CN114417712B - Airship propeller reliability estimation method based on chaos initialization SSA-BP neural network - Google Patents

Airship propeller reliability estimation method based on chaos initialization SSA-BP neural network Download PDF

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CN114417712B
CN114417712B CN202210000110.2A CN202210000110A CN114417712B CN 114417712 B CN114417712 B CN 114417712B CN 202210000110 A CN202210000110 A CN 202210000110A CN 114417712 B CN114417712 B CN 114417712B
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刘坤澎
王海峰
职鑫鑫
聂波
程柳开
口启慧
江泓鑫
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Abstract

The invention discloses a method for estimating the reliability of an airship propeller based on a chaos initialization SSA-BP neural network, which is used for determining main factors influencing the strain of a blade under the design resident air working condition of the propeller; constructing a training/testing input data set of the chaotic initialization SSA-BP neural network; solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set; establishing a chaos initialization SSA-BP neural network model; performing normal distribution dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set, and performing normal distribution dispersion on the allowable strain value of the propeller according to a 3 sigma principle according to a variation coefficient of the allowable strain value of the propeller; solving the failure rate of the airship propeller and the mean time between failure and working (MTBF). The method effectively avoids the situation of sinking into a local optimal solution, improves the prediction precision and the prediction efficiency, can rapidly estimate the reliability of the propeller, and has great engineering value.

Description

Airship propeller reliability estimation method based on chaos initialization SSA-BP neural network
Technical Field
The invention belongs to the technical field of reliability evaluation, and particularly relates to a reliability evaluation method for airship propellers.
Background
Reliability estimation of composite propellers is a key content in high altitude airship safety indicators, mean Time Between Failure (MTBF) is a capability that embodies the propeller to maintain its thrust for a prescribed period of time without damage. The high-altitude airship is required to fly for an ultra-long time within a specified working height without falling due to the specificity of the working condition, and aiming at the special unmanned aerial vehicle, the accurate estimation of the MTBF of the composite propeller is very important for the airship, and the design and technical improvement of the propeller are also greatly facilitated.
At present, two main ways of estimating MTBF are adopted, namely, continuous rotation test of a propeller is adopted, destructive test is adopted, and cost is too high and the MTBF is rarely used. The strength failure of the composite propeller can be judged by a maximum strain failure criterion, a second estimation method is led out, the maximum strain of the propeller under the corresponding working condition is solved through a finite element and compared with the allowable strain, if the allowable strain is exceeded, the failure is recorded once, and then the estimation is carried out through the relationship between failure rate and MTBF. The aircraft speed and the aircraft flight altitude are not always accurately located on the design point, so that the aircraft speed and the aircraft flight altitude can be understood as normal distribution based on the design point, working conditions required to be calculated are quite many, finite element calculation is time-consuming, strain is not well found along with the change rule of the aircraft flight altitude and the rotating speed, and therefore a BP neural network can be added to estimate the strain, and further the MTBF is estimated.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an airship propeller reliability estimation method based on a chaos initialization SSA-BP neural network, which determines main factors influencing the blade strain under the design resident air working condition of the propeller; constructing a training/testing input data set of the chaotic initialization SSA-BP neural network; solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set; establishing a chaos initialization SSA-BP neural network model; performing normal distribution dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set, and performing normal distribution dispersion on the allowable strain value of the propeller according to a 3 sigma principle according to a variation coefficient of the allowable strain value of the propeller; solving the failure rate and the Mean Time Between Failure (MTBF) of the airship propeller. According to the invention, the BP neural network prediction result is utilized, the sparrow search algorithm is adopted to optimize the BP neural network structure, and the chaotic initialization method is used to determine the initial population position of the SSA, so that the situation of sinking into a local optimal solution is effectively avoided, the prediction precision and the prediction efficiency are improved, the reliability of the propeller can be rapidly estimated, and the method has great engineering value.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
