Bulb biconical reentry vehicle reliability analysis method

Abstract

The invention discloses a reliability analysis method for a ball-head biconical reentry vehicle. The method comprises the following steps: constructing a maximum temperature prediction model for the boundary of an internal cavity of the ball-head biconical reentry vehicle according to a deep neural network and a generalized chaotic polynomial; obtaining a labeled training data set and a non-labeled training data set; constructing a loss function based on the property of the generalized chaotic polynomial; based on the loss function, training a maximum temperature prediction model of the boundary of the internal cavity of the ball-head biconical reentry vehicle by using the labeled training data set and the unlabeled training data set; and performing prediction analysis on the maximum temperature of the boundary of the internal cavity of the ball-head biconical reentry vehicle by using the trained prediction model for the maximum temperature of the boundary of the internal cavity of the ball-head biconical reentry vehicle. According to the method, the maximum temperature of the boundary of the inner cavity of the ball-head biconical reentry vehicle can be accurately predicted under the condition that the geometric parameters and the material parameters of the ball-head biconical reentry vehicle are given, the calculation cost is reduced, and the analysis efficiency is improved.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft design, and in particular to a reliability analysis method for a spherical-head double-conical reentry vehicle. Background Art

[0002] The Sphere-Biconic Reentry Flight Vehicle (SBRFV) is a commonly used high-altitude, high-speed aircraft. Figure 1-4 The spherical head double cone reentry vehicle is generally a rotating geometric body around the central axis, including a top, an internal heat insulation metal structure and an external heat protection layer. The top is composed of a spherical geometric body and a truncated cone. The external heat protection layer is a rotating geometric body whose generatrix is ​​a circular arc. The internal heat insulation metal structure is a cavity rotating geometric body. The top and the internal heat insulation metal structure are made of alloy structural steel, and the external heat protection layer is made of fiberglass. Based on the above-mentioned structure of the spherical head double cone reentry vehicle, the structural parameters corresponding to the spherical head double cone reentry vehicle include 12 geometric parameters and 7 material parameters. The 2 geometric parameters include: the length of the top D1, the radius of the spherical geometric body r1, the angle between the truncated cone generatrix and the central axis ω, the radius r2 corresponding to the generatrix arc of the external heat protection layer, the length D2 of the external heat protection layer, the top wall thickness d2, the side wall thickness d1, the bottom thickness d3 and the bottom circle radius r3, the top thickness d4, the side wall thickness d5 and the bottom thickness d6 of the internal insulation metal structure. The 7 material parameters include: the density ρ1 of the alloy structural steel, the specific heat capacity and thermal conductivity Density ρ2 and specific heat capacity of FRP and thermal conductivity and the surface radiation coefficient R of the external thermal protection layer ehs Among them, Figure 4 In (a x ,a y ) is the coordinate of the center of the generatrix arc of the external heat protection layer. After determining the above structural parameters, the corresponding ball-headed double-conical reentry vehicle can be designed.

[0003] In order to verify whether the designed ball-headed double-conical reentry vehicle is reliable, it is necessary to conduct a simulation analysis of the ball-headed double-conical reentry vehicle. Specifically, a heat flux is loaded on the surface of the ball-headed double-conical reentry vehicle, and a high-fidelity finite element model is used to analyze and calculate the maximum temperature T of the internal cavity boundary of the ball-headed double-conical reentry vehicle. SBRFV , if the maximum temperature T SBRFV If the temperature is lower than the preset temperature threshold, the currently designed spherical-headed double-conical reentry vehicle is reliable; otherwise, the currently designed spherical-headed double-conical reentry vehicle has poor reliability and needs to be redesigned.

[0004] However, in actual engineering applications, random factors such as ambient temperature changes and material molding condition disturbances will lead to uncertainty in material density ρ1 and ρ2, and random factors such as processing and manufacturing deviations will lead to uncertainty in 12 geometric parameters. In order to improve the accuracy of the results, a large number of simulation analyses are required. In the use of high-fidelity finite element models to analyze and calculate the maximum temperature T of the internal cavity boundary of the ball-headed double-conical reentry vehicle, the maximum temperature T of the internal cavity boundary of the ball-headed double-conical reentry vehicle is calculated. SBRFV When performing a single finite element analysis, the computational cost is high, more computing resources are required, and the computational time is long. If a large number of finite element analyses are performed, the computational cost increases dramatically and the efficiency is low. Summary of the invention

[0005] In order to solve part or all of the technical problems existing in the above-mentioned prior art, the present invention provides a reliability analysis method for a spherical-headed double-conical reentry vehicle.

[0006] The technical solution of the present invention is as follows:

[0007] A reliability analysis method for a ball-headed double-cone reentry vehicle is provided, the method comprising:

[0008] A prediction model for the maximum temperature of the inner cavity boundary of a spherical-headed biconical reentry vehicle is constructed based on deep neural networks and generalized chaotic polynomials.

[0009] Obtain a labeled training data set and an unlabeled training data set, the labeled training data includes input data and its corresponding output data, the unlabeled training data includes input data, the input data includes geometric parameters and material parameters of the spherical-headed biconical reentry vehicle, and the output data includes the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle;

[0010] Based on the properties of generalized chaotic polynomials, a loss function is constructed;

[0011] Based on the loss function, the maximum temperature prediction model of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle is trained using the labeled training data set and the unlabeled training data set;

[0012] The trained prediction model for the maximum temperature of the boundary of the internal cavity of the spherical-headed double-conical reentry vehicle is used to perform prediction analysis on the maximum temperature of the boundary of the internal cavity of the spherical-headed double-conical reentry vehicle.

