An intelligent diagnosis method for fan faults based on improved fireworks algorithm

Abstract

An intelligent diagnosis method for fan faults using an improved fireworks algorithm has the following basic steps: (1) signal sampling; (2) data preprocessing; (3) feature extraction; (4) data normalization processing; (5) intelligent diagnosis of fan faults. In view of the limitations of existing fan fault diagnosis systems, the present invention designs an intelligent diagnosis method for fan faults using an improved fireworks algorithm to optimize a BP neural network. An improved Gaussian density function is used to optimize the enhanced fireworks algorithm to calculate the optimal weights and thresholds of the BP neural network, thereby improving the performance of the BP neural network. By using the correlation kurtosis deconvolution algorithm (MCKD) and the fan bearing data processed by time domain features for testing, the method of the present invention can meet the user's set functional and performance requirements in diagnosing fan fault bearing data. A large number of comparative experiments have shown that the intelligent diagnosis method for fan faults using the improved fireworks algorithm can achieve a higher accuracy rate.

Description

Technical Field

[0001] The invention relates to an intelligent diagnosis method for a fan, in particular to an intelligent diagnosis method for a fan fault with an improved fireworks algorithm. Background Art

[0002] With the development of industrial society, industrial equipment is becoming larger and more integrated. Once a failure occurs, it will not only pollute the environment and cause significant economic losses, but also endanger the lives of workers. At the same time, people pay more attention to the safety of the working environment, which undoubtedly puts higher standards on equipment safety and reliability. There are a large number of parts in large-scale mechanical equipment, and each small part is crucial. Once some parts fail, and the maintenance personnel fail to find and replace them in time, it will lead to a crisis for the entire equipment, or even a disaster for the entire factory. If the equipment is frequently shut down for maintenance and inspection, it will undoubtedly affect production and increase the labor cost of workers. Therefore, detecting the status of industrial equipment parts and using artificial intelligence technology to determine whether the parts have failed and need to be replaced can not only maximize the service life of the parts, but also overcome the shortcomings of traditional fault diagnosis, which has important social significance. Summary of the invention

[0003] In order to solve the above problems, the present invention provides an intelligent diagnosis method for fan faults with an improved fireworks algorithm.

[0004] The object of the present invention is achieved through the following technical solution: a method for clustering incomplete data with generative adversarial network valuation, the steps of which are:

[0005] An intelligent diagnosis method for fan faults based on an improved fireworks algorithm, comprising the following steps:

[0006] 1) Signal sampling: Use an accelerometer to collect bearing vibration data, and select fan bearing data with a digital signal sampling frequency of 12000 Hz;

[0007] 2) Noise reduction processing;

[0008] 3) Feature selection: select mean μ x , peak value x p , the square sum of the amplitude x c , standard deviation ω, these four time domain feature parameters are used for feature extraction;

[0009] 4) Data normalization: The time domain feature vector is normalized to obtain the final data as the input of the model, and the data obtained by deconvolution and denoising using the maximum correlation kurtosis is converted into data in the range of [0,1] after feature selection;

[0010] 5) Intelligent diagnosis of fan fault:

[0011] 5.1) Improved fireworks algorithm:

[0012] 5.1.1) Spark analysis: First, according to the defined explosion radius R i and the number of explosion sparks S i Generate an explosion spark through the explosion operation, and then randomly extract a spark x from the spark population at this moment i , and the extracted spark x i Execute the d-dimensional Gaussian mutation behavior. Finally, after the two sparks explode and mutate, the newly generated sparks may cross the boundary. i When the feasible domain φ is exceeded in the d dimension, a mapping rule is defined to map the firework to a new position;

[0013] 5.1.2) Select strategy:

[0014] After the explosion and mutation sparks are generated, the selection strategy is executed so that the excellent information in the population can be inherited to the next generation of sparks. A part of individuals are selected from the candidate set γ of fireworks, explosion sparks and mutation sparks as the next generation of fireworks population, and the population size is Z; the firework individual with the smallest fitness is directly selected as the next generation of fireworks, and the remaining next generation of fireworks individuals are selected from Z-1 current individuals using the roulette algorithm; in the candidate fireworks set, if a firework is surrounded by many other candidate fireworks individuals, the probability of this firework being selected will decrease, that is, the greater the density of fireworks individuals, the smaller the probability of being selected by the roulette algorithm;