step 1: determining factors influencing the strain of the blade under the design resident air working condition of the propeller;
factors influencing the stress of the blade under the air-resident working condition comprise aerodynamic force and rotational inertia force, and only the flying height and the rotating speed are considered for 2 indirect factors influencing the aerodynamic force and the rotational inertia force within the design tolerance range of the blade size through DOE analysis;
step 2: constructing a training/testing input data set of the chaotic initialization SSA-BP neural network;
step 2-1: according to the task section analysis, the flying height change of the airship design takes the value H= { H 1 ,h 2 …,h k Value n= { n } corresponding to the change of the rotating speed of the propeller 1 ,n 2 ,…,n k -a }; k represents the number of the designed flying heights of the airship;
step 2-2: according to the flying height and the rotating speed change range, taking the corresponding rotating speed at each height as the center, taking the situation that the interval c is discretized by 7k as the calculation working conditions, namely I= { (h) 1 ,n 1 -3c),(h 1 ,n 1 -2c),…,(h 1 ,n 1 +3c),…,(h k ,n k +3c) } to form a 7k 2 input set matrix;
step 3: solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set;
constructing a propeller geometric model to divide a structured grid, carrying out pneumatic calculation on the propellers under working conditions of different task stages, obtaining the aerodynamic force of the surfaces of the propellers, carrying out strength analysis on the propellers through structural finite element analysis software, and calculating the maximum strain value of the blades under corresponding input parameters as an output data set;
step 4: establishing a chaos initialization SSA-BP neural network model, and determining the optimal node number of an hidden layer of the SSA-BP neural network through simulation trial calculation; determining the initial population position of a sparrow search algorithm SSA through Logistic chaotic mapping; optimizing initial threshold values and weight values of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm; training and testing the optimized SSA-BP neural network;
step 4-1: determining the initial population position of the sparrow search algorithm SSA through Logistic chaotic mapping:
using Logistic mapping to replace a pseudo-random number generator to generate chaos numbers between 0 and 1;
the Logistic chaotic mapping model is as follows:
z m+1 ＝μz m (1-z m )
wherein z is m Represents a chaotic variable, mu E [0,4]]；
The chaos initialization formula is as follows:
z(i+1,j)＝μ×z(i,j)×(1-z(i,j))
in the formula, generating an optimal chaotic variable of the (i+1) th individual through the optimal chaotic variable of the (i) th individual; z (i, j) represents the optimal chaotic variable of the i-th individual, and z (i+1, j) represents the optimal chaotic variable of the i+1-th individual;
x(i,j)＝x min (j)+(x max (j)-x min (j))×z(i,j)
wherein x (i, j) represents the position of the ith individual, x min (j) Representing the lower bound of the variable j search space, x max (j) Representing the upper bound of the variable j search space;
step 4-2: optimizing initial threshold values and weights of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm:
the SSA-BP neural network is a multi-layer feedforward network, the initial weight and the threshold number of the SSA-BP neural network depend on the network structure, the number of input parameters, the number of output parameters and the number of hidden layer nodes, and for the three-layer SSA-BP neural network, the total number Q of the initial weight and the threshold is as follows:
Q＝inputnum*hiddennum+hiddennum+hiddennum*outputnum+outputnum
wherein, inputnum and outputnum are respectively the number of input/output parameters, and hiddennum is the number of hidden layer nodes;
the initial weight and the threshold are determined by random seeds, the prediction accuracy of the neural network is affected by different initial values, the positions of the weight and the threshold are continuously updated by a sparrow search algorithm, the fitness is compared, and then the optimal weight and threshold are selected;
