Thick and large nodular cast iron defect prediction method based on phase-space reconstruction

Abstract

The invention discloses a thick and large nodular cast iron defect prediction method based on phase-space reconstruction, which relates to a nondestructive testing technology, and comprises the following steps: acquiring measurement data with thick and large nodular cast iron defects, and dividing the measurement data into a training set and a test set; converting measurement data in the training set from low-dimensional data into high-dimensional data through phase-space reconstruction, and mapping the high-dimensional data into a one-dimensional real number field through a prediction algorithm to obtain prediction output of a next time point so as to obtain a prediction value; establishing a BP neural network structure according to the predicted value of the prediction algorithm, and seeking an optimal BP neural network weight and an optimal initial value of a threshold value through an improved HGAPSO algorithm; and inputting collected real-time data of the thick and large nodular cast iron to be tested into the BP neural network structure to obtain a defect output result of the thick and large nodular cast iron. The method can predict the defects of the thick and large nodular cast iron in the next furnace, reduces the defects and abnormities of the nodular cast iron, and facilitates the comprehensive prediction of the defects of the nodular cast iron.

Description

Technical Field

[0001] The invention relates to nondestructive testing technology, and more particularly to a thick ductile iron defect prediction method based on phase space reconstruction. Background Art

[0002] Ductile iron has many excellent properties such as high strength, high toughness, good wear resistance, processing performance, thermal conductivity and electrical conductivity due to its unique spheroidal graphite structure. Its material composition mainly includes elements such as iron, carbon, silicon, manganese, and spheroidizers and other alloying elements are added to improve mechanical properties. Before the formation of ductile iron, the temperature of the molten iron is as high as 1350-1450℃, which causes the chemical elements to react with the refractory materials to form brittle compounds. At the same time, due to inaccurate control of carbon equivalent, phosphorus, rare earth elements and temperature, it is easy to produce defects such as shrinkage, acid shrinkage, slag inclusion, subcutaneous pores, graphite floating, and poor spheroidization. Traditionally, macro-control of the formation process of ductile iron relies heavily on the operating experience of on-site personnel and cannot achieve automatic control. With the advancement of science and technology, researchers have established a variety of mechanism mathematical models to reveal the internal phenomena of molten iron and reflect the formation mechanism of ductile iron. However, these models have disadvantages such as low accuracy and time-consuming calculations. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a defect prediction method for thick ductile iron based on phase space reconstruction in view of the deficiencies in the prior art.

[0004] The present invention discloses a method for predicting defects of thick ductile iron based on phase space reconstruction, the method comprising the following steps:

[0005] S1, obtaining measurement data of thick ductile iron defects, and dividing the measurement data into a training set and a test set;

[0006] S2, converting the measured data in the training set from low-dimensional data to high-dimensional data through phase space reconstruction, and then performing prediction processing on the high-dimensional data through a prediction algorithm to obtain a prediction value;

[0007] S3, establishing a BP neural network structure according to the predicted value of the prediction algorithm, and seeking the optimal initial value of the BP neural network weight and threshold through the improved HGAPSO algorithm;

[0008] S4, the BP neural network structure uses the optimal initial values ​​of weights and thresholds to train the training set, and stops training when the mean square error of the BP neural network structure reaches the minimum mean square error; uses the trained BP neural network structure to test the test data of the test group, and compares it with the actual value of the thick and large ductile iron defects corresponding to the data of the test group. If they are consistent, it means that the construction of the BP neural network structure meets the requirements;

[0009] S5. Collecting real-time data of the thick ductile iron to be tested and inputting it into the BP neural network structure in step S4 to obtain defect output results of the thick ductile iron.

[0010] Preferably, the prediction algorithm is specifically:

[0011] S21, set k = 1 ~ N, ξ is the area radius, r * is the prediction accuracy, l is the prediction sample length; N is the total number of test data in the training set;

[0012] S22. Searching for high-dimensional data H k The domain point H within the domain radius ξ k1 ,H k2 ,...,H kn(ξ) , and satisfy:

[0013]

[0014] Among them, ‖.‖ represents the infinite norm;

[0015] S23, determine the next iteration point H of n(ξ) domain points k1+1 ,H k2+1 ,...,H kn(ξ)+1 , and find the next iteration point H k1+1 ,H k2+1 ,...,H kn(ξ)+1 The first component