[0013] In some possible implementations, the generalized chaotic polynomial is:

[0014]

[0015] The properties of the generalized chaotic polynomial include:

[0016] E[y (p)(ξ)]=c1

[0017]

[0018] Where ξ is the input data, ξ={ξ k |k=1,2,…,d}, d represents the number of variables contained in the input data ξ, c i is the expansion coefficient, Φ i (ξ) is a multidimensional standard orthogonal basis {Φ1(ξ),…,Φ M (ξ)}, M is a multidimensional orthogonal basis {Φ1(ξ),…,Φ M (ξ)}, M = (d+p)! / (d!p!), E[y (p) (ξ)] represents y (p) The mean value of (ξ), V[y (p) (ξ)] represents y (p) The variance of (ξ).

[0019] In some possible implementations, the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle includes:

[0020] An input layer, comprising a plurality of input neurons, wherein the output of each of the input neurons is respectively connected to the input of a plurality of intermediate neurons, and the input neurons are used to receive and output input data corresponding to the ball-headed bi-conical reentry vehicle;

[0021] An orthogonal polynomial layer comprises a plurality of intermediate neurons, the outputs of the plurality of intermediate neurons are connected to output neurons respectively, and the value of the ith intermediate neuron is configured as the ith multidimensional polynomial Φ of the generalized chaotic polynomial i (ξ);

[0022] The output layer includes an output neuron for outputting the maximum temperature value of the boundary of the internal cavity of the spherical head double cone reentry vehicle according to the input of the plurality of intermediate neurons, and the weight corresponding to the i-th intermediate neuron is configured as the i-th expansion coefficient c of the generalized chaotic polynomial i .

[0023] In some possible implementations, the loss function is:

[0024]

[0025] in, represents the loss function, represents the supervised loss function, represents the unsupervised loss function, represents the first unsupervised loss function, represents the second unsupervised loss function, λ1 and λ2 represent hyperparameters.

[0026] In some possible implementations, the supervised loss function is expressed as:

[0027]

[0028] Among them, N LD represents the amount of labeled training data set, and They represent the standardized input data of the lth labeled training data and the maximum temperature of the inner cavity boundary of the spherical-headed biconical reentry vehicle, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c represents the expansion coefficient.

[0029] In some possible implementations, the first unsupervised loss function is expressed as:

[0030]

[0031] The second unsupervised loss function is expressed as:

[0032]

[0033] in,

[0034]

[0035] Indicates the predicted maximum temperature The mean value, N UD represents the amount of unlabeled training data, represents the standardized input data of the l′th unlabeled training data, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c i represents the i-th expansion coefficient, Represents input data The corresponding i-th multidimensional polynomial, Indicates the predicted maximum temperature The variance of .

[0036] In some possible implementations, based on the loss function, training the maximum temperature prediction model of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle using the labeled training data set and the unlabeled training data set includes the following steps:

[0037] Step S41, preprocessing the labeled training data set and the unlabeled training data set to convert the input data into standardized data;

[0038] Step S42, initializing the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle according to the labeled training data set;

[0039] Step S43, respectively inputting the input data of the labeled training data in the labeled training data set and the input data of the unlabeled training data in the unlabeled training data set into the prediction model for the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle, to obtain the prediction value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the labeled training data and the prediction value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the unlabeled training data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle;

[0040] Step S44, calculating a loss function according to the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle with labeled training data and the corresponding predicted value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle, and the predicted value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the unlabeled training data;

[0041] Step S45, using the loss function to update the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle;

[0042] Step S46, determine whether the preset training stop condition is reached. If so, use the current ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model as the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model that has completed training. If not, return to step S43.

[0043] In some possible implementations, training the maximum temperature prediction model for the internal cavity boundary of the spherical-headed double-conical reentry vehicle further includes the following steps:

[0044] Acquire a validation data set, the validation data including standardized input data and corresponding output data, the input data including geometric parameters and material parameters of the spherical-headed biconical reentry vehicle, and the output data including the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle;

[0045] After each update of the parameters of the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the input data of the verification data in the verification data set is input into the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, and the prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle corresponding to the verification data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle is obtained; according to the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle of the verification data and the corresponding prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the accuracy evaluation index is calculated, and it is determined whether the currently obtained accuracy evaluation index is less than the accuracy evaluation index obtained in the previous iteration; if so, the currently obtained expansion coefficient is saved as the optimal expansion coefficient; otherwise, the saved optimal expansion coefficient is kept unchanged;

[0046] After completing the iterative training of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle, the saved optimal expansion coefficient is extracted as the final expansion coefficient of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle.

[0047] In some possible implementations, the method further includes:

[0048] The reliability of the spherical-headed double-conical reentry vehicle is quantitatively analyzed using the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

[0049] In some possible implementations, the reliability of the ball-headed double-conical reentry vehicle is quantitatively analyzed by using the maximum temperature prediction model of the internal cavity boundary of the ball-headed double-conical reentry vehicle, including:

[0050] Based on the value range of geometric parameters and material parameters of the spherical-headed double-conical reentry vehicle, a random data set is obtained, the random data includes input data, the input data includes geometric parameters and material parameters of the spherical-headed double-conical reentry vehicle, and the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle is used to predict the maximum temperature prediction value of the internal cavity boundary of the spherical-headed double-conical reentry vehicle corresponding to each random data, and the failure rate and reliability of the spherical-headed double-conical reentry vehicle are calculated according to the maximum temperature prediction value of the internal cavity boundary of the spherical-headed double-conical reentry vehicle;

[0051] The failure rate is calculated using the following formula:

[0052]

[0053] Reliability is calculated using the following formula:

[0054] R SBRFV =1-P f

[0055] Among them, P f represents the failure rate of the spherical-headed biconical reentry vehicle, R SBRFV represents the reliability of the spherical-headed biconical reentry vehicle, N MCS represents the amount of random data, represents the standardized input data of the lth random data, Δ lim It indicates the temperature threshold for the normal operation of the pre-set spherical-headed bi-conical reentry vehicle. The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, IF(·) is the indicator function, expressed as:

[0056]

[0057] The main advantages of the technical solution of the present invention are as follows:

[0058] The reliability analysis method of the ball-headed bi-conical reentry vehicle of the present invention constructs a maximum temperature prediction model for the internal cavity boundary of the ball-headed bi-conical reentry vehicle based on a deep neural network and a generalized chaotic polynomial, constructs a loss function of the prediction model using the properties of the generalized chaotic polynomial, and trains the maximum temperature prediction model for the internal cavity boundary of the ball-headed bi-conical reentry vehicle using a labeled training data set and an unlabeled training data set. A high-precision maximum temperature prediction model for the internal cavity boundary of the ball-headed bi-conical reentry vehicle can be obtained, thereby enabling accurate prediction of the maximum temperature of the internal cavity boundary of the ball-headed bi-conical reentry vehicle under given geometric parameters and material parameters of the ball-headed bi-conical reentry vehicle, thereby reducing computational costs and improving the design and analysis efficiency of the ball-headed bi-conical reentry vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0060] Figure 1 It is a structural schematic diagram of an existing ball-head double-cone reentry vehicle;

[0061] Figure 2 for Figure 1 AA section view in the figure;

[0062] Figure 3 for Figure 1 BB section view in the figure;

[0063] Figure 4 for Figure 1 The schematic diagram of the relevant parameters of the ball-nosed double-conical reentry vehicle shown;

[0064] Figure 5 It is a flow chart of a reliability analysis method of a ball-headed double-conical reentry vehicle according to an embodiment of the present invention;

[0065] Figure 6 It is a schematic diagram of the structure of an existing single hidden layer neural network;

[0066] Figure 7 A schematic diagram of a maximum temperature prediction model for the internal cavity boundary of a spherical-headed double-conical reentry vehicle according to an embodiment of the present invention.

[0067] Figure 8 The figure is a schematic diagram of the training process of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0069] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0070] refer to Figure 5 An embodiment of the present invention provides a reliability analysis method for a ball-headed double-conical reentry vehicle, comprising the following steps:

[0071] Step S1, constructing a maximum temperature prediction model for the internal cavity boundary of a spherical-headed double-conical reentry vehicle based on a deep neural network and a generalized chaotic polynomial;

[0072] Step S2, obtaining a labeled training data set and an unlabeled training data set, wherein the labeled training data includes input data and its corresponding output data, and the unlabeled training data includes input data, wherein the input data includes geometric parameters and material parameters of the ball-headed biconical reentry vehicle, and the output data includes the maximum temperature of the internal cavity boundary of the ball-headed biconical reentry vehicle;

[0073] Step S3, constructing a loss function based on the properties of the generalized chaotic polynomial;

[0074] Step S4, based on the loss function, using the labeled training data set and the unlabeled training data set to train the maximum temperature prediction model of the internal cavity boundary of the spherical head double cone reentry vehicle;

[0075] Step S5, using the trained prediction model for the maximum temperature prediction of the internal cavity boundary of the spherical-headed double-conical reentry vehicle to perform prediction analysis on the maximum temperature of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

[0076] A reliability analysis method for a ball-headed bi-conical reentry vehicle provided in an embodiment of the present invention constructs a maximum temperature prediction model for the boundary of the internal cavity of a ball-headed bi-conical reentry vehicle based on a deep neural network and a generalized chaotic polynomial, constructs a loss function of the prediction model using the properties of the generalized chaotic polynomial, and trains the maximum temperature prediction model for the boundary of the internal cavity of a ball-headed bi-conical reentry vehicle using a labeled training data set and an unlabeled training data set. A high-precision maximum temperature prediction model for the boundary of the internal cavity of a ball-headed bi-conical reentry vehicle can be obtained, thereby enabling accurate prediction of the maximum temperature of the boundary of the internal cavity of a ball-headed bi-conical reentry vehicle under given geometric parameters and material parameters of the ball-headed bi-conical reentry vehicle, thereby reducing computational costs and improving the design and analysis efficiency of the ball-headed bi-conical reentry vehicle.

[0077] The steps and principles of a reliability analysis method for a ball-headed double-conical reentry vehicle provided in one embodiment of the present invention are further described below.

[0078] Step S1, constructing a maximum temperature prediction model for the internal cavity boundary of a spherical-headed bi-conical reentry vehicle based on a deep neural network and a generalized chaotic polynomial.

[0079] In actual engineering applications, random factors such as ambient temperature changes and material molding condition disturbances will lead to uncertainty in material densities ρ1 and ρ2, and random factors such as processing and manufacturing deviations will lead to uncertainty in 12 geometric parameters. According to the design standards GJB2150A-2005, GJB 3759-99, GB / T-1804-2000 and engineering experience, the two material densities and 12 geometric parameters are modeled as random variables obeying normal distribution, and the thermal conductivity of alloy structural steel is and specific heat capacity Thermal conductivity of FRP and specific heat capacity and the surface radiation coefficient R of the external thermal protection layer ehs Modeled as a random variable that follows a uniform distribution. The seven structural parameters ρ2,ρ1, R ehs Represented as a 7-dimensional vector X mp =[X1 X2 … X7] T, the 12 geometric parameters d4, d5, d6, r3, r2, d2, d3, d1, D2, D1, r1, ω are represented as a 12-dimensional vector X gp =[X8 X9 … X 19 ] T Tables 1 and 2 below show the uncertainty information of material parameters and geometric parameters of a spherical-headed double-conical reentry vehicle.