the fitness calculating method comprises the following steps:
the output value of the fitness function fit is the mean square error of the test set, and the fitness function has the following calculation formula:
Figure GDA0004261616180000031
wherein, error i Representing the error of the ith predicted output value and the true value;
step 5: performing normal distribution dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set; normal distribution dispersion is carried out on the allowable strain value of the propeller according to the variation coefficient and the 3 sigma principle;
the propeller stays at the designed flight height with equal probability, when staying at the corresponding height layer, the fluctuation range of delta h exists, meanwhile, the motor control error is considered to be delta n, the variation of the flight height and the rotation speed is assumed to be compliant with normal distribution, and the flight height and the rotation speed are obtained according to 3 sigma criteria and are compliant with the normal distribution as follows:
Figure GDA0004261616180000032
randomly generating a large number of discrete points by using MATLAB as an input data set;
according to allowable strain [ epsilon ] of the propeller composite material and the material variation coefficient is CV, the allowable strain obeys normal distribution as follows:
N([ε],σ CV 2 )
wherein sigma CV ＝[ε]CV, CV is the coefficient of variation;
step 6: solving the failure rate of the airship propeller and the mean time between failure and working (MTBF);
step 6-1: the input data set is imported into a trained SSA-BP neural network model for simulation calculation, and the output strain value and allowable strain N ([ epsilon ])],σ CV 2 ) Obtaining total failure times, and recording as one failure when the output strain is greater than the allowable strain, and further calculating to obtain the reliability R of the blade as follows:
Figure GDA0004261616180000041
in n f For the total number of failures, 1, N is added to the value 1 times per failure 1 The total comparison times;
step 6-2: failure rate after the working time t of the propeller is calculated through reliability:
failure rate of
Figure GDA0004261616180000042
Step 6-3: the mean failure free operating time MTBF of the propeller is calculated through failure rate to evaluate the reliability of the propeller:
mean time to failure
Figure GDA0004261616180000043
Preferably, the μ=2.
The beneficial effects of the invention are as follows:
the invention provides an airship propeller reliability estimation method based on a chaos initialization SSA-BP neural network. Compared with the conventional BP neural network estimation method, the method has the advantages that a sparrow search algorithm is adopted to optimize the neural network structure, the initial weight and the threshold value of the neural network layer are determined through random seeds, different initial values influence the prediction accuracy of the neural network, the positions of the weight and the threshold value are continuously updated through the sparrow search algorithm, the magnitudes of errors are compared, and then the optimal weight and threshold value are selected. Meanwhile, the initial population position of the SSA is determined by a chaos initialization method, the situation of sinking into a local optimal solution is effectively avoided, the prediction precision and the prediction efficiency are improved, the reliability of the propeller can be rapidly estimated, the method has certain universality, and the method is greatly helpful for solving the problems, for example, the service life of a bolt can be estimated by the method.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a geometric model of a propeller in an embodiment of the invention.
Fig. 3 is a flowchart of a chaotic initialization sparrow search algorithm for optimizing a BP neural network in an embodiment of the present invention.
Fig. 4 is a chaotic initialization SSA-BP neural network structure in an embodiment of the present invention.
FIG. 5 is a discrete view of an input dataset in an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
Aiming at the existing problems, the invention provides an airship propeller reliability estimation method based on a chaos initialization SSA-BP neural network, through the prediction capability of the neural network, the output value can be accurately predicted under the condition of unknown input and mapping relation, further the failure rate and Mean Time Between Failure (MTBF) are obtained, and the method has strong universality and is suitable for engineering application.