[0015] Candidate Fireworks x i The probability of being selected is:

[0016]

[0017]

[0018] Among them, R(x i ) is the current firework individual x i The sum of the distances to all fireworks in the candidate fireworks set Z-1;

[0019] First, the explosion radius is limited. The spark explosion radius limit in dimension k is as follows:

[0020]

[0021]

[0022] Among them, R min,k is the minimum value of the explosion radius of the fireworks in the k-dimensional space, t is the current number of iterations, and t max is the maximum number of iterations, R firstis the initial spark explosion radius, R last is the final spark explosion radius;

[0023] Secondly, change the mutation rules of the fireworks algorithm mutation operator

[0024] x' ik =x ik +(x Bk -x ik )×g(R) (15)

[0025]

[0026] Where g(R) is the improved Gaussian probability density function, o is the stage distribution coefficient, N is the number of distribution coefficients set, which is set to 2 in this system, and σ i is the proportional coefficient of the i-th distribution, and the two coefficients are set to 0.7 and 0.3 respectively, τ i is the mean of the ith distribution, is the standard deviation of the ith distribution;

[0027] Finally, modify the mapping rules:

[0028] x ik =x l,k +U(0,1)·(x u,k -x l,k ) (17)

[0029] Where U(0,1) is a random number with a value between 0 and 1 and uniform distribution, x u,k , x l,k are the upper and lower boundaries on dimension k respectively;

[0030] 5.2)ImFWA optimizes BP neural network model.

[0031] In the step 5.2), the specific method is:

[0032] 5.2.1) Set the number of iterations and the initial value of population size Z;

[0033] 5.2.2) Randomly initialize Z fireworks x in the solution space i ;

[0034] 5.2.3) Let i = 1, the maximum number of iterations is T, and evaluate the current firework x i The fitness value f(x i ), calculate the explosion radius R i and the number of explosion sparks S i ;

[0035] 5.2.4) Produce explosion sparks;

[0036] 5.2.5) Generate mutation sparks;

[0037] 5.2.6) Execute mapping rules for newly generated out-of-bounds explosion sparks and mutation sparks;

[0038] 5.2.7) In Fireworks x i , select the next generation of sparks from the explosion and mutation sparks, and execute i=i+1;

[0039] 5.2.8) Repeat steps 5.2.2) to 5.2.6) and if i=T, output the optimization result;

[0040] 5.2.9) The optimization result obtained in step 5.2.8) is the weight and threshold of the proposed model;

[0041] 5.2.10) Input the feature vector of the training set;

[0042] 5.2.11) Perform forward propagation according to the following formula. The input signal is x i , ω is the weight, and the net input value after weighting the j-th neuron in the next layer (hidden layer) of the input layer is:

[0043]

[0044] g(x) is the hidden layer activation function, and the hidden layer output is:

[0045]

[0046] The neural network predicts the output as:

[0047]

[0048] Where b is the threshold of the neural network. Calculate the error v between the predicted and actual output.

[0049] 5.2.12) Perform back propagation according to the following formula,

[0050] The learning rate is η, and the update thresholds a and b are:

[0051]

[0052] b k =b k +v k ,(k=1,2,···,n) (22)

[0053] Update weight ω:

[0054]

[0055] ω jk=ω jk +ηH j v k ,(j=1,2,···,n,k=1,2,···,n) (24)

[0056] Calculate the error, update the weights and thresholds;

[0057] 5.2.13) Repeat steps 5.2.11) to 5.2.12). If the error reaches the target value, stop training.

[0058] In step 2), the specific method is: using the maximum kurtosis deconvolution technology, by extracting the impact component in the periodic fault signal, using the correlation kurtosis as the characteristic parameter, and through deconvolution, the correlation kurtosis of the fault signal after noise reduction processing is maximized, thereby highlighting the continuous pulse sequence submerged by the noise in the signal, and more effectively displaying the bearing fault information.