[0080] Table 1 Uncertainty information of material parameters in the spherical-headed biconical reentry vehicle

[0081]

[0082] Table 2 Uncertainty information of geometric parameters in the spherical-headed biconical reentry vehicle

[0083]

[0084]

[0085] in, represents the relative limit deviation. Assume that the random variable X k The mean value of For a random variable X that follows a uniform distribution k (k=1,2,5,6,7), and its upper and lower bounds are and For a random variable X that follows a normal distribution k (k=3,4,8,9,…,19), its standard deviation Determined using the "6σ" criterion, namely:

[0086] In order to facilitate the description of the steps and principles of the reliability analysis method of the ball-headed double-conical reentry vehicle provided in one embodiment of the present invention, without loss of generality, the 7 structural parameters and 12 geometric parameters of the ball-headed double-conical reentry vehicle are expressed as input ξ={ξ k |k=1,2,…,d}, d represents the number of variables contained in the input data ξ, that is, d=19, and the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle is expressed as a random system Y=f(ξ).

[0087] Generalized Polynomial Chaos (gPC) uses different types of orthogonal polynomials to construct mixed polynomials. Assuming that the random system Y = f (ξ) is approximated by a p-order generalized chaotic polynomial, the p-order generalized chaotic polynomial adopts the truncation method that only retains the multidimensional standard orthogonal polynomials whose order does not exceed p. Then the p-order gPC model of the random system Y = f (ξ) can be expressed as:

[0088]

[0089] Where ξ is the input data, ξ={ξ k |k=1,2,…,d}, d represents the number of variables contained in the input data ξ, c i is the expansion coefficient, Φ i (ξ) is a multidimensional standard orthogonal basis {Φ1(ξ),…,Φ M (ξ)}, M is a multidimensional orthogonal basis {Φ1(ξ),…,Φ M The number of multidimensional polynomials in (ξ)}, M = (d+p)! / (d!p!).

[0090] Based on the orthogonality of multidimensional orthonormal basis, y (p) The mean, variance and expansion coefficient of (ξ) satisfy the following two properties:

[0091] Mean E[y (p) (ξ)] is equal to the first expansion coefficient c1, that is:

[0092] E[y (p) (ξ)]=c1Formula 2

[0093] Variance V[y (p) (ξ)] is equal to the expansion coefficients {c2,c3,…,c M}, that is:

[0094]

[0095] For the i-th multidimensional polynomial Φ i (ξ), which is the random variable ξ k The product of univariate polynomials (k=1,2,…,d) is specifically expressed as:

[0096]

[0097] in, is a multivariate index set s i The kth index in To form a univariate standard orthogonal basis The standard orthogonal polynomials of .

[0098] For a univariate orthonormal basis It is orthogonal to the probability measure Γ, which can be expressed as:

[0099]

[0100] Among them, Ω is the event space, δ jj′is the Kronecker delta.

[0101] Univariate Orthonormal Basis is the random variable ξ k The origin moment of is constructed, where the probability measure Γ can be any type of probability distribution. To this end, in one embodiment of the present invention, the method proposed in the technical document "Oladyshkin S, Nowak W. Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion [J]. Reliability Engineering & System Safety. 2012, 106: 179–190" is used to construct a univariate standard orthogonal basis.

[0102] For the kth random variable ξ k , j-order (j=0,1,…,p) polynomial is defined as:

[0103]

[0104] in, is a polynomial The coefficient of Calculated by the following formula:

[0105]

[0106] in, is a random variable ξ k The j-order origin moment of .

[0107] Based on the above formula 6, the random variable ξ k The j-order standard orthogonal polynomial It can be expressed as:

[0108]

[0109]

[0110] Furthermore, in order to simplify the coefficients (j=0,1,…,p), the random variable ξ k Through linear transformation, it is transformed into a standardized random variable with a mean of 0 and a variance of 1, which is specifically expressed as:

[0111]

[0112] Among them, μ k is a random variable ξk The mean value, σ k is a random variable ξ k The standard deviation of .

[0113] Furthermore, in order to simplify the formula notation, we assume that ξ={ξ k |k=1,2,…,d} is already a standardized input. Based on the above formulas 7 and 10, polynomials of different orders can be obtained. The coefficients of , thus obtaining the univariate standard orthogonal basis according to the above formula eight According to the above formula 4, we can obtain the multidimensional standard orthogonal basis {Φ1(ξ),…,Φ M (ξ)}.

[0114] Further, refer to Figure 6 , assuming that the random system Y = f(ξ) is approximated by a single hidden layer neural network, the single hidden layer neural network model of the random system Y = f(ξ) can be expressed as:

[0115]

[0116] Among them, θ represents the parameters of a single hidden layer neural network, θ=(W d×M ,b 1×M ,W M×1 ,b),W d×M and W M×1 represents the weight, b 1×M and b represents the bias, ξ 1×d =[ξ1,ξ2,…,ξ M ] represents input data, H 1×M =[h1,h2,…,h M ],h1,h2,…,h M They represent the values ​​of the M neurons in the hidden layer of a single hidden layer neural network, Represents the output of a single hidden layer neural network corresponding to the input data ξ.

[0117] Set the weight W M×1 =[W1,W2,…,W M ] T ,W1,W2,…,W M They represent the weights corresponding to the M neurons in the hidden layer of a single hidden layer neural network, then It can be expressed as:

[0118]

[0119] Furthermore, based on the above-mentioned analysis process of generalized chaotic polynomials and single hidden layer neural networks, in one embodiment of the present invention, a maximum temperature prediction model for the boundary of the internal cavity of a spherical-headed bi-conical reentry vehicle is constructed according to deep neural networks and generalized chaotic polynomials, and the deep neural network is specifically a single hidden layer neural network.

[0120] refer to Figure 7 In one embodiment of the present invention, the constructed maximum temperature prediction model of the internal cavity boundary of the spherical head double cone reentry vehicle includes:

[0121] An input layer, comprising a plurality of input neurons, wherein the output of each input neuron is respectively connected to the input of a plurality of intermediate neurons, and the input neuron is used to receive and output input data corresponding to the ball-headed bi-conical reentry vehicle;

[0122] The orthogonal polynomial layer includes multiple intermediate neurons, the outputs of the multiple intermediate neurons are connected to the output neurons respectively, and the value of the i-th intermediate neuron is configured as the i-th multidimensional polynomial Φ of the generalized chaotic polynomial i (ξ);

[0123] The output layer includes an output neuron for outputting the maximum temperature value of the internal cavity boundary of the spherical head double cone reentry vehicle according to the input of multiple intermediate neurons, and the weight corresponding to the i-th intermediate neuron is configured as the i-th expansion coefficient c of the generalized chaotic polynomial i .