A airship propeller reliability estimation method based on a chaos initialization SSA-BP neural network comprises the following steps:
step 1: determining factors influencing the strain of the blade under the design resident air working condition of the propeller;
factors influencing the stress of the blade under the air-resident working condition comprise aerodynamic force and rotational inertia force, and only the flying height and the rotating speed are considered for 2 indirect factors influencing the aerodynamic force and the rotational inertia force within the design tolerance range of the blade size through DOE analysis;
step 2: constructing a training/testing input data set of the chaotic initialization SSA-BP neural network;
step 2-1: according to the task section analysis, the flying height change of the airship design takes the value H= { H 1 ,h 2 …,h k Value n= { n } corresponding to the change of the rotating speed of the propeller 1 ,n 2 ,…,n k }；
Step 2-2: according to the flying height and the rotating speed change range, taking the corresponding rotating speed at each height as the center, taking the situation that the interval c is discretized by 7k as the calculation working conditions, namely I= { (h) 1 ,n 1 -3c),(h 1 ,n 1 -2c),…,(h 1 ,n 1 +3c),…,(h k ,n k +3c) } to form a 7k 2 input set matrix;
step 3: solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set;
constructing a propeller geometric model to divide a structured grid, carrying out pneumatic calculation on the propellers under working conditions of different task stages, obtaining the aerodynamic force of the surfaces of the propellers, carrying out strength analysis on the propellers through structural finite element analysis software, and calculating the maximum strain value of the blades under corresponding input parameters as an output data set;
step 4: establishing a chaos initialization SSA-BP neural network model, and determining the optimal node number of an hidden layer of the SSA-BP neural network through simulation trial calculation; determining the initial population position of a sparrow search algorithm SSA through Logistic chaotic mapping; optimizing initial threshold values and weight values of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm; training and testing the optimized SSA-BP neural network;
the feeding process of the sparrow population is taken as inspiration, and the sparrow population is divided into a finder part and a jointer part in the feeding process, which are respectively responsible for providing the direction of the population feeding andfollow and acquire food. When the sparrow population becomes aware of the danger, then anti-predation will occur and the population location will be updated. The location update and anti-predation behavior of the discoverer and the joiner can be represented by mathematical expressions. The position of each sparrow can be expressed as x= (X) 1 ,x 2 ,…,x D ) The best position of each sparrow population can be used as a finder, and the fitness value can be expressed as f i ＝f(x 1 ,x 2 ,…,x D ) Discoverers with better fitness values will take food preferentially during the search process. Where D represents the dimension of the algorithmic solution space.
Step 4-1: determining the initial population position of the sparrow search algorithm SSA through Logistic chaotic mapping:
using Logistic mapping to replace a pseudo-random number generator to generate chaos numbers between 0 and 1;
the common population uniformity initialization adopts a pseudo-random number mode, and an initialization model is as follows:
x(i,j)＝x min (j)+(x max (j)-x min (j))×rand
wherein rand is a uniform random number.
The Logistic chaotic mapping model is as follows:
z m+1 ＝μz m (1-z m )
wherein z is m Represents a chaotic variable, mu E [0,4]]；
The chaos initialization formula is as follows:
z(i+1,j)＝μ×z(i,j)×(1-z(i,j))
in the formula, generating an optimal chaotic variable of the (i+1) th individual through the optimal chaotic variable of the (i) th individual;
x(i,j)＝x min (j)+(x max (j)-x min (j))×z(i,j)
SSA population initialization is carried out through the chaos variable z (i, j), so that better effect is achieved compared with conventional pseudo random number initialization, and optimization can be effectively prevented from being trapped into local optimum.