[0059] In step 3), the mean μ x , peak value x p , the square sum of the amplitude x c , the extraction formula of standard deviation ω is:

[0060]

[0061] x p =max|x i | (2)

[0062]

[0063]

[0064] Where: μ x is the mean, x i is the input data, x p is the peak value, x c is the sum of squares of amplitude, ω is the standard deviation, and n is the sampling point;

[0065] In step 4), the formula used is:

[0066]

[0067] Where: X t is the normalized result; X is the original data; n is the minimum sample value; m is the maximum sample value.

[0068] In step 5.1.1), the explosion radius R i and the number of explosion sparks S i The extreme formula is:

[0069]

[0070]

[0071] Among them, a and b are constants, a is used to control the size of the explosion radius, b controls the number of explosion sparks, c is a machine minimum value, f(x) is the problem to be solved, and the calculation method of the minimum fitness of the spark population at this moment in the formula is y min =min(f(x i ), (i=1,2,···N), the maximum fitness value in the spark population at this moment is calculated as y max =max(f(x i ),(i=1,2,···N);

[0072] Add restrictions to formula (7):

[0073]

[0074] Wherein, p and q are both constants, round(·) is the integer function, and the integer principle is rounding.

[0075] In step 5.1.1), the extracted spark x i Perform d-dimensional Gaussian mutation behavior,

[0076] x' id =x id ×e (9)

[0077] Among them, e is a Gaussian distribution, in which the mean and variance are both 1, that is, e~N(1,1).

[0078] In step 5.1.1), the specific formula for mapping fireworks to their new positions is:

[0079] x' id =x L,d +|x' id |%(x U,d -x L,d ) (10)

[0080] Among them, x U,d is the upper boundary of the solution set of dimension d, x L,d is the lower bound of the solution set of dimension d.

[0081] The beneficial effects created by the present invention are as follows: In view of the fact that the performance of the traditional BP neural network is greatly affected by weights and thresholds, and if the values ​​are not selected properly, the convergence speed will be slow, etc., the present invention proposes an ImFWA algorithm to optimize the BP neural network model, and uses an intelligent optimization algorithm to calculate better weights and thresholds to improve the performance of the BP neural network. The fireworks algorithm is prone to fall into the local optimum during calculation and cannot jump out of the current solution process. By improving the Gaussian density function and using it to optimize the enhanced fireworks algorithm, the illusion of rapid convergence caused by FWA is prevented. The present invention proposes an improved fireworks algorithm to optimize the intelligent diagnosis method of wind turbines. Compared with the traditional wind turbine fault diagnosis model, it can more accurately identify the fault type and reduce the losses caused by equipment failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is the vibration signal image before denoising.

[0083] Figure 2 It is the vibration signal image after denoising.

[0084] Figure 3 It is a BP neural network construction model.

[0085] Figure 4 This is the convergence graph of the four algorithms under the Rastrigin function.

[0086] Figure 5 These are the convergence graphs of the four algorithms under the Scherfel function.

[0087] Figure 6 This is the convergence graph of the four algorithms under the Ackley function.

[0088] Figure 7 It is an image of the wind turbine intelligent diagnosis test results. DETAILED DESCRIPTION

[0089] An intelligent diagnosis method for fan faults based on an improved fireworks algorithm, the basic steps are as follows:

[0090] 1) Signal sampling: Use an accelerometer to collect bearing vibration data, and select fan bearing data with a digital signal sampling frequency of 12000 Hz;

[0091] 2) Noise reduction processing: The maximum kurtosis deconvolution technology is used to extract the impact components in the periodic fault signal. The relevant kurtosis is used as the characteristic parameter. The relevant kurtosis of the fault signal after noise reduction processing is maximized through deconvolution, thereby highlighting the continuous pulse sequence submerged by the noise in the signal, and more effectively displaying the bearing fault information.