[0016] S24, using the least squares method to fit the parameters a0, α T , and make it satisfy:

[0017]

[0018] Among them, min S is the minimum value of the least squares fitting parameters mentioned above; is the state vector The first component The estimated output; j is the index parameter of the input data, and is the number of input data in the test data;

[0019] S25, a0 and α obtained in S24 T Substitute into the local linear model and use the local linear model to Make a prediction and get the predicted value

[0020] S26, update k = k + 1, repeat S22-S25 until k = N + 1, thus obtaining The predicted value of All predicted values Combine and finally get the combination of predicted values

[0021] S27. Calculate the prediction accuracy:

[0022]

[0023] in, is the estimated output of the i-th prediction sample from the first data starting from N, It is the actual output of the i-th predicted sample from the first data starting from N;

[0024] Compare the prediction accuracy r with the preset accuracy threshold r * The size of r, if r≤r * , then stop the calculation; if r>r*, then modify ξ, k=N, and repeat S22-S26.

[0025] Preferably, the local linear model is:

[0026]

[0027] Among them, ε k+1 is a noise signal that follows a normal distribution.

[0028] Preferably, the correction method of the domain radius ξ is:

[0029] ξ k+1 =ξ k +Δξ;

[0030] Where Δξ is a positive adjustment, ξ k is the radius ξ of the kth domain.

[0031] Preferably, the improved HGAPSO algorithm is specifically:

[0032] S31, initializing parameters in the HGAPSO algorithm;

[0033] S32. Calculate the position of the next generation of particles based on the particle velocity vector and the random perturbation function:

[0034]

[0035] in, is the particle position of the i-th particle after iteration k+1; is the velocity vector of the k+1th generation particle; k t is a random perturbation function;

[0036] S33, calculate the particle position as The global fitness value of the particle is determined, and whether the particle is accepted is determined according to the global fitness value. If the particle is accepted, S34 is performed; otherwise, S35 is performed;

[0037] S34, performing boundary constraints on the particles:

[0038] if but:

[0039]

[0040] if but:

[0041]

[0042] Among them, lb is the lower boundary of the particle group size, and ub is the upper boundary of the particle group size;

[0043] S35. Repeat steps S32-S34 until the maximum number of iterations is reached to form a new particle swarm, extract weights and threshold data from the particle dimension D containing weight and threshold information in the particle swarm, and use the weights and threshold data as the optimal initial values ​​of weights and thresholds for BP neural network structure training.

[0044] Preferably, in S33, the global fitness value is calculated by the following formula:

[0045]

[0046] Among them, NEW(k) is the global fitness value after dynamic adjustment in the kth generation of particles, β is the hyperparameter that controls the decay rate; MSE(k (i) ) refers to the mean square error between the actual output defect percentage and the estimated output defect percentage of the neural network corresponding to the i-th particle of the particle swarm at the k-th iteration.

[0047] Preferably, the optimal global fitness value PRENEW(k) is sought by the following formula:

[0048]

[0049] Preferably, whether the particle is accepted is determined by the following formula:

[0050]

[0051] Among them, if NEW(k) is the best global fitness value, PRENEW(k)=NEW(k), PRENEW(k+1)=NEW(k+1); if MSE(k (i)) as the best global fitness value, PRENEW(k)=MSE(k (i) ), PRENEW(k+1)=MSE(k+1 (i) ).

[0052] Preferably, the mean square error MSE(k (i) ) is calculated by the following formula:

[0053]

[0054] in, The particle position is The particle contains the estimated output value of the neural network after forward feedback under D-dimensional weight value and threshold data; The particle position is The particles contain the D-dimensional weights and the actual output values ​​under the threshold data.

[0055] Beneficial Effects

[0056] The advantages of the present invention are:

[0057] 1. Through phase space reconstruction, prediction algorithm and BP neural network structure, the chaotic characteristics and mutual influence of chemical elements in the formation process of ductile iron can be captured, and the thick and large ductile iron defects of the next furnace can be predicted, reducing the occurrence of ductile iron defects and anomalies, which is helpful to comprehensively predict the defects of ductile iron.