Step 4-2: optimizing initial threshold values and weights of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm:
the SSA-BP neural network is a multi-layer feedforward network, the initial weight and the threshold number of the SSA-BP neural network depend on the network structure, the number of input parameters, the number of output parameters and the number of hidden layer nodes, and for the three-layer SSA-BP neural network, the total number Q of the initial weight and the threshold is as follows:
Q＝inputnum*hiddennum+hiddennum+hiddennum*outputnum+outputnum
wherein, inputnum and outputnum are respectively the number of input/output parameters, and hiddennum is the number of hidden layer nodes;
the initial weight and the threshold are determined by random seeds, the prediction accuracy of the neural network is affected by different initial values, the positions of the weight and the threshold are continuously updated by a sparrow search algorithm, the fitness is compared, and then the optimal weight and threshold are selected;
the fitness calculating method comprises the following steps:
the output value of the fitness function fit is the mean square error of the test set, and the fitness function has the following calculation formula:
Figure GDA0004261616180000071
wherein, error i Representing the error of the ith predicted output value and the true value;
step 5: performing normal distribution dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set; normal distribution dispersion is carried out on the allowable strain value of the propeller according to the variation coefficient and the 3 sigma principle;
the propeller stays at the designed flight height with equal probability, when staying at the corresponding height layer, the fluctuation range of delta h exists, meanwhile, the motor control error is considered to be delta n, the variation of the flight height and the rotation speed is assumed to be compliant with normal distribution, and the flight height and the rotation speed are obtained according to 3 sigma criteria and are compliant with the normal distribution as follows:
Figure GDA0004261616180000072
randomly generating a large number of discrete points by using MATLAB as an input data set;
according to allowable strain [ epsilon ] of the propeller composite material and the material variation coefficient is CV, the allowable strain obeys normal distribution as follows:
N([ε],σ CV 2 )
wherein sigma CV ＝[ε]CV, CV is the coefficient of variation;
step 6: solving the failure rate of the airship propeller and the mean time between failure and working (MTBF);
step 6-1: the input data set is imported into a trained SSA-BP neural network model for simulation calculation, and the output strain value and allowable strain N ([ epsilon ])],σ CV 2 ) Obtaining total failure times, and recording as one failure when the output strain is greater than the allowable strain, and further calculating to obtain the reliability R of the blade as follows:
Figure GDA0004261616180000081
in n f For the total number of failures, 1, N is added to the value 1 times per failure 1 The total comparison times;
step 6-2: failure rate after the working time t of the propeller is calculated through reliability:
failure rate of
Figure GDA0004261616180000082
Step 6-3: the mean failure free operating time MTBF of the propeller is calculated through failure rate to evaluate the reliability of the propeller:
mean time to failure
Figure GDA0004261616180000083
Specific examples:
the airship propeller reliability estimation method based on the chaotic initialization SSA-BP neural network comprises the following steps of:
determining main factors influencing the strain of the blade under the design resident working condition of the propeller;
constructing a training/testing input data set of the chaotic initialization SSA-BP neural network;
solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set;
establishing a chaotic initialization SSA-BP neural network model;
performing normal distribution and dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set, and performing normal distribution and dispersion on the allowable strain value of the propeller according to a variation coefficient according to the 3 sigma principle in the same way;
solving the failure rate and the Mean Time Between Failure (MTBF) of the airship propeller.
The method comprises the following steps:
1. determining main factors influencing blade strain under design resident air working condition of the propeller: the main factors influencing the blade stress during the idle mission stage include aerodynamic forces and rotational inertial forces, which in turn are related to flight altitude, rotational speed, blade size, etc. Through DOE analysis, the influence of the blade size on the stress is small within the design tolerance range of the blade size, so that 2 influence factors of the flying height and the rotating speed are considered.
2. The training/testing input data set for constructing the chaotic initialization SSA-BP neural network is specifically as follows:
firstly, according to task profile analysis, designing a flying height change value H= {18,19,20,21,22} (unit: km) of the airship, and corresponding to a change value n= {200,300,400,500,600} (unit: rpm) of a propeller rotating speed requirement;
and secondly, taking corresponding rotating speeds at each height as a center according to the flying height and the rotating speed change range, and taking 35 conditions of interval 3 (rpm) as calculation working conditions, namely, I= { (18,191), (18,194), …, (18,209), …, (22,609) }, and forming a 35×2 input set matrix.
3. The solving of the strain value of the maximum strain position of the propeller under the working condition of taking the input data set is specifically as follows:
the first step: a propeller geometry model was constructed as shown in fig. 2. The structural grids are divided, the structural grids can easily realize boundary fitting of the region, and the fitting of the curved surface or space adopts a parameterization or spline interpolation method, so that the structural grids are closer to an actual model.