[0092] 3) Feature selection: select mean μ x , peak value x p, the square sum of the amplitude x c , standard deviation ω, these four time domain feature parameters are used for feature extraction:

[0093]

[0094] x p =max|x i | (2)

[0095]

[0096]

[0097] Where: μ x is the mean, x i is the input data, x p is the peak value, x c is the sum of squares of amplitude, ω is the standard deviation, and n is the sampling point;

[0098] 4) Data normalization: The time domain feature vector is normalized to obtain the final data as the input of the model. The data obtained by deconvolution and denoising using the maximum correlation kurtosis is converted into data in the range of [0,1] by feature selection. The formula used is:

[0099]

[0100] Where: X t is the normalized result; X is the original data; n is the minimum sample value; m is the maximum sample value;

[0101] 5) Intelligent diagnosis of fan faults:

[0102] 5.1) Improved fireworks algorithm:

[0103] The fireworks algorithm can be roughly divided into two parts: spark analysis and strategy selection:

[0104] (1) Spark analysis

[0105] Sparks are divided into two types: explosion and mutation. First, according to the defined explosion radius R i and the number of explosion sparks S i An explosion spark is generated by an explosive operation.

[0106]

[0107]

[0108] Among them, a and b are constants. a is used to control the size of the explosion radius, and b controls the number of explosion sparks. c is a machine minimum value, the purpose is to prevent the numerator or denominator from being zero, which makes the formula meaningless. f(x) is the problem to be solved. The calculation method of the minimum fitness of the spark population at this moment in the formula is y min =min(f(x i ), (i=1,2,···N), on the contrary, the maximum fitness calculation method in the spark population is y max =max(f(x i ),(i=1,2,···N).

[0109] Add restrictions to formula (7):

[0110]

[0111] Wherein, p and q are both constants, round(·) is the integer function, and the integer principle is rounding.

[0112] Then, at this moment, a spark x is randomly drawn from the spark population. i , and the extracted spark x i Performs a Gaussian mutation in dimension d.

[0113] x' id =x id ×e (9)

[0114] Among them, e is a Gaussian distribution, in which the mean and variance are both 1. That is, e~N(1,1).

[0115] After the two sparks explode and mutate, the newly generated sparks may cross the boundary. i When the feasible domain φ is exceeded in the d dimension, a mapping rule is defined to map the firework to a new position:

[0116] x' id =x L,d +|x' id |%(x U,d -x L,d ) (10)

[0117] Among them, x U,d is the upper boundary of the solution set of dimension d, x L,d is the lower bound of the solution set of dimension d.

[0118] (2) Strategy selection

[0119] After the above operations generate explosion and mutation sparks, the selection strategy will be executed so that the excellent information in the population can be inherited to the next generation of sparks. A part of individuals are selected from the candidate set γ of fireworks, explosion sparks and mutation sparks as the next generation of fireworks population, and the population size is Z. The firework individual with the smallest fitness is directly selected as the next generation of fireworks, and the remaining next generation of fireworks individuals are selected from Z-1 current individuals using the roulette algorithm. In the candidate fireworks set, if a firework is surrounded by many other candidate fireworks individuals, the probability of this firework being selected will decrease, that is, the greater the density of fireworks individuals, the smaller the probability of being selected using the roulette algorithm.

[0120] Candidate Fireworks x i The probability of being selected is:

[0121]

[0122]

[0123] Among them, R(x i ) is the current firework individual x i The sum of the distances to all fireworks individuals in the candidate fireworks set Z-1 (excluding x i ).

[0124] The traditional fireworks algorithm has certain limitations, that is, it is easy to fall into the local optimum, and it is easy to exceed the boundary and increase the amount of calculation when calculating the next generation of fireworks. The root cause is related to the definition of the fireworks algorithm. When calculating, it is extremely easy to fall into the local optimum when the solution is at the origin or close to the origin, and it is impossible to jump out of the current area. According to the introduction of the fireworks algorithm, two improvements are proposed. The first point is to modify the mutation method of the mutation operator so that the mutation spark has higher randomness and accuracy; the second point is to modify the mapping rules of the algorithm.

[0125] First, we limit the explosion radius in formula (8). If the explosion radius is too small, the information mined by the algorithm is not very meaningful. The spark explosion radius limit in dimension k is as follows:

[0126]

[0127]

[0128] Among them, R min,k is the minimum value of the explosion radius of the fireworks in the k-dimensional space, t is the current number of iterations, and t max is the maximum number of iterations, R first is the initial spark explosion radius, R last is the final spark explosion radius.