[0058] 2. Compared with the traditional HGAPSO algorithm, the present invention uses the improved HGAPSO algorithm to optimize the weights and thresholds of the BP neural network, which can enhance the global exploration ability, increase the convergence speed, improve the algorithm speed and ensure the stability of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic flow chart of the method for predicting defects of thick ductile iron of the present invention;

[0060] Figure 2 It is a schematic diagram of the BP neural network structure dimensions of the present invention. DETAILED DESCRIPTION

[0061] The present invention will be further described below in conjunction with the embodiments, but it does not constitute any limitation to the present invention. Any limited number of modifications made by anyone within the scope of the claims of the present invention are still within the scope of the claims of the present invention.

[0062] See also Figure 1 The present invention provides a method for predicting defects of thick ductile iron based on phase space reconstruction, and the specific steps are as follows:

[0063] S1. Obtain measurement data. The factors affecting ductile iron defects mainly come from the content of 8 chemical elements, cooling rate and wall thickness. The specific collection method is: use direct reading spectrometer, high-frequency infrared carbon and sulfur analyzer and thermal analyzer to collect chemical element content, and use temperature sensor to measure cooling rate. Collect chemical element content data of 5220 furnaces in a 2-hour cycle, of which the first 5000 furnace data are used for training and the last 220 furnace data are used for testing.

[0064] The cooling rate can be expressed as follows:

[0065]

[0066] The wall thickness can be expressed as follows:

[0067]

[0068] Where v is the propagation speed of sound waves in the material, t r It is the time it takes for the sound wave to travel back and forth.

[0069] S2. The collected 8 chemical element contents, cooling rates and wall thicknesses are normalized. The measured data in the training set after processing will be converted from low-dimensional data to high-dimensional data through phase space reconstruction, and then the high-dimensional data will be mapped to a one-dimensional real number domain through a prediction algorithm to obtain the prediction output at the next time point.

[0070] S3. Construct a BP neural network structure according to the output of the prediction algorithm, and obtain the optimal initial values ​​of the weights and thresholds in the BP neural network structure through the improved GAPSO algorithm, so that the BP neural network structure has a more efficient training capability.

[0071] S4, BP neural network structure uses the optimal initial values ​​of weights and thresholds to train the training set (i.e., 5000 furnace data). When the minimum mean square error is reached, the network stops training. Finally, the trained BP neural network structure is used to test the data of the test group (i.e., 220 furnace data), and the actual values ​​corresponding to the data of the test group are compared. If they are consistent, it means that the construction of the BP neural network structure meets the requirements. The collected real-time data is input into the BP neural network structure, and the output result of the expected defect is obtained through the prediction of the BP neural network structure.

[0072] S5. Input the real-time data of the thick ductile iron to be tested into the BP neural network structure in step S4 to obtain the defect output result of the thick ductile iron, thereby realizing the prediction of the defects of the thick ductile iron.

[0073] In the above S2, the specific implementation method of phase space reconstruction is as follows:

[0074] Assume: y j :R n →R is a second-order differentiable measurement function, where R n →R is a process of mapping n-dimensional vectors to the real number field, y j is the mapping function; R n is an n-dimensional Euclidean space, the input vector is n-dimensional; R is a one-dimensional real number field. The measurement sequence is: in is the output variable; x i is the input measurement data; j is an input element representing different chemical elements, cooling rates and wall thicknesses, in this embodiment j=10 (i.e. 8 chemical elements+1 cooling rate+1 wall thickness); N=5000, i.e. 5000 furnace test data in the training set.

[0075] Embed the above measurement sequence into d j In the dimensional phase space, the state vector can be expressed as:

[0076]

[0077] In this formula, Indicates the data output under the kth furnace and the jth index. If k = 2000, j = 10, it indicates the wall thickness data under the 2000th furnace test data. τ j and d j are the embedding delay and embedding dimension of the measurement sequence respectively. And in the above state vector expression, it must satisfy k=max{(d1-1)τ1, (d2-1)τ2,...,(d 10 -1)τ 10}+1,...,N. And d is the total dimension of the space.

[0078] On the embedded delay τ j and embedding dimension d j , the chemical element composition data, cooling rate and wall thickness of 5000 furnaces are normalized to make their mean 0 and amplitude 1. After normalization, the length of the time series is set to n>>10d, and then the embedded time lag τ is determined as follows j and embedding dimension d j :

[0079] 1) Embedded time delay τ j Determination of:

[0080] Based on the autocorrelation function C j (τ), discretize τ to get τ-C j (τ) chart, and 10 time-delay data τ1, τ2, ..., τ are obtained respectively.10 . The autocorrelation function formula is:

[0081]

[0082] in, It represents the average value of the sum of all i discrete times in the j-th data of the measurement sequence.