And a second step of: and carrying out pneumatic calculation on the propellers under working conditions in different task stages to obtain the surface aerodynamic force of the propellers. Aerodynamic force is used as one of the loads of the propeller, and is loaded on the finite element model of the propeller structure through multi-point interpolation.
And a third step of: and carrying out intensity analysis on the propeller by structural finite element analysis software, and calculating the maximum strain value of the blade under the corresponding input parameters. The method comprises the following steps:
the load applied by the blade is aerodynamic, gravitational, centrifugal force F=m· (2n) 2 R, where m is blade mass, n is rotational speed, r is propeller radius;
the blade applies a constraint at the root of the blade;
the partial intensity analysis data are shown in table 1 below:
TABLE 1 intensity analysis data
Figure GDA0004261616180000091
Figure GDA0004261616180000101
4. The establishment of the chaotic initialization SSA-BP neural network model specifically comprises the following steps:
the first step, determining the optimal node number of the hidden layer of the BP neural network through simulation trial calculation, circulating the different hidden layer node numbers, comparing output errors, and determining the optimal hidden layer node number corresponding to the minimum value of the output errors.
Secondly, determining the initial population position of a Sparrow Search Algorithm (SSA) through Logistic chaotic mapping, wherein the method comprises the following steps:
the Logistic mapping can replace a pseudo-random number generator to generate chaos numbers between 0 and 1, and has proved to have better effect than pseudo-random numbers in algorithm population initialization.
The common population uniformity initialization adopts a pseudo-random number mode, and an initialization model is as follows:
x(i,j)＝x min (j)+(x max (j)-x min (j))×rand
where i represents the ith individual, j represents the jth variable, and rand is a uniform random number.
The Logistic chaotic mapping model is as follows:
z k+1 ＝μz k (1-z k )
where z represents a chaotic variable, mu.e [0,4], generally 2 or 4, in this example 2.
Figure GDA0004261616180000102
These values may cause the chaotic system to fail, eventually converge, or cause the chaotic system to have regularity.
The chaos initialization formula is as follows:
z(i+1,j)＝μ×z(i,j)×(1-z(i,j))
wherein the optimal chaotic variable of the (i+1) th individual is generated through the optimal chaotic variable of the (i) th individual.
x(i,j)＝x min (j)+(x max (j)-x min (j))×z(i,j)
Compared with rand random numbers, the chaotic variable z (i, j) has better effect on the initialization of SSA algorithm population, and can effectively prevent optimization from falling into local optimum.
Third, optimizing initial threshold values and weights of the BP neural network input layer and the middle layer through a sparrow search algorithm, wherein the flow is shown in a figure 3, and the specific method is as follows:
as shown in fig. 4, the present embodiment employs a three-layer BP neural network having an input layer, a hidden layer, and an output layer. The number of the initial weights and the number of the threshold values to be optimized are calculated according to the number of the input parameters, the number of the output parameters and the number of the hidden layer nodes, and the number is as follows:
n＝inputnum*hiddennum+hiddennum+hiddennum*outputnum+outputnum
where inputnum and outputnum are the number of input/output parameters and hiddennum is the number of hidden layer nodes.
The initial weight and the threshold are determined by random seeds, different initial values influence the prediction accuracy of the neural network, and the positions of the weight and the threshold are continuously updated by a sparrow search algorithm. The optimal weight and the threshold position are determined by the size of the fitness, the fitness is the mean square error of the test set, and the smaller the value of the fitness function is, the higher the prediction precision of the model is.
The calculation method comprises the following steps:
Figure GDA0004261616180000111
where error represents the error of the predicted output value from the true value.
And fourthly, importing the optimized SSA-BP neural network into an input/output data set to perform network training and testing, and obtaining a trained propeller reliability neural network model.