[0129] Secondly, the mutation rule of the fireworks algorithm mutation operator is changed to improve formula (9):

[0130] x' ik =x ik +(x Bk -x ik )×g(R) (15)

[0131]

[0132] Where g(R) is the improved Gaussian probability density function, o is the stage distribution coefficient, N is the number of distribution coefficients set, which is set to 2 in this system, and σ i is the proportional coefficient of the i-th distribution, and the two coefficients are set to 0.7 and 0.3 respectively, τ i is the mean of the ith distribution, is the standard deviation of the ith distribution.

[0133] Finally, modify the mapping rules of the traditional fireworks algorithm:

[0134] x ik =x l,k +U(0,1)·(x u,k -x l,k ) (17)

[0135] Where U(0,1) is a random number with a value between 0 and 1 and uniform distribution, x u,k , x l,k are the upper and lower boundaries on dimension k respectively.

[0136] 5.2) ImFWA optimizes BP neural network model:

[0137] The performance of traditional BP neural network is greatly affected by weights and thresholds, so the improved fireworks algorithm is used to optimize it. The ImFWA optimization process of BP neural network is as follows:

[0138] 5.2.1) Set the number of iterations and the initial value of population size Z.

[0139] 5.2.2) Randomly initialize Z fireworks x in the solution space i .

[0140] 5.2.3) Let i = 1, the maximum number of iterations is T, and evaluate the current firework x i The fitness value f(x i ), calculate the explosion radius R i and the number of explosion sparks S i .

[0141] 5.2.4) Generate explosion sparks according to formulas (6), (7), (8), (9), and (10).

[0142] 5.2.5) Generate variant sparks according to formulas (15) and (16).

[0143] 5.2.6) Execute mapping rules for newly generated out-of-bounds explosion sparks and mutation sparks according to formula (17).

[0144] 5.2.7) According to formulas (11) and (12), at the fireworks x i , select the next generation of sparks from the explosion and mutation sparks and execute i=i+1.

[0145] 5.2.8) Repeat steps 5.2.2) to 5.2.6). If i=T, output the optimization result.

[0146] 5.2.9) The optimization result obtained in step 5.2.8) is the weight and threshold of the proposed model.

[0147] 5.2.10) Input the feature vector of the training set.

[0148] 5.2.11) Perform forward propagation according to the following formula. The input signal is x i , ω is the weight, and the net input value after weighting the j-th neuron in the next layer (hidden layer) of the input layer is:

[0149]

[0150] g(x) is the hidden layer activation function, and the hidden layer output is:

[0151]

[0152] The neural network predicts the output as:

[0153]

[0154] Where b is the threshold of the neural network. Calculate the error v between the predicted and actual output.

[0155] 5.2.12) Perform back propagation according to the following formula,

[0156] The learning rate is η, and the update thresholds a and b are:

[0157]

[0158] b k =b k +v k ,(k=1,2,···,n) (22)

[0159] Update weight ω:

[0160]

[0161] ω jk =ω jk +ηH j v k ,(j=1,2,···,n,k=1,2,···,n) (24)

[0162] Calculate the error and update the weights and thresholds.

[0163] 5.2.13) Repeat steps 5.2.11) to 5.2.12). If the error reaches the target value, stop training.

[0164] Embodiment 1:

[0165] 1. Theoretical basis of the present invention:

[0166] 1. BP Neural Network

[0167] The BP (back propagation) neural network was pioneered by Rumelhart, McClelland and others. In 1986, scientists used the back propagation learning algorithm combined with the forward network of unidirectional step-by-step propagation. It is the most commonly used neural network.

[0168] BP neural network has the characteristics of strong nonlinear mapping ability and complex and changeable network structure. It uses the gradient descent method to minimize the difference between the actual and expected output values ​​of the neural network. There are three types of structures: input layer, hidden layer and output layer. The number of hidden layers and the number of neurons in each layer can be set by yourself. The calculation of BP neural network is divided into two parts: forward propagation and back propagation. The error output is calculated from front to back, and the weights and thresholds are adjusted from back to front.