[0083] Observe the time delay curve and take C j (τ) The first one drops to e -1 The τ at this time is the optimal time delay, and the τ at this time is marked as the embedded delay τ j .

[0084] 2) Embedding dimension d j Determination of:

[0085] Step 1: Set the initial value: d j =1, counter M j (d)=0.

[0086] Step 2: At d = d1 + d2 + ... + d 10 In the dimensional space, calculation and its nearest area point The Euclidean distance is:

[0087]

[0088] Step 3: Update d=d+1. At this time, the d+1 dimension distance is:

[0089]

[0090] If j / s≥φ, it is considered that when the dimension d→d+1, a pair of pseudo-neighborhood points appear, and accordingly, the counter M j (d) = M j (d) + 1. Here, φ is a threshold parameter for determining whether the nearest vector point in the phase space is a pseudo-neighborhood point.

[0091] Step 4: Change the value of k and repeat steps 2 and 3 until k passes through all points in the phase space orbit. If M j (d)>δ, then d j =d j +1. Among them, δ is the upper limit of the percentage of pseudo-neighborhood points, and the reconstruction process stops when this upper limit is exceeded.

[0092] Step 5: Update d = d + p, where p is M j (d) The number of counters greater than δ. Repeat steps 2-4 until all M j(d)<δ, then the optimal embedding dimension d is obtained j .

[0093] The state of phase space reconstruction evolves according to the following functional relationship:

[0094] H k+1 =F(H k ).

[0095] Based on the output of the above phase space reconstruction, in the prediction algorithm, for j = 10 input data, there is the following function mapping:

[0096]

[0097] To predict For example, predict it through a local linear model:

[0098]

[0099] In the formula, yes The predicted value of k+1 is a noise signal that obeys the normal distribution, a0 is a deviation value of the local linear model, is the unknown coefficient, obtained by the least square method. Therefore, the prediction algorithm specifically includes:

[0100] S21: Set ξ to be the radius of the domain, r * is the prediction accuracy, and l is the prediction sample length.

[0101] S22: Searching for H k The ξ field point H k1 ,H k2 ,...,H kn(ξ) , that is, satisfying:

[0102]

[0103] Among them, ‖.‖ represents the infinite norm.

[0104] S23: Determine the next iteration point H of n(ξ) domain points k1+1 ,H k2+1 ,...,H kn(ξ)+1 , and find their first component

[0105] S24: Fitting parameters a0, α using the least squares method T , and satisfies the following formula:

[0106]

[0107] In this formula, min S is the minimum value of the least squares fitting parameters mentioned above, and then a0 and α are respectively T Find the partial derivative equal to 0, and get a0, α T data.

[0108] S25: a0 and α obtained in S24 T Substitute into the local linear model and use the local linear model to Make a prediction and get

[0109] S26: Update k=k+1, and repeat S22-S25 until k=N+1.

[0110] Step 7: Calculate the prediction accuracy:

[0111]

[0112] in, is the estimated output of the i-th prediction sample from the first data starting from N, It is the actual output of the i-th predicted sample starting from N for the first data.

[0113] Compare r and r * The size of r, if r≤r * , then stop the calculation; if r>r*, then modify ξ, k=N, and repeat steps 2-6.

[0114] Here we use the linear correction method:

[0115] ξ k+1 =ξ k +Δξ;

[0116] Among them, Δξ is a positive adjustment amount.

[0117] The final combination of predicted values Based on data from j = 10 and N = 5000 furnaces, the predicted value It is 10*5000 dimensional data.

[0118] The BP neural network structure is established based on the predicted value of the prediction algorithm. The neural network structure is established based on the principle that the embedding dimension is equal to the input node of the neural network, such as Figure 2 As shown, the BP neural network structure is as follows: the number of neural network nodes is 10, the number of hidden layer nodes is 2*10+1 according to the empirical formula, and the number of output layer nodes is the percentage of the five specific defect types.