[0124] Specifically, in the above-constructed prediction model for the maximum temperature of the internal cavity boundary of the ball-headed biconical reentry vehicle, the number of input neurons is the same as the number of variables contained in the input data corresponding to the ball-headed biconical reentry vehicle, and the number of intermediate neurons is the same as the number of multidimensional polynomials in the generalized chaotic polynomial. For example, if the above-mentioned input data includes 19 parameters, namely 12 geometric parameters and 7 structural parameters, then the number of input neurons is 19, and there are M multidimensional polynomials in the above-mentioned generalized chaotic polynomial, then the number of intermediate neurons is M.

[0125] In one embodiment of the present invention, by using an orthogonal polynomial layer {Φ1(ξ),Φ2(ξ),…,Φ M (ξ)} replaces the hidden layer in the single hidden layer neural network to construct a prediction model for the maximum temperature of the internal cavity boundary of a spherical head double cone reentry vehicle. Among them, the orthogonal polynomial layer does not contain any parameters that need to be learned, and the values ​​of all neurons in the orthogonal polynomial layer H 1×M for:

[0126] H 1×M =[Φ1(ξ) Φ2(ξ) … Φ M (ξ)] Formula 13

[0127] At the same time, the expansion coefficient c=[c1 c2 … c M ] T is parameterized as the weight W of the output neuron M×1 , the bias of the output neuron is configured to be 0, and the expansion coefficient c is the parameter to be learned of the prediction model of the maximum temperature of the internal cavity boundary of the spherical head double cone reentry vehicle. According to the above formula 12, the output value of the output neuron of the prediction model of the maximum temperature of the internal cavity boundary of the spherical head double cone reentry vehicle is expressed as:

[0128]

[0129] Step S2, obtaining a labeled training data set and an unlabeled training data set, wherein the labeled training data includes input data and its corresponding output data, and the unlabeled training data includes the input data.

[0130] Taking into account the difficulty of obtaining labeled training data when designing a ball-headed bi-conical reentry vehicle, in one embodiment of the present invention, a small amount of labeled training data and a large amount of unlabeled training data are obtained, and a loss function is constructed based on a generalized chaotic polynomial. The labeled training data, the unlabeled training data and the constructed loss function are used to train a prediction model for the maximum temperature of the internal cavity boundary of a ball-headed bi-conical reentry vehicle to solve the expansion coefficient, thereby improving the prediction accuracy of the prediction model for the maximum temperature of the internal cavity boundary of a ball-headed bi-conical reentry vehicle.

[0131] Furthermore, since the maximum temperature of the boundary of the internal cavity of the spherical-headed bi-conical reentry vehicle is related to 19 parameters of the spherical-headed bi-conical reentry vehicle (including 7 material parameters and 12 geometric parameters), in order to realize the accurate prediction of the maximum temperature of the boundary of the internal cavity of the spherical-headed bi-conical reentry vehicle by the maximum temperature prediction model of the boundary of the internal cavity of the spherical-headed bi-conical reentry vehicle, in one embodiment of the present invention, the input data in the labeled training data includes 12 geometric parameters and 7 material parameters of the spherical-headed bi-conical reentry vehicle, the output data includes the maximum temperature of the boundary of the internal cavity of the spherical-headed bi-conical reentry vehicle corresponding to the input data, and the input data in the unlabeled training data includes 12 geometric parameters and 7 material parameters of the spherical-headed bi-conical reentry vehicle.

[0132] In one embodiment of the present invention, labeled training data can be obtained from known data, or by "selecting a set of input data from a predetermined range of geometric parameters and material parameters of a spherical-headed biconical reentry vehicle, and using finite element analysis to obtain the corresponding maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle based on the selected input data" to obtain a set of labeled training data, and multiple sets of labeled training data can be obtained by performing multiple selections and finite element analyses. Unlabeled training data can be obtained from known data, or by "selecting a set of input data from a predetermined range of geometric parameters and material parameters of a spherical-headed biconical reentry vehicle" to obtain a set of unlabeled training data, and multiple sets of unlabeled training data can be obtained by performing multiple selections.

[0133] Step S3, constructing a loss function based on the properties of the generalized chaotic polynomial.

[0134] Specifically, set: N LD Data pairs Composing a labeled training dataset in, For input data, is the corresponding output label; N UD unlabeled input data Composing an unlabeled training dataset

[0135] For l=1,2,…,N LD , refer to formula 10, there will be a labeled training data set Each input data Convert to standardized input data Prediction of the maximum temperature of the internal cavity boundary of a spherical-headed biconical reentry vehicle using a prediction model The corresponding maximum temperature of the internal cavity boundary of the spherical double-conical reentry vehicle is calculated by predicting the maximum temperature With output label (l=1,2,…,N LD ) constructs a supervised loss function using the L1 norm of the deviation between Specifically expressed as:

[0136]

[0137] Among them, N LD represents the amount of labeled training data, and They represent the standardized input data of the lth labeled training data and the maximum temperature of the inner cavity boundary of the spherical-headed biconical reentry vehicle, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c represents the expansion coefficient.

[0138] For l′=1,2,…,N UD , refer to Formula 10, and convert the unlabeled training dataset Each input data Convert to standardized input data Prediction of the maximum temperature of the inner cavity boundary of a spherical-headed biconical reentry vehicle using a prediction model The corresponding maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle is calculated by the following formula to calculate the mean and variance of the maximum temperature prediction value:

[0139]

[0140]

[0141] in, Indicates the predicted maximum temperature The mean value, N UD represents the amount of unlabeled training data, represents the standardized input data of the l′th unlabeled training data, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c i represents the i-th expansion coefficient, Represents input data The corresponding i-th multidimensional polynomial, Indicates the predicted maximum temperature The variance of .