5. The flight height and the rotating speed of the propeller design under the task profile are subjected to normal distribution and dispersion according to a 3 sigma principle, a new input data set is obtained, and the allowable strain value of the propeller is subjected to normal distribution and dispersion according to a 3 sigma principle by the same principle according to a variation coefficient, specifically:
in the present embodiment, when the corresponding height layer stays, there is a fluctuation range of about ±100m, and considering that the motor control error is ±9rpm, assuming that the changes of the flying height and the rotating speed both obey the normal distribution, according to the 3σ criterion, the flying height and the rotating speed can be obtained as follows:
N(18,0.033 2 )，N(19,0.033 2 )，N(20,0.033 2 )，N(21,0.033 2 )，N(22,0.033 2 )
N(200,3 2 )，N(300,3 2 )，N(400,3 2 )，N(500,3 2 )，N(600,3 2 )
the random generation of 5E+8 discrete points as input data sets using MATLAB according to the distribution is shown in FIG. 5.
According to the allowable strain of the propeller composite material being 3000 mu epsilon and the material variation coefficient being 10%, the allowable strain obeys the normal distribution as follows:
N(3000,300 2 )
1E+8 discrete points were randomly generated using MATLAB.
6. Solving the failure rate and the Mean Time Between Failure (MTBF) of the airship propeller, specifically:
the input data set is imported into a trained SSA-BP neural network model for simulation calculation, and the output strain value and allowable strain N ([ epsilon ])],σ CV 2 ) The total failure times (the output strain is greater than the allowable strain and is marked as one failure) are obtained, and then the reliability R of the blade is calculated as follows:
Figure GDA0004261616180000121
in n f For the total number of failures, 1, N is added to the value 1 times per failure 1 The total number of comparisons.
Further, failure rate after the working time t of the propeller is calculated through reliability.
Failure rate of
Figure GDA0004261616180000122
Further, the reliability of the propeller is evaluated by calculating the Mean Time Between Failure (MTBF) of the propeller.
Mean time to failure
Figure GDA0004261616180000123

Claims (2)

1. The airship propeller reliability estimation method based on the chaotic initialization SSA-BP neural network is characterized by comprising the following steps of:
step 1: determining factors influencing the strain of the blade under the design resident air working condition of the propeller;
factors influencing the stress of the blade under the air-resident working condition comprise aerodynamic force and rotational inertia force, and only the flying height and the rotating speed are considered for 2 indirect factors influencing the aerodynamic force and the rotational inertia force within the design tolerance range of the blade size through DOE analysis;
step 2: constructing a training/testing input data set of the chaotic initialization SSA-BP neural network;
step 2-1: according to the task section analysis, the flying height change of the airship design takes the value H= { H 1 ,h 2 …,h k Value n= { n } corresponding to the change of the rotating speed of the propeller 1 ,n 2 ,…,n k -a }; k represents the number of the designed flying heights of the airship;
step 2-2: according to the flying height and the rotating speed change range, taking the corresponding rotating speed at each height as the center, taking the situation that the interval c is discretized by 7k as the calculation working conditions, namely I= { (h) 1 ,n 1 -3c),(h 1 ,n 1 -2c),…,(h 1 ,n 1 +3c),…,(h k ,n k +3c) } to form a 7k 2 input set matrix;
step 3: solving a strain value of a maximum strain position of the propeller under the working condition of taking the input data set;
constructing a propeller geometric model to divide a structured grid, carrying out pneumatic calculation on the propellers under working conditions of different task stages, obtaining the aerodynamic force of the surfaces of the propellers, carrying out strength analysis on the propellers through structural finite element analysis software, and calculating the maximum strain value of the blades under corresponding input parameters as an output data set;
step 4: establishing a chaos initialization SSA-BP neural network model, and determining the optimal node number of an hidden layer of the SSA-BP neural network through simulation trial calculation; determining the initial population position of a sparrow search algorithm SSA through Logistic chaotic mapping; optimizing initial threshold values and weight values of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm; training and testing the optimized SSA-BP neural network;