[0169] Nowadays, BP neural network has been widely used in pattern recognition, data compression, classification prediction and other fields.

[0170] 1.1BP Neural Network Structure

[0171] BP neural network is a back propagation learning network with simple structure and convenient calculation. BP neural network consists of three parts: input layer, hidden layer, and output layer. Figure 3 As shown:

[0172] like Figure 5As shown in the figure, the upper and lower layers of the BP neural network are connected to each other, but the neurons on each layer are not connected. During forward propagation, the input signal is input to the hidden layer after weighted operation, and propagates to the output layer under the joint action of the hidden layer activation function and the threshold. If the actual output does not match the expected output at this time, the difference between the actual and expected outputs is propagated forward through the hidden layer layer by layer until the input layer enters the back propagation process. Forward propagation and back propagation are performed alternately until the error drops to an acceptable range. The specific steps are:

[0173] (1) Forward propagation

[0174] The signal after feature extraction is input into the input layer, and after weighted operation, the signal is input into the next hidden layer for the next step of calculation. i , ω is the weight, and the net input value after weighting the j-th neuron in the next layer (hidden layer) of the input layer is:

[0175]

[0176] g(x) is the hidden layer activation function, and the hidden layer output is:

[0177]

[0178] The neural network predicts the output as:

[0179]

[0180] Where b is the threshold of the neural network. Calculate the error v between the predicted and actual output.

[0181] (2) Back Propagation

[0182] The learning rate is η, and the update thresholds a and b are:

[0183]

[0184] b k =b k +v k ,(k=1,2,···,n) (22)

[0185] Update weight ω:

[0186]

[0187] ω jk =ω jk +ηH j v k ,(j=1,2,···,n,k=1,2,···,n) (24)

[0188] Repeat the above two steps until the error drops to the set value. The two sets of parameters in the BP neural network, weights and thresholds, are randomly generated, resulting in instability. Inappropriate weights and thresholds will not only affect the efficiency of the neural network, but also have a great impact on the recognition accuracy. This system uses intelligent algorithms to optimize it, which can make up for the shortcomings of the BP neural network.

[0189] 2. Implementation process of the technical solution of the present invention:

[0190] 1. Signal sampling: Use an accelerometer to collect bearing vibration data, and select bearing data with a digital signal sampling frequency of 12000Hz;

[0191] 2. Noise reduction: Using the characteristic that the maximum kurtosis deconvolution (MCKD) is sensitive to the periodic shock contained in the signal, the vibration signal is deconvolved to amplify the periodic pulses covered by the noise in the signal and extract effective signal features from it;

[0192] 3. Feature selection: Select the four time domain feature parameters of mean, peak, square sum of amplitude, and standard deviation for feature extraction;

[0193] 4. Normalization: The time domain feature vector is normalized to obtain the final data as the input of the model. The data obtained by maximum kurtosis deconvolution MCKD denoising is converted into data in the range of [0,1] after feature selection;

[0194] 5. Intelligent diagnosis of wind turbines: Use the improved fireworks algorithm to find the optimal weights and thresholds of the BP neural network, and use the intelligent optimization algorithm to calculate the better weights and thresholds to improve the performance of the BP neural network. The fireworks algorithm is prone to fall into local optimality during calculation and cannot jump out of the current solution process. This paper improves the Gaussian density function and uses it to optimize the enhanced fireworks algorithm, thereby preventing FWA from easily causing the illusion of rapid convergence. This paper proposes an improved fireworks algorithm to optimize the wind turbine intelligent diagnosis system model. Compared with the traditional wind turbine fault diagnosis model, it can more accurately identify the fault type and reduce the losses caused by equipment failure.

[0195] 3. Feasibility Analysis

[0196] (1) Performance analysis of improved fireworks algorithm

[0197] In order to test the superiority of the improved fireworks algorithm over the original algorithm, the two algorithms and the fitness curves of the particle swarm algorithm and genetic algorithm are compared under different fitness functions. The test dimension is 30, the population size is 100, and the operation is performed 10 times to take the average value. The following is the convergence of the algorithms under three functions and their analysis.