[0142] According to the above formula 2, by calculating the mean The first unsupervised loss function is constructed by taking the L1 norm of the deviation from the first expansion coefficient c1 Specifically expressed as:

[0143]

[0144] According to the above formula 3, by calculating the variance With the second to last expansion coefficients {c2,c3,…,c M The L1 norm of the squared deviation between the two constructs the second unsupervised loss function Specifically expressed as:

[0145]

[0146] Therefore, based on the unlabeled training dataset Constructed unsupervised loss function It is expressed as:

[0147]

[0148] In summary, the loss function constructed for training and learning the maximum temperature prediction model of the internal cavity boundary of the spherical head double cone reentry vehicle is It is expressed as:

[0149]

[0150] Among them, λ1 and λ2 are hyperparameters. Generally, the less labeled training data there is, the larger the value of the hyperparameter is. This means that when labeled training data is insufficient, sufficient unlabeled training data plays an important role in accurately solving the expansion coefficients. In addition, solving nonlinear random systems requires larger hyperparameters than solving linear random systems.

[0151] Step S4, based on the loss function, using the labeled training data set and the unlabeled training data set to train the maximum temperature prediction model of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle.

[0152] refer to Figure 8 In one embodiment of the present invention, based on the loss function, a maximum temperature prediction model of the internal cavity boundary of a spherical-headed bi-conical reentry vehicle is trained using a labeled training data set and an unlabeled training data set, including the following steps:

[0153] Step S41 , preprocessing the labeled training data set and the unlabeled training data set to convert the input data into standardized data.

[0154] In one embodiment of the present invention, the input data is preprocessed with reference to Formula 10, and each input data in the labeled training data set and the unlabeled training data set is converted into standardized data.

[0155] Step S42, initializing the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle according to the labeled training data set.

[0156] In one embodiment of the present invention, based on labeled training data Use the following formula to calculate the corresponding column vector y LD and the matrix A LD :

[0157]

[0158]

[0159] The initial value c of the expansion coefficient c is calculated using the following formula: 0 :

[0160]

[0161] in, Represents input data The corresponding M-th multidimensional polynomial.

[0162] Since the parameter to be updated and learned in the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle is the expansion coefficient, the parameter of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle is initialized, that is, the expansion coefficient is initialized.

[0163] Step S43, respectively input the input data of the labeled training data in the labeled training data set and the input data of the unlabeled training data in the unlabeled training data set into the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle, and obtain the prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle corresponding to the labeled training data and the prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle corresponding to the unlabeled training data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle.

[0164] In one embodiment of the present invention, the standardized input data of the labeled training data in the labeled training data set and the standardized input data of the unlabeled training data in the unlabeled training data set are respectively input from the input end of the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model, sequentially processed by each layer of the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model, and output from the output end of the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model, and the information output from the output end of the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model is the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction value corresponding to the input data.

[0165] Step S44, calculate the loss function according to the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle in the labeled training data and the corresponding predicted value of the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle, and the predicted value of the maximum temperature of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle corresponding to the unlabeled training data.

[0166] In one embodiment of the present invention, the loss function is calculated using the above formulas 15 to 21 based on information output by a maximum temperature prediction model for the internal cavity boundary of a spherical-headed bi-conical reentry vehicle.

[0167] Step S45, using the loss function to update the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

[0168] Specifically, the loss function is used to update the expansion coefficients in the maximum temperature prediction model of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle.

[0169] In one embodiment of the present invention, a stochastic gradient descent method is used to train and update the parameters of a maximum temperature prediction model for the internal cavity boundary of a spherical-headed double-conical reentry vehicle.

[0170] Specifically, the following formula is used to update the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle:

[0171]

[0172] Among them, c t+1 represents the expansion coefficient of the model at the t+1th iteration, c t represents the expansion coefficient of the model at the tth iteration, Δ[] represents the optimizer, η represents the learning rate, represents the loss function, and c represents the expansion coefficient of the model. The optimizer is set according to the actual situation, such as Adam, etc. The learning rate is pre-set to control the speed of updating the model parameters.

[0173] Step S46, determine whether the preset training stop condition is reached. If so, use the current ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model as the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model that has completed training. If not, return to step S43.

[0174] In one embodiment of the present invention, the training stop condition is specifically set according to the actual situation, for example, when the number of training iterations reaches the set number of iterations. At this time, a parameter ep is set to record the number of training iterations. Each time an iteration is performed, the value of the parameter ep is increased by 1. When the number of training iterations reaches the set number of iterations, that is, ep is equal to the set number of iterations ep. max When , the training is finished, and the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle that has completed the training is obtained.

[0175] Furthermore, in one embodiment of the present invention, in order to further improve the prediction accuracy of the maximum temperature prediction model of the internal cavity boundary of the ball-headed double-conical reentry vehicle that has finally completed the training, when training the maximum temperature prediction model of the internal cavity boundary of the ball-headed double-conical reentry vehicle, the following steps are also included:

[0176] Acquire a validation data set, the validation data including standardized input data and corresponding output data, the input data including geometric parameters and material parameters of the spherical-headed biconical reentry vehicle, and the output data including the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle;

[0177] After each update of the parameters of the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the input data of the verification data in the verification data set is input into the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, and the prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle corresponding to the verification data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle is obtained; according to the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle of the verification data and the corresponding prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the accuracy evaluation index is calculated, and it is determined whether the currently obtained accuracy evaluation index is less than the accuracy evaluation index obtained in the previous iteration; if so, the currently obtained expansion coefficient is saved as the optimal expansion coefficient; otherwise, the saved optimal expansion coefficient is kept unchanged;

[0178] After completing the iterative training of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle, the saved optimal expansion coefficient is extracted as the final expansion coefficient of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle.