step 4-1: determining the initial population position of the sparrow search algorithm SSA through Logistic chaotic mapping:
using Logistic mapping to replace a pseudo-random number generator to generate chaos numbers between 0 and 1;
the Logistic chaotic mapping model is as follows:
z m+1 ＝μz m (1-z m )
wherein z is m Represents a chaotic variable, mu E [0,4]]；
The chaos initialization formula is as follows:
z(i+1,j)＝μ×z(i,j)×(1-z(i,j))
in the formula, generating an optimal chaotic variable of the (i+1) th individual through the optimal chaotic variable of the (i) th individual; z (i, j) represents the optimal chaotic variable of the i-th individual, and z (i+1, j) represents the optimal chaotic variable of the i+1-th individual;
x(i,j)＝x min (j)+(x max (j)-x min (j))×z(i,j)
wherein x (i, j) represents the position of the ith individual, x min (j) Representing the lower bound of the variable j search space, x max (j) Representing the upper bound of the variable j search space;
step 4-2: optimizing initial threshold values and weights of an SSA-BP neural network input layer and an intermediate layer through a sparrow search algorithm:
the SSA-BP neural network is a multi-layer feedforward network, the initial weight and the threshold number of the SSA-BP neural network depend on the network structure, the number of input parameters, the number of output parameters and the number of hidden layer nodes, and for the three-layer SSA-BP neural network, the total number Q of the initial weight and the threshold is as follows:
q=inputnum+hiddennum+hiddennum +. Hiddennum in the formula outputnum + outputnum, inputnum and outputnum are respectively the number of input/output parameters, and hiddennum is the number of hidden layer nodes;
the initial weight and the threshold are determined by random seeds, the prediction accuracy of the neural network is affected by different initial values, the positions of the weight and the threshold are continuously updated by a sparrow search algorithm, the fitness is compared, and then the optimal weight and threshold are selected;
the fitness calculating method comprises the following steps:
the output value of the fitness function fit is the mean square error of the test set, and the fitness function has the following calculation formula:
Figure FDA0004261616170000021
wherein, error i Representing the error of the ith predicted output value and the true value;
step 5: performing normal distribution dispersion on the design flight height and the rotating speed of the propeller under the task profile according to a 3 sigma principle to obtain a new input data set; normal distribution dispersion is carried out on the allowable strain value of the propeller according to the variation coefficient and the 3 sigma principle;
the propeller stays at the designed flight height with equal probability, when staying at the corresponding height layer, the fluctuation range of delta h exists, meanwhile, the motor control error is considered to be delta n, the variation of the flight height and the rotation speed is assumed to be compliant with normal distribution, and the flight height and the rotation speed are obtained according to 3 sigma criteria and are compliant with the normal distribution as follows:
Figure FDA0004261616170000022
randomly generating a large number of discrete points by using MATLAB as an input data set;
according to allowable strain [ epsilon ] of the propeller composite material and the material variation coefficient is CV, the allowable strain obeys normal distribution as follows:
N([ε],σ CV 2 )
wherein sigma CV ＝[ε]CV, CV is the coefficient of variation;
step 6: solving the failure rate of the airship propeller and the mean time between failure and working (MTBF);
step 6-1: the input data set is imported into a trained SSA-BP neural network model for simulation calculation, and the output strain value and allowable strain N ([ epsilon ])],σ CV 2 ) Obtaining total failure times, and recording as one failure when the output strain is greater than the allowable strain, and further calculating to obtain the reliability R of the blade as follows:
Figure FDA0004261616170000031
in n f For the total number of failures, 1, N is added to the value 1 times per failure 1 The total comparison times;
step 6-2: failure rate after the working time t of the propeller is calculated through reliability:
Figure FDA0004261616170000032
step 6-3: the mean failure free operating time MTBF of the propeller is calculated through failure rate to evaluate the reliability of the propeller:
mean time to failure
Figure FDA0004261616170000033
2. The airship propeller reliability estimation method based on the chaotic initialization SSA-BP neural network according to claim 1, wherein μ=2.
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