[0198] Figure 4The convergence of the four algorithms under the Rastrigin function shows that the proposed ImFWA algorithm converges earlier and converges close to zero. Table 1 compares the standard deviation and average value, and Table 2 compares the time.

[0199] Table 1 Comparison of standard deviation and average value of four algorithms under Rastrigin function

[0200]

[0201] Table 2 Time comparison of four algorithms under Rastrigin function

[0202]

[0203] Figure 5 The convergence of the four algorithms under the Scherfel function shows that the proposed ImFWA algorithm converges earlier and converges close to zero. Table 3 compares the standard deviation and average value, and Table 4 compares the time.

[0204] Table 3 Comparison of standard deviation and average value of four algorithms under Scherfel function

[0205]

[0206] Table 4 Time comparison of four algorithms under Scherfel function

[0207]

[0208] Figure 6 The convergence of the four algorithms under the Ackley function shows that the proposed ImFWA algorithm converges earlier and converges close to zero. Table 5 shows the comparison of standard deviation and average value, and Table 6 shows the time comparison.

[0209] Table 5 Comparison of standard deviation and average value of four algorithms under Ackley function

[0210]

[0211] Table 6 Time comparison of four algorithms under Ackley function

[0212]

[0213] From the above results, it can be seen that the improved fireworks algorithm proposed in this paper shows good performance. Compared with FWA, PSO, and GA algorithms, the ImFWA algorithm has higher search accuracy and prevents the calculation from falling into the local optimum within a certain range. It can also be found from the experiment that the ImFWA algorithm takes a long time, but the number of iterations is small when reaching convergence, that is, the time required from the start of the calculation to reaching convergence is not long, so the ImFWA algorithm can be adopted.

[0214] (2) ImFWA optimized BP neural network performance test

[0215] For the proposed ImFWA optimized BP neural network model, the performance analysis was performed using the processed fan bearing data with loads of 0, 1, 2, and 3. The number of spark populations in the algorithm parameters was 1000, the number of iterations was set to 100, the ratio of the training set to the test set was selected to be 4:1, and the BP neural network and RBF network models were trained with the same data at the same time. The experiment was repeated 10 times to obtain the average classification accuracy. The accuracy of the three models under four loads is shown in Table 7, and the average accuracy and time under each load are shown in Table 8:

[0216] Table 7 Accuracy under four load conditions

[0217]

[0218] Table 8 Accuracy and time

[0219]

[0220]

[0221] According to Tables 7 and 8, although the ImFWA neural network model proposed in this paper takes slightly more time than the traditional BP neural network model and the traditional RBF neural network model, its accuracy is greatly improved. Experiments show that the improved fireworks algorithm optimized fan intelligent fault diagnosis system model proposed in this invention can classify fan bearing faults more accurately.