[0179] Specifically, taking the current ep-th training iteration as an example, the accuracy evaluation index is calculated using the following formula:

[0180]

[0181] If ε ep <ε ep-1 , then c * =c ep Otherwise, keep c * constant.

[0182] Among them, ε ep represents the accuracy evaluation index at the epth training iteration, ε ep-1 represents the accuracy evaluation index at the ep-1th training iteration, N val Indicates the amount of verification data, and denote the standardized input data of the l″th verification data and the maximum temperature of the inner cavity boundary of the spherical-headed biconical reentry vehicle, respectively. represents the output and input data of the maximum temperature prediction model of the internal cavity boundary of the spherical head double cone reentry vehicle obtained by the epth training iteration The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, cep represents the expansion coefficient determined at the epth training iteration, c * represents the optimal expansion coefficient.

[0183] Step S5, using the trained prediction model for the maximum temperature prediction of the internal cavity boundary of the spherical-headed double-conical reentry vehicle to perform prediction analysis on the maximum temperature of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

[0184] Furthermore, in one embodiment of the present invention, after completing the training of the prediction model of the maximum temperature of the internal cavity boundary of the ball-headed double-conical reentry vehicle, the prediction analysis of the maximum temperature of the internal cavity boundary of the ball-headed double-conical reentry vehicle is performed using the prediction model of the maximum temperature of the internal cavity boundary of the ball-headed double-conical reentry vehicle. Specifically, when performing the prediction, the geometric parameters and material parameters of the ball-headed double-conical reentry vehicle whose internal cavity boundary maximum temperature is to be predicted are input into the prediction model of the maximum temperature of the internal cavity boundary of the ball-headed double-conical reentry vehicle to obtain the predicted value of the maximum temperature of the internal cavity boundary of the ball-headed double-conical reentry vehicle.

[0185] Furthermore, in one embodiment of the present invention, the reliability analysis method of the ball-headed double-conical reentry vehicle further includes:

[0186] The reliability of the spherical-headed double-conical reentry vehicle is quantitatively analyzed using the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

[0187] Specifically, when conducting a quantitative analysis on the reliability of a ball-headed bi-conical reentry vehicle, a random data set is obtained based on the value ranges of the geometric parameters and material parameters of the ball-headed bi-conical reentry vehicle, and the random data includes input data. The input data includes the geometric parameters and material parameters of the ball-headed bi-conical reentry vehicle. A maximum temperature prediction model for the internal cavity boundary of the ball-headed bi-conical reentry vehicle is used to predict the predicted value of the maximum temperature of the internal cavity boundary of the ball-headed bi-conical reentry vehicle corresponding to each random data. The failure rate and reliability of the ball-headed bi-conical reentry vehicle are calculated based on the predicted value of the maximum temperature of the internal cavity boundary of the ball-headed bi-conical reentry vehicle.

[0188] In one embodiment of the present invention, the failure rate is calculated using the following formula:

[0189]

[0190] Among them, P f represents the failure rate of the spherical-headed biconical reentry vehicle, N MCS represents the amount of random data, represents the standardized input data of the lth random data, Δ lim It indicates the temperature threshold for the normal operation of the pre-set spherical-headed bi-conical reentry vehicle. The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, IF(·) is the indicator function, which is specifically expressed as:

[0191]

[0192] Reliability is calculated using the following formula:

[0193] R SBRFV =1-P f Formula 29

[0194] Among them, R SBRFV Indicates the reliability of the ball-nosed bi-conical reentry vehicle.

[0195] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "upper" and "lower" in this article are all referenced to the placement state shown in the accompanying drawings.

[0196] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability analysis method for a spherical-headed biconical reentry vehicle, characterized in that: include: A prediction model for the maximum temperature of the inner cavity boundary of a spherical-headed biconical reentry vehicle is constructed based on deep neural networks and generalized chaotic polynomials. Obtain a labeled training data set and an unlabeled training data set, the labeled training data includes input data and its corresponding output data, the unlabeled training data includes input data, the input data includes geometric parameters and material parameters of the spherical-headed biconical reentry vehicle, and the output data includes the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle; Based on the properties of generalized chaotic polynomials, a loss function is constructed; Based on the loss function, the maximum temperature prediction model of the internal cavity boundary of the spherical-headed bi-conical reentry vehicle is trained using the labeled training data set and the unlabeled training data set; The trained prediction model for the maximum temperature of the boundary of the internal cavity of the spherical-headed double-conical reentry vehicle is used to perform prediction analysis on the maximum temperature of the boundary of the internal cavity of the spherical-headed double-conical reentry vehicle.

2. The reliability analysis method of the ball-headed double-conical reentry vehicle according to claim 1 is characterized in that: The generalized chaos polynomial is: The properties of the generalized chaotic polynomial include: Hey (p) (ξ)]=c1 Where ξ is the input data, ξ={ξ k |k=1,2,…,d}, d represents the number of variables contained in the input data ξ, c i is the expansion coefficient, Φ i (ξ) is a multidimensional standard orthogonal basis {Φ1(ξ),…,Φ M (ξ)}, M is a multidimensional orthogonal basis {Φ1(ξ),…,Φ M (ξ)}, M = (d+p)! / (d!p!), E[y (p) (ξ)] represents y (p) The mean value of (ξ), V[y (p) (ξ)] represents y (p) The variance of (ξ).