[0119] After the BP neural network structure is established, the optimal initial value of the BP neural network weights and thresholds is sought through the improved HGAPSO algorithm. For the traditional HGAPSO algorithm, the iteration of the particle swarm requires continuous mutation and update, which increases the amount of calculation of the algorithm. Here, the dynamic adjustment factor and Gaussian mutation operator are introduced to improve the calculation speed of HGAPSO and reduce the number of iterations. The improved HGAPSO algorithm mainly includes the following steps:

[0120] S31, algorithm initialization:

[0121] S311, population initialization:

[0122] Set the population size to N, the maximum number of iterations to T, and the particle dimension to D. The particle swarm is an N×D-dimensional matrix. The particle dimension D contains the weights and threshold information between different nodes. For example, the first 10×21 dimensions of the particle are the weights between the input layer and the hidden layer, the 10×21+1 to 10×21+21×5 dimensions of the particle are the weights between the hidden layer and the output layer, and the 10×21+21×5+1 to 10×21+21×5+21 dimensions of the particle are the thresholds of the hidden layer nodes. Then randomly generate particle positions. Where i=1,2,…,N.

[0123] S312, parameter initialization:

[0124] Initialize the parameters c1, c2, r1, r2, and the decay factor λ in the particle swarm algorithm formula.

[0125] S32, particle position update:

[0126] The formula for calculating the velocity vector of the next generation of particles is:

[0127]

[0128] is the velocity vector of the k+1th generation particle; w is the inertia weight; c1 and c2 are both learning factors; r1 and r2 are both random numbers distributed in [0,1]; is the individual optimal value in the kth generation particle; is the global optimal value in the kth generation of particles; σ is the Gaussian variation parameter, i.e. the standard deviation of the noise. In the velocity vector formula represents the independent evolutionary patterns of individuals in each generation, and Represents the evolutionary pattern of the population in each generation.

[0129] The random perturbation function is:

[0130] k t =k0e -λt. Where k0 is the initial adjustment factor.

[0131] Calculate the position of the next generation of particles based on the particle's velocity vector and random perturbation function:

[0132]

[0133] in, is the particle position of the i-th particle after iteration k+1.

[0134] S33, calculate the particle position as The fitness of the particle is calculated and whether the particle is accepted is determined based on the fitness:

[0135] S331, calculate the mean square error between each particle after the optimization algorithm iteration and the particle before the iteration:

[0136]

[0137] Among them, MSE(k (i) ) refers to the mean square error between the actual output defect percentage and the estimated output defect percentage of the neural network corresponding to the i-th particle of the k-th iteration of the particle swarm; The particle position is The particle contains the estimated output value of the neural network after forward feedback under D-dimensional weight value and threshold data; The particle position is The particles contain the D-dimensional weights and the actual output values ​​under the threshold data.

[0138] S332, dynamically adjust the fitness value:

[0139]

[0140] Among them, NEW(k) is the global fitness value after dynamic adjustment in the kth generation of particles, β is the hyperparameter that controls the decay rate, and t is the current number of iterations, which is 1~T.

[0141] After finding the fitness values ​​of N particles, we seek the optimal global fitness value PRENEW(K). Specifically,

[0142]

[0143] S333, update particle swarm position:

[0144]

[0145] S334, Boundary Constraints:

[0146] if but:

[0147]

[0148] if but:

[0149]

[0150] S35. Repeat steps S32-S34 until the maximum number of iterations is reached to form a new particle swarm, extract weights and threshold data from the particle dimension D containing weight and threshold information in the particle swarm, and use the weights and threshold data as the optimal initial values ​​of weights and thresholds for BP neural network structure training.

[0151] The above is only a preferred embodiment of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the structure of the present invention, which will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A method for predicting defects in thick ductile iron based on phase space reconstruction, characterized in that: The method comprises the following steps: S1, obtaining measurement data of thick ductile iron defects, and dividing the measurement data into a training set and a test set; S2, converting the measured data in the training set from low-dimensional data to high-dimensional data through phase space reconstruction, and then performing prediction processing on the high-dimensional data through a prediction algorithm to obtain a prediction value; S3, establishing a BP neural network structure according to the predicted value, and seeking the optimal initial value of the BP neural network weight and threshold through the improved HGAPSO algorithm; S4, the BP neural network structure uses the optimal initial values ​​of weights and thresholds to train the training set, and stops training when the mean square error of the BP neural network structure reaches the minimum mean square error; uses the trained BP neural network structure to test the test data of the test group, and compares it with the actual value of the thick and large ductile iron defects corresponding to the data of the test group. If they are consistent, it means that the construction of the BP neural network structure meets the requirements; S5. Input the collected real-time data of the thick ductile iron to be tested into the BP neural network structure in step S4 to obtain the defect output result of the thick ductile iron.

2. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 1 is characterized in that: The prediction algorithm is specifically: S21, set k = 1 ~ N, ξ is the area radius, r * is the prediction accuracy, l is the prediction sample length; N is the total number of test data in the training set; S22. Searching for high-dimensional data H k The domain point H within the domain radius ξ k1 ,H k2 ,...,H kn(ξ) , and satisfy it: Among them, ‖.‖ represents the infinite norm; S23, determine the next iteration point H of n(ξ) domain points k1+1 ,H k2+1 ,...,H kn(ξ)+1 , and find the next iteration point H k1+1 ,H k2+1 ,...,H kn(ξ)+1 The first component S24, using the least squares method to fit the parameters a0, α T , and satisfy it: Among them, min S is the minimum value of the least squares fitting parameters mentioned above; is the state vector The first component The estimated output; j is the index parameter of the input data; S25, a0 and α obtained in S24 T Substitute into the local linear model and use the local linear model to Make a prediction and get the predicted value S26, update k = k + 1, repeat S22-S25 until k = N + 1, thus obtaining The predicted value of All predicted values Combine and finally get the combination of predicted values S27. Calculate the prediction accuracy: in, is the estimated output of the i-th prediction sample from the first data starting from N, It is the actual output of the i-th predicted sample from the first data starting from N; Compare the prediction accuracy r with the preset accuracy threshold r * The size of r, if r≤r * , then stop the calculation; if r>r*, then modify ξ, k=N, and repeat S22-S26.

3. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 2 is characterized in that: The local linear model is: Among them, ε k+1 is a noise signal that follows a normal distribution.

4. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 2 is characterized in that: The correction method of the domain radius ξ is: x k+1 =ξ k +Dx; Where Δξ is a positive adjustment, ξ k is the radius ξ of the kth domain.

5. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 1, characterized in that: The improved HGAPSO algorithm is specifically: S31, initializing parameters in the HGAPSO algorithm; S32. Calculate the position of the next generation of particles based on the particle velocity vector and the random perturbation function: in, is the particle position of the i-th particle after iteration k+1; is the velocity vector of the k+1th generation particle; k t is the random perturbation function; S33, calculate the particle position as The global fitness value of the particle is determined, and whether the particle is accepted is determined according to the global fitness value. If the particle is accepted, S34 is performed; otherwise, S35 is performed; S34, performing boundary constraints on the particles: if but: if but: Among them, lb is the lower boundary of the particle group size, and ub is the upper boundary of the particle group size; S35. Repeat steps S32-S34 until the maximum number of iterations is reached to form a new particle swarm, extract weights and threshold data from the particle dimension D containing weight and threshold information in the particle swarm, and use the weights and threshold data as the optimal initial values ​​of weights and thresholds for BP neural network structure training.

6. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 5, characterized in that: In S33, the global fitness value is calculated by the following formula: Among them, NEW(k) is the global fitness value after dynamic adjustment in the kth generation of particles, β is the hyperparameter that controls the decay rate; MSE(k (i) ) refers to the mean square error between the actual output defect percentage and the estimated output defect percentage of the neural network corresponding to the i-th particle of the particle swarm at the k-th iteration.

7. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 6 is characterized in that: The optimal global fitness value PRENEW(k) is found by the following formula:

8. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 7, characterized in that: Whether the particles are accepted is determined by the following formula: Among them, if NEW(k) is the best global fitness value, PRENEW(k) = NEW(k), PRENEW(k+1)=NEW(k+1); if MSE(k (i) ) as the best global fitness value, PRENEW(k)=MSE(k (i) ),PRENEW(k+1)=MSE(k+1 (i) )。 9. The method for predicting defects of thick ductile iron based on phase space reconstruction according to claim 6, characterized in that: Mean square error MSE(k (i) ) is calculated by the following formula: in, The particle position is The particle contains the estimated output value of the neural network after forward feedback under D-dimensional weight value and threshold data; The particle position is The particles contain the D-dimensional weights and the actual output values ​​under the threshold data.

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