Claims

1. An intelligent diagnosis method for fan bearing faults based on an improved fireworks algorithm, comprising the following steps: 1) Signal sampling: Use an accelerometer to collect bearing vibration data, and select fan bearing data with a digital signal sampling frequency of 12000 Hz; 2) Noise reduction processing: The maximum kurtosis deconvolution technology is used to extract the impact component in the periodic fault signal, and the relevant kurtosis is used as the characteristic parameter. The relevant kurtosis of the fault signal after noise reduction processing is maximized through deconvolution, thereby highlighting the continuous pulse sequence submerged by noise in the signal and displaying the bearing fault information; 3) Feature selection: select mean μ x , peak value x p , the square sum of the amplitude x c , standard deviation θ, these four time domain feature parameters are used for feature extraction; 4) Data normalization: The time domain feature vector is normalized to obtain the final data as the input of the model, and the data obtained by deconvolution and denoising using the maximum correlation kurtosis is converted into data in the range of [0,1] after feature selection; 5) Intelligent diagnosis of fan faults: 5.1) Improved fireworks algorithm: 5.1.1) Fireworks analysis: First, according to the defined explosion radius R i and the number of explosion fireworks S i Generate explosion fireworks through the explosion operation, and then randomly extract a firework x from the fireworks population at this moment i , and the extracted fireworks x i Execute the d-dimensional Gaussian mutation behavior. Finally, after the two fireworks produce explosions and mutation operations respectively, when the fireworks x i When the feasible domain φ is exceeded in the d dimension, a mapping rule is defined to map the firework to a new position; 5.1.2) Select strategy: After the explosion and mutation fireworks are generated, the selection strategy is executed so that the excellent information in the population can be inherited to the next generation of fireworks. A part of individuals are selected from the candidate set γ of fireworks, explosion fireworks and mutation fireworks as the next generation of fireworks population, and the population size is Z; the firework individual with the smallest fitness is directly selected as the next generation of fireworks, and the remaining next generation of fireworks individuals are selected from Z-1 current individuals using the roulette algorithm; in the candidate fireworks set, if a firework is surrounded by many other candidate fireworks individuals, the probability of this firework being selected will decrease, that is, the greater the density of fireworks individuals, the smaller the probability of being selected by the roulette algorithm; Current firework individual x i The probability of being selected p(x i )for: in, R(x i ) is the current firework individual x i The sum of the distances to all fireworks in the candidate fireworks set Z-1; x s Indicates the sth firework; First, we limit the explosion radius. The explosion radius R of fireworks in dimension k ik The restrictions are as follows: Among them, R min,k is the minimum value of the explosion radius of the fireworks in the k-dimensional space, t is the current number of iterations, and t max is the maximum number of iterations, R first is the initial firework explosion radius, R last is the final explosion radius of the fireworks; Secondly, change the mutation rules of the fireworks algorithm mutation operator x i ′ k =x ik +(x Bk -x ik )×g (15) Where g is the improved Gaussian probability density function, o is the stage distribution coefficient, N is the number of distribution coefficients set, which is set to 2 in this system, and σ i is the proportional coefficient of the i-th distribution, the two coefficients are set to 0.7 and 0.3 respectively, τ i is the mean of the ith distribution, is the standard deviation of the ith distribution; Finally, modify the mapping rules: x ik =x l,k +U(0,1)·(x u,k -x l,k ) (17) Where U(0,1) is a random number with a value between 0 and 1 and uniform distribution, x u,k , x l,k are the upper and lower boundaries on dimension k respectively; 5.2) Improve the fireworks algorithm to optimize the BP neural network model; 5.2.1) Set the number of iterations and the initial value of population size Z; 5.2.2) Randomly initialize Z fireworks x in the solution space i ; 5.2.3) Let i = 1, the maximum number of iterations is T, and evaluate the current firework x i The fitness value f(x i ), calculate the explosion radius R i and the number of explosion fireworks S i ; 5.2.4) Generate explosive fireworks; 5.2.5) Generate mutant fireworks; 5.2.6) Execute mapping rules for newly generated out-of-bounds explosion fireworks and mutant fireworks; 5.2.7) In Fireworks x i , select the next generation of fireworks from the explosion and mutation fireworks, and execute i=i+1; 5.2.8) Repeat steps 5.2.2) to 5.2.6) and if i=T, output the optimization result; 5.2.9) The optimization result obtained in step 5.2.8) is the weight and threshold of the proposed model; 5.2.10) Input the feature vector of the training set; 5.2.11) Perform forward propagation according to the following formula; the input signal is x i , ω is the weight, and the net input value after weighting the j-th neuron in the next layer of the input layer is: g(x) is the hidden layer activation function, and the hidden layer output is: The neural network predicts the output as: Where b is the threshold of the neural network; calculate the error v between the prediction and the actual output; 5.2.12) Perform back propagation according to the following formula, The learning rate is η, and the update thresholds a and b are: b k =b k +v k ,k=1,2,…,n (22) Update weight ω: oh jk =ω jk +ηH j v k ,j=1,2,…,n,k=1,2,…,n (24) Calculate the error, update the weights and thresholds; 5.2.13) Repeat steps 5.2.11) to 5.2.12). If the error reaches the target value, stop training and improve the intelligent diagnosis model of fan bearing faults based on the fireworks algorithm to classify the fan bearing fault types.

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