3. The reliability analysis method of the ball-headed double-conical reentry vehicle according to claim 2 is characterized in that: The maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle includes: An input layer, comprising a plurality of input neurons, wherein the output of each of the input neurons is respectively connected to the input of a plurality of intermediate neurons, and the input neurons are used to receive and output input data corresponding to the ball-headed bi-conical reentry vehicle; An orthogonal polynomial layer comprises a plurality of intermediate neurons, the outputs of the plurality of intermediate neurons are connected to output neurons respectively, and the value of the ith intermediate neuron is configured as the ith multidimensional polynomial Φ of the generalized chaotic polynomial i (ξ); The output layer includes an output neuron for outputting the maximum temperature value of the boundary of the internal cavity of the spherical head double cone reentry vehicle according to the input of the plurality of intermediate neurons, and the weight corresponding to the i-th intermediate neuron is configured as the i-th expansion coefficient c of the generalized chaotic polynomial i .

4. The reliability analysis method of the ball-headed double-conical reentry vehicle according to claim 3 is characterized in that: The loss function is: in, represents the loss function, represents the supervised loss function, represents the unsupervised loss function, represents the first unsupervised loss function, represents the second unsupervised loss function, λ1 and λ2 represent hyperparameters.

5. The reliability analysis method of the ball-headed double-conical reentry vehicle according to claim 4 is characterized in that: The supervised loss function is expressed as: Among them, N LD represents the amount of labeled training data set, and They represent the standardized input data of the lth labeled training data and the maximum temperature of the inner cavity boundary of the spherical-headed biconical reentry vehicle, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c represents the expansion coefficient.

6. The reliability analysis method of a ball-headed bi-conical reentry vehicle according to claim 4, characterized in that: The first unsupervised loss function is expressed as: The second unsupervised loss function is expressed as: in, Indicates the predicted maximum temperature The mean value, N UD represents the amount of unlabeled training data, represents the standardized input data of the l′th unlabeled training data, The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, c i represents the i-th expansion coefficient, Represents input data The corresponding i-th multidimensional polynomial, Indicates the predicted maximum temperature The variance of .

7. The reliability analysis method of a ball-headed bi-conical reentry vehicle according to claim 4, characterized in that: Based on the loss function, the maximum temperature prediction model of the internal cavity boundary of the ball-headed double-conical reentry vehicle is trained using the labeled training data set and the unlabeled training data set, including the following steps: Step S41, preprocessing the labeled training data set and the unlabeled training data set to convert the input data into standardized data; Step S42, initializing the parameters of the maximum temperature prediction model of the internal cavity boundary of the ball-headed double-conical reentry vehicle according to the labeled training data set; Step S43, respectively inputting the input data of the labeled training data in the labeled training data set and the input data of the unlabeled training data in the unlabeled training data set into the prediction model for the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle, to obtain the prediction value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the labeled training data and the prediction value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the unlabeled training data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle; Step S44, calculating a loss function according to the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle with labeled training data and the corresponding predicted value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle, and the predicted value of the maximum temperature of the internal cavity boundary of the spherical head biconical reentry vehicle corresponding to the unlabeled training data; Step S45, using the loss function to update the parameters of the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle; Step S46, determine whether the preset training stop condition is reached. If so, use the current ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model as the ball-headed bi-conical reentry vehicle internal cavity boundary maximum temperature prediction model that has completed training. If not, return to step S43.

8. The reliability analysis method of a ball-headed bi-conical reentry vehicle according to claim 7, characterized in that: Training the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle also includes the following steps: Acquire a validation data set, the validation data including standardized input data and corresponding output data, the input data including geometric parameters and material parameters of the spherical-headed biconical reentry vehicle, and the output data including the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle; After each update of the parameters of the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the input data of the verification data in the verification data set is input into the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, and the prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle corresponding to the verification data output by the prediction model for the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle is obtained; according to the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle of the verification data and the corresponding prediction value of the maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, the accuracy evaluation index is calculated, and it is determined whether the currently obtained accuracy evaluation index is less than the accuracy evaluation index obtained in the previous iteration; if so, the currently obtained expansion coefficient is saved as the optimal expansion coefficient; otherwise, the saved optimal expansion coefficient is kept unchanged; After completing the iterative training of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle, the saved optimal expansion coefficient is extracted as the final expansion coefficient of the maximum temperature prediction model for the inner cavity boundary of the spherical-headed double-conical reentry vehicle.

9. The reliability analysis method of a ball-headed bi-conical reentry vehicle according to any one of claims 1 to 8, characterized in that: The method further comprises: The reliability of the spherical-headed double-conical reentry vehicle is quantitatively analyzed using the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle.

10. The reliability analysis method of a ball-headed double-conical reentry vehicle according to claim 9, characterized in that: The reliability of the spherical-headed double-conical reentry vehicle is quantitatively analyzed by using the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle, including: Based on the value range of geometric parameters and material parameters of the spherical-headed double-conical reentry vehicle, a random data set is obtained, the random data includes input data, the input data includes geometric parameters and material parameters of the spherical-headed double-conical reentry vehicle, and the maximum temperature prediction model of the internal cavity boundary of the spherical-headed double-conical reentry vehicle is used to predict the maximum temperature prediction value of the internal cavity boundary of the spherical-headed double-conical reentry vehicle corresponding to each random data, and the failure rate and reliability of the spherical-headed double-conical reentry vehicle are calculated according to the maximum temperature prediction value of the internal cavity boundary of the spherical-headed double-conical reentry vehicle; The failure rate is calculated using the following formula: Reliability is calculated using the following formula: R SBRFV =1-P f Among them, P f represents the failure rate of the spherical-headed biconical reentry vehicle, R SBRFV represents the reliability of the spherical-headed biconical reentry vehicle, N MCS represents the amount of random data, represents the standardized input data of the lth random data, Δ lim It indicates the temperature threshold for the normal operation of the pre-set spherical-headed bi-conical reentry vehicle. The output and input data of the maximum temperature prediction model for the internal cavity boundary of a spherical-headed biconical reentry vehicle The corresponding predicted maximum temperature of the internal cavity boundary of the spherical-headed biconical reentry vehicle, IF(·) is the indicator function, expressed as:

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