 to 0.5.
In this embodiment, step S2 specifically includes the following steps:
step S21: the purpose of the retarder design problem is to minimize the self weight of the retarder. The self-weight of the reducer is influenced by factors such as bending stress of the gear, surface stress, lateral deflection, stress constraint of the shaft and the like. The present embodiment sets the dead weight design problem of the speed reducer to be composed of four linear constraints and seven nonlinear constraints. The mathematical model of the reducer design problem is as follows:
the defining variables are:
the objective function is:
the constraint conditions are as follows:
the domain is defined as:
as shown in FIG. 3, x1Representing the width, x, of a gear wheel in the output shaft2Pinion width, x, of the intermediate shaft3Indicating the distance, x, of the bearing from the pinion in the input shaft4Representing the axial spacing, x, of the input shaft5Indicating the distance, x, of the gearwheel in the output shaft from the bearing6Denotes the diameter, x, of the input shaft7Indicating the diameter of the output shaft;
step S22: and applying an improved locust algorithm to the solution of the mathematical model, wherein the aim is to minimize an objective function and obtain a reducer with the minimum dead weight.
In this embodiment, step S22 specifically includes the following steps:
step S221: initializing all parameters including a population size N and iteration times t;
step S222: chaotic initialization of the population by adopting Logistic mapping;
step S223: setting T as an optimal solution;
step S224: judging whether the current iteration number is smaller than the maximum iteration number, if so, entering a step S225, otherwise, entering a step S228;
step S225: checking the upper bound and the lower bound of the solution, and updating the adaptive coefficient c in the traditional locust individual position updating formula;
step S226: calculating according to the objective function to obtain a fitness value, and judging whether the current individual i is smaller than the population size N, if so, entering step S227, otherwise, entering step S228;
step S227: defining a speed vector by adopting a speed disturbance mechanism, and updating the speed; simultaneously, updating the position;
step S228: and substituting the optimal position into the solution calculated by the objective function, namely outputting the optimal solution T by the optimal solution.
Preferably, the embodiment uses the improved locust algorithm (CV-GOA) to solve the reducer design problem, and compares the design result with the traditional locust algorithm (GOA), teaching and learning optimization algorithm (TLBO), and the data result is shown in fig. 2. The aim is to minimize the objective function, i.e. to design a reducer with minimum deadweight.
The program was set to population 25, the maximum number of iterations was 200, the program was run 30 times repeatedly, and the output results are shown in fig. 2. As can be seen from FIG. 2, CV-GOA optimizes 7 structural parameters, among which X1, X5 and X6, X7 are better design optimization. In addition, the design effect of the final objective function of the CV-GOA algorithm is obviously superior to that of other 2 algorithms, the CV-GOA algorithm calculates the minimum objective function value, and then the TLBO algorithm and finally the GOA algorithm are carried out. This means that CV-GOA (the method of the present embodiment) can effectively solve the problems in designing the reduction gear, and can design a reduction gear with a smaller self weight than other methods.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (3)
1. A speed reducer dead weight design method combined with a speed disturbance mechanism chaotic locust algorithm is characterized by comprising the following steps: the method comprises the following steps:
step S1: improving the traditional locust algorithm by adopting a chaos strategy and a speed disturbance mechanism;
step S2: adopting the locust algorithm improved in the step S1 to solve the dead weight design method of the speed reducer;
in step S1, the chaos strategy is adopted to improve the traditional locust algorithm, specifically: chaotic initialization of the population by adopting Logistic mapping:
Cn＝μCn-1(1-Cn-1)
in the formula, CnWhen the parameter mu is 4, a group of sequences in complete chaos can be obtained;
the traditional locust algorithm is improved by adopting a speed disturbance mechanism, and the method specifically comprises the following steps: introducing a group of velocity vectors and velocity updating formulas in the traditional locust algorithm, wherein the velocity of an individual is defined as a d-dimensional vector: vi d＝(Vi1,Vi2,...Vid) (ii) a To velocity Vi dPerforming random initialization, speed and position update of the ith individualThe formula is as follows:
wherein w is the inertial weight; r is a number satisfying a Gaussian distribution between 0 and 1; ranging between-0.5 and 0.5;
step S2 specifically includes the following steps:
step S21: the self-weight design problem of the speed reducer is set to be composed of four linear constraints and seven nonlinear constraints; the mathematical model of the reducer design problem is as follows:
the defining variables are:
the objective function is:
the constraint conditions are as follows:
the domain is defined as:
in the formula, x1,x2,x3,x4,x5,x6,x7Respectively representing the width of a bull gear in an output shaft of a speed reducer, the width of a pinion gear of an intermediate shaft, the distance between a bearing and the pinion gear in the input shaft, the shaft spacing of the input shaft, the distance between the bull gear and the bearing in the output shaft, the diameter of the input shaft and the diameter of the output shaft;
step S22: applying an improved locust algorithm to the solution of the mathematical model, wherein the aim is to minimize an objective function and obtain a reducer with the minimum dead weight;
step S22 specifically includes the following steps:
step S221: initializing all parameters including a population size N and iteration times t;
step S222: chaotic initialization of the population by adopting Logistic mapping;
step S223: setting T as an optimal solution;
step S224: judging whether the current iteration number is smaller than the maximum iteration number, if so, entering a step S225, otherwise, entering a step S228;
step S225: checking the upper bound and the lower bound of the solution, and updating the adaptive coefficient c in the traditional locust individual position updating formula;
step S226: calculating according to the objective function to obtain a fitness value, and judging whether the current individual i is smaller than the population size N, if so, entering step S227, otherwise, entering step S228;
step S227: defining a speed vector by adopting a speed disturbance mechanism, and updating the speed; simultaneously, updating the position;
step S228: and substituting the optimal position into the solution calculated by the objective function, namely outputting the optimal solution T by the optimal solution.
2. The reducer dead weight design method combining the speed disturbance mechanism chaotic locust algorithm according to claim 1, characterized in that: the value of the inertial weight w is 0.9.
3. The reducer dead weight design method combined with the speed disturbance mechanism chaotic locust algorithm according to claim 1, characterized in that: speed V of locust individuali dIn the range of-0.5 to 0.5